SeminarTitle[20021101]= "Analysis and Geometry"; Location[20021101]= "509LA"; Title[20021101]= "TBA"; Abstract[20021101]= "TBA"; Speaker[20021101]= "Roland Duduchava"; SpeakerLink[20021101]= "http://www.rmi.acnet.ge/~duduch/"; PictureLink[20021101]= "http://www.rmi.acnet.ge/~duduch/duduch70.jpg"; University[20021101]= "Razmadze Mathematical Institute (Georgia)"; UniversityLink[20021101]= " http://www.rmi.acnet.ge/"; SecondUniversity[20021101]= " "; SecondUniversityLink[20021101]= " "; DateOfTalk[20021101]= "November 1, 2002"; DayOfWeek[20021101]= "Friday"; TimeOfTalk[20021101]= "2PM"; IsTimeDefault[20021101]= "1"; IsDateDefault[20021101]= "1"; Entry[20021101]= "1"; Comments[20021101]= " "; SeminarTitle[20020920]= "Analysis and Geometry"; Location[20020920]= "509LA"; Title[20020920]= "Differential operators, brackets and connections"; Abstract[20020920]= "I am going to describe remarkable relations between differential operators and bracket structures. It is known that an operator of the second order acting on functions defines a \"bracket\", i.e. a symmetric bilinear operation on functions satisfying the Leibniz rule (basically, the polarized principal symbol). This works on ordinary manifolds as well as on supermanifolds. In the super context, this gives a relation between odd Laplacians (or \"Batalin-Vilokovisky D-operators\") and odd Poisson brackets. I will show how this relation between differential operators and brackets can be made 1-1 if one considers the algebra of densities instead of the algebra of functions. This construction implicitly involves \"generalized\" connections: notice that every differential operator of the second order acting on functions encodes in its coefficients an \"upper connection\" in the bundle of volume forms (basically, the subprincipal symbol). An extension of these ideas to operators of higher order would lead to homotopy algebras. This is a joint work with Hovhannes Khudaverdian."; Speaker[20020920]= "Theodore Voronov"; SpeakerLink[20020920]= "http://www.ma.umist.ac.uk/tv/"; PictureLink[20020920]= "http://www.ma.umist.ac.uk/tv/ted252.jpg"; University[20020920]= "University of Manchester (UMIST)"; UniversityLink[20020920]= "http://www2.umist.ac.uk/mathematics/"; SecondUniversity[20020920]= " "; SecondUniversityLink[20020920]= " "; DateOfTalk[20020920]= "September 20, 2002"; DayOfWeek[20020920]= "Friday"; TimeOfTalk[20020920]= "2PM"; IsTimeDefault[20020920]= "1"; IsDateDefault[20020920]= "1"; Entry[20020920]= "1"; Comments[20020920]= " "; SeminarTitle[20021011]= "Analysis and Geometry"; Location[20021011]= "509LA"; Title[20021011]= "TBA"; Abstract[20021011]= "TBA"; Speaker[20021011]= "Stanislav Dubrovskiy"; SpeakerLink[20021011]= " "; PictureLink[20021011]= " "; University[20021011]= "Northeastern University"; UniversityLink[20021011]= "http://www.math.neu.edu/"; SecondUniversity[20021011]= " "; SecondUniversityLink[20021011]= " "; DateOfTalk[20021011]= "October 11, 2002"; DayOfWeek[20021011]= "Friday"; TimeOfTalk[20021011]= "2PM"; IsTimeDefault[20021011]= "1"; IsDateDefault[20021011]= "1"; Entry[20021011]= "1"; Comments[20021011]= " "; SeminarTitle[20021025]= "Analysis and Geometry"; Location[20021025]= "509LA"; Title[20021025]= "TBA"; Abstract[20021025]= "TBA"; Speaker[20021025]= "Megan M. Kerr"; SpeakerLink[20021025]= "http://palmer.wellesley.edu/~mkerr/"; PictureLink[20021025]= "http://palmer.wellesley.edu/~mkerr/mmk.jpeg"; University[20021025]= "Wellesley College"; UniversityLink[20021025]= "http://www.wellesley.edu/Math/mathhome.html"; SecondUniversity[20021025]= " "; SecondUniversityLink[20021025]= " "; DateOfTalk[20021025]= "October 25, 2002"; DayOfWeek[20021025]= "Friday"; TimeOfTalk[20021025]= "2PM"; IsTimeDefault[20021025]= "1"; IsDateDefault[20021025]= "1"; Entry[20021025]= "1"; Comments[20021025]= " "; SeminarTitle[20021011]= "Analysis and Geometry"; Location[20021011]= "509LA"; Title[20021011]= " Moduli space of symmetric connections"; Abstract[20021011]= "We are interested in local differential invariants of a symmetric connection, under smooth coordinate changes. We consider the action of origin-preserving diffeomorphisms on a space of jets of connections and calculate dimensions of moduli spaces in generic case. We show that the corresponding Poincarè series is a rational function. This confirms one more time the 1894\' finitness claim of Tresse, stated for any \"natural\" differential-geometric structure."; Speaker[20021011]= "Stanislav Dubrovskiy"; SpeakerLink[20021011]= " "; PictureLink[20021011]= " "; University[20021011]= "Northeastern University"; UniversityLink[20021011]= "http://www.math.neu.edu/"; SecondUniversity[20021011]= " "; SecondUniversityLink[20021011]= " "; DateOfTalk[20021011]= "October 11, 2002"; DayOfWeek[20021011]= "Friday"; TimeOfTalk[20021011]= "2PM"; IsTimeDefault[20021011]= "1"; IsDateDefault[20021011]= "1"; Entry[20021011]= "1"; Comments[20021011]= " "; SeminarTitle[20021025]= "Analysis and Geometry"; Location[20021025]= "509LA"; Title[20021025]= "TBA"; Abstract[20021025]= "TBA"; Speaker[20021025]= "Mikhail Shubin"; SpeakerLink[20021025]= "http://www.math.neu.edu/~shubin/"; PictureLink[20021025]= "http://www.math.neu.edu/~shubin/shubin.jpg"; University[20021025]= "Northeastern University"; UniversityLink[20021025]= "http://www.math.neu.edu/"; SecondUniversity[20021025]= " "; SecondUniversityLink[20021025]= " "; DateOfTalk[20021025]= "October 25, 2002"; DayOfWeek[20021025]= "Friday"; TimeOfTalk[20021025]= "2PM"; IsTimeDefault[20021025]= "1"; IsDateDefault[20021025]= "1"; Entry[20021025]= "1"; Comments[20021025]= " "; SeminarTitle[20021004]= "Analysis and Geometry"; Location[20021004]= "509LA"; Title[20021004]= "Bounds for eigenfunctions of the Laplacian on compact Riemannian manifolds"; Abstract[20021004]= "Suppose that φ is an eigenfunction of -Δ with eigenvalue λ≠0. It is proved that ||φ||_∞≤   c₁λ^(n-^1)/4||φ||₂, where n is the dimension of M and c₁ depends only upon a bound for the absolute value of the sectional curvature of M and a lower bound for the injectivity radius of M. It is then shown that if M admits an isometric circle action, and the metric is generic, one has exceptional sequences of eigenfunctions satisfying the complementary bounds ||φ_k||_∞≥   c₂λ _k^(n-^1)/8 ||φ_k|| ² ."; Speaker[20021004]= "Harold G. Donnelly"; SpeakerLink[20021004]= " "; PictureLink[20021004]= " "; University[20021004]= "Purdue University"; UniversityLink[20021004]= " http://www.math.purdue.edu/"; SecondUniversity[20021004]= " "; SecondUniversityLink[20021004]= " "; DateOfTalk[20021004]= "October 4, 2002"; DayOfWeek[20021004]= "Friday"; TimeOfTalk[20021004]= "2PM"; IsTimeDefault[20021004]= "1"; IsDateDefault[20021004]= "1"; Entry[20021004]= "1"; Comments[20021004]= " "; SeminarTitle[20021101]= "Analysis and Geometry"; Location[20021101]= "509LA"; Title[20021101]= " Mathematical theory of cracks: the Wiener-Hopf method"; Abstract[20021101]= "A crack in elastic media is modelled by the Neumann boundary value problem for a homogeneous second order partial differential equation with constant coefficients. We use potentials and the Wiener-Hopf method to obtain a full asymptotic expansion of the solution. We show that these asymptotics do not contain logarithmic terms."; Speaker[20021101]= "Roland Duduchava"; SpeakerLink[20021101]= "http://www.rmi.acnet.ge/~duduch/"; PictureLink[20021101]= "http://www.rmi.acnet.ge/~duduch/duduch70.jpg"; University[20021101]= "Razmadze Mathematical Institute (Georgia)"; UniversityLink[20021101]= " http://www.rmi.acnet.ge/"; SecondUniversity[20021101]= " "; SecondUniversityLink[20021101]= " "; DateOfTalk[20021101]= "November 1, 2002"; DayOfWeek[20021101]= "Friday"; TimeOfTalk[20021101]= "2PM"; IsTimeDefault[20021101]= "1"; IsDateDefault[20021101]= "1"; Entry[20021101]= "1"; Comments[20021101]= " "; SeminarTitle[20021018]= "Analysis and Geometry"; Location[20021018]= "509LA"; Title[20021018]= "Milnor numbers of minimal surfaces in 4-manifolds"; Abstract[20021018]= "When a sequence of smooth embedded complex curves (C_n) in CP^2 degenerates to a branched curve C₀, we lose topology ( g(C_n)>g(C₀) ) and gain singularity. Milnor gave a precise meaning to this assertion. There is a quantity - now called the Milnor number - we can compute on the branch points of C₀ which tells us how much topology we have lost going from C_n to C₀.
   So we ask: is there anything even remotely similar if the C_n\'s and C₀ are more general surfaces (e.g. minimal surfaces) in a 4-manifold? Can we define a Milnor number for a sequence of minimal surfaces? It turns out that we have to define not one, but two Milnor numbers (the "tangent\'\' and the "normal\'\' one); these numbers coincide in the complex case.
   We will define these Milnor numbers, give explain geometric and topological interpretations and show how they give a partial answer to our question above."; Speaker[20021018]= "Marina Ville"; SpeakerLink[20021018]= " "; PictureLink[20021018]= " "; University[20021018]= "Boston University"; UniversityLink[20021018]= "http://math.bu.edu/"; SecondUniversity[20021018]= " "; SecondUniversityLink[20021018]= " "; DateOfTalk[20021018]= "October 18, 2002"; DayOfWeek[20021018]= "Friday"; TimeOfTalk[20021018]= "2PM"; IsTimeDefault[20021018]= "1"; IsDateDefault[20021018]= "1"; Entry[20021018]= "1"; Comments[20021018]= " "; SeminarTitle[20021018]= "Analysis and Geometry"; Location[20021018]= "509LA"; Title[20021018]= "Milnor numbers of minimal surfaces in 4-manifolds"; Abstract[20021018]= "When a sequence of smooth embedded complex curves (C_n) in CP^2 degenerates to a branched curve C₀, we lose topology ( g(C_n)>g(C₀) ) and gain singularity. Milnor gave a precise meaning to this assertion. There is a quantity - now called the Milnor number - we can compute on the branch points of C₀ which tells us how much topology we have lost going from C_n to C₀.
   So we ask: is there anything even remotely similar if the C_n\'s and C₀ are more general surfaces (e.g. minimal surfaces) in a 4-manifold? Can we define a Milnor number for a sequence of minimal surfaces? It turns out that we have to define not one, but two Milnor numbers (the "tangent\'\' and the "normal\'\' one); these numbers coincide in the complex case.
   We will define these Milnor numbers, give explain geometric and topological interpretations and show how they give a partial answer to our question above."; Speaker[20021018]= "Marina Ville"; SpeakerLink[20021018]= " "; PictureLink[20021018]= " "; University[20021018]= "CNRS"; UniversityLink[20021018]= "http://www.spm.cnrs-dir.fr/"; SecondUniversity[20021018]= "Boston University"; SecondUniversityLink[20021018]= " http://math.bu.edu/"; DateOfTalk[20021018]= "October 18, 2002"; DayOfWeek[20021018]= "Friday"; TimeOfTalk[20021018]= "2PM"; IsTimeDefault[20021018]= "1"; IsDateDefault[20021018]= "1"; Entry[20021018]= "1"; Comments[20021018]= " "; SeminarTitle[20021025]= "Analysis and Geometry"; Location[20021025]= "509LA"; Title[20021025]= "A new family of necessary and sufficient discreteness of spectrum conditions for Schr\"odinger operators"; Abstract[20021025]= " I will explain new criteria of discreteness of spectrum for the Schr\"odinger operators with semi-bounded below potentials. They extend a well known result by A.Molchanov (1953) who was the first to formulate a necessary and sufficient condition for the discreteness of spectrum in terms of the Wiener capacity.
   We provide a new family of such conditions which depend on a functional parameter describing \"negligible\" sets.
   (This is a joint work with V.Maz\'ya.)"; Speaker[20021025]= "Mikhail Shubin"; SpeakerLink[20021025]= "http://www.math.neu.edu/~shubin/"; PictureLink[20021025]= "http://www.math.neu.edu/~shubin/shubin.jpg"; University[20021025]= "Northeastern University"; UniversityLink[20021025]= " http://www.math.neu.edu/"; SecondUniversity[20021025]= " "; SecondUniversityLink[20021025]= " "; DateOfTalk[20021025]= "October 25, 2002"; DayOfWeek[20021025]= "Friday"; TimeOfTalk[20021025]= "2PM"; IsTimeDefault[20021025]= "1"; IsDateDefault[20021025]= "1"; Entry[20021025]= "1"; Comments[20021025]= " "; SeminarTitle[20021025]= "Analysis and Geometry"; Location[20021025]= "509LA"; Title[20021025]= "A new family of necessary and sufficient discreteness of spectrum conditions for Schrödinger operators"; Abstract[20021025]= " I will explain new criteria of discreteness of spectrum for the Schr\\\"odinger operators with semi-bounded below potentials. They extend a well known result by A.Molchanov (1953) who was the first to formulate a necessary and sufficient condition for the discreteness of spectrum in terms of the Wiener capacity.
   We provide a new family of such conditions which depend on a functional parameter describing \"negligible\" sets.
   (This is a joint work with V.Maz\'\'ya.)"; Speaker[20021025]= "Mikhail Shubin"; SpeakerLink[20021025]= "http://www.math.neu.edu/~shubin/"; PictureLink[20021025]= "http://www.math.neu.edu/~shubin/shubin.jpg"; University[20021025]= "Northeastern University"; UniversityLink[20021025]= " http://www.math.neu.edu/"; SecondUniversity[20021025]= ""; SecondUniversityLink[20021025]= " "; DateOfTalk[20021025]= "October 25, 2002"; DayOfWeek[20021025]= "Friday"; TimeOfTalk[20021025]= "2PM"; IsTimeDefault[20021025]= "1"; IsDateDefault[20021025]= "1"; Entry[20021025]= "0"; Comments[20021025]= " "; SeminarTitle[20021025]= "Analysis and Geometry"; Location[20021025]= "509LA"; Title[20021025]= "A new family of necessary and sufficient discreteness of spectrum conditions for Schrödinger operators"; Abstract[20021025]= "I will explain new criteria of discreteness of spectrum for the Schrödinger operators with semi-bounded below potentials. They extend a well known result by A.Molchanov (1953) who was the first to formulate a necessary and sufficient condition for the discreteness of spectrum in terms of the Wiener capacity.
   We provide a new family of such conditions which depend on a functional parameter describing \"negligible\" sets.
   (This is a joint work with V.Maz\'ya.)"; Speaker[20021025]= "Mikhail Shubin"; SpeakerLink[20021025]= "http://www.math.neu.edu/~shubin/mathindex.html"; PictureLink[20021025]= "http://www.math.neu.edu/~shubin/shubin.jpg"; University[20021025]= "Northeastern University"; UniversityLink[20021025]= " http://www.math.neu.edu/"; SecondUniversity[20021025]= " "; SecondUniversityLink[20021025]= " "; DateOfTalk[20021025]= "October 25, 2002"; DayOfWeek[20021025]= "Friday"; TimeOfTalk[20021025]= "2PM"; IsTimeDefault[20021025]= "1"; IsDateDefault[20021025]= "1"; Entry[20021025]= "1"; Comments[20021025]= " "; SeminarTitle[20021206]= "Analysis and Geometry"; Location[20021206]= "509LA"; Title[20021206]= "TBA"; Abstract[20021206]= "TBA"; Speaker[20021206]= "Hubert Bray"; SpeakerLink[20021206]= "http://www-math.mit.edu/~bray/"; PictureLink[20021206]= "http://www-math.mit.edu/~bray/bray.jpg"; University[20021206]= "MIT"; UniversityLink[20021206]= "http://www-math.mit.edu/"; SecondUniversity[20021206]= " "; SecondUniversityLink[20021206]= " "; DateOfTalk[20021206]= "December 6, 2002"; DayOfWeek[20021206]= "Friday"; TimeOfTalk[20021206]= "2PM"; IsTimeDefault[20021206]= "1"; IsDateDefault[20021206]= "1"; Entry[20021206]= "1"; Comments[20021206]= " "; SeminarTitle[20021108]= "Analysis and Geometry"; Location[20021108]= "509LA"; Title[20021108]= "TBA"; Abstract[20021108]= "TBA"; Speaker[20021108]= "Mihaela Iftime"; SpeakerLink[20021108]= " "; PictureLink[20021108]= " "; University[20021108]= "Northeastern University"; UniversityLink[20021108]= " http://www.math.neu.edu/"; SecondUniversity[20021108]= " "; SecondUniversityLink[20021108]= " "; DateOfTalk[20021108]= "November 8, 2002"; DayOfWeek[20021108]= "Friday"; TimeOfTalk[20021108]= "2PM"; IsTimeDefault[20021108]= "1"; IsDateDefault[20021108]= "1"; Entry[20021108]= "1"; Comments[20021108]= " "; SeminarTitle[20021108]= "Analysis and Geometry"; Location[20021108]= "509LA"; Title[20021108]= "TBA"; Abstract[20021108]= "TBA"; Speaker[20021108]= "Mihaela Iftime"; SpeakerLink[20021108]= " "; PictureLink[20021108]= " "; University[20021108]= "Northeastern University"; UniversityLink[20021108]= "http://www.math.neu.edu/"; SecondUniversity[20021108]= " "; SecondUniversityLink[20021108]= " "; DateOfTalk[20021108]= "November 8, 2002"; DayOfWeek[20021108]= "Friday"; TimeOfTalk[20021108]= "2PM"; IsTimeDefault[20021108]= "1"; IsDateDefault[20021108]= "1"; Entry[20021108]= "1"; Comments[20021108]= " "; SeminarTitle[20021206]= "Analysis and Geometry"; Location[20021206]= "509LA"; Title[20021206]= "TBA"; Abstract[20021206]= "TBA"; Speaker[20021206]= "Hubert Bray"; SpeakerLink[20021206]= "http://www-math.mit.edu/~bray/"; PictureLink[20021206]= "http://www-math.mit.edu/~bray/bray.jpg"; University[20021206]= "MIT"; UniversityLink[20021206]= "http://www-math.mit.edu/"; SecondUniversity[20021206]= " "; SecondUniversityLink[20021206]= " "; DateOfTalk[20021206]= "December 6, 2002"; DayOfWeek[20021206]= "Friday"; TimeOfTalk[20021206]= "2PM"; IsTimeDefault[20021206]= "1"; IsDateDefault[20021206]= "1"; Entry[20021206]= "1"; Comments[20021206]= " "; SeminarTitle[20021004]= "Analysis and Geometry"; Location[20021004]= "509LA"; Title[20021004]= "A new family of necessary and sufficient discreteness of spectrum conditions for Schrödinger operators"; Abstract[20021004]= "I will explain new criteria of discreteness of spectrum for the Schrödinger operators with semi-bounded below potentials. They extend a well known result by A.Molchanov (1953) who was the first to formulate a necessary and sufficient condition for the discreteness of spectrum in terms of the Wiener capacity.
   We provide a new family of such conditions which depend on a functional parameter describing \"negligible\" sets.
   (This is a joint work with V.Maz\'ya.)"; Speaker[20021004]= "Mikhail Shubin"; SpeakerLink[20021004]= "http://www.math.neu.edu/~shubin/mathindex.html"; PictureLink[20021004]= "http://www.math.neu.edu/~shubin/shubin.jpg"; University[20021004]= "Northeastern University"; UniversityLink[20021004]= " http://www.math.neu.edu/"; SecondUniversity[20021004]= " "; SecondUniversityLink[20021004]= " "; DateOfTalk[20021004]= "October 4, 2002"; DayOfWeek[20021004]= "Friday"; TimeOfTalk[20021004]= "2PM"; IsTimeDefault[20021004]= "1"; IsDateDefault[20021004]= "1"; Entry[20021004]= "1"; Comments[20021004]= " "; SeminarTitle[20021025]= "Analysis and Geometry"; Location[20021025]= "509LA"; Title[20021025]= "A new family of necessary and sufficient discreteness of spectrum conditions for Schrödinger operators"; Abstract[20021025]= "I will explain new criteria of discreteness of spectrum for the Schrödinger operators with semi-bounded below potentials. They extend a well known result by A.Molchanov (1953) who was the first to formulate a necessary and sufficient condition for the discreteness of spectrum in terms of the Wiener capacity.
   We provide a new family of such conditions which depend on a functional parameter describing \"negligible\" sets.
   (This is a joint work with V.Maz\'ya.)"; Speaker[20021025]= "Mikhail Shubin"; SpeakerLink[20021025]= "http://www.math.neu.edu/~shubin/mathindex.html"; PictureLink[20021025]= "http://www.math.neu.edu/~shubin/shubin.jpg"; University[20021025]= "Northeastern University"; UniversityLink[20021025]= " http://www.math.neu.edu/"; SecondUniversity[20021025]= ""; SecondUniversityLink[20021025]= " "; DateOfTalk[20021025]= "October 25, 2002"; DayOfWeek[20021025]= "Friday"; TimeOfTalk[20021025]= "2PM"; IsTimeDefault[20021025]= "1"; IsDateDefault[20021025]= "1"; Entry[20021025]= "1"; Comments[20021025]= " "; SeminarTitle[20021018]= "Analysis and Geometry"; Location[20021018]= "509LA"; Title[20021018]= "TBA"; Abstract[20021018]= "When a sequence of smooth embedded complex curves (C_n) in CP^2 degenerates to a branched curve C₀, we lose topology ( g(C_n)>g(C₀) ) and gain singularity. Milnor gave a precise meaning to this assertion. There is a quantity - now called the Milnor number - we can compute on the branch points of C₀ which tells us how much topology we have lost going from C_n to C₀.
   So we ask: is there anything even remotely similar if the C_n\\'s and C₀ are more general surfaces (e.g. minimal surfaces) in a 4-manifold? Can we define a Milnor number for a sequence of minimal surfaces? It turns out that we have to define not one, but two Milnor numbers (the "tangent\" and the "normal\" one); these numbers coincide in the complex case.
   We will define these Milnor numbers, give explain geometric and topological interpretations and show how they give a partial answer to our question above."; Speaker[20021018]= "Marina Ville"; SpeakerLink[20021018]= " "; PictureLink[20021018]= " "; University[20021018]= "CNRS"; UniversityLink[20021018]= "http://www.spm.cnrs-dir.fr/"; SecondUniversity[20021018]= "Boston University"; SecondUniversityLink[20021018]= "http://math.bu.edu"; DateOfTalk[20021018]= "October 18, 2002"; DayOfWeek[20021018]= "Friday"; TimeOfTalk[20021018]= "2PM"; IsTimeDefault[20021018]= "1"; IsDateDefault[20021018]= "1"; Entry[20021018]= "1"; Comments[20021018]= " "; SeminarTitle[20021018]= "Analysis and Geometry"; Location[20021018]= "509LA"; Title[20021018]= "Milnor numbers of minimal surfaces in 4-manifolds"; Abstract[20021018]= "When a sequence of smooth embedded complex curves (C_n) in CP^2 degenerates to a branched curve C₀, we lose topology ( g(C_n)>g(C₀) ) and gain singularity. Milnor gave a precise meaning to this assertion. There is a quantity - now called the Milnor number - we can compute on the branch points of C₀ which tells us how much topology we have lost going from C_n to C₀.
   So we ask: is there anything even remotely similar if the C_n\\'s and C₀ are more general surfaces (e.g. minimal surfaces) in a 4-manifold? Can we define a Milnor number for a sequence of minimal surfaces? It turns out that we have to define not one, but two Milnor numbers (the "tangent\" and the "normal\" one); these numbers coincide in the complex case.
   We will define these Milnor numbers, give explain geometric and topological interpretations and show how they give a partial answer to our question above."; Speaker[20021018]= "Marina Ville"; SpeakerLink[20021018]= " "; PictureLink[20021018]= " "; University[20021018]= "CNRS"; UniversityLink[20021018]= " http://www.spm.cnrs-dir.fr/"; SecondUniversity[20021018]= "Boston University"; SecondUniversityLink[20021018]= " http://math.bu.edu"; DateOfTalk[20021018]= "October 18, 2002"; DayOfWeek[20021018]= "Friday"; TimeOfTalk[20021018]= "2PM"; IsTimeDefault[20021018]= "1"; IsDateDefault[20021018]= "1"; Entry[20021018]= "1"; Comments[20021018]= " "; SeminarTitle[20021101]= "Analysis and Geometry"; Location[20021101]= "509LA"; Title[20021101]= "Mathematical theory of cracks: the Wiener-Hopf method"; Abstract[20021101]= "A crack in elastic media is modelled by the Neumann boundary value problem for a homogeneous second order partial differential equation with constant coefficients. We use potentials and the Wiener-Hopf method to obtain a full asymptotic expansion of the solution. We show that these asymptotics do not contain logarithmic terms."; Speaker[20021101]= "Roland Duduchava"; SpeakerLink[20021101]= "http://www.rmi.acnet.ge/~duduch/"; PictureLink[20021101]= "http://www.rmi.acnet.ge/~duduch/duduch70.jpg"; University[20021101]= "Razmadze Mathematical Institute (Tbilisi, Georgia)"; UniversityLink[20021101]= "http://www.rmi.acnet.ge/"; SecondUniversity[20021101]= " "; SecondUniversityLink[20021101]= " "; DateOfTalk[20021101]= "November 1, 2002"; DayOfWeek[20021101]= "Friday"; TimeOfTalk[20021101]= "2PM"; IsTimeDefault[20021101]= "1"; IsDateDefault[20021101]= "1"; Entry[20021101]= "1"; Comments[20021101]= " "; SeminarTitle[20021004]= "Analysis and Geometry"; Location[20021004]= "509LA"; Title[20021004]= "Bounds for eigenfunctions of the Laplacian on compact Riemannian manifolds"; Abstract[20021004]= "Suppose that φ is an eigenfunction of -Δ with eigenvalue λ≠0. It is proved that ||φ||_∞≤   c₁λ^(n-^1)/4||φ||₂, where n is the dimension of M and c₁ depends only upon a bound for the absolute value of the sectional curvature of M and a lower bound for the injectivity radius of M. It is then shown that if M admits an isometric circle action, and the metric is generic, one has exceptional sequences of eigenfunctions satisfying the complementary bounds ||φ_k||_∞≥   c₂λ _k^(n-^1)/8 ||φ_k|| ² ."; Speaker[20021004]= "Harold G. Donnelly"; SpeakerLink[20021004]= " "; PictureLink[20021004]= " "; University[20021004]= "Purdue University"; UniversityLink[20021004]= "http://www.math.purdue.edu/"; SecondUniversity[20021004]= " "; SecondUniversityLink[20021004]= " "; DateOfTalk[20021004]= "October 4, 2002"; DayOfWeek[20021004]= "Friday"; TimeOfTalk[20021004]= "2PM"; IsTimeDefault[20021004]= "1"; IsDateDefault[20021004]= "1"; Entry[20021004]= "1"; Comments[20021004]= " "; SeminarTitle[20021004]= "Analysis and Geometry"; Location[20021004]= "509LA"; Title[20021004]= "Moduli space of symmetric connections"; Abstract[20021004]= "We are interested in local differential invariants of a symmetric connection, under smooth coordinate changes. We consider the action of origin-preserving diffeomorphisms on a space of jets of connections and calculate dimensions of moduli spaces in generic case. We show that the corresponding Poincarè series is a rational function. This confirms one more time the 1894\' finitness claim of Tresse, stated for any \"natural\" differential-geometric structure."; Speaker[20021004]= "Stanislav Dubrovskiy"; SpeakerLink[20021004]= " "; PictureLink[20021004]= " "; University[20021004]= "Northeastern University"; UniversityLink[20021004]= " http://www.math.neu.edu/"; SecondUniversity[20021004]= " "; SecondUniversityLink[20021004]= " "; DateOfTalk[20021004]= "October 4, 2002"; DayOfWeek[20021004]= "Friday"; TimeOfTalk[20021004]= "2PM"; IsTimeDefault[20021004]= "1"; IsDateDefault[20021004]= "1"; Entry[20021004]= "1"; Comments[20021004]= " "; SeminarTitle[20021025]= "Analysis and Geometry"; Location[20021025]= "509LA"; Title[20021025]= "A new family of necessary and sufficient discreteness of spectrum conditions for Schrödinger operators"; Abstract[20021025]= "I will explain new criteria of discreteness of spectrum for the Schrödinger operators with semi-bounded below potentials. They extend a well known result by A.Molchanov (1953) who was the first to formulate a necessary and sufficient condition for the discreteness of spectrum in terms of the Wiener capacity.
   We provide a new family of such conditions which depend on a functional parameter describing \"negligible\" sets.
   (This is a joint work with V.Maz\'ya.)"; Speaker[20021025]= "Mikhail Shubin"; SpeakerLink[20021025]= "http://www.math.neu.edu/~shubin/mathindex.html"; PictureLink[20021025]= "http://www.math.neu.edu/~shubin/shubin.jpg"; University[20021025]= "Northeastern University"; UniversityLink[20021025]= " http://www.math.neu.edu/"; SecondUniversity[20021025]= "CNRS"; SecondUniversityLink[20021025]= " http://www.spm.cnrs-dir.fr/"; DateOfTalk[20021025]= "October 25, 2002"; DayOfWeek[20021025]= "Friday"; TimeOfTalk[20021025]= "2PM"; IsTimeDefault[20021025]= "1"; IsDateDefault[20021025]= "1"; Entry[20021025]= "1"; Comments[20021025]= " "; SeminarTitle[20021018]= "Analysis and Geometry"; Location[20021018]= "509LA"; Title[20021018]= "Milnor numbers of minimal surfaces in 4-manifolds"; Abstract[20021018]= "When a sequence of smooth embedded complex curves (C_n) in CP^2 degenerates to a branched curve C₀, we lose topology ( g(C_n)>g(C₀) ) and gain singularity. Milnor gave a precise meaning to this assertion. There is a quantity - now called the Milnor number - we can compute on the branch points of C₀ which tells us how much topology we have lost going from C_n to C₀.
   So we ask: is there anything even remotely similar if the C_n\\'\'s and C₀ are more general surfaces (e.g. minimal surfaces) in a 4-manifold? Can we define a Milnor number for a sequence of minimal surfaces? It turns out that we have to define not one, but two Milnor numbers (the "tangent\" and the "normal\" one); these numbers coincide in the complex case.
   We will define these Milnor numbers, give explain geometric and topological interpretations and show how they give a partial answer to our question above."; Speaker[20021018]= "Marina Ville"; SpeakerLink[20021018]= " "; PictureLink[20021018]= " "; University[20021018]= "CNRS"; UniversityLink[20021018]= " http://www.spm.cnrs-dir.fr/"; SecondUniversity[20021018]= "CNRS"; SecondUniversityLink[20021018]= " http://www.spm.cnrs-dir.fr/"; DateOfTalk[20021018]= "October 18, 2002"; DayOfWeek[20021018]= "Friday"; TimeOfTalk[20021018]= "2PM"; IsTimeDefault[20021018]= "1"; IsDateDefault[20021018]= "1"; Entry[20021018]= "1"; Comments[20021018]= " "; SeminarTitle[20021025]= "Analysis and Geometry"; Location[20021025]= "509LA"; Title[20021025]= "A new family of necessary and sufficient discreteness of spectrum conditions for Schrödinger operators"; Abstract[20021025]= "I will explain new criteria of discreteness of spectrum for the Schrödinger operators with semi-bounded below potentials. They extend a well known result by A.Molchanov (1953) who was the first to formulate a necessary and sufficient condition for the discreteness of spectrum in terms of the Wiener capacity.
   We provide a new family of such conditions which depend on a functional parameter describing \"negligible\" sets.
   (This is a joint work with V.Maz\'ya.)"; Speaker[20021025]= "Mikhail Shubin"; SpeakerLink[20021025]= "http://www.math.neu.edu/~shubin/mathindex.html"; PictureLink[20021025]= "http://www.math.neu.edu/~shubin/shubin.jpg"; University[20021025]= "Northeastern University"; UniversityLink[20021025]= " http://www.math.neu.edu/"; SecondUniversity[20021025]= "CNRS"; SecondUniversityLink[20021025]= " http://www.spm.cnrs-dir.fr/"; DateOfTalk[20021025]= "October 25, 2002"; DayOfWeek[20021025]= "Friday"; TimeOfTalk[20021025]= "2PM"; IsTimeDefault[20021025]= "1"; IsDateDefault[20021025]= "1"; Entry[20021025]= "1"; Comments[20021025]= " "; SeminarTitle[20021025]= "Analysis and Geometry"; Location[20021025]= "509LA"; Title[20021025]= "A new family of necessary and sufficient discreteness of spectrum conditions for Schrödinger operators"; Abstract[20021025]= "I will explain new criteria of discreteness of spectrum for the Schrödinger operators with semi-bounded below potentials. They extend a well known result by A.Molchanov (1953) who was the first to formulate a necessary and sufficient condition for the discreteness of spectrum in terms of the Wiener capacity.
   We provide a new family of such conditions which depend on a functional parameter describing \"negligible\" sets.
   (This is a joint work with V.Maz\'ya.)"; Speaker[20021025]= "Mikhail Shubin"; SpeakerLink[20021025]= "http://www.math.neu.edu/~shubin/mathindex.html"; PictureLink[20021025]= "http://www.math.neu.edu/~shubin/shubin.jpg"; University[20021025]= "Northeastern University"; UniversityLink[20021025]= " http://www.math.neu.edu/"; SecondUniversity[20021025]= "CNRS"; SecondUniversityLink[20021025]= " http://www.spm.cnrs-dir.fr/"; DateOfTalk[20021025]= "October 25, 2002"; DayOfWeek[20021025]= "Friday"; TimeOfTalk[20021025]= "2PM"; IsTimeDefault[20021025]= "1"; IsDateDefault[20021025]= "1"; Entry[20021025]= "1"; Comments[20021025]= " "; SeminarTitle[20021025]= "Analysis and Geometry"; Location[20021025]= "509LA"; Title[20021025]= "A new family of necessary and sufficient discreteness of spectrum conditions for Schrödinger operators"; Abstract[20021025]= "I will explain new criteria of discreteness of spectrum for the Schrödinger operators with semi-bounded below potentials. They extend a well known result by A.Molchanov (1953) who was the first to formulate a necessary and sufficient condition for the discreteness of spectrum in terms of the Wiener capacity.
   We provide a new family of such conditions which depend on a functional parameter describing \"negligible\" sets.
   (This is a joint work with V.Maz\'ya.)"; Speaker[20021025]= "Mikhail Shubin"; SpeakerLink[20021025]= "http://www.math.neu.edu/~shubin/mathindex.html"; PictureLink[20021025]= "http://www.math.neu.edu/~shubin/shubin.jpg"; University[20021025]= "Northeastern University"; UniversityLink[20021025]= " http://www.math.neu.edu/"; SecondUniversity[20021025]= "CNRS"; SecondUniversityLink[20021025]= " http://www.spm.cnrs-dir.fr/"; DateOfTalk[20021025]= "October 25, 2002"; DayOfWeek[20021025]= "Friday"; TimeOfTalk[20021025]= "2PM"; IsTimeDefault[20021025]= "1"; IsDateDefault[20021025]= "1"; Entry[20021025]= "1"; Comments[20021025]= " "; SeminarTitle[20020920]= "Analysis and Geometry"; Location[20020920]= "509LA"; Title[20020920]= "Differential operators, brackets and connections"; Abstract[20020920]= "I am going to describe remarkable relations between differential operators and bracket structures. It is known that an operator of the second order acting on functions defines a \"bracket\", i.e. a symmetric bilinear operation on functions satisfying the Leibniz rule (basically, the polarized principal symbol). This works on ordinary manifolds as well as on supermanifolds. In the super context, this gives a relation between odd Laplacians (or \"Batalin-Vilokovisky D-operators\") and odd Poisson brackets. I will show how this relation between differential operators and brackets can be made 1-1 if one considers the algebra of densities instead of the algebra of functions. This construction implicitly involves \"generalized\" connections: notice that every differential operator of the second order acting on functions encodes in its coefficients an \"upper connection\" in the bundle of volume forms (basically, the subprincipal symbol). An extension of these ideas to operators of higher order would lead to homotopy algebras.
   This is a joint work with Hovhannes Khudaverdian."; Speaker[20020920]= "Theodore Voronov"; SpeakerLink[20020920]= "http://www.ma.umist.ac.uk/tv/"; PictureLink[20020920]= "http://www.ma.umist.ac.uk/tv/ted252.jpg"; University[20020920]= "University of Manchester (UMIST)"; UniversityLink[20020920]= " http://www2.umist.ac.uk/mathematics/"; SecondUniversity[20020920]= " "; SecondUniversityLink[20020920]= " "; DateOfTalk[20020920]= "September 20, 2002"; DayOfWeek[20020920]= "Friday"; TimeOfTalk[20020920]= "2PM"; IsTimeDefault[20020920]= "1"; IsDateDefault[20020920]= "1"; Entry[20020920]= "1"; Comments[20020920]= " "; SeminarTitle[20021011]= "Analysis and Geometry"; Location[20021011]= "509LA"; Title[20021011]= "Moduli space of symmetric connections"; Abstract[20021011]= "We are interested in local differential invariants of a symmetric connection, under smooth coordinate changes. We consider the action of origin-preserving diffeomorphisms on a space of jets of connections and calculate dimensions of moduli spaces in generic case. We show that the corresponding Poincarè series is a rational function. This confirms one more time the 1894\' finitness claim of Tresse, stated for any \"natural\" differential-geometric structure."; Speaker[20021011]= "Stanislav Dubrovskiy"; SpeakerLink[20021011]= " "; PictureLink[20021011]= " "; University[20021011]= "Northeastern University"; UniversityLink[20021011]= " http://www.math.neu.edu/"; SecondUniversity[20021011]= " "; SecondUniversityLink[20021011]= " "; DateOfTalk[20021011]= "October 11, 2002"; DayOfWeek[20021011]= "Friday"; TimeOfTalk[20021011]= "2PM"; IsTimeDefault[20021011]= "1"; IsDateDefault[20021011]= "1"; Entry[20021011]= "1"; Comments[20021011]= " "; SeminarTitle[20021004]= "Analysis and Geometry"; Location[20021004]= "509LA"; Title[20021004]= "Bounds for eigenfunctions of the Laplacian on compact Riemannian manifolds"; Abstract[20021004]= "Suppose that φ is an eigenfunction of -Δ with eigenvalue λ≠0. It is proved that ||φ||_∞≤   c₁λ^(n-^1)/4||φ||₂, where n is the dimension of M and c₁ depends only upon a bound for the absolute value of the sectional curvature of M and a lower bound for the injectivity radius of M. It is then shown that if M admits an isometric circle action, and the metric is generic, one has exceptional sequences of eigenfunctions satisfying the complementary bounds ||φ_k||_∞≥   c₂λ _k^(n-^1)/8 ||φ_k|| ² ."; Speaker[20021004]= "Harold G. Donnelly"; SpeakerLink[20021004]= " "; PictureLink[20021004]= " "; University[20021004]= "Purdue University"; UniversityLink[20021004]= " http://www.math.purdue.edu/"; SecondUniversity[20021004]= " "; SecondUniversityLink[20021004]= " "; DateOfTalk[20021004]= "October 4, 2002"; DayOfWeek[20021004]= "Friday"; TimeOfTalk[20021004]= "2PM"; IsTimeDefault[20021004]= "1"; IsDateDefault[20021004]= "1"; Entry[20021004]= "1"; Comments[20021004]= " "; SeminarTitle[20021025]= "Analysis and Geometry"; Location[20021025]= "509LA"; Title[20021025]= "A new family of necessary and sufficient discreteness of spectrum conditions for Schrödinger operators"; Abstract[20021025]= "I will explain new criteria of discreteness of spectrum for the Schrödinger operators with semi-bounded below potentials. They extend a well known result by A.Molchanov (1953) who was the first to formulate a necessary and sufficient condition for the discreteness of spectrum in terms of the Wiener capacity.
   We provide a new family of such conditions which depend on a functional parameter describing \"negligible\" sets.
   (This is a joint work with V.Maz\'ya.)"; Speaker[20021025]= "Mikhail Shubin"; SpeakerLink[20021025]= "http://www.math.neu.edu/~shubin/mathindex.html"; PictureLink[20021025]= "http://www.math.neu.edu/~shubin/shubin.jpg"; University[20021025]= "Northeastern University"; UniversityLink[20021025]= " http://www.math.neu.edu/"; SecondUniversity[20021025]= " "; SecondUniversityLink[20021025]= " "; DateOfTalk[20021025]= "October 25, 2002"; DayOfWeek[20021025]= "Friday"; TimeOfTalk[20021025]= "2PM"; IsTimeDefault[20021025]= "1"; IsDateDefault[20021025]= "1"; Entry[20021025]= "1"; Comments[20021025]= " "; SeminarTitle[20021108]= "Analysis and Geometry"; Location[20021108]= "509LA"; Title[20021108]= "On cylindrically symmetric solutions of Einstein\'s field equation"; Abstract[20021108]= "I will present a stationary cylindrically symmetric solution of Einstein\'s equation with dust and positive cosmological constant. The solution approaches Einstein static universe on the axis of rotation."; Speaker[20021108]= "Mihaela Iftime"; SpeakerLink[20021108]= " "; PictureLink[20021108]= " "; University[20021108]= "Northeastern University"; UniversityLink[20021108]= " http://www.math.neu.edu/"; SecondUniversity[20021108]= " "; SecondUniversityLink[20021108]= " "; DateOfTalk[20021108]= "November 8, 2002"; DayOfWeek[20021108]= "Friday"; TimeOfTalk[20021108]= "2PM"; IsTimeDefault[20021108]= "1"; IsDateDefault[20021108]= "1"; Entry[20021108]= "1"; Comments[20021108]= " "; SeminarTitle[20021018]= "Analysis and Geometry"; Location[20021018]= "509LA"; Title[20021018]= "Milnor numbers of minimal surfaces in 4-manifolds"; Abstract[20021018]= "When a sequence of smooth embedded complex curves (C_n) in CP^2 degenerates to a branched curve C₀, we lose topology ( g(C_n)>g(C₀) ) and gain singularity. Milnor gave a precise meaning to this assertion. There is a quantity - now called the Milnor number - we can compute on the branch points of C₀ which tells us how much topology we have lost going from C_n to C₀.
   So we ask: is there anything even remotely similar if the C_n\'s and C₀ are more general surfaces (e.g. minimal surfaces) in a 4-manifold? Can we define a Milnor number for a sequence of minimal surfaces? It turns out that we have to define not one, but two Milnor numbers (the "tangent\" and the "normal\" one); these numbers coincide in the complex case.
   We will define these Milnor numbers, give explain geometric and topological interpretations and show how they give a partial answer to our question above."; Speaker[20021018]= "Marina Ville"; SpeakerLink[20021018]= " "; PictureLink[20021018]= " "; University[20021018]= "CNRS"; UniversityLink[20021018]= " http://www.spm.cnrs-dir.fr/"; SecondUniversity[20021018]= "Boston University"; SecondUniversityLink[20021018]= " http://math.bu.edu"; DateOfTalk[20021018]= "October 18, 2002"; DayOfWeek[20021018]= "Friday"; TimeOfTalk[20021018]= "2PM"; IsTimeDefault[20021018]= "1"; IsDateDefault[20021018]= "1"; Entry[20021018]= "1"; Comments[20021018]= " "; SeminarTitle[20021122]= "Analysis and Geometry"; Location[20021122]= "509LA"; Title[20021122]= "TBA"; Abstract[20021122]= "TBA"; Speaker[20021122]= "Jeff Viaclovsky"; SpeakerLink[20021122]= "http://www-math.mit.edu/~jeffv/"; PictureLink[20021122]= "http://www-math.mit.edu/~jeffv/Jeff1.jpg"; University[20021122]= "MIT"; UniversityLink[20021122]= " http://www-math.mit.edu/"; SecondUniversity[20021122]= " "; SecondUniversityLink[20021122]= " "; DateOfTalk[20021122]= "November 22, 2002"; DayOfWeek[20021122]= "Friday"; TimeOfTalk[20021122]= "2PM"; IsTimeDefault[20021122]= "1"; IsDateDefault[20021122]= "1"; Entry[20021122]= "1"; Comments[20021122]= " "; SeminarTitle[20021122]= "Analysis and Geometry"; Location[20021122]= "509LA"; Title[20021122]= "TBA"; Abstract[20021122]= "TBA"; Speaker[20021122]= "Jeff Viaclovsky"; SpeakerLink[20021122]= "http://www-math.mit.edu/~jeffv/"; PictureLink[20021122]= "http://www-math.mit.edu/~jeffv/Jeff1.jpg"; University[20021122]= "MIT"; UniversityLink[20021122]= " http://www-math.mit.edu/"; SecondUniversity[20021122]= ""; SecondUniversityLink[20021122]= " "; DateOfTalk[20021122]= "November 22, 2002"; DayOfWeek[20021122]= "Friday"; TimeOfTalk[20021122]= "2PM"; IsTimeDefault[20021122]= "1"; IsDateDefault[20021122]= "1"; Entry[20021122]= "1"; Comments[20021122]= " "; SeminarTitle[20021101]= "Analysis and Geometry"; Location[20021101]= "509LA"; Title[20021101]= "Mathematical theory of cracks: the Wiener-Hopf method"; Abstract[20021101]= "A crack in elastic media is modelled by the Neumann boundary value problem for a homogeneous second order partial differential equation with constant coefficients. We use potentials and the Wiener-Hopf method to obtain a full asymptotic expansion of the solution. We show that these asymptotics do not contain logarithmic terms."; Speaker[20021101]= "Roland Duduchava"; SpeakerLink[20021101]= "http://www.rmi.acnet.ge/~duduch/"; PictureLink[20021101]= "http://www.rmi.acnet.ge/~duduch/duduch70.jpg"; University[20021101]= "Razmadze Mathematical Institute (Tbilisi, Georgia)"; UniversityLink[20021101]= " http://www.rmi.acnet.ge/"; SecondUniversity[20021101]= " "; SecondUniversityLink[20021101]= " "; DateOfTalk[20021101]= "November 1, 2002"; DayOfWeek[20021101]= "Friday"; TimeOfTalk[20021101]= "2PM"; IsTimeDefault[20021101]= "1"; IsDateDefault[20021101]= "1"; Entry[20021101]= "1"; Comments[20021101]= " "; SeminarTitle[20020104]= "Analysis and Geometry"; Location[20020104]= "509LA"; Title[20020104]= "Noncommutative index on the quantum sphere"; Abstract[20020104]= "Noncommutative (NC) index was introduced by A.Connes.
Given a NC algebra A, NC index is defined as a pairing
            K₀(A) x K⁰(A)→ K
where K₀(A) is defined by projective A-modules,
K⁰(A) is defined by finite-dimensional A-modules,
and K is the basic field. In the talk I will introduce
quantum orbits whose particular case is a quantum sphere,
define a version of the NC index well adapted to the algebras
in question and compute NC index on this sphere.
"; Speaker[20020104]= "Dimitri Gourevitch"; SpeakerLink[20020104]= " "; PictureLink[20020104]= " "; University[20020104]= "Université de Valenciennes"; UniversityLink[20020104]= " http://www.univ-valenciennes.fr/lamath/"; SecondUniversity[20020104]= ""; SecondUniversityLink[20020104]= " "; DateOfTalk[20020104]= "January 4, 2002"; DayOfWeek[20020104]= "Friday"; TimeOfTalk[20020104]= "2PM"; IsTimeDefault[20020104]= "1"; IsDateDefault[20020104]= "1"; Entry[20020104]= "0"; Comments[20020104]= " "; SeminarTitle[20030110]= "Analysis and Geometry"; Location[20030110]= "509LA"; Title[20030110]= "Noncommutative index on the quantum sphere"; Abstract[20030110]= "Noncommutative (NC) index was introduced by A.Connes.
Given a NC algebra A, NC index is defined as a pairing
            K₀(A) x K⁰(A)→ K
where K₀(A) is defined by projective A-modules,
K⁰(A) is defined by finite-dimensional A-modules,
and K is the basic field. In the talk I will introduce
quantum orbits whose particular case is a quantum sphere,
define a version of the NC index well adapted to the algebras
in question and compute NC index on this sphere.
"; Speaker[20030110]= "Dimitri Gourevitch"; SpeakerLink[20030110]= " "; PictureLink[20030110]= " "; University[20030110]= "Université de Valenciennes"; UniversityLink[20030110]= " http://www.univ-valenciennes.fr/lamath/"; SecondUniversity[20030110]= " "; SecondUniversityLink[20030110]= " "; DateOfTalk[20030110]= "January 10, 2003"; DayOfWeek[20030110]= "Friday"; TimeOfTalk[20030110]= "2PM"; IsTimeDefault[20030110]= "1"; IsDateDefault[20030110]= "1"; Entry[20030110]= "1"; Comments[20030110]= " "; SeminarTitle[20030110]= "Analysis and Geometry"; Location[20030110]= "509LA"; Title[20030110]= "Noncommutative index on the quantum sphere"; Abstract[20030110]= "Noncommutative (NC) index was introduced by A.Connes.
Given a NC algebra A, NC index is defined as a pairing
            K₀(A) x K⁰(A)→ K
where K₀(A) is defined by projective A-modules, K⁰(A) is defined by finite-dimensional A-modules, and K is the basic field. In the talk I will introduce quantum orbits whose particular case is a quantum sphere, define a version of the NC index well adapted to the algebras in question and compute NC index on this sphere."; Speaker[20030110]= "Dimitri Gourevitch"; SpeakerLink[20030110]= " "; PictureLink[20030110]= " "; University[20030110]= "Université de Valenciennes"; UniversityLink[20030110]= " http://www.univ-valenciennes.fr/lamath/"; SecondUniversity[20030110]= " "; SecondUniversityLink[20030110]= " "; DateOfTalk[20030110]= "January 10, 2003"; DayOfWeek[20030110]= "Friday"; TimeOfTalk[20030110]= "2PM"; IsTimeDefault[20030110]= "1"; IsDateDefault[20030110]= "1"; Entry[20030110]= "1"; Comments[20030110]= " "; SeminarTitle[20021101]= "Analysis and Geometry"; Location[20021101]= "509LA"; Title[20021101]= "TBA"; Abstract[20021101]= "TBA"; Speaker[20021101]= "Jeff Viaclovsky"; SpeakerLink[20021101]= "http://www-math.mit.edu/~jeffv/"; PictureLink[20021101]= "http://www-math.mit.edu/~jeffv/Jeff1.jpg"; University[20021101]= "MIT"; UniversityLink[20021101]= " http://www-math.mit.edu/"; SecondUniversity[20021101]= " "; SecondUniversityLink[20021101]= " "; DateOfTalk[20021101]= "November 1, 2002"; DayOfWeek[20021101]= "Friday"; TimeOfTalk[20021101]= "2PM"; IsTimeDefault[20021101]= "1"; IsDateDefault[20021101]= "1"; Entry[20021101]= "1"; Comments[20021101]= " "; SeminarTitle[20021115]= "Analysis and Geometry"; Location[20021115]= "509LA"; Title[20021115]= "Associative cones and integrable system"; Abstract[20021115]= "(joint work with Shengli Kong)"; Speaker[20021115]= "Eric Wang"; SpeakerLink[20021115]= " "; PictureLink[20021115]= " "; University[20021115]= "Northeastern University"; UniversityLink[20021115]= " http://www.math.neu.edu/"; SecondUniversity[20021115]= " "; SecondUniversityLink[20021115]= " "; DateOfTalk[20021115]= "November 15, 2002"; DayOfWeek[20021115]= "Friday"; TimeOfTalk[20021115]= "2PM"; IsTimeDefault[20021115]= "1"; IsDateDefault[20021115]= "1"; Entry[20021115]= "1"; Comments[20021115]= " "; SeminarTitle[20021101]= "Analysis and Geometry"; Location[20021101]= "509LA"; Title[20021101]= "TBA"; Abstract[20021101]= "TBA"; Speaker[20021101]= "Jeff Viaclovsky"; SpeakerLink[20021101]= "http://www-math.mit.edu/~jeffv/"; PictureLink[20021101]= "http://www-math.mit.edu/~jeffv/Jeff1.jpg"; University[20021101]= "MIT"; UniversityLink[20021101]= " http://www-math.mit.edu/"; SecondUniversity[20021101]= " "; SecondUniversityLink[20021101]= " "; DateOfTalk[20021101]= "November 1, 2002"; DayOfWeek[20021101]= "Friday"; TimeOfTalk[20021101]= "2PM"; IsTimeDefault[20021101]= "1"; IsDateDefault[20021101]= "1"; Entry[20021101]= "0"; Comments[20021101]= " "; SeminarTitle[20021101]= "Analysis and Geometry"; Location[20021101]= "509LA"; Title[20021101]= "TBA"; Abstract[20021101]= "TBA"; Speaker[20021101]= "Jeff Viaclovsky"; SpeakerLink[20021101]= "http://www-math.mit.edu/~jeffv/"; PictureLink[20021101]= "http://www-math.mit.edu/~jeffv/Jeff1.jpg"; University[20021101]= "MIT"; UniversityLink[20021101]= " http://www-math.mit.edu/"; SecondUniversity[20021101]= " "; SecondUniversityLink[20021101]= " "; DateOfTalk[20021101]= "November 1, 2002"; DayOfWeek[20021101]= "Friday"; TimeOfTalk[20021101]= "2PM"; IsTimeDefault[20021101]= "1"; IsDateDefault[20021101]= "1"; Entry[20021101]= "1"; Comments[20021101]= " "; SeminarTitle[20021122]= "Analysis and Geometry"; Location[20021122]= "509LA"; Title[20021122]= "TBA"; Abstract[20021122]= "TBA"; Speaker[20021122]= "Jeff Viaclovsky"; SpeakerLink[20021122]= "http://www-math.mit.edu/~jeffv/"; PictureLink[20021122]= "http://www-math.mit.edu/~jeffv/Jeff1.jpg"; University[20021122]= "MIT"; UniversityLink[20021122]= " http://www-math.mit.edu/"; SecondUniversity[20021122]= " "; SecondUniversityLink[20021122]= " "; DateOfTalk[20021122]= "November 22, 2002"; DayOfWeek[20021122]= "Friday"; TimeOfTalk[20021122]= "2PM"; IsTimeDefault[20021122]= "1"; IsDateDefault[20021122]= "1"; Entry[20021122]= "1"; Comments[20021122]= " "; SeminarTitle[20021115]= "Analysis and Geometry"; Location[20021115]= "509LA"; Title[20021115]= "Associative cones and integrable system"; Abstract[20021115]= "Associative 3-manifolds play an important role in calibrated geometry of G₂manifolds. We study associative cones in R⁷ with isolated singularity. In particular, we give an integrable system formulation using moving frame. We will discuss some applications.
                   (joint work with Shengli Kong)"; Speaker[20021115]= "Eric Wang"; SpeakerLink[20021115]= " "; PictureLink[20021115]= " "; University[20021115]= "Northeastern University"; UniversityLink[20021115]= " http://www.math.neu.edu/"; SecondUniversity[20021115]= " "; SecondUniversityLink[20021115]= " "; DateOfTalk[20021115]= "November 15, 2002"; DayOfWeek[20021115]= "Friday"; TimeOfTalk[20021115]= "2PM"; IsTimeDefault[20021115]= "1"; IsDateDefault[20021115]= "1"; Entry[20021115]= "1"; Comments[20021115]= " "; SeminarTitle[20021101]= "Analysis and Geometry"; Location[20021101]= "509LA"; Title[20021101]= "TBA"; Abstract[20021101]= "TBA"; Speaker[20021101]= "Jeff Viaclovsky"; SpeakerLink[20021101]= "http://www-math.mit.edu/~jeffv/"; PictureLink[20021101]= "http://www-math.mit.edu/~jeffv/Jeff1.jpg"; University[20021101]= "MIT"; UniversityLink[20021101]= " http://www-math.mit.edu/"; SecondUniversity[20021101]= " "; SecondUniversityLink[20021101]= " "; DateOfTalk[20021101]= "November 1, 2002"; DayOfWeek[20021101]= "Friday"; TimeOfTalk[20021101]= "2PM"; IsTimeDefault[20021101]= "1"; IsDateDefault[20021101]= "1"; Entry[20021101]= "0"; Comments[20021101]= " "; SeminarTitle[20021101]= "Analysis and Geometry"; Location[20021101]= "509LA"; Title[20021101]= " Mathematical theory of cracks: the Wiener-Hopf method"; Abstract[20021101]= " A crack in elastic media is modelled by the Neumann boundary value problem for a homogeneous second order partial differential equation with constant coefficients. We use potentials and the Wiener-Hopf method to obtain a full asymptotic expansion of the solution. We show that these asymptotics do not contain logarithmic terms."; Speaker[20021101]= "Roland Duduchava"; SpeakerLink[20021101]= "http://www.rmi.acnet.ge/~duduch/"; PictureLink[20021101]= "http://www.rmi.acnet.ge/~duduch/duduch70.jpg"; University[20021101]= "Razmadze Mathematical Institute (Tbilisi, Georgia)"; UniversityLink[20021101]= " http://www.rmi.acnet.ge/"; SecondUniversity[20021101]= ""; SecondUniversityLink[20021101]= " "; DateOfTalk[20021101]= "November 1, 2002"; DayOfWeek[20021101]= "Friday"; TimeOfTalk[20021101]= "2PM"; IsTimeDefault[20021101]= "1"; IsDateDefault[20021101]= "1"; Entry[20021101]= "1"; Comments[20021101]= " "; SeminarTitle[20021101]= "Analysis and Geometry"; Location[20021101]= "509LA"; Title[20021101]= " Mathematical theory of cracks: the Wiener-Hopf method"; Abstract[20021101]= " A crack in elastic media is modelled by the Neumann boundary value problem for a homogeneous second order partial differential equation with constant coefficients. We use potentials and the Wiener-Hopf method to obtain a full asymptotic expansion of the solution. We show that these asymptotics do not contain logarithmic terms."; Speaker[20021101]= "Roland Duduchava"; SpeakerLink[20021101]= "http://www.rmi.acnet.ge/~duduch/"; PictureLink[20021101]= "http://www.rmi.acnet.ge/~duduch/duduch70.jpg"; University[20021101]= "Razmadze Mathematical Institute (Tbilisi, Georgia)"; UniversityLink[20021101]= " http://www.rmi.acnet.ge/"; SecondUniversity[20021101]= " "; SecondUniversityLink[20021101]= " "; DateOfTalk[20021101]= "November 1, 2002"; DayOfWeek[20021101]= "Friday"; TimeOfTalk[20021101]= "2PM"; IsTimeDefault[20021101]= "1"; IsDateDefault[20021101]= "1"; Entry[20021101]= "1"; Comments[20021101]= " "; SeminarTitle[20021122]= "Analysis and Geometry"; Location[20021122]= "509LA"; Title[20021122]= "TBA"; Abstract[20021122]= "TBA"; Speaker[20021122]= "Roland Duduchava"; SpeakerLink[20021122]= "http://www.rmi.acnet.ge/~duduch/"; PictureLink[20021122]= "http://www.rmi.acnet.ge/~duduch/duduch70.jpg"; University[20021122]= "Razmadze Mathematical Institute (Tbilisi, Georgia)"; UniversityLink[20021122]= " http://www.rmi.acnet.ge/"; SecondUniversity[20021122]= " "; SecondUniversityLink[20021122]= " "; DateOfTalk[20021122]= "November 22, 2002"; DayOfWeek[20021122]= "Friday"; TimeOfTalk[20021122]= "2PM"; IsTimeDefault[20021122]= "1"; IsDateDefault[20021122]= "1"; Entry[20021122]= "0"; Comments[20021122]= " "; SeminarTitle[20021122]= "Analysis and Geometry"; Location[20021122]= "509LA"; Title[20021122]= "Fully nonlinear equations on Riemannian manifolds"; Abstract[20021122]= "We define a conformal invariant using maximal volumes, and use this to prove existence of solutions to a class of conformally invariant fully nonlinear second order PDEs."; Speaker[20021122]= "Jeff Viaclovsky"; SpeakerLink[20021122]= "http://www-math.mit.edu/~jeffv/"; PictureLink[20021122]= "http://www-math.mit.edu/~jeffv/Jeff1.jpg"; University[20021122]= "MIT"; UniversityLink[20021122]= " http://www-math.mit.edu/"; SecondUniversity[20021122]= " "; SecondUniversityLink[20021122]= " "; DateOfTalk[20021122]= "November 22, 2002"; DayOfWeek[20021122]= "Friday"; TimeOfTalk[20021122]= "2PM"; IsTimeDefault[20021122]= "1"; IsDateDefault[20021122]= "1"; Entry[20021122]= "1"; Comments[20021122]= " "; SeminarTitle[20030110]= "Analysis and Geometry"; Location[20030110]= "509LA"; Title[20030110]= "Noncommutative index on the quantum sphere"; Abstract[20030110]= "Noncommutative (NC) index was introduced by A.Connes.
Given a NC algebra A, NC index is defined as a pairing
            K₀(A) x K⁰(A)→ K
where K₀(A) is defined by projective A-modules, K⁰(A) is defined by finite-dimensional A-modules, and K is the basic field. In the talk I will introduce quantum orbits whose particular case is a quantum sphere, define a version of the NC index well adapted to the algebras in question and compute NC index on this sphere."; Speaker[20030110]= "Dimitri Gourevitch"; SpeakerLink[20030110]= " "; PictureLink[20030110]= " "; University[20030110]= "Université de Valenciennes"; UniversityLink[20030110]= " http://www.univ-valenciennes.fr/lamath/"; SecondUniversity[20030110]= ""; SecondUniversityLink[20030110]= " "; DateOfTalk[20030110]= "January 10, 2003"; DayOfWeek[20030110]= "Friday"; TimeOfTalk[20030110]= "2PM"; IsTimeDefault[20030110]= "1"; IsDateDefault[20030110]= "1"; Entry[20030110]= "1"; Comments[20030110]= " "; SeminarTitle[20030110]= "Analysis and Geometry"; Location[20030110]= "509LA"; Title[20030110]= "Noncommutative index on the quantum sphere"; Abstract[20030110]= "Noncommutative (NC) index was introduced by A.Connes.
Given a NC algebra A, NC index is defined as a pairing
            K₀(A) x K⁰(A)→ K
where K₀(A) is defined by projective A-modules, K⁰(A) is defined by finite-dimensional A-modules, and K is the basic field. In the talk I will introduce quantum orbits whose particular case is a quantum sphere, define a version of the NC index well adapted to the algebras in question and compute NC index on this sphere."; Speaker[20030110]= "Dimitri Gourevitch"; SpeakerLink[20030110]= " "; PictureLink[20030110]= " "; University[20030110]= "Université de Valenciennes"; UniversityLink[20030110]= " http://www.univ-valenciennes.fr/lamath/"; SecondUniversity[20030110]= " "; SecondUniversityLink[20030110]= " "; DateOfTalk[20030110]= "January 10, 2003"; DayOfWeek[20030110]= "Friday"; TimeOfTalk[20030110]= "2PM"; IsTimeDefault[20030110]= "1"; IsDateDefault[20030110]= "1"; Entry[20030110]= "1"; Comments[20030110]= " "; SeminarTitle[20021206]= "Analysis and Geometry"; Location[20021206]= "509LA"; Title[20021206]= "Classification of Prime 3-Manifolds with Yamabe Invariant Greater Than RP³"; Abstract[20021206]= "In a joint work with Andre Neves, we classify prime 3-manifolds with Yamabe invariant greater than Y₂, the Yamabe invariant of RP³. The Yamabe invariant of a closed manifold is a smooth topological invariant which is defined geometrically and reduces to the Euler characteristic in dimension 2 by the Gauss Bonnet formula. However, prior to this work, the only known values of the Yamabe invariant for 3-manifolds had been 0 and
                    Y₁ = 6 (2p²)^2/3,
the Yamabe invariant of S³. We increase the number of known values by 50% by proving that the Yamabe invariants of RP³ and RP²xS¹ are equal to Y₂ = Y₁/2^2/3. We also prove that any 3-manifold with Yamabe invariant Y > Y₂ must either be S³ or a connect sum with an S² bundle over S² (S²xS¹ or the 3-dimensional Klein bottle). Hence, the Poincare conjecture for manifolds with Y > Y₂ (which includes an infinite number of 3-manifolds) follows. Also, since the classification of 3-manifolds reduces to the classification of prime 3-manifolds, it is natural to try to make a list of prime 3-manifolds. Ordered by their Yamabe invariants, we conclude that the first five prime 3-manifolds are S³, S² xS¹, K (the 3-dimensional Klein bottle), RP³, and RP² xS¹."; Speaker[20021206]= "Hubert Bray"; SpeakerLink[20021206]= "http://www-math.mit.edu/~bray/"; PictureLink[20021206]= "http://www-math.mit.edu/~bray/bray.jpg"; University[20021206]= "MIT"; UniversityLink[20021206]= " http://www-math.mit.edu/"; SecondUniversity[20021206]= "Torun, Poland"; SecondUniversityLink[20021206]= " http://www.mat.uni.torun.pl/en/"; DateOfTalk[20021206]= "December 6, 2002"; DayOfWeek[20021206]= "Friday"; TimeOfTalk[20021206]= "2PM"; IsTimeDefault[20021206]= "1"; IsDateDefault[20021206]= "1"; Entry[20021206]= "1"; Comments[20021206]= " "; SeminarTitle[20021206]= "Analysis and Geometry"; Location[20021206]= "509LA"; Title[20021206]= "Classification of Prime 3-Manifolds with Yamabe Invariant Greater Than RP³"; Abstract[20021206]= "In a joint work with Andre Neves, we classify prime 3-manifolds with Yamabe invariant greater than Y₂, the Yamabe invariant of RP³. The Yamabe invariant of a closed manifold is a smooth topological invariant which is defined geometrically and reduces to the Euler characteristic in dimension 2 by the Gauss Bonnet formula. However, prior to this work, the only known values of the Yamabe invariant for 3-manifolds had been 0 and
                    Y₁ = 6 (2p²)^2/3,
the Yamabe invariant of S³. We increase the number of known values by 50% by proving that the Yamabe invariants of RP³ and RP²xS¹ are equal to Y₂ = Y₁/2^2/3. We also prove that any 3-manifold with Yamabe invariant Y > Y₂ must either be S³ or a connect sum with an S² bundle over S² (S²xS¹ or the 3-dimensional Klein bottle). Hence, the Poincare conjecture for manifolds with Y > Y₂ (which includes an infinite number of 3-manifolds) follows. Also, since the classification of 3-manifolds reduces to the classification of prime 3-manifolds, it is natural to try to make a list of prime 3-manifolds. Ordered by their Yamabe invariants, we conclude that the first five prime 3-manifolds are S³, S² xS¹, K (the 3-dimensional Klein bottle), RP³, and RP² xS¹."; Speaker[20021206]= "Hubert Bray"; SpeakerLink[20021206]= "http://www-math.mit.edu/~bray/"; PictureLink[20021206]= "http://www-math.mit.edu/~bray/bray.jpg"; University[20021206]= "MIT"; UniversityLink[20021206]= " http://www-math.mit.edu/"; SecondUniversity[20021206]= " "; SecondUniversityLink[20021206]= " "; DateOfTalk[20021206]= "December 6, 2002"; DayOfWeek[20021206]= "Friday"; TimeOfTalk[20021206]= "2PM"; IsTimeDefault[20021206]= "1"; IsDateDefault[20021206]= "1"; Entry[20021206]= "1"; Comments[20021206]= " "; SeminarTitle[20021206]= "Analysis and Geometry"; Location[20021206]= "509LA"; Title[20021206]= "Classification of Prime 3-Manifolds with Yamabe Invariant Greater Than RP³"; Abstract[20021206]= "In a joint work with Andre Neves, we classify prime 3-manifolds with Yamabe invariant greater than Y₂, the Yamabe invariant of RP³. The Yamabe invariant of a closed manifold is a smooth topological invariant which is defined geometrically and reduces to the Euler characteristic in dimension 2 by the Gauss Bonnet formula. However, prior to this work, the only known values of the Yamabe invariant for 3-manifolds had been 0 and
                    Y₁ = 6 (2p²)^2/3,
the Yamabe invariant of S³. We increase the number of known values by 50% by proving that the Yamabe invariants of RP³ and RP²xS¹ are equal to Y₂ = Y₁/2^2/3. We also prove that any 3-manifold with Yamabe invariant Y > Y₂ must either be S³ or a connect sum with an S² bundle over S² (S²xS¹ or the 3-dimensional Klein bottle). Hence, the Poincare conjecture for manifolds with Y > Y₂ (which includes an infinite number of 3-manifolds) follows. Also, since the classification of 3-manifolds reduces to the classification of prime 3-manifolds, it is natural to try to make a list of prime 3-manifolds. Ordered by their Yamabe invariants, we conclude that the first five prime 3-manifolds are S³, S²xS¹, K (the 3-dimensional Klein bottle), RP³, and RP² xS¹."; Speaker[20021206]= "Hubert Bray"; SpeakerLink[20021206]= "http://www-math.mit.edu/~bray/"; PictureLink[20021206]= "http://www-math.mit.edu/~bray/bray.jpg"; University[20021206]= "MIT"; UniversityLink[20021206]= " http://www-math.mit.edu/"; SecondUniversity[20021206]= ""; SecondUniversityLink[20021206]= " "; DateOfTalk[20021206]= "December 6, 2002"; DayOfWeek[20021206]= "Friday"; TimeOfTalk[20021206]= "2PM"; IsTimeDefault[20021206]= "1"; IsDateDefault[20021206]= "1"; Entry[20021206]= "1"; Comments[20021206]= " "; SeminarTitle[20021206]= "Analysis and Geometry"; Location[20021206]= "509LA"; Title[20021206]= "Classification of Prime 3-Manifolds with Yamabe Invariant Greater Than RP³"; Abstract[20021206]= "In a joint work with Andre Neves, we classify prime 3-manifolds with Yamabe invariant greater than Y₂, the Yamabe invariant of RP³. The Yamabe invariant of a closed manifold is a smooth topological invariant which is defined geometrically and reduces to the Euler characteristic in dimension 2 by the Gauss Bonnet formula. However, prior to this work, the only known values of the Yamabe invariant for 3-manifolds had been 0 and
                    Y₁ = 6 (2p²)^2/3,
the Yamabe invariant of S³. We increase the number of known values by 50% by proving that the Yamabe invariants of RP³ and RP²xS¹ are equal to Y₂ = Y₁/2^2/3. We also prove that any 3-manifold with Yamabe invariant Y > Y₂ must either be S³ or a connect sum with an S² bundle over S² (S²xS¹ or the 3-dimensional Klein bottle). Hence, the Poincare conjecture for manifolds with Y > Y₂ (which includes an infinite number of 3-manifolds) follows. Also, since the classification of 3-manifolds reduces to the classification of prime 3-manifolds, it is natural to try to make a list of prime 3-manifolds. Ordered by their Yamabe invariants, we conclude that the first five prime 3-manifolds are S³, S²xS¹, K (the 3-dimensional Klein bottle), RP³, and RP² xS¹."; Speaker[20021206]= "Hubert Bray"; SpeakerLink[20021206]= "http://www-math.mit.edu/~bray/"; PictureLink[20021206]= "http://www-math.mit.edu/~bray/bray.jpg"; University[20021206]= "MIT"; UniversityLink[20021206]= " http://www-math.mit.edu/"; SecondUniversity[20021206]= " "; SecondUniversityLink[20021206]= " "; DateOfTalk[20021206]= "December 6, 2002"; DayOfWeek[20021206]= "Friday"; TimeOfTalk[20021206]= "2PM"; IsTimeDefault[20021206]= "1"; IsDateDefault[20021206]= "1"; Entry[20021206]= "1"; Comments[20021206]= " "; SeminarTitle[20021206]= "Analysis and Geometry"; Location[20021206]= "509LA"; Title[20021206]= "Classification of Prime 3-Manifolds with Yamabe Invariant Greater Than RP³"; Abstract[20021206]= "In a joint work with Andre Neves, we classify prime 3-manifolds with Yamabe invariant greater than Y₂, the Yamabe invariant of RP³. The Yamabe invariant of a closed manifold is a smooth topological invariant which is defined geometrically and reduces to the Euler characteristic in dimension 2 by the Gauss Bonnet formula. However, prior to this work, the only known values of the Yamabe invariant for 3-manifolds had been 0 and
                    Y₁ = 6 (2p²)^2/3,
the Yamabe invariant of S³. We increase the number of known values by 50% by proving that the Yamabe invariants of RP³ and RP²xS¹ are equal to Y₂ = Y₁/2^2/3. We also prove that any 3-manifold with Yamabe invariant Y > Y₂ must either be S³ or a connect sum with an S² bundle over S² (S²xS¹ or the 3-dimensional Klein bottle). Hence, the Poincare conjecture for manifolds with Y > Y₂ (which includes an infinite number of 3-manifolds) follows. Also, since the classification of 3-manifolds reduces to the classification of prime 3-manifolds, it is natural to try to make a list of prime 3-manifolds. Ordered by their Yamabe invariants, we conclude that the first five prime 3-manifolds are S³, S²xS¹, K (the 3-dimensional Klein bottle), RP³, and RP² xS¹."; Speaker[20021206]= "Hubert Bray"; SpeakerLink[20021206]= "http://www-math.mit.edu/~bray/"; PictureLink[20021206]= "http://www-math.mit.edu/~bray/bray.jpg"; University[20021206]= "MIT"; UniversityLink[20021206]= " http://www-math.mit.edu/"; SecondUniversity[20021206]= ""; SecondUniversityLink[20021206]= " "; DateOfTalk[20021206]= "December 6, 2002"; DayOfWeek[20021206]= "Friday"; TimeOfTalk[20021206]= "2PM"; IsTimeDefault[20021206]= "1"; IsDateDefault[20021206]= "1"; Entry[20021206]= "1"; Comments[20021206]= " "; SeminarTitle[20021206]= "Analysis and Geometry"; Location[20021206]= "509LA"; Title[20021206]= "Classification of Prime 3-Manifolds with Yamabe Invariant Greater Than RP³"; Abstract[20021206]= "In a joint work with Andre Neves, we classify prime 3-manifolds with Yamabe invariant greater than Y₂, the Yamabe invariant of RP³. The Yamabe invariant of a closed manifold is a smooth topological invariant which is defined geometrically and reduces to the Euler characteristic in dimension 2 by the Gauss Bonnet formula. However, prior to this work, the only known values of the Yamabe invariant for 3-manifolds had been 0 and
                    Y₁ = 6 (2p²)^2/3,
the Yamabe invariant of S³. We increase the number of known values by 50% by proving that the Yamabe invariants of RP³ and RP²xS¹ are equal to Y₂ = Y₁/2^2/3. We also prove that any 3-manifold with Yamabe invariant Y > Y₂ must either be S³ or a connect sum with an S² bundle over S² (S²xS¹ or the 3-dimensional Klein bottle). Hence, the Poincare conjecture for manifolds with Y > Y₂ (which includes an infinite number of 3-manifolds) follows. Also, since the classification of 3-manifolds reduces to the classification of prime 3-manifolds, it is natural to try to make a list of prime 3-manifolds. Ordered by their Yamabe invariants, we conclude that the first five prime 3-manifolds are S³, S²xS¹, K (the 3-dimensional Klein bottle), RP³, and RP² xS¹."; Speaker[20021206]= "Hubert Bray"; SpeakerLink[20021206]= "http://www-math.mit.edu/~bray/"; PictureLink[20021206]= "http://www-math.mit.edu/~bray/bray.jpg"; University[20021206]= "MIT"; UniversityLink[20021206]= " http://www-math.mit.edu/"; SecondUniversity[20021206]= " "; SecondUniversityLink[20021206]= " "; DateOfTalk[20021206]= "December 6, 2002"; DayOfWeek[20021206]= "Friday"; TimeOfTalk[20021206]= "2PM"; IsTimeDefault[20021206]= "1"; IsDateDefault[20021206]= "1"; Entry[20021206]= "1"; Comments[20021206]= " "; SeminarTitle[20021206]= "Analysis and Geometry"; Location[20021206]= "509LA"; Title[20021206]= "Classification of Prime 3-Manifolds with Yamabe Invariant Greater Than RP³"; Abstract[20021206]= "In a joint work with Andre Neves, we classify prime 3-manifolds with Yamabe invariant greater than Y₂, the Yamabe invariant of RP³. The Yamabe invariant of a closed manifold is a smooth topological invariant which is defined geometrically and reduces to the Euler characteristic in dimension 2 by the Gauss Bonnet formula. However, prior to this work, the only known values of the Yamabe invariant for 3-manifolds had been 0 and
                    Y₁ = 6 (2p²)^2/3,
the Yamabe invariant of S³. We increase the number of known values by 50% by proving that the Yamabe invariants of RP³ and RP²xS¹ are equal to Y₂ = Y₁/2^2/3. We also prove that any 3-manifold with Yamabe invariant Y > Y₂ must either be S³ or a connect sum with an S² bundle over S² (S²xS¹ or the 3-dimensional Klein bottle). Hence, the Poincare conjecture for manifolds with Y > Y₂ (which includes an infinite number of 3-manifolds) follows. Also, since the classification of 3-manifolds reduces to the classification of prime 3-manifolds, it is natural to try to make a list of prime 3-manifolds. Ordered by their Yamabe invariants, we conclude that the first five prime 3-manifolds are S³, S²xS¹, K (the 3-dimensional Klein bottle), RP³, and RP² xS¹."; Speaker[20021206]= "Hubert Bray"; SpeakerLink[20021206]= "http://www-math.mit.edu/~bray/"; PictureLink[20021206]= "http://www-math.mit.edu/~bray/bray.jpg"; University[20021206]= "MIT"; UniversityLink[20021206]= " http://www-math.mit.edu/"; SecondUniversity[20021206]= ""; SecondUniversityLink[20021206]= " "; DateOfTalk[20021206]= "December 6, 2002"; DayOfWeek[20021206]= "Friday"; TimeOfTalk[20021206]= "2PM"; IsTimeDefault[20021206]= "1"; IsDateDefault[20021206]= "1"; Entry[20021206]= "1"; Comments[20021206]= " "; SeminarTitle[20021206]= "Analysis and Geometry"; Location[20021206]= "509LA"; Title[20021206]= "Classification of Prime 3-Manifolds with Yamabe Invariant Greater Than RP³"; Abstract[20021206]= "In a joint work with Andre Neves, we classify prime 3-manifolds with Yamabe invariant greater than Y₂, the Yamabe invariant of RP³. The Yamabe invariant of a closed manifold is a smooth topological invariant which is defined geometrically and reduces to the Euler characteristic in dimension 2 by the Gauss Bonnet formula. However, prior to this work, the only known values of the Yamabe invariant for 3-manifolds had been 0 and
                    Y₁ = 6 (2p²)^2/3,
the Yamabe invariant of S³. We increase the number of known values by 50% by proving that the Yamabe invariants of RP³ and RP²xS¹ are equal to Y₂ = Y₁/2^2/3. We also prove that any 3-manifold with Yamabe invariant Y > Y₂ must either be S³ or a connect sum with an S² bundle over S² (S²xS¹ or the 3-dimensional Klein bottle). Hence, the Poincare conjecture for manifolds with Y > Y₂ (which includes an infinite number of 3-manifolds) follows. Also, since the classification of 3-manifolds reduces to the classification of prime 3-manifolds, it is natural to try to make a list of prime 3-manifolds. Ordered by their Yamabe invariants, we conclude that the first five prime 3-manifolds are S³, S²xS¹, K (the 3-dimensional Klein bottle), RP³, and RP² xS¹."; Speaker[20021206]= "Hubert Bray"; SpeakerLink[20021206]= "http://www-math.mit.edu/~bray/"; PictureLink[20021206]= "http://www-math.mit.edu/~bray/bray.jpg"; University[20021206]= "MIT"; UniversityLink[20021206]= " http://www-math.mit.edu/"; SecondUniversity[20021206]= " "; SecondUniversityLink[20021206]= " "; DateOfTalk[20021206]= "December 6, 2002"; DayOfWeek[20021206]= "Friday"; TimeOfTalk[20021206]= "2PM"; IsTimeDefault[20021206]= "1"; IsDateDefault[20021206]= "1"; Entry[20021206]= "1"; Comments[20021206]= " "; SeminarTitle[20021206]= "Analysis and Geometry"; Location[20021206]= "509LA"; Title[20021206]= "Classification of Prime 3-Manifolds with Yamabe Invariant Greater Than RP³"; Abstract[20021206]= "In a joint work with Andre Neves, we classify prime 3-manifolds with Yamabe invariant greater than Y₂, the Yamabe invariant of RP³. The Yamabe invariant of a closed manifold is a smooth topological invariant which is defined geometrically and reduces to the Euler characteristic in dimension 2 by the Gauss Bonnet formula. However, prior to this work, the only known values of the Yamabe invariant for 3-manifolds had been 0 and
                    Y₁ = 6 (2p²)^2/3,
the Yamabe invariant of S³. We increase the number of known values by 50% by proving that the Yamabe invariants of RP³ and RP²xS¹ are equal to Y₂ = Y₁/2^2/3. We also prove that any 3-manifold with Yamabe invariant Y > Y₂ must either be S³ or a connect sum with an S² bundle over S² (S²xS¹ or the 3-dimensional Klein bottle). Hence, the Poincare conjecture for manifolds with Y > Y₂ (which includes an infinite number of 3-manifolds) follows. Also, since the classification of 3-manifolds reduces to the classification of prime 3-manifolds, it is natural to try to make a list of prime 3-manifolds. Ordered by their Yamabe invariants, we conclude that the first five prime 3-manifolds are S³, S²xS¹, K (the 3-dimensional Klein bottle), RP³, and RP² xS¹."; Speaker[20021206]= "Hubert Bray"; SpeakerLink[20021206]= "http://www-math.mit.edu/~bray/"; PictureLink[20021206]= "http://www-math.mit.edu/~bray/bray.jpg"; University[20021206]= "MIT"; UniversityLink[20021206]= " http://www-math.mit.edu/"; SecondUniversity[20021206]= " "; SecondUniversityLink[20021206]= " "; DateOfTalk[20021206]= "December 6, 2002"; DayOfWeek[20021206]= "Friday"; TimeOfTalk[20021206]= "2PM"; IsTimeDefault[20021206]= "1"; IsDateDefault[20021206]= "1"; Entry[20021206]= "1"; Comments[20021206]= " "; SeminarTitle[20021206]= "Analysis and Geometry"; Location[20021206]= "509LA"; Title[20021206]= "Classification of Prime 3-Manifolds with Yamabe Invariant Greater Than RP³"; Abstract[20021206]= "In a joint work with Andre Neves, we classify prime 3-manifolds with Yamabe invariant greater than Y₂, the Yamabe invariant of RP³. The Yamabe invariant of a closed manifold is a smooth topological invariant which is defined geometrically and reduces to the Euler characteristic in dimension 2 by the Gauss Bonnet formula. However, prior to this work, the only known values of the Yamabe invariant for 3-manifolds had been 0 and
                    Y₁ = 6 (2p²)^2/3,
the Yamabe invariant of S³. We increase the number of known values by 50% by proving that the Yamabe invariants of RP³ and RP²xS¹ are equal to Y₂ = Y₁/2^2/3. We also prove that any 3-manifold with Yamabe invariant Y > Y₂ must either be S³ or a connect sum with an S² bundle over S² (S²xS¹ or the 3-dimensional Klein bottle). Hence, the Poincare conjecture for manifolds with Y > Y₂ (which includes an infinite number of 3-manifolds) follows. Also, since the classification of 3-manifolds reduces to the classification of prime 3-manifolds, it is natural to try to make a list of prime 3-manifolds. Ordered by their Yamabe invariants, we conclude that the first five prime 3-manifolds are S³, S²xS¹, K (the 3-dimensional Klein bottle), RP³, and RP² xS¹."; Speaker[20021206]= "Hubert Bray"; SpeakerLink[20021206]= "http://www-math.mit.edu/~bray/"; PictureLink[20021206]= "http://www-math.mit.edu/~bray/bray.jpg"; University[20021206]= "MIT"; UniversityLink[20021206]= " http://www-math.mit.edu/"; SecondUniversity[20021206]= "Torun, Poland"; SecondUniversityLink[20021206]= " http://www.mat.uni.torun.pl/en/"; DateOfTalk[20021206]= "December 6, 2002"; DayOfWeek[20021206]= "Friday"; TimeOfTalk[20021206]= "2PM"; IsTimeDefault[20021206]= "1"; IsDateDefault[20021206]= "1"; Entry[20021206]= "1"; Comments[20021206]= " "; SeminarTitle[20021206]= "Analysis and Geometry"; Location[20021206]= "509LA"; Title[20021206]= "Classification of Prime 3-Manifolds with Yamabe Invariant Greater Than RP³"; Abstract[20021206]= "In a joint work with Andre Neves, we classify prime 3-manifolds with Yamabe invariant greater than Y₂, the Yamabe invariant of RP³. The Yamabe invariant of a closed manifold is a smooth topological invariant which is defined geometrically and reduces to the Euler characteristic in dimension 2 by the Gauss Bonnet formula. However, prior to this work, the only known values of the Yamabe invariant for 3-manifolds had been 0 and
                    Y₁ = 6 (2p²)^2/3,
the Yamabe invariant of S³. We increase the number of known values by 50% by proving that the Yamabe invariants of RP³ and RP²xS¹ are equal to Y₂ = Y₁/2^2/3. We also prove that any 3-manifold with Yamabe invariant Y > Y₂ must either be S³ or a connect sum with an S² bundle over S² (S²xS¹ or the 3-dimensional Klein bottle). Hence, the Poincare conjecture for manifolds with Y > Y₂ (which includes an infinite number of 3-manifolds) follows. Also, since the classification of 3-manifolds reduces to the classification of prime 3-manifolds, it is natural to try to make a list of prime 3-manifolds. Ordered by their Yamabe invariants, we conclude that the first five prime 3-manifolds are S³, S²xS¹, K (the 3-dimensional Klein bottle), RP³, and RP² xS¹."; Speaker[20021206]= "Hubert Bray"; SpeakerLink[20021206]= "http://www-math.mit.edu/~bray/"; PictureLink[20021206]= "http://www-math.mit.edu/~bray/bray.jpg"; University[20021206]= "MIT"; UniversityLink[20021206]= " http://www-math.mit.edu/"; SecondUniversity[20021206]= " "; SecondUniversityLink[20021206]= " "; DateOfTalk[20021206]= "December 6, 2002"; DayOfWeek[20021206]= "Friday"; TimeOfTalk[20021206]= "2PM"; IsTimeDefault[20021206]= "1"; IsDateDefault[20021206]= "1"; Entry[20021206]= "1"; Comments[20021206]= " ";