The current organizer of the seminar is Maxim Braverman.
 

• November 1, 2000

Speaker: Andreas M Kollross (Northeastern)
Title: Locally symmetric spaces
Abstract: This talk is meant to be a short introduction to the theory of locally and globally Riemannian symmetric spaces.  We will talk about some of their elementary properties, curvature, examples, duality and the classification.
 
• November 8, 2000

Speaker: Maxim Braverman (Northeastern)
Title: Dirac operators and their determinants
Abstract: In the first part of the talk I will give a brief introduction to the theory of Clifford algebras  and Dirac operators. The notion of spinors will be introduced and discussed. In the second part of the talk I'll discuss the notion of a determinant of an elliptic operator on a compact manifold.
 
• September 24, 2004 at 204 BK (Note the unusual place)
  Speaker: Maxim Braverman (Northeastern)
  Title: Pseudo-Differential Operators
  Abstract: I will review the construction and the basic properties of pseudo-differential operators on manifolds. I will explain why the pseudo-differential operators are useful. I will also discuss some other algebras of symbols and explain the reason people look at those algebras. 
     This talk will provide a necessary background for the talk of  Pablo Ramacher on Analysis and Geometry Seminar
  .
• October 15, 2004
at 511 LA
Speaker: Maxim Braverman (Northeastern)
Title: Witten's proof of Morse inequalities
Abstract: In 1982 Ed Witten suggested a new analytic approach to the proof of the Morse inequalities. This method proved to be very useful in the study of spectral invariant of differential operators on manifolds: the spectral invariants tie together the geometric and the topological properties of the manifold.   In essence, Witten's method allows to separate the "geometry" from the "topology".
    I will describe the Witten's proof of the Morse inequalities and will explain how it can be generalized to the study of other spectral problems. I will indicate several applications to topology and complex geometry.
   This talk will provide some background for my talk on Analysis and Geometry Seminar.


• October 22, 2004
at 511 LA
Speaker: Nilufer  Koldan (Northeastern)
Title: A Compactness Condition for Fedosov Manifolds
Abstract: A Fedosov manifold is a triple (M, w, G) where M is a C^∞ manifold, w is a non-degenerate closed exterior 2-form on M and G  is a symmetric connection which preserves the form w  in the sense that w =0.  I will give a definition of sectional curvature on Fedosov manifold and two examples that lead one to believe that Myers theorem about compactness of a Riemannian manifold might also hold for Fedosov manifolds.


• October 29, 2004
at 511 LA
Speaker: Mikhail Shubin (Northeastern)
Title: Distributions and Sobolev spaces on the real line
Abstract: The theory of distributions, created in 1930-1940's by S.Sobolev and L.Schwartz, includes all locally integrable functions into a larger space of distributions which can be differentiated infinitely many times. Restricting growth at infinity we may take Fourier transform of distributions.
     Sobolev spaces are particular Hilbert (or Banach) spaces of distributions which simplify full scale application of functional analysis to differential equations. I will explain definitions and elementary properties of distributions and Sobolev spaces on the real line.
   This talk will provide some background  for my talk on Analysis and Geometry Seminar.

• December 3, 2004
  Speaker:  Gideon Maschler (University of Toronto)
  Title: Kahler-Einstein Manifolds
   
• January 21, 2005
  Speaker:  Gabriel Katz (Bennington College)
  Title: How to compute the homology of a fat S in terms of its height function?
  Abstract:  I will explain how to construct the Morse-Smale complex  for a Morse function on a manifold with boundary  (the function is not constant on the boundary). The homology  of this complex  is isomorphic to the absolute homology of the  manifold.
     This talk will provide some background  for my talk on Analysis and Geometry Seminar.
    
• February 3, 2005,  11:30 AM (Note the special date and time)
  Speaker:  Mikhail Agranovich (Moscow Institute of Electronics and Mathematics, Russia)
  Title: Elliptic Boundary Value Problem
   
•   February 11, 2005,  11:30 AM
  Speaker:  Joseph Coffey (New York University)
  Title:  Introduction to the H-principal
  Abstract:  TBA



• March 25, 2005  10:30 AM (Note the special time)
  Speaker:  Raphaël Ponge (Ohio State University)
  Title: Introduction to the non-commutative residue.
  Abstract:  The noncommutative residue is a trace on the algebra of pseudodifferential operators which was independently discovered by Wodzicki and Guillemin. It has many applications in geometric analysis, noncommutative geometry and mathematical physics. The aim of this talk will be to present an elementary construction of the noncommutative residue and to give an overview of its main properties.
   

• January 20, 2006
  Speaker:  Peter Topalov (Northeastern University)
  Title: Integrable equations, conservation laws and  Lax pairs
   
• March 24, 2006
  Speaker:  Mihai Stoiciu (Williams College)
  Title: Orthogonal Polynomials on the Unit Circle and CMV Matrices
  Abstract: We will give a brief introduction to orthogonal polynomials on the unit circle and CMV matrices. We will present a few important results on the spectral theory of CMV matrices.
   
• March 31, 2006
  Speaker:  Mikhail Shubin (Northeastern University)
  Title: Spectral theory of periodic Schrödinger operators
  Abstract: The spectrum of the Schrödinger operator with a periodic potential has a band structure which can be understood through the Bloch decomposition. This decomposition allows to present any  L²  function as a superposition of Bloch waves, parametrized by points of a torus of quasimomenta, and is similar to the Fourier transform.

 

Seminars and Colloquia

 

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Created: August 20, 2000. Last modified: October 20, 2002

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