The current organizer of the seminar is Maxim Braverman.
 

• September 22, 2006, 11 AM-1 PM (Note the special time)
  Speaker:  Victor Ivrii (University of Toronto)
  Title: Everything Started From Weyl
  Abstract: Hermann Weyl  was the first who studied seriously  asymptotic distribution of eigenvalues (1911) and formulated what was later called  Weyl's conjecture. In the first part of my talk I will discuss the history of the subject and ideas leading to the proof.
       This proof was worked out in the framework of Microlocal Analysis which is  based on the idea of quantization, and the most useful quantization method was also suggested by H.Weyl (1927):
                          http://en.wikipedia.org/wiki/Weyl_quantization
       In the second part of the talk I will discuss quantization, uncertainty principle, the role of periodic trajectories in the remainder estimate and their possible contribution to the main part
                          http://www.math.toronto.edu/ivrii/Research/preprints/Grad_Talk_3.php
   
• September 29, 2006
  Speaker:  Steven Rosenberg (Boston University)
  Title: Chern-Weil Theory
   
• October 13, 2006
  Speaker:  Peter Topalov (Northeastern University)
  Title: Mathematical theory of billiards
  Abstract: Billiard dynamical systems are mathematical idealizations of the game of billiards, but where the "billiard tables'' can have shapes other than rectangular or even have non-Euclidean geometry. Since the works of G. Birkhoff, billiards became a popular topic of investigation where various mathematical subjects intertwine (Ergodic theory, Topology, Number theory, KAM etc). It is a general belief that billiards are simplified models that capture all the complexity of dynamical systems -- from integrability to chaotic motion. On the other hand, billiards naturally appear in a number of important problems in classical mechanics and physics.
   
• October 27, 2006
  Speaker:  Jonathan Weitsman (University of California Santa Cruz)
  Title: Equivariant Morse theory, old and new:  Morse theory, equivariant topology, and symplectic geometry
  Abstract: In 1980 Raoul Bott gave his Poincare Symposium Lectures on Morse Theory, Old and New, at the end of which he previewed his work with M. Atiyah on Yang Mills theory in two dimensions. These ideas have since given rise to an explosion in the understanding of equivariant Morse theory. In the talk I will overview the works of Atiyah, Bott, Kirwan, Guillemin, Sternberg, and others on equivariant Morse theory, focusing on its role in the context of symplectic geometry.
   
• November 3, 2006
  Speaker: Maxim Braverman (Northeastern University)
  Title: Regularized determinants and regularized traces  of (pseudo-)differential operators
  Abstract: To define a trace and a determinant of an unbounded (pseudo-)differential operator one needs to use a regularization procedure in order to get rid of infinities. Such a regularization destroy some good properties of these objects and lead to, so called, anomalies, closely related to different anomalies in quantum field theory. In the talk I will present the most standard renormalization methods and define the regularized trace and determinant. I will describe the anomalies which the regularized objects have and explain where this anomalies come from. Finally, I will try to convince you that despite the anomalies the regularized trace and determinant are useful and interesting objects.

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