Colloquium 2008-09

September 4
September 9* Louis Rowen (Bar Ilan University)   Host: Andrei Rapinchuk
  Title: Supertropical algebra (Joint work with Z. Izhakian)
September 11 Sasha Kleshchev (University of Oregon/UVa)   Host: Weiqiang Wang
  Title: Recent developments in representation theory of symmetric groups
September 18
September 25
October 2 Rafael Benguria (P. Universidad Catolica de Chile)   Host: Lawrence Thomas
  Title: The zeroes of the Fourier transform of the characteristic function of a domain and their relation with the eigenvalues of the Laplacian
October 9 Ruth Williams (UCSD)   Host: Christian Gromoll
  Title: Stochastic networks with resource sharing
October 16
October 23 Math Club  &nbsp
October 30 Michael Jolly (Indiana University)   Host: Zoran Grujic
  Title: Computation of Invariant Manifolds
November 6 Charles Rezk (U Illinois, Urbana)   Host: Nick Kuhn
November 13 David Hemmer (Buffalo)   Host: Brian Parshall
  Title: A tour of symmetric group representation theory via Specht module filtrations
November 20
November 27 Thanksgiving Recess
December 4 Ivan Losev (MIT)   Host: Weiqiang Wang
  Title: W-algebras
December 11 Victor Isakov (Wichita State University)   Host: Roberto Triggiani
  Title: Carleman estimates with two large parameters and applications to elasticity with residual stress

January 22 No colloquium
January 29 No colloquium
February 5 Michael Chipot (University of Zürich)
Title: On Correctors in Anisotropic Singular Perturbations Problems
Host: Irena Lasiecka
February 12 No colloquium
Departmental Meeting
February 19 No colloquium
February 26 Samuel Krushkal (Bar-Ilan University and UVA)
Title: Moser's conjecture and geometry of Teichmüller spaces Teichmüller spaces are the deformation spaces of conformal structures on Riemann surfaces. They have various applications in Mathematics and in String theory in Physics. I plan to discuss mainly the universal Teichmüller space, containing copies of all such spaces. It is a complex Banach manifold with rich complex geometry and pluripotential theory. An application to solving several long standing problems, including Moser's conjecture on Grunsky and Teichmüller norms, will be briefly presented.
March 5 No colloquium
Spring Recess
March 12 **cancelled** Dan Nakano (University of Georgia)
Title: Invertible Modules, Cohomology, and Nilpotent Matrices
Host: Brian Parshall
March 19 Pascal Lambrechts (Universite catholique de Louvain)
Title: Understanding immersions and embeddings: the cut and paste strategy We will consider smooth immersions and smooth embeddings of a manifold into a Euclidean space. At the beginning of my talk I will review Smale's strategy for proving his famous result that the sphere can be turned inside-out through immersions. I will then explain how this strategy has been generalized to understand not only immersions, but also embeddings. Finally, I will show how these ideas can help us to understand better the spaces of embeddings of the circle into a Euclidean space, that is of the space of knots.

Host: Greg Arone
March 26 Said Sidki (Univeristy of Brasilia, Brazil)
Title: Virtual endomorphisms of groups A virtual endomorphism of a group G is a homomorphism f :H → G where H is a subgroup of G of finite index m. A recursive construction using f produces a so called state-closed (or, self-similar) representation of G on a 1-rooted regular m-ary tree. The kernel of this representation is the maximal subgroup K of H which is both normal in G and is f -invariant, in the sense that Kf ≤ K; it is called the f -core (H). The map f is called simple provided the f -core (H) is trivial. We will discuss the implications for groups- especially those which are nilpotent - to admit simple virtual endomorphisms of a fixed degree m. This material is based on work with Nekrashevych, Berlatto and Brunner.

Host: Andrei Rapinchuk
April 2 **cancelled** C. Ward Henson (UIUC)
Title: Model theory for metric structures A metric structure is based on a complete metric space (M,d); the rest of the structure consists of operations, which are distinguished M-valued functions on M; predicates, which are distinguished real-valued functions on M, and constants, which are distinguished elements of M. The restriction of each operation and predicate to an arbitrary bounded subset of its domain must be bounded and uniformly continuous. Metric structures arise in all areas of mathematics, especially in analysis, probability, and geometry. For example: Banach spaces, -lattices, -algebras, etc; C*-algebras; measure algebras; asymptotic cones of finitely generated groups; and metric spaces themselves. Logicians view model theory as a set of concepts and tools for applying first order logic (predicate logic) to structures arising in mathematics. A more congenial starting point for non-logicians is the ultraproduct construction, which has been used in natural ways in many parts of algebra. There is a nice generalization of the ultraproduct construction to metric structures, and it has found important uses since the 1960s in several areas of analysis. (For example, ultraproducts of Banach spaces are routinely used as a tool by specialists in the geometric theory of Banach spaces.) We will use this ultraproduct from analysis as a starting point for explaining how model theory is beginning to be applied to metric structures. One very recent outcome of these investigations has been the development of a real-valued analogue of classical first order logic. In this generalization, boolean connectives are replaced by continuous functions on the reals and the classical quantifiers "for all" and "there exists" are replaced by the operations of supremum and infimum on the reals. The resulting continuous logic is a beautiful and natural extension of classical logic with suitable analogues of essentially all the key properties: logical compactness, existence of rich and highly homogeneous models, characterizations of quantifier elimination and categoricity, fundamental tools of model-theoretic stability, etc. Moreover, this continuous logic for metric structures resonates effectively with the mathematical properties of many important examples of metric structures.

Host: David Sherman
April 9 Bill Graham (University of Georgia)
Title: Localization in Equivariant Cohomology and K-Theory
Host: Weiqiang Wang
April 16 No colloquium
April 23 Laura De Marco (University of Illinois at Chicago)
Title: Deformations of complex dynamical systems
Host: Tom Kriete
April 30 Michael Hill (UVa)
Title: On the non-existence of Kervaire invariant one manifolds I will describe joint work with Hopkins and Ravenel in which we show that there are no smooth Kervaire invariant one manifolds in dimensions larger than 126. I will begin by describing the classical reductions from the study of manifolds to the study of the Adams spectral sequence, and then I will describe some new, equivariant techniques which further recast the problem into one of algebra.


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