UW Algebra Seminar
Autumn 2006
Tuesday 1:30pm, Padelford C-36

Speaker: Eliot Brenner, Center for Advanced Studies in Mathematics at Ben Gurion University
Title: Heat Eisenstein Series and Applications
Date: October 3
Abstract: I will define the heat Eisenstein series and sketch some of their theory, as developed by Jorgenson and Lang in the 90s and early 00s. Then, I will describe their role in an ongoing project to generalize theta relations and spectral zeta functions to arithmetic quotients of real Lie groups in higher rank. Finally, I will state some of my results on exact fundamental domains and explain how they are used or are expected to be used in this program.
Speaker: Jon Hanke, Duke University
Title: The 290-Theorem and Representing Numbers by Quadratic Forms
Date: October 10
Abstract: This talk will describe several finiteness theorems for quadratic forms, and progress on the question: "Which positive definite integer-valued quadratic forms represent all positive integers?". The answer to this question depends on settling the related question "Which integers are represented by a given quadratic form?" for finitely many forms. The answer to this question can involve both arithmetic and analytic techniques, though only recently has the analytic approach become practical. We will describe the theory of quadratic forms as it relates to answering these questions, its connections with the theory of modular forms, and give an idea of how one can obtain explicit bounds to describe which numbers are represented by a given quadratic form.
Speaker: Nicole Lemire, University of Western Ontario and MSRI
Title: Galois Module Structure of Galois Cohomology and Applications
Date: October 17
Abstract: For a cyclic p-extension of fields E/F where F contains a primitive p-th root of unity, we determine the $\F_p[\Gal(E/F)]$ module structure of $H^m(G_E,\F_p)$ in terms of the field extension E/F. We apply this to determine restrictions on the group structure of an absolute Galois group $G_F$ (with Dave Benson) and to determine the cohomological dimension of the maximal pro-p quotient $G_F(p)$ (with John Labute).
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Date: October 24
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Speaker: Daniel Chan, University of New South Wales
Title: Clifford algebras and Conic Bundles
Date: October 31
Abstract: Maximal orders on surfaces are examples of noncommutative surfaces. We consider the question of constructing and studying such orders in the case where the rank is 4 over the centre. The approach is via the even Clifford algebra. We also study the relationship of these orders with conic bundles.
Speaker: Kevin Knudson, University of Mississipi and MSRI
Title: Generating discrete Morse functions from point data
Date: November 7
Abstract: If $K$ is a finite simplicial complex and $h$ is an injective map from the vertices of $K$ to $\R$ we show how to extend $h$ to a discrete Morse function in the sense of Forman in a reasonably efficient manner so that the resulting discrete Morse function mirrors the large-scale behavior of $h$. Examples and an explicit algorithm will be presented.
Speaker: Julia Hartmann, University of Heidelberg and University of Pennsylvania
Title: Differential Galois Groups and Patching
Date: November 14
Abstract: The talk gives an introduction to differential Galois theory, and then addresses the inverse problem: Which groups can occur as differential Galois groups over a given field? Recent results employ patching methods to attack the problem (joint work with D. Harbater).
Speaker: Steve Mitchell, University of Washington
Title: Schubert varieties in the affine Grassmannian
Date: November 21
Abstract: The loop space of a compact Lie group is homotopy equivalent to a certain infinite-dimensional projective algebraic variety, the "affine Grassmannian". This variety shares many of the beautiful features of ordinary Grassmannians; for example, it has a decomposition into Schubert cells whose closures are ordinary projective varieties. There are two striking differences, however: The affine Grassmannian is a topological group, and the principal bundle defining it as a homogeneous space is topologically trivial. In these largely expository talks I will present a topologist's perspective on the affine Grassmannian, and discuss some ongoing work involving its Schubert varieties: For example, which of these are nonsingular? This question is closely related to the combinatorics of the Bruhat order on the affine Weyl group, a beautiful subject in its own right.
Speaker: Steve Mitchell, University of Washington
Title: Schubert varieties in the affine Grassmannian
Date: November 28
Abstract: The loop space of a compact Lie group is homotopy equivalent to a certain infinite-dimensional projective algebraic variety, the "affine Grassmannian". This variety shares many of the beautiful features of ordinary Grassmannians; for example, it has a decomposition into Schubert cells whose closures are ordinary projective varieties. There are two striking differences, however: The affine Grassmannian is a topological group, and the principal bundle defining it as a homogeneous space is topologically trivial. In these largely expository talks I will present a topologist's perspective on the affine Grassmannian, and discuss some ongoing work involving its Schubert varieties: For example, which of these are nonsingular? This question is closely related to the combinatorics of the Bruhat order on the affine Weyl group, a beautiful subject in its own right.
Speaker: Hsian-hua Tseng, UBC
Title: Gromov-Witten theory of twisted projective lines and integrable hierarchies
Date: December 5
Abstract: It has been expected that the totality of Gromov-Witten invariants of a Kahler manifold admits certain integrable structures. More precisely, the generating function of descendant Gromov-Witten invariants should be a tau-function of certain integrable hierarchy. Examples of manifolds with this property include a point (Witten's conjecture) and complex projective line (Toda conjecture). In this talk we discuss this problem in a class of new examples--the twisted projective lines. This is based on the joint work with Todor Milanov.
To request disability accommodations, contact the Office of the ADA Coordinator, ten days in advance of the event or as soon as possible: 543-6450 (voice); 543-6452 (TDD); 685-3885 (FAX); access@u.washington.edu (E-mail).

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