Department of

Mathematics


Seminar Calendar
for events the day of Thursday, February 6, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, February 6, 2014

1:00 pm in Altgeld Hall 347,Thursday, February 6, 2014

Large and symmetric

Anton Klyachko (Moscow State University)

Abstract: I shall talk about our (joint with Maria Milentyeva) generalisation of the Khukhro--Makarenko theorem on large characteristic subgroups with laws. This generalised theorem implies new facts on groups, algebras, and even graphs and other structures.

2:00 pm in 243 Altgeld Hall,Thursday, February 6, 2014

Vector analysis and intrinsic metrics on fractals

Dan Kelleher (University of Connecticut)

Abstract: We will discuss a possibility of defining vector analysis for measurable Dirichlet forms (quadratic forms on functions). In particular we shall talk about results on the existence and properties of intrinsic metrics on Dirichlet and Resistance spaces, as well as the construction of a Dirac operator using techniques from non-commutative functional analysis. If time permits, we will also discuss how this Dirac operator gives rise to spectral triples on fractal spaces.

4:00 pm in 245 Altgeld Hall,Thursday, February 6, 2014

Equivariant structures in mirror symmetry and distinguished bases from symplectic geometry

James Pascaleff (University of Texas at Austin)

Abstract: To a symplectic manifold M one can associate various algebraic structures built from pseudo-holomorphic curves, such as the quantum cohomology ring and the Fukaya category. One way to formulate the phenomenon of mirror symmetry is to say that structures associated to the symplectic geometry of M are typically equivalent to structures associated to the algebraic geometry of a rather different space X. In one direction, this allows us to use tools from algebraic geometry to study symplectic manifolds. In the other direction, the symplectic interpretation may make manifest a structure that is surprising from the algebraic point of view. In this talk, I will describe a line of research that incorporates both directions. On the one hand, we can translate an algebraic group action on X into the notion of an equivariant Lagrangian submanifold in M. This gives us representations of Lie algebras in Floer cohomology groups. On the other hand, the symplectic geometry yields certain distinguished bases of these Floer cohomology groups, related to the "theta functions" of Gross-Hacking-Keel, and we expect to the canonical bases arising in representation theory.