Department of

Mathematics


Seminar Calendar
for events the day of Friday, January 24, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, January 24, 2014

2:00 pm in 443 Altgeld Hall,Friday, January 24, 2014

Organizational Meeting

Sheldon Katz (Illinois Math)

Abstract: I am proposing a RAP on the interaction between geometry and supersymmetric quantum field theories. While the exact choice of topics will be participant-dependent, the initial proposal includes the physics of super Yang-Mills, dimensional reduction, and topological twisting, with geometric applications such as Higgs bundles, geometric Langlands, and geometric engineering. Participation is sought from faculty, postdocs, and grad students in the math and physics departments. If you are interested in participating in the RAP but cannot attend the organizational meeting, please let me know.

4:00 pm in 245 Altgeld Hall,Friday, January 24, 2014

The arithmetic of special values of L-functions

Robert W. Harron (University of Wisconsin–Madison)

Abstract: L-functions have played an important role in number theory since the work of Dirichlet in the 19th century. Today, they continue to intrigue us, taking up two of the seven Clay Millennium Problems: the Riemann Hypothesis and the Conjecture of Birch and Swinnerton-Dyer. This talk will concentrate on ideas related to the latter problem, namely the arithmetic meaning hidden within the values L-functions take at integers. I will go over some motivating examples and illustrate how we use modular forms, Galois representations, and techniques of p-adic variation to understand what L-functions are trying to tell us. I will end by discussing some recent results concerning mysterious quantities that can sometimes occur: L-invariants.

4:00 pm in 241 Altgeld Hall,Friday, January 24, 2014

Stability approached by means of Symplectic Geometry

Georgios Kydonakis (UIUC Math)

Abstract: We will focus on N. Hitchin's approach to the notion of stability from the perspective of Symplectic Geometry in order to describe the relationship between flatness of connections and stability, as explained in the Theorem of Narasimhan and Seshadri. Moreover, we will see how this approach is used to end up with an appropriate definition of a stable Higgs bundle.