UIUC Dept. of Mathematics Seminar Calendar

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Thursday, January 26, 2012

Number Theory Seminar
11:00 am in 241 Altgeld Hall, Thursday, January 26, 2012

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Submitted by ford.

Scott Ahlgren (UIUC Math)
Mock modular grids
Abstract: We study infinite grids of mock modular forms which are "dual'' in the sense that while reading across the grid gives the coefficients of the first family, reading down the grid gives the coefficients of the second. Each of these grids contains a generating function of number-theoretic or combinatorial interest as its first entry (for example, the ``smallest parts" function of Andrews, or a mock theta function of Ramanujan) and we deduce many corollaries for these functions.

Lunch Seminar on NetMath
12:05 pm in 102 Altgeld Hall, Thursday, January 26, 2012

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Debra Woods [email] (Mathematics/Urbana)
History and Vision of NetMath
Abstract: NetMath is the distance education program of the Mathematics Department of the University of Illinois (Urbana). Its mission is to extend the high quality curriculum of the Mathematics Department at the University of Illinois to students worldwide. Combining innovative pedagogy with tools tailored to our course offerings, NetMath delivers flexible courses that engage students to learn according to their own schedule and learning style. Conceived by Jerry Uhl, Bill Davis and Horatio Porta, the founders of the Calculus and Mathematica Program, NetMath has grown from a few dozen students to over a thousand annually in the two decades of its existence. NetMath‚Äôs vision is to become the premier university program for all students seeking online math instruction worldwide, continuing to set a high standard for online education, and serving as a center for knowledge exchange and springboard for developing and testing innovative learning technology.

Graduate Geometry and Topology Seminar
2:00 pm in 241 Altgeld Hall, Thursday, January 26, 2012

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Mee Seong Im (UIUC Math)
The Hamiltonian reduction of a certain affine variety
Abstract: I will discuss certain theories in symplectic geometry and in algebraic geometry which give us various ways to view the same complex manifold. More specifically, the Hamiltonian reduction of the cotangent bundle of a certain variety can be thought of as the symmetric product of the complex plane while the GIT quotient of the same cotangent bundle but which is twisted by a character of the general linear group can be thought of as a certain Hilbert scheme. These varieties are related by the Hilbert-Chow morphism in the sense that one is a desingularization of the other. I will end with an analogous construction in which a notion of noncommutativity appears in the algebro-geometric quotient. Lots of examples will be provided throughout my talk.