UIUC Dept. of Mathematics Seminar Calendar

     October 2009          November 2009          December 2009    
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
              1  2  3    1  2  3  4  5  6  7          1  2  3  4  5
  4  5  6  7  8  9 10    8  9 10 11 12 13 14    6  7  8  9 10 11 12
 11 12 13 14 15 16 17   15 16 17 18 19 20 21   13 14 15 16 17 18 19
 18 19 20 21 22 23 24   22 23 24 25 26 27 28   20 21 22 23 24 25 26
 25 26 27 28 29 30 31   29 30                  27 28 29 30 31

Monday, November 16, 2009

Math 499: Introduction to Graduate Mathematics
4:00 pm in 245 Altgeld Hall, Monday, November 16, 2009

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Submitted by seminar.

Matthew Ando (Department of Mathematics, University of Illinois)
Integration-like formulas in algebraic topology
Abstract: One of the oldest questions in algebraic topology is how many times two compact submanifolds of a manifold must intersect. Thanks to the de Rham Theorem, theanswer to this question can often be expressed as an integral: connecting something apparently continuous (an integral) to something discrete (an integer). I'll describe a variety of situations similar to this, in which a discrete quantity is extracted from an analytic situation.

Tuesday, November 17, 2009

Logic Seminar
1:00 pm in 345 Altgeld Hall, Tuesday, November 17, 2009

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Submitted by w-henson.

Justin Moore (Cornell)
Forcing Axioms and the Continuum Hypothesis.
Abstract: Woodin asked whether there are two $\Pi_2$-sentences $\psi_i$ $i = 0,1$ such that for each $i$, it is forcible that $H(\omega_2)$ satisfies $\psi_i$ and $2^{\aleph_0} = \aleph_1$ but such that $\psi_0 \land \psi_1$ proves $2^{\aleph_0} > \aleph_1$. This is a precise formulation of the vague question ``Is there an optimal forcing axiom which is consistent with the Continuum Hypothesis?'' I will discuss recent joint work with D. Aspero and P. Larson in which we demonstrate a positive solution to Woodin's problem (and hence that there is no optimal forcing axiom consistent with CH).

Number Theory Seminar
1:00 pm in 241 Altgeld Hall, Tuesday, November 17, 2009

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Submitted by jarouse.

Youness Lamzouri (The Institute for Advanced Study)
On the Distribution of large values of L-functions at the edge of the critical strip
Abstract: In this talk we will construct a class of probabilistic random Euler products to study large values of various families of $L$-functions at the edge of the critical strip. In particular this class includes the random models constructed recently by A. Granville and K. Soundararajan to study large values of the Riemann zeta function and Dirichlet $L$-functions on the $1$-line. Among new applications, we study families of symmetric power $L$-functions of holomorphic cusp forms in the level aspect (assuming the automorphy of these $L$-functions) at $s=1$, functions in the Selberg class (in the height aspect), and the family of $L$-functions of quadratic twists of a fixed $GL(m)/{\Bbb Q}$-automorphic cusp form at $s=1$.

Probability Seminar
2:00 pm in 347 Altgeld Hall, Tuesday, November 17, 2009

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Submitted by rsong.

Prof. Elton Hsu (Northwestern University)
Volume Growth and Escape Rate of Brownian motion on a Complete Riemannian manifold
Abstract: We show that the question of how fast Brownian motion on a complete Riemannian manifold escapes to infinity can be effectively answered solely based on the volume growth of the manifold. In this talk time reversal of reflecting Brownian motion and volumes of geodesic balls all come together in this problem and give an elegant and often sharp upper bound of the escaping rate solely in terms of the volume growth function without any extra geometric restriction besides geodesic completeness.

Geometry Seminar
2:00 pm in 243 Altgeld Hall, Tuesday, November 17, 2009

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Submitted by sba.

Vincent Matsko (IMSA)
Envelopes of Conic Sections
Abstract: In one of the classic nineteenth-century geometry texts, Salmon's *A Treatise on Conic Sections*, conics are discussed in the context of the projective plane. As a result, the duality of conic sections and their envelopes is easily represented. This talk will extend ideas of previous talks based on Salmon. In particular, use of the tangential equation to produce an envelope of lines for a conic will be discussed. Several examples will be described, followed by a brief slide show of attempts at creating an art gallery of pleasing geometric forms. An introduction to all necessary ideas is included in the talk. Interested undergraduates are encouraged to attend.

Wednesday, November 18, 2009

Algebra, Geometry and Combinatorics Seminar
12:00 pm in 445 Altgeld Hall, Wednesday, November 18, 2009

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Submitted by llpku.

Jonah Blasiak (University of Chicago)
Cyclage, catabolism, and the affine Hecke algebra
Abstract: It is classically known that the ring of coinvariants C[y_1,...,y_n]/(e_1,...,e_n), thought of as an S_n-module with S_n acting by permuting the variables, is a graded version of the regular representation of S_n. However, how a decomposition of the coinvariants into irreducibles is compatible with its ring structure remains a mystery. In particular, there are difficult combinatorial conjectures for the graded characters of certain subquotients of this ring. We describe a promising approach to understanding such subquotients using the canonical basis of the extended affine Hecke algebra. We show that a subalgebra of this Hecke algebra has a cellular subquotient which is a q-analog of the ring of coinvariants and, further, that this subquotient has cellular quotients which are q-analogs of the Garsia-Procesi modules. This cellular picture gives a clear explanation of the appearance of cyclage and catabolism in the combinatorial description of these modules.

Thursday, November 19, 2009

Mathematical and theoretical physics
11:30 am in 464 Loomis or 322 Loomis, Thursday, November 19, 2009

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Submitted by mando.

Prof. Aki Hashimoto (University of Wisconsin/Madison)
Branes and fluxes in manifolds of special holonomy and cascading field theories
Abstract: In this talk, I will motivate and describe some generalizations of ABJM construction, which can be viewed as decoupled theories of M2-branes in transverse eight dimensional manifolds of sp(2) holonomy, to cases involving holonomy groups spin(7) and sp(1)xsp(1). I will comment on the threshold of dynamical supersymmetry breaking in these models, and speculate on the features of the dual gravity description of the dynamically broken supersymmetry

Number Theory Seminar
1:00 pm in 241 Altgeld Hall, Thursday, November 19, 2009

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Submitted by jarouse.

Andrew Shallue (Illinois Wesleyan)
Enumerating class group structures of real quadratic number fields
Abstract: There are many classic conjectures surrounding the structure of the ideal class group of real quadratic number fields. Among them are the Cohen-Lenstra heuristics, which give precise information about the expected structure of such class groups. Supporting such conjectures provides motivation to tabulate class numbers of quadratic number fields. I will discuss the present progress of a project to enumerate the structure of all class groups for discriminants of real quadratic number fields up to 10^11, and to do so without relying on the Extended Riemann Hypothesis. In essence, this has two main components. First, there are algorithms for computing the structure of an abelian group given group operations as a black box. Second, these group operations must be instantiated. This is nontrivial in the case of the ideal class group of a real quadratic number field. In addition to first computing the regulator, elements of the group do not have a unique representative, making identity testing a difficult proposition. We will see how these difficulties are overcome, and discuss exciting new developments in algorithms for finding the structure of a generic group.

Friday, November 20, 2009