Department of

Mathematics


Seminar Calendar
for events the day of Thursday, October 17, 2013.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, October 17, 2013

11:00 am in 241 Altgeld Hall,Thursday, October 17, 2013

Torsion homology of Bianchi Groups and Arithmetic

Mehmet Haluk Sengun (University of Warwick / ICERM)

Abstract: Bianchi groups are groups of the form SL(2,R) where R is the ring of integers of an imaginary quadratic field. They form an important class of arithmetic Kleinian groups and moreover they hold a key role for the development of the Langlands program for GL(2) beyond totally real fields. In this talk, I will discuss several interesting questions related to the torsion in the homology of Bianchi groups. After discussing the importance of torsion from the perspective of number theory, I will talk on the recent results on the asymptotic behavior of the size of torsion, including joint work with N.Bergeron and A.Venkatesh on the cycle complexity of arithmetic manifolds and torsion growth.

12:30 pm in 464 Loomis Laboratory,Thursday, October 17, 2013

A Holographic View on Higher Spin Black Holes

Kewang Jin (Illinois Physics)

Abstract: The Minimal Model Holography, relating 3d higher spin gravity on the AdS side and W_N minimal model on the CFT side is reviewed in this talk. In particular, explicit black hole solutions carrying higher spin charges are constructed with proper thermodynamics. We compute the free energy of a charged black hole from the holographic dual at large central charge, using the modular properties of 2d CFT and commutation relations of the W-algebra, and find exact match with the bulk thermodynamics. Furthermore, scalar fields are coupled to the gravity and higher spin corrections to the two-point functions are computed both from the AdS side and the CFT side. Again, a perfect match is found, which gives further support to the minimal model holography.

1:00 pm in 241 Altgeld Hall,Thursday, October 17, 2013

The evolution of invariant theory: from classics to modern

Mee Seong Im (UIUC Math )

Abstract: Invariant theory is prominent in many areas of mathematics. After giving a few motivations for the study of invariant theory, I will state some classical problems leading us to more recent representation-theoretic problems and results. I will end by discussing some interesting applications.

1:00 pm in Altgeld Hall 347,Thursday, October 17, 2013

Subgroups of $Out(F_n)$ generated by two Dehn twists

Funda Gultepe (UIUC Math)

Abstract: Based on analogies between mapping class group of a surface with one puncture and $Out(F_n)$, it is possible to investigate groups generated by two Dehn twist automorphisms. We will discuss when such a subgroup is free by working on the 3-dimensional model $M=\sharp_n(S^2\times S^1)$ for $Out(F_n)$ and defining Dehn twists along tori in $M$.

2:00 pm in 243 Altgeld Hall,Thursday, October 17, 2013

Equilibrium distribution of a charge in the presence of an external field

Igor Pritsker (University of Oklahoma)

Abstract: It is well known that the equilibrium distribution of a unit charge on a conductor is characterized by a minimum energy problem. When we consider this distribution in the presence of an external field, a similar characterization exists, going back to Gauss. However, the location of this equilibrium position of charge varies with external field, which makes finding explicit equilibrium distributions difficult even for simple conductors and fields. We shall address the problem when the external field is generated by finitely many point charges. These problems have surprisingly diverse applications in approximation theory and orthogonal polynomials, combinatorics and number theory, random matrices, etc.

2:00 pm in 149 Henry Administration Building,Thursday, October 17, 2013

Bipartite Ramanujan Graphs of All Degrees

Michelle Delcourt (UIUC Math)

Abstract: This talk is based primarily on the paper Interlacing Families I: Bipartite Ramanujan Graphs of All Degrees by Marcus, Spielman, and Srivastava. By proving a variant of a conjecture of Bilu and Linial, they show that there exist infi nite families of d-regular bipartite Ramanujan graphs for d>2. Of particular interest in the paper by Marcus, Spielman, and Srivastava is their "method of interlacing polynomials".

3:00 pm in 243 Altgeld Hall,Thursday, October 17, 2013

Mather-Jacobian multiplier ideal and its applications

Wenbo Niu (Purdue University)

Abstract: In the past twenty years, the theory of multiplier ideals on nonsingular varieties has been developed significantly and found many amazing applications in analytic geometry, algebraic geometry, and commutative algebra. Recently, the theory of multiplier ideals on arbitrary varieties have been established independently by Ein-Ishii-Mustata and de Fernex-Docampo. This is called Mather-Jacobian multiplier ideal. In this talk, I will introduce this new theory and discuss its basic algebraic and geometric properties. Then I will show two applications to Nullstellensatz problem and symbolic powers problem.

4:00 pm in 245 Altgeld Hall,Thursday, October 17, 2013

Foliations - Thurston Zebras to Cantor Geometries

Steve Hurder (University of Illinois at Chicago)

Abstract: It was forty years ago that William Thurston electrified the theory of foliations with his celebrated constructions of foliations, and raised the hope of classifying these geometric structures on manifolds. This was followed by an intense period of development over the next ten years of the theory of characteristic classes for foliations. The study of foliations since then has taken many twists and turns, finding applications in dynamical systems and ergodic theory, and incorporating many new ideas in the quest for a viable classification scheme.

In this talk, I will survey three aspects of these developments: the role of algebra in the works of Kamber and Tondeur in the 1970's on secondary class theory; the rise of dynamical and ergodic theory methods in the 1980's and 1990's; and the current development of topological methods and the techniques of Cantor actions to gain a new understanding of the structure of foliations.