Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, April 15, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, April 15, 2014

1:00 pm in Altgeld Hall 243,Tuesday, April 15, 2014

#### Evolving structures and uniform growth rate

###### Kasra Rafi (University of Toronto)

Abstract: During his 60th birthday conference, Thurston asserted that the growth rate of mapping class group is independent of genus. In this talk, we attempt to understand why and to what extend this is true. It turns out, given the right choice of generating sets, the mapping class group, Out(F_n) and SL(n,Z) all have uniform growth rates. We use the ideas and the work of Sleator-Tarjan-Thurston.

1:00 pm in 345 Altgeld Hall,Tuesday, April 15, 2014

#### Buchi's Problem and Uniform Undecidability for rings of functions of positive characteristic

###### Thanases Pheidas (Purdue/University of Crete)

Abstract: We address the question: Is there an algorithm which can decide, given a polynomial equations (in many variables), with coefficients in F_p[z] (polynomials over z, with coefficients in the finite field with p elements, p a prime), whether the polynomial has solutions in F_p(z) for almost all primes p (or for infinitely many p, or for all primes p congruent to 1 mod 4)? We will present a negative answer to this question. A critical element of the proof is the solution to an analogue of Buchi's problem, a problem in Number Theory of independent interest.

1:00 pm in 347 Altgeld Hall,Tuesday, April 15, 2014

#### Layered Media Scattering: Fokas Integral Equations and Boundary Perturbation Methods

###### David Nicholls (UIC)

Abstract: In this talk we describe a class of Integral Equations to compute Dirichlet-Neumann operators for the Helmholtz equation on periodic domains inspired by the recent work of Fokas and collaborators on novel solution formulas for boundary value problems. These Integral Equations have a number of advantages over standard alternatives including: (i.) ease of implementation (high-order spectral accuracy is realized without sophisticated quadrature rules), (ii.) seamless enforcement of the quasiperiodic boundary conditions (no periodization of the fundamental solution, e.g. via Ewald summation, is required), and (iii.) reduced regularity requirements on the interface proles (derivatives of the deformations do not appear explicitly in the formulation). We show how these can be efficiently discretized and utilized in the simulation of scattering of linear acoustic waves by families of periodic layered media which arise in geoscience applications.

2:00 pm in 241 Altgeld Hall,Tuesday, April 15, 2014
###### Canceled

2:00 pm in Altgeld Hall 347,Tuesday, April 15, 2014

#### Poincar\'e inequalities in Noncommutative $L_p$ spaces

###### Qiang Zeng (UIUC Math)

Abstract: It is known in probability theory that good estimates of moments of random variables lead to concentration inequalities. The Poincar\'e inequalities provide upper bounds for the moments of random variables using their derivatives. In this talk, I will first give some motivating examples of $L_p$ Poincar\'e inequalities with satisfactory constants in classical probability and Fourier analysis. Then I will explain the consequences of these inequalities and a general theory in the context of noncommutative $L_p$ spaces. The talk is based on joint work with Marius Junge.

3:00 pm in 347 Altgeld Hall,Tuesday, April 15, 2014

#### Replication and Optimization in Causal Inference

###### Wendy K. Tam Cho (UIUC Political Science/Statistics)

Abstract: A common thread throughout scientific endeavors is the desire to identify and understand causal relationships. Randomized experiments are the gold standard for isolating treatment effects and identifying causal relationships. When experiments are not practical or not possible, researchers sometimes turn to observational data. Matching methods comprise one strategy for making causal inferences with observational data. We present a new paradigm and method for making causal inferences in the absence of experimental data. Our method incorporates an optimization approach that illuminates important scientific notions of replication. While observational studies have obvious pitfalls, we demonstrate how our computational approach highlights previously unseen opportunities with these data.

3:00 pm in 241 Altgeld Hall,Tuesday, April 15, 2014

#### Online Ramsey Theory for Planar Graphs

###### Sarka Petrickova (UIUC Math)

Abstract: An online Ramsey game $(G,\mathcal{H})$ is a game between Builder and Painter, alternating in turns. During each turn, Builder draws an edge, and Painter colors it blue or red. Builder's goal is to force Painter to create a monochromatic copy of $G$, while Painter's goal is to prevent this. The only limitation for Builder is that after each of his moves, the resulting graph has to belong to the class of graphs $\mathcal{H}$. It was conjectured by Grytczuk, Haluszczak, and Kierstead (2004) that if $\mathcal{H}$ is the class of planar graphs, then Builder can force a monochromatic copy of a planar graph G if and only if G is outerplanar. Here we show that the only if'' part does not hold while the if'' part does.

3:00 pm in 243 Altgeld Hall,Tuesday, April 15, 2014

#### Holomorphic one-forms on varieties of general type

###### Mihnea Popa (UIC Math)

Abstract: I will explain recent work with C. Schnell, in which we prove that every holomorphic one-form on a variety of general type has non-empty zero locus (together with a suitable generalization to arbitrary Kodaira dimension). The proof makes use of generic vanishing theory for Hodge D-modules on abelian varieties.

4:00 pm in Altgeld Hall,Tuesday, April 15, 2014

#### Schemes as Functors

###### Matej Penciak (UIUC Math)

Abstract: Replacing schemes with their functor of points offers a useful perspective to tackle moduli problems. In this talk I will explain this interpretation of schemes, characterize the functors that come from this construction, and try to motivate this viewpoint through various examples. Along the way I will discuss the Quot and Hilbert schemes--two schemes that represent common moduli problems.