Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, September 9, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2014           September 2014          October 2014
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2       1  2  3  4  5  6             1  2  3  4
3  4  5  6  7  8  9    7  8  9 10 11 12 13    5  6  7  8  9 10 11
10 11 12 13 14 15 16   14 15 16 17 18 19 20   12 13 14 15 16 17 18
17 18 19 20 21 22 23   21 22 23 24 25 26 27   19 20 21 22 23 24 25
24 25 26 27 28 29 30   28 29 30               26 27 28 29 30 31
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Tuesday, September 9, 2014

1:00 pm in 243 Altgeld Hall,Tuesday, September 9, 2014

#### Directions in Hyperbolic Lattices

Abstract: Let Gamma be a lattice in PSO(n,1). Given two points w and z in H^n, we analyze local statistics of the set of directions of orbit Gamma.w as viewed from z. Watch at http://youtu.be/rzHbyreE8oQ

1:00 pm in Altgeld Hall,Tuesday, September 9, 2014

#### Co-analytic constructions

###### Kostas Beros (University of North Texas)

Abstract: In a 1996 paper, Greg Hjorth showed that there is a complete co-analytic equivalence relation. I will discuss a simple proof of this theorem which eliminates Hjorth's use of effective theory specific to the class of co-analytic sets. Assuming PD, my proof generalizes Hjorth's theorem to all odd-numbered pi-classes in the projective hierarchy. Additionally, I will present some further results of my own which use these techniques.

2:00 pm in Altgeld Hall 347,Tuesday, September 9, 2014

#### High temperature limits for (1+1)-dimensional directed polymer with heavy-tailed disorder

###### Partha Dey (UIUC Math)

Abstract: The directed polymer model at intermediate disorder regime was introduced by Alberts-Khanin-Quastel in 2012. It was proved that at inverse temperature $\beta n^{-\gamma}$ with $\gamma=1/4$ the partition function, centered appropriately, converges in distribution and the limit is given in terms of the solution of the stochastic heat equation. This result was obtained under the assumption that the disorder variables posses exponential moments, but its universality was also conjectured under the assumption of six moments. We show that this conjecture is valid and we further extend it by exhibiting the non-universal limiting behavior in the case of less than six moments. We also explain the behavior of the scaling exponent for the log-partition function under different moment assumptions and values of $\gamma$. Based on joint work with Nikos Zygouras.

4:00 pm in 245 Altgeld Hall,Tuesday, September 9, 2014

#### ﻿A modern synthesis of analysis, mechanics and probability

###### Richard Lehoucq (Sandia)

Abstract: My presentation considers the role of modern applied mathematics in support of the evolving peridynamic mechanical model. The peridynamic model is of mathematical interest because the classical balance laws posed in terms of partial differential equations are replaced with nonlocal balance laws involving integral equations. The model is of mechanical interest because the integral operators allow the dynamic formation of jump discontinuities and so allow the modeling of material failure. I also consider the broader aspects of attempting to impact a largely engineering endeavor in modeling and simulation with modern tools of mathematics.

5:00 pm in 239 Altgeld Hall,Tuesday, September 9, 2014

Abstract: For Math graduate students. PI4 poster session and mingling with today's MSS speaker Richard Lehoucq (Sandia National Labs).