Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, April 16, 2015.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      March 2015             April 2015              May 2015
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1  2  3  4  5  6  7             1  2  3  4                   1  2
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Thursday, April 16, 2015

11:00 am in 241 Altgeld Hall,Thursday, April 16, 2015

#### Relative trace formula and relative Weyl laws

###### Heekyoung Hahn (Duke Univ. Math)

Abstract: In this talk we prove a relative trace formula for all pairs of connected algebraic groups $H \leq G \times G$ with $G$ a reductive group and $H$ the direct product of a reductive group and a unipotent group given that the test function satisfies simplifying hypotheses. As an application, we prove a relative analogue of the Weyl law, giving an asymptotic formula for the number of eigenfunctions of the Laplacian on a locally symmetric space associated to $G$ weighted by their $L^2$-restriction norm over a locally symmetric subspace associated to $H_0 \leq G$. Time permitting, we discuss how this relative Weyl law can be used to systematically construct families of automorphic forms with “large periods.” This is joint work with J. R. Getz and M. Lipnowski.

1:00 pm in Altgeld Hall,Thursday, April 16, 2015

#### A multi-scale modeling challenge for disparate crop models

###### Amy Marshall-Colon (Plant Biology, UIUC)

Abstract: The rate of change of our atmosphere and climate present significant threat to food security by imposing environmental challenges that present day germplasm are not adapted to handle. Computational models capable of predicting emergent crop phenotypes in response to climate change are needed to rapidly evaluate risk to food security and direct research efforts toward making educated decisions about metabolic pathways to modify. However, models that simulate responses at a single biological scale are limited in their ability to provide a holistic view of ecosystem or even whole plant response to global change. This limitation can be addressed by integrative, multi-scale modeling. Here I will present two types of models at singular biological levels followed by discussion of current multi-scale modeling attempts and future challenges that could be addressed by collaborative efforts between math and biology.

1:00 pm in Altgeld Hall 243,Thursday, April 16, 2015

#### Boundaries of (some) $Out(F_n)$-complexes

###### Mladen Bestvina (University of Utah)

Abstract: It has recently been shown that Out(F_n) acts on several interesting hyperbolic complexes in analogy with mapping class groups acting on the curve (or arc) complex. In the talk I will try to describe what the boundaries of two of these (free factor and splitting) complexes look like. The answer is modelled on Klarreich's description of the boundary of the curve complex as the space of ending laminations. This is joint work with Reynolds and with Feighn-Reynolds (in progress) respectively.

2:00 pm in 140 Henry Administration Bldg,Thursday, April 16, 2015

#### Computer Algebra Algorithms for Proving Theta Function Identities

###### Liangjie Ye (Research Institute for Symbolic Computation (RISC), Austria)

Abstract: In the past, researchers working on mathematical problems in number theory used some quite technical arithmetic manipulations to prove some basic theta function relations which, done by hand, is a tedious (perhaps unfeasible) task for more complicated identities. Now by our new algorithmic approach one can prove all identities from a general class in a computer-assisted way. The main tools are elliptic functions and modular forms. In this talk, I give an overview of my research and its main results, including some underlying concepts from complex analysis I use (e.g., compact Riemann surfaces and zero recognition of elliptic and modular functions).

4:00 pm in 245 Altgeld Hall,Thursday, April 16, 2015

#### Hyperbolicity and asymptotic dimension

###### Mladen Bestvina (University of Utah)

Abstract: Asymptotic dimension (asdim) is the large scale version of the concept of dimension, introduced by Gromov. It applies to metric spaces, and in particular to finitely generated groups. A celebrated theorem of Guoliang Yu implies the Novikov conjecture in manifold theory for groups with finite asdim. In this talk I will discuss some basic examples and explain how hyperbolicity properties of a space can be used to prove finiteness of asdim. If there is time, I will talk about the recent work with Bromberg and Fujiwara that proves that mapping class groups have finite asdim.