Department of

# Mathematics

Seminar Calendar
for events the day of Friday, April 1, 2016.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      March 2016             April 2016              May 2016
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1  2  3  4  5                   1  2    1  2  3  4  5  6  7
6  7  8  9 10 11 12    3  4  5  6  7  8  9    8  9 10 11 12 13 14
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Friday, April 1, 2016

2:00 pm in 445 Altgeld Hall,Friday, April 1, 2016

#### Heat and wave equations in fractal sets

###### Fernando Roman-Garcia (UIUC Math)

Abstract: Have you ever heated up a Sierpinski-Gasket-shaped pizza slice and wonder how long you have to wait for the heat to dissipate so you can enjoy your snack at the right temperature? In this talk we develop the necessary tools to answer this question by defining heat and wave equations in fractal sets. We start with an explicit approach to construct a suitable Laplace operator on the Sierpinski Gasket (SG) which will then be used to define second order differential equations with the SG as their spatial domain. Dirichlet (and/or Neumann) Spectral analysis for such an operator will be introduced if time permits.

3:00 pm in 245 Altgeld Hall,Friday, April 1, 2016

#### Finite-size effects and switching times for Moran dynamics with mutation

###### Meghan Galiardi (UIUC)

Abstract: A standard tool used in evolutionary dynamics is to formulate the model as a Markov chain on a lattice, where the discrete points on the lattice correspond to integer sizes of the various subpopulations. In the limit of large populations, this Markov chain converges to an ordinary differential equation. For populations large but finite, however, the system is still noisy and this stochastic system gives a finer picture of the dynamics than the deterministic limit does. We demonstrate the advantage of studying the stochastic system for a 1-D system using Moran dynamics.

4:00 pm in 345 Altgeld Hall,Friday, April 1, 2016

#### A foundational look at entropy and the second law of thermodynamics after Lieb and Yngvason

###### Slawomir Solecki (UIUC)

Abstract: We will go over "A guide to entropy and the second law of thermodynamics" by Elliott H. Lieb and Jakob Yngvason, Notices of the AMS, 1998.

4:00 pm in 241 Altgeld Hall,Friday, April 1, 2016

#### Pure Braid Groups and Mapping Class Groups

###### Marissa Loving (UIUC Math)

Abstract: In 2009, Leininger and Margalit proved that given any two elements of the pure braid group they either commute or generate a free group. Their proof exploited the connection between the pure braid group and the mapping class group of a punctured sphere as well as using results from 3 dimensional topology and Bass-Serre Theory. I will give a sketch of their proof and talk about some current research in the area, namely generalizing this result to pure surface braid groups.

4:00 pm in 347 Altgeld Hall,Friday, April 1, 2016

#### Matrix Schubert varieties and Gaussian conditional independence models

###### Jenna Rajchgot   [email] (U Michigan)

Abstract: Matrix Schubert varieties are subvarieties in the affine space of square matrices determined by putting rank conditions on submatrices. I will discuss analogs of these varieties for the spaces of upper triangular and symmetric matrices and show that, as in the traditional matrix Schubert setting, defining ideals have nice Grobner bases, and primary decomposition of sums of defining ideals can be computed combinatorially. Our motivation for discussing these upper triangular and symmetric matrix Schubert varieties comes from algebraic statistics. I will explain how to use these varieties to solve two problems concerning Gaussian random variables. This is joint work with Alex Fink and Seth Sullivant.