# Probability Seminar

# Fall 2016

**Thursdays in 901 Van Vleck Hall at 2:25 PM**, unless otherwise noted.

**
If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu.
**

## Thursday, September 8, Daniele Cappelletti, UW-Madison

Title: **Reaction networks: comparison between deterministic and stochastic models**

Abstract: Mathematical models for chemical reaction networks are widely used in biochemistry, as well as in other fields. The original aim of the models is to predict the dynamics of a collection of reactants that undergo chemical transformations. There exist two standard modeling regimes: a deterministic and a stochastic one. These regimes are chosen case by case in accordance to what is believed to be more appropriate. It is natural to wonder whether the dynamics of the two different models are linked, and whether properties of one model can shed light on the behavior of the other one. Some connections between the two modelling regimes have been known for forty years, and new ones have been pointed out recently. However, many open questions remain, and the issue is still largely unexplored.

## Friday, September 16, 11 am Elena Kosygina, Baruch College and the CUNY Graduate Center

** Please note the unusual day and time **

The talk will be in Van Vleck 910 as usual.

Title: **Homogenization of viscous Hamilton-Jacobi equations: a remark and an application.**

Abstract: It has been pointed out in the seminal work of P.-L. Lions, G. Papanicolaou, and S.R.S. Varadhan that for the first order Hamilton-Jacobi (HJ) equation, homogenization starting with affine initial data should imply homogenization for general uniformly continuous initial data. The argument utilized the properties of the HJ semi-group, in particular, the finite speed of propagation. The last property is lost for viscous HJ equations. We remark that the above mentioned implication holds under natural conditions for both viscous and non-viscous Hamilton-Jacobi equations. As an application of our result, we show homogenization in a stationary ergodic setting for a special class of viscous HJ equations with a non-convex Hamiltonian in one space dimension. This is a joint work with Andrea Davini, Sapienza Università di Roma.

## Thursday, September 22, Philip Matchett Wood, UW-Madison

Title: Low-degree factors of random polynomials

Abstract: TBA

## Thursday, September 29, Joseph Najnudel, University of Cincinnati

Title: TBA

## Thursday, October 6, TBA, TBA

Title: TBA

## Thursday, October 13, No Seminar due to Midwest Probability Colloquium

For details, see Midwest Probability Colloquium.

## Thursday, October 20, Amol Aggarwal, Harvard

Title: TBA

## Thursday, October 27, TBA, TBA

Title: TBA

## Thursday, November 3, TBA, TBA

Title: TBA

## Thursday, November 10, TBA, TBA

Title: TBA

## Thursday, November 17, TBA, TBA

Title: TBA

## Thursday, November 24, No Seminar due to Thanksgiving

## Thursday, December 1, TBA, TBA

Title: TBA

## Thursday, December 8, TBA, TBA

Title: TBA

## Thursday, December 15, TBA, TBA

Title: TBA