Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted.
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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
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: We study the probability that a monic polynomial with integer coefficients has a low-degree factor over the integers. It is known that certain models are very likely to produce random polynomials that are irreducible, and our project can be viewed as part of a general program of testing whether this is a universal behavior exhibited by many random polynomial models. Interestingly, though the question comes from algebra and number theory, we primarily use tools from combinatorics, including additive combinatorics, and probability theory. We prove for a variety of models that it is very unlikely for a random polynomial with integer coefficients to have a low-degree factor—suggesting that this is, in fact, a universal behavior. For example, we show that the characteristic polynomial of random matrix with independent +1 or −1 entries is very likely to be irreducible. Joint work with Sean O’Rourke. The talk will also discuss joint work with UW-Madison undergraduates Christian Borst, Evan Boyd, Claire Brekken, and Samantha Solberg, who were supported by NSF grant DMS-1301690 and co-supervised by Melanie Matchett Wood.
Thursday, September 29, Joseph Najnudel, University of Cincinnati
Thursday, October 6, TBA, TBA
Thursday, October 13, No Seminar due to Midwest Probability Colloquium
For details, see Midwest Probability Colloquium.
Thursday, October 20, Amol Aggarwal, Harvard
Thursday, October 27, TBA, TBA
Thursday, November 3, TBA, TBA
Thursday, November 10, TBA, TBA
Thursday, November 17, TBA, TBA
Thursday, November 24, No Seminar due to Thanksgiving
Thursday, December 1, TBA, TBA
Thursday, December 8, TBA, TBA
Thursday, December 15, TBA, TBA