Dear colleagues, I would like to invite you to the following online seminar organized by the Probability group of the University of Pisa. The two talks will be accessible under the link Click here to join the meeting<https://teams.microsoft.com/l/meetup-join/19%3A17115d7f6ef44c5e91974362906cfc95%40thread.tacv2/1615820667134?context=%7B%22Tid%22%3A%22c7456b31-a220-47f5-be52-473828670aa1%22%2C%22Oid%22%3A%22dfd1e5f6-331d-43e0-a180-4bb6ce727fb7%22%7D> Best regards, Giacomo Tuesday, March 23, 16:00 Speaker: Michela Ottobre (Heriot-Watt University Edinburgh) Title: Uniform in time approximations of stochastic dynamics Abstract: Complicated models, for which a detailed analysis is too far out of reach, are routinely approximated via a variety of procedures; this is the case when we use multiscale methods, when we take many particle limits and obtained a simplified, coarse-grained dynamics, or, simply, when we use numerical methods. While approximating, we make an error which is small over small time-intervals but it typically compounds over longer time-horizons. Hence, in general, the approximation error grows in time so that the results of our ``predictions" are less reliable when we look at longer time-hormizons. However this is not necessarily the case and one may be able to find dynamics and corresponding approximation procedures for which the error remains bounded, uniformly in time. We will discuss a very general approach to understand when this is possible. I will show how the approach we take is very broad and show how it can be used for all of the approximation procedures mentioned above. This is based on a series of joint works with a number of people: L. Angeli, J. Barre', D. Crisan, P. Dobson, I. Souttar and E. Zatorska. Tuesday, March 23, 17:00 Speaker: Andrea Agazzi (Duke University) Title: Large deviations for stochastic models of chemical reaction networks Abstract: At the microscopic level, the dynamics of arbitrary networks of chemical reactions can be modeled as jump Markov processes whose sample paths converge, in the limit of large number of molecules, to the solutions of a set of algebraic ordinary differential equations. Fluctuations around these asymptotic trajectories and the corresponding phase transitions can in principle be studied through large deviations theory in path space, also called Wentzell-Freidlin (W-F) theory. However, the specific form of the jump rates for this family of processes does not satisfy the standard regularity assumptions imposed by such theory. This talk discusses how such conditions can be relaxed. In this talk, I will discuss sufficient stability and nondegeneracy conditions on the given family of Markov jump processes to obtain the desired large deviations estimates, and show how some of these conditions can be translated into structural ones, facilitating their verification for large chemical networks. ************************ Giacomo Di Gesù Dipartimento di Matematica Università di Pisa Largo Bruno Pontecorvo 5 56127 - Pisa, Italy giacomo.digesu@unipi.it<mailto:giacomo.digesu@unipi.it> https://sites.google.com/site/giacomodigesu/