Stochastic Homogenization of Hamilton-Jacobi Equations: An Overview of Results and Challenges

Topic: 
Stochastic Homogenization of Hamilton-Jacobi Equations: An Overview of Results and Challenges
Date & Time: 
Thursday, November 14, 2024 - 17:00 to 18:00
Speaker: 
Elena Kosygina, NYU Shanghai & Baruch College, City University of New York
Location: 
W923, West Hall, NYU Shanghai New Bund Campus

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Abstract:  

Since the pioneering unpublished paper of P.-L. Lions, G. Papanicolaou, S.R.S. Varadhan (circa 1987), where they proposed two different treatments of the homogenization problem for Hamilton-Jacobi equations with periodic Hamitonians, the subject of homogenization of inviscid and viscous Hamilton-Jacobi equations in stationary ergodic media has received a lot of attention. In this talk I shall first give a very brief overview of the topic and then focus on our latest results and open questions. These latest results are the joint work with Atilla Yilmaz from Temple University.

Biography:  

Elena Kosygina is a Visiting Professor of Mathematics at NYU Shanghai and a Professor of Mathematics at Baruch College and the CUNY Graduate Center. After completing her PhD at the Courant Institute of Mathematical Sciences, NYU, she was a (non-tenure-track) R. Boas Assistant Professor at Northwestern University, and then moved to CUNY to a tenure-track position and received tenure. She was a member of the Institute of Advanced Studies (Spring 2009) and a Simons Fellow in Mathematics (2014-2015). Prof. Kosygina's research is in probability, stochastic processes, and partial differential equations. In particular, she is interested in scaling limits of self-interacting random walks and in homogenization of Hamilton-Jacobi equations in random media.

Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai

This event is open to the NYU Shanghai community and Math community.