LSU Department of Mathematics Professor P. Sundar and graduate student Christian Ennis are working on a collaborative research project with graduate students and postdoctoral researchers from the Bergische Universität Wuppertal in Wuppertal, Germany starting from the Spring of 2022 with research visits arranged at LSU and Wuppertal University. The research will focus on the probabilistic behavior of solutions of stochastic partial differential equations that arise in applications with the goal of obtaining tunneling properties for stochastic processes with multiple limit distributions. It would lead to an understanding of rare transitions from the vicinity of one limit distribution to another. Though this research is theoretical in nature, it has applications in thermodynamics as well as mathematical finance and will lead to new aspects of risk theory in various applications.

The objective is to obtain sufficient conditions for the existence of multiple limit distributions for the solution of a SPDE, and to obtain sharp estimates on the probability of certain rare events related to transitions between limit distributions. If the solution of a stochastic partial differential equation starts in the domain of attraction of a limiting distribution, then find the probability that it transitions to a vicinity of a different limiting distribution. “SPDEs for which we aim to analyze tunneling properties may in future be obtained as fluctuation limits of thermodynamical systems with for e.g., double well potentials”.

Dr. Sundar came to the LSU Department of Mathematics after receiving his Ph.D. from Purdue University in 1985. He has authored many papers and has a prolific history of mentorship and collaboration. In future research visits, he plans to work on large deviation theory of SPDEs with multiple limit distributions, hold discussions and lectures, write papers, mentor, and meet other mathematicians working in statistical physics. When asked about his experience in the LSU Department of Mathematics he offered that the department is nationally well-ranked, dedicated to teaching and research, and attracts strong graduate students who assist in research.

Christian Ennis was first interested in mathematics when he began tutoring and realized he enjoyed math enough to teach it. He read about open problems in mathematics and discovered questions that hadn’t been answered. He finds joy in the challenge of solving problems, and after taking a proof course knew that he wanted to continue in academia to become a professor and help future students learn about mathematics, by teaching but also mentoring in research in the field of probability theory after receiving his Ph.D.

The collaboration project will extend beyond the Spring 2022 semester with graduate students and postdoctoral researchers visiting Dr. Sundar at LSU as well as Christian Ennis and Dr. Sundar travelling to Wuppertal to perform research with his collaborator Dr. Barbara Rüdiger. He and his collaborator, Dr. Barbara Rüdiger, plan to form an international group of young researchers to further the growth of this research area.

(Photo and Contact: Jolie Cornay)