# Carl Mueller

Department of Mathematics

University of Rochester

Rochester, NY 14627

carl dot e dot mueller at rochester dot e du

## Classes

### Fall 2024

- Math 504, Stochastic Processes

### Spring 2025

- Math 201, Introduction to Probability

## Research Interests

Probability and related parts of analysis. I am interested in multiparameter models driven by noise, often related to models in statistical physics. Currently, my main interest is in stochastic partial differential equations (SPDE). Most physical systems are described in terms of partial differential equations, and random noise influences most of these systems. This leads to the study of SPDE. I usually study the qualitative properties of solutions to nonlinear SPDE, such as blow-up, support, die-out, phase transitions, SPDE with singular solutions, and SPDE with vector-valued solutions. I have also dealt with the convergence of particle systems to SPDE. Some of my research is inspired by connections between SPDE and a particle system called the Dawson-Watanabe process (or super-Brownian motion). More recently I have studied hitting properties of vector-valued solutions to SPDE, and SPDE and other models which penalize self-intersections.

## Biography

I received my Ph.D. from the Berkeley Statistics Department in 1979. I was an NSF postdoc at the University of Illinois from 1979 - 1981, an assistant professor at the University of Texas from 1981 - 1984, and then came to Rochester. Now I’m a full professor. I’ve taken sabbaticals at the University of Minnesota, University of British Columbia, the Simons-Lauffer Mathematical Sciences Institute at Berkeley, the Mittag-Leffler Institute outside of Stockholm, and again at the Simons-Lauffer Mathematical Sciences Institute at Berkeley.