# Carl Mueller

Department of Mathematics

University of Rochester

Rochester, NY 14627

carl dot e dot mueller at rochester dot e du

## Classes

### Fall 2022

- Math 210, Introduction to Financial Mathematics
- Math 255, Differential Geometry I

### Spring 2023

- Math 506, Topics in Probability

## Research Interests

Probability and related parts of analysis. I am interested in stochastic processes in which there is not only a time parameter, but an extra parameter such as space. 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 Math Sciences Research Institute at Berkeley, the Mittag-Leffler Institute outside of Stockholm, and again at the Math Sciences Research Institute at Berkeley.