# Faculty

## Carl Mueller

*Professor of Mathematics*

PhD, University of California, Berkeley, 1979

802 Hylan Hall

(585) 441-5029

Fax: (585) 273-4655

carl.e.mueller@rochester.edu

Office Hours: Mondays and Wednesdays, 10:30 - 12:00

### Biography

I received my PhD from the Berkeley Statistics Department in 1979. I was an NSF postdoc at the University of Illinois from 1979 - 1981, an assistant professor at theUniversity 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.

### Research Overview

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). Recently I have studied hitting properties of vector-valued solutions to SPDE.

### Courses Offered (subject to change)

- MTH 201H Introduction to Probability, Honors Version (Fall 2016)
- MTH 165 Linear Algebra with Differential Equations (Spring 2017)

### Selected Publications

- (with R. Dalang and Y. Xiao) Polarity of points for Gaussian random fields,
*Ann. Prob*. - (with L. Mytnik and E. Perkins) Nonuniqueness for a parabolic SPDE with 3/4−ε Holder diffusion coefficients,
*Ann. Prob*. 42, 5, 2032-2112 (2014). - (with L. Mytnik and J. Quastel) Effect of noise on front propagation in reaction-diffusion equations of KPP type,
*Invent. Math*. 184, 2, 405-453 (2011). - (with R. Tribe) Hitting properties of a random string,
*Electronic J. Probab**.*, 7, paper 10, 1-29, (2002). - Long time existence for the heat equation with a noise term,
*Probab. Th. and Related Fields*, 90, 505-518, (1991).