My research interests intersect probability, geometry, and analysis. More particularly, they include infinite-dimensional analysis, Gaussian measures and processes, stochastic differential equations on Lie groups (and sometimes more general manifolds), Markov processes and semigroups, differential operators and hypoellipticity theory. My articles on arXiv.

I co-organize the UVa Probability seminar

I am founder of and coordinate activities for Women in Probability.

I am faculty coordinator for the UVa Math Ambassadors.

All course materials for classes I am teaching may be found on the UVa Canvas course page.

Department of Mathematics

University of Virginia

Charlottesville, VA 22903 USA


Tel: (434) 982-2782

Fax: (434) 982-3084

Office: 205 Kerchof

E-mail: melcher "at"