Tai Melcher

Tai Melcher I am an associate professor in the Department of Mathematics at the University of Virginia.
		Contact 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" virginia.edu Homepage: http://faculty.virginia.edu/melcher I coorganize the UVA Probability Seminar. I am founder of and coordinate activities for Women in Probability. I am faculty coordinator for the UVa Math Ambassadors.

Research

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.

Stochastic integrals and Brownian motion on abstract nilpotent Lie groups
preprint.

Convergence rates of the empirical spectral measure of unitary Brownian motion with E. Meckes

Annales Henri Lebesgue, 1, 247-265, 2018.

Small-time asymptotics for subelliptic Hermite functions on SU(2) and the CR sphere with J. Campbell

to appear in Potential Analysis, 2019.

Hypoelliptic heat kernels on infinite-dimensional Heisenberg groups with B. Driver and N. Eldredge

Transactions of the AMS, 368, 989-1022, 2016.

Small deviations for time-changed Brownian motions and applications to second-order chaos with D. Dobbs

Electronic Journal of Probability, 19, 1-23 2014.

Smoothness of heat kernel measures on infinite-dimensional Heisenberg-like groups with D. Dobbs

Journal of Functional Analysis, 264, 2206-2223, 2013.

Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups with F. Baudoin and M. Gordina

Transactions of the AMS, 365, 4313-4350, 2013.

A subelliptic Taylor isomorphism on infinite-dimensional Heisenberg groups with M. Gordina

Probability Theory and Related Fields, 155, 379-426, 2013.

Heat kernel analysis on semi-infinite Lie groups

Journal of Functional Analysis, 257, 3552-3592, 2009.

Malliavin calculus for Lie group-valued Wiener functions with note

Infinite Dimensional Analysis, Quantum Probability and Related Topics, 12, 67-89, 2009.

Hypoelliptic heat kernel inequalities on Lie groups

Stochastic Processes and their Applications, 118, 368-388, 2008.

Hypoelliptic heat kernel inequalities on the Heisenberg group with B. Driver

Journal of Functional Analysis, 221, 340-365, 2005.

My articles on arXiv.

Teaching (links only for those with access to UVa Collab)

i

Spring '16:	MATH 7310, Real Analysis and Linear Spaces I
Fall '15:	MATH 4110, Introduction to Stochastic Processes
Fall '14:	MATH 7360, Probability Theory I
Spring '14:	MATH 2310, Calculus III
Fall '13:	MATH 7000
	MATH 7360, Probability Theory I
Spring '13:	MATH 7370, Probability Theory II
Fall '12:	MATH 3250, Ordinary Differential Equations
Fall '11:	MATH 5110, Introduction to Stochastic Processes
	MATH 7360, Probability Theory I
Spring '11:	MATH 5110, Introduction to Stochastic Processes
Fall '10:	MATH 3100, Introduction to Probability
	MATH 7360, Probability Theory I
Spring '09:	MATH 736, Probability Theory I
Fall '08:	MATH 310, Introduction to Probability
	MATH 511, Introduction to Stochastic Processes
Spring '08:	MATH 736, Probability Theory I
Fall '07:	APMA 310, Probability
Spring '07:	MATH 122, Applied Calculus II
Fall '06:	APMA 308, Linear Algebra

UVA

Department of Mathematics

email me