tai melcher

Tai Melcher I am an assistant 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: 219 Kerchof E-mail: melcher "at" virginia.edu Homepage: http://faculty.virginia.edu/melcher I coorganize the UVA Probability Seminar.

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.

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

To appear in Transactions of the AMS, 2011.

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.

Some upcoming conferences

Oberwolfach workshop on Heat Kernels, Stochastic Processes, and Functional Inequalities, 5-11 May 2013
2013 Southeastern Probability Conference, 13-14 May 2013 at Duke University
36th Conference on Stochastic Processes and their Applications, 29 Jul-2 Aug, 2013 at UC Boulder

Teaching

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

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