Professor Xue-Mei Li graduated from Hebei University in 1983. While studying at Xi’an Jiaotong University, she was awarded the Sino-British Friendship Scholarship, a highly selective national scholarship at the time. She went on to receive her Ph.D. from University of Warwick.
She held an EPSRC Research Associate position at the University of Warwick before joining the University of Connecticut, where she was granted tenure and received several competitive research grants and fellowships, including NSF support and a research fellowship at the Mathematical Sciences Research Institute (Berkeley). She returned to the UK in 2001, where she was awarded a Senior Royal Society Leverhulme Research Fellowship.
Li’s research lies at the interface of probability, geometry, and analysis. Her early contributions include the Bismut–Elworthy–Li formula, a fundamental tool for differentiating heat semigroups and studying ergodicity in stochastic PDEs, as well as work on strict local martingales, later influential in mathematical finance for modeling bubbles and arbitrage. She has also made significant contributions to geometric stochastic analysis, in particular to analysis on path spaces based on Malliavin calculus and infinite-dimensional geometry and geometry of diffusion operators, contributing to a broader program aimed at understanding the structure of diffusion measures and the geometry and topology of infinite-dimensional spaces.
She resolved the longstanding open problem of strong completeness for stochastic differential equations on non-compact manifolds, establishing conditions for global stochastic flows with smooth dependence on initial data, with implications for both numerical analysis and stochastic dynamical systems. More recently, her work develops multi-scale methods with long-range dependent noise beyond the classical Markovian framework. In particular, she has used rough path theory to analyse non-Markovian two-scale stochastic systems, while her work on stochastic PDEs with spatial long-range dependence shows that decay of correlations can play a role analogous to dimension. She has also contributed to quantitative and multi-scale analysis on manifolds.
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Sino-British Friendship Scholarship: Thatcher’s speech and memo
Lecture Notes:
Markov Processes Stochastic Analysis Markov Processes-semi-group Measure and Integration