Tatyana Barron

Tatyana Barron is a Professor in the Department of Mathematics at the University of Western Ontario since July 2022. She holds a Ph.D. from Pennsylvania State University (1998) and has held academic positions at institutions like the University of Michigan and the University of Arizona. Her research focuses on geometric quantization, complex geometry, and mathematical physics. She has supervised five Ph.D. students and has an extensive publication record spanning topics from Toeplitz operators to entropy analysis in quantum systems.

Education:

• Ph.D. in Mathematics, Pennsylvania State University (1998)
• Bachelor's Degree, Moscow Institute of Physics and Technology (1994)

Research Interests: Tatyana Barron explores geometric quantization techniques applied to complex manifolds, with particular emphasis on Kähler and multisymplectic structures. Her work bridges differential geometry, algebraic geometry, and quantum mechanics, addressing topics like automorphic forms, entropy in quantum systems, and the asymptotic properties of geometric operators. She has contributed to understanding Berezin-Toeplitz operators, entanglement in mixed states, and geometric models for therapeutic approaches involving electromagnetic fields.

Her recent publications (2023-2025) highlight advancements in geometric signal theory, entanglement quantification, and semiclassical asymptotics. She has also explored mathematical models for medical applications using electromagnetic principles.

Advising: Supervised five Ph.D. students focusing on topics ranging from holomorphic differentials to singular Lagrangian submanifolds. She co-supervised three of these students with colleagues in geometric analysis and differential geometry.