Donald Youmans

I am interested on one hand in the underlying mathematical structures of physical problems, and on the other hand how physical intuition can help us solve mathematical problems. For example, I am currently studying which role Virasoro coadjoint orbits (which are a priori purely mathematical objects) play in the theory of two-dimensional (quantum) gravity. Another project I am currently working on is counting holomorphic maps from complex two-dimensional manifolds into toric manifolds. Theoretical physics has developped powerful techniques which can be used to tackle this problem.

• A. Alekseev, O. Chekeres, and D. R. Youmans. Towards bosonization of Virasoro coadjoint orbits, Ann. Henri Poincaré (2023).
• O. Chekeres, A. Losev, P. Mnev, and D. R. Youmans, Two field-theoretic viewpoints on the Fukaya-Morse A∞ category, Lett. Math. Phys. 112, 125 (2022)
• J. Pulmann, P. Ševera, and D. R. Youmans, Renormalization group flow of Chern-Simons boundary conditions and generalized Ricci tensor, J. High Energ. Phys. 2020, 96 (2020)
• F. Valach, and D. R. Youmans, Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of BF theory, J. High Energ. Phys. 2020, 189 (2020)
• A. Losev, P. Mnev, and D. R. Youmans, Two-Dimensional Non-abelian BF Theory in Lorenz Gauge as a Solvable Logarithmic TCFT Commun. Math. Phys. 376, 993–1052 (2020)