Supersymmetry and trace formulas - Leon Takhtajan (part 1)

Stony Brook Mathematics Colloquium September 14, 2023 Leon Takhtajan, Stony Brook University Supersymmetry and trace formulas: from Atiyah-Singer to Jacobi-Poisson and Selberg Supersymmetry is a physics concept that related bosons and fermions, particles with integer and half-integer spins. Though it lacks experimental confirmation, supersymmetry has numerous applications in mathematics. I will explain, in simple terms, mathematical origin of the supersymmetry, leading to a derivation of the Atiyah-Singer formula for the index of the Dirac operator, and will outline its new application leading to the classical trace formulas of Jacobi-Poisson and Selberg. Based on the joint work with Changha Choi, arXiv: 2112.07942 and arXiv: 2306.13636.