Member Seminar Speaker: Kai Xu (CMSA) Title: Moduli of vector bundles on curve and semiorthogonal decomposition Abstract: In this talk we construct semiorthogonal decompositions of moduli of vector bundles on a curve into its symmetric powers. The essential ingredients in the proof include Borel-Weil-Bott theory for loop groups, derived Schur-Weyl duality for current groups and derived […]

Member Seminar Speaker: Benjamin McKenna Title: Random matrices and large deviations Abstract: We give a generalist overview of random matrices and their (a)typical behaviors. In recent years, classical results have been complemented by a variety of new ones, in both the math and physics literatures, whose proofs leverage connections with special integrals over matrix groups. Some of these […]

Member Seminar Speaker: Puskar Mondal (CMSA) Title: On the Breakdown of Einstein's Gravity Abstract: It is important to understand under which conditions, the solutions of non-linear hyperbolic PDEs break down in finite time. In the context of Einstein's gravity, this is very closely tied to naked singularity formation and Penrose's weak cosmic censorship conjecture. In this talk, […]

Member Seminar Speaker: Daniel Kapec (CMSA) Title: Black Holes as Quantum Systems Abstract: To an outside observer, a black hole appears to be an ordinary quantum mechanical system with finite entropy and highly chaotic internal dynamics. Nevertheless, the low-temperature thermodynamics of the Kerr black hole presents several puzzles. For instance, the leading order semiclassical approximation to the […]

Member Seminar Speaker: Iacopo Brivio (CMSA) Title: Extension of pluricanonical forms in positive and mixed characteristics Abstract: The geometry of a complex manifold $X$ is to a large extent determined by its pluricanonical forms, i.e. global sections of $(\Omega^{\dim X}_X)^{\otimes m}$ for $m\geq 0$. A famous theorem of Siu states that when $X\to D$ is a smooth […]

Member Seminar Speaker: Zi Yang Kang Title: Deformations of Landau-Ginzburg models and their fibers Abstract: In mirror symmetry, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w, but not all such pairs correspond to Fano varieties under mirror symmetry, so a […]