Thursday, October 10, 2019
10/10/2019 - 4:00pm
Abstract: Random matrix theory has played an important role in recent work on statistical network analysis. In this talk, I will review recent results on regimes of concentration of random graphs around their expectation, showing that dense graphs concentrate, and sparse graphs concentrate after regularization. I will also discuss some new results and open problems regarding spectra of random graphs, with applications to the problem of community detection.
10/10/2019 - 4:15pm
Abstract: Perverse sheaves are, by now, classical objects of algebraic topology. They occupy the middle position between sheaves (“functions”) and cosheaves (“distributions”). Remarkably, in many instances, perverse sheaves admit natural categorical analogs called perverse schobers. I will explain this concept and sketch its applications to such areas as Fukaya catgories with coefficients, derived categories of flops and algebra of the infrared of Gaiotto-Moore-Witten.