Calendar
- 22September 22, 2020
Triangular Prism equations and categorification
Fusion categories have been extensively studied by Mathematicians and have proved to have many important applications in quantum physics. A fusion category is completely determined by a set of F-symbols which satisfies the pentagon equations. In general, the fusion categories are constructed by different approaches and their F-symbols remain unknown. In this talk, we introduce the triangular prism equations for fusion categories and show that they are equivalent to the pentagon equations. Moreover, we provide a relevant way to manage the complexity by localization, and thus a possible approach to solve them for the F-symbols. As applications, we provided new criteria for categorification and a categorical approach to the neargroup construction, improving Izumi’s equations.
CMSA Computer Science for Mathematicians: Cybersecurity research in the wild
Cybersecurity research exhibits classic yet complex challenges, melding together cryptography, programming language design, and computational complexity, along with psychology and industrial design.One example of these challenges is crafting an expressive yet safe programming language. SQL — the most popular database querying language — is, however, far from being safe; its expressiveness and lack of care in design result in countless SQL injection attacks to this day. The approaches to mitigating this design flaw vary between academia and industry and involve a mixture of graph analysis, system engineering and new designs of programming interfaces.During this talk I will review the different participants in frontier research: industry, academia, nationstates and hobbyists. The first part of the talk will focus on these participants and their incentives, while the second part will contrast how academia is approaching them compared to industry and nationstates.K-stability of cubic fourfolds
Recently there has been tremendous progress on constructing (projective) moduli spaces of Fano varieties using K-stability. In this talk, we will show that the K-moduli space of cubic fourfolds coincide with their GIT moduli space. In particular, all smooth cubic fourfolds are K-stable as well as those with simple singularities. The key ingredients are local volume estimates in dimension 3 due to Liu-Xu, Ambro-Kawamata non-vanishing theorem for Fano 4-folds, and degeneration of K3 surfaces.
Zoom: https://harvard.zoom.us/j/91794282895?pwd=VFZxRWdDQ0VNT0hsVTllR0JCQytoZz09