Presentations

Presenters:  Jackie Stapleton, Caitlin Carter, Laura Bredahl

A presentation for LAAUW members outlining the process and outcomes of a scoping review we conducted from September 2019 to April 2020.

video of the talk: part I

video of the talk: part II

Abstract:  Remarkable work of Braverman-Finkelberg-Nakajima has constructed, based on some fancy quantum field theory, a fascinating collection of spaces called "Coulomb branches." The definition of these involves the geometry of affine Grassmannians, and thus is not so easy for many people think about.  Luckily, the algebraic tools for understanding the most...

video of the talk  

Soergel bimodules have natural manifestations in 3 different contexts: combinatorial (i.e. diagrammatic calculus), geometric (i.e. perverse sheaves on the flag variety) and representation theoretic (i.e. Harish-Chandra bimodules/category O).  

In each of these contexts, there are generalizations that might interest you:

• on the combinatorial side, there is a categorification of the kth tensor power of C^n via KLRW algebras, studied by Khovanov-Lauda-Sussan-Yonezawa...

video of the talk

One of the central topics of the interaction between QFT and math is mirror symmetry for 2d theories. This theory has a more mysterious and exotic friend one dimension higher, sometimes called 3d mirror symmetry, which relates two 3-dimensional theories with N=4 supersymmetry. For roughly a decade, I struggled to understand this phenomenon without understanding what most of the words in the previous sentence meant. Eventually, I wised up and based on work of Braverman, Finkelberg, Nakajima, Dimofte,...