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Categorification in Mathematical Physics: April 9 – 13, 2018

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Organized by: Eugene Gorsky, Sergei Gukov, Mikhail Khovanov, Andrei Negut, and Piotr Sułkowski

Categorification is one of the deepest ideas in contemporary mathematics. As the name indicates, it aims to generalize various statements to a categorical level, replacing sets by categories, functions by functors, etc. It led to important developments in various branches of mathematics, among others in knot theory (where polynomial knot invariants turned out to arise simply as dimensions of certain homological spaces, such as Khovanov homology and its generalizations), or in the algebro-geometric setting (involving objects such as coherent sheaves on Hilbert schemes of points). At the same time, categorification turns out to be related to physics, in particular to the process of quantization, and to various fundamental aspects of quantum field theory and string theory.

This workshop will focus on various aspects of categorification in mathematical physics, with particular emphasis on geometric and representation theoretic approaches to conceptualizing and computing knot invariants, and their relations with supersymmetric field theories and string theory.

Talk Schedule


Time Title Presenter Location
9:00am Vertex operator algebras and Higgs branches Christopher Beem SCGP 102
10:00am Coffee Break N/A SCGP Cafe
10:30am On the gluing law in non-topological QFTs Mykola Dedushenko SCGP 102
11:30am   Short Break  
11:45am Representations of DAHA from Hitchin moduli space Satoshi Nawata SCGP 102
12:45pm Lunch N/A SCGP Cafe
2:30pm Categorification of the ring of integers with two inverted Mikhail Khovanov SCGP Cafe
3:30pm Tea N/A SCGP 515
4:00pm  Hall algebras of surfaces Ben Cooper SCGP 102


Time Title Presenter Location
9:00am  Foams and categorification Robert Louis-Hedrien SCGP 102
10:00am Coffee Break N/A SCGP Cafe
10:30am  On categorification of skein modules and algebras Paul Wedrich SCGP 102
11:30am   Short Break  
11:45am  Artin groups and categorification Tony Licata SCGP 102
12:45pm Lunch N/A SCGP Cafe
2:30pm Fermionic finite group gauge theories and (de)categorification Pavel Putrov SCGP Cafe
3:30pm Tea N/A SCGP 515


Time Title Presenter Location
9:00am  Knot contact homology and colored HOMFLY-PT recursion Lenny Ng SCGP 102
10:00am Coffee Break N/A SCGP Cafe
10:30am  Links of surface singularities and planar contact structures Olga Plamenevskaya SCGP 102
11:30am   Short Break  
11:45am  Floer homology for manifolds with torus boundary Jake Rasmussen SCGP 102
12:45pm Lunch N/A SCGP Cafe
2:30pm  Some geometric applications of the link Floer homology Beibei Liu SCGP Cafe
3:30pm Tea N/A SCGP 515
4:00pm  q-skein algebras as integrable systems Shamil Shakirov SCGP 102


Time Title Presenter Location
9:00am  DGA Representations, Ruling Polynomials, and the Colored HOMFLY-PT Polynomial Caitlin Leverson SCGP 102
10:00am Coffee Break N/A SCGP Cafe
10:30am iply graded HOMFLY-PT link homology from a stack of D2 branes. Lev Rozansky SCGP 102
11:30am   Short Break  
11:45am Categorical Chern character and sheaves on the Hilbert scheme of points on plane Alexei Oblomkov SCGP 102
12:45pm Lunch N/A SCGP Cafe
2:30pm Curved complexes, Khovanov-Rozansky homology, and Hilbert schemes Matt Hogancamp SCGP Cafe
3:30pm Tea N/A SCGP 515
4:00pm Knots-quivers correspondence Piotr Sulkowski SCGP 102


Time Title Presenter Location
9:00am On categorification of the WRT invariant Du Pei SCGP 102
10:00am Coffee Break N/A SCGP Cafe
10:30am From Donaldson-Thomas to Haydys-Witten Sergei Gukov SCGP 102
11:30am   Short Break  
11:45am  (0,2) theories and the 4-simplex Tudor Dimofte SCGP 102
12:45pm Lunch N/A SCGP Cafe
2:30pm From Painlevé equations to quantum curves via gauge theory. Alba Grassi SCGP 102
3:30pm Tea N/A SCGP 515