Andrea Brini (Imperial College), “Knot invariants from mirror symmetry”
–
Events at: MSRI: SIMONS AUDITORIUM
Geordie Williamson (University of Sydney), “Top heaviness and hard Lefschetz in combinatorics”
–
ABSTRACT: How many faces in each dimension can a simplicial polytope have? This question turns out to have a beautiful answer, which was conjectured by McMullen in 1971 and proved by Stanley and Billera-Lee in the 80s. It is natural to ask what one can say for other combinatorial structures. I will review several instances where hard Lefschetz provides the … Read More
Zijun Zhou (Stanford University), “GW/DT correspondence for local gerby curves with transversal A_n singularity”
–
ABSTRACT: In this talk, I will discuss an ongoing joint project with Zhengyu Zong on the Gromov-Witten/Donaldson-Thomas correspondence for local gerby curves, as an orbifold generalization of the corresponding work on the smooth case by Bryan-Pandharipande and Okounkov-Pandharipande. By applying degeneration formulas, the correspondence can be reduced to the case of [C^2/Z_{n+1}] \times P^1, where the 3-point relative GW/DT invariants … Read More
Hiroshi Iritani (Kyoto University), “Toric flips and quantum D-modules”
–
ABSTRACT: I will discuss the change of quantum cohomology of toric stacks under flips.
Andrei Negut (MIT), “Hecke correspondences for general surfaces, II”
–
ABSTRACT: On February 5, I discussed the problem of understanding the representation theory of Hecke correspondences between moduli spaces of stable sheaves on a smooth projective surface S (and presented reasons why one would care, stemming from mathematical physics and algebraic geometry). In this talk, I will give details on the proof, by studying the geometry and intesection theory of … Read More
Evgeny Gorsky (UC Davis), “Knot homology and Hilbert schemes”
–
ABSTRACT: I will describe recent results and conjectures relating knot invariants (such as HOMFLY-PT polynomial and Khovanov-Rozansky homology) to algebraic geometry of the Hilbert scheme of points on the plane. The talk is based on joint works with Andrei Negut, Jacob Rasmussen and Matthew Hogancamp.
Sven Meinhardt (University of Sheffield), “Monoidal Gerbes and Cohomological Hall (co)Algebras”
–
ABSTRACT: I will introduce the concept of monoidal gerbes and show how to use them to twist suitable monoidal tensor categories. We will see interesting examples of this construction related to moduli stacks of objects in Calabi-Yau categories. For 3-Calabi-Yau categories we can go even further by constructing interesting monoidal functors. This allows us to define the Cohomological Hall (co)Algebra.
Raphael Rouquier (UCLA), “Toroidal algebras, Hilbert schemes and finite groups of Lie type”
–
Martijn Kool (Rijksuniversiteit te Utrecht), “New directions in Vafa-Witten theory”
–
ABSTRACT: In the 1990’s, Vafa-Witten tested S-duality of N=4 SUSY Yang-Mills theory on a complex algebraic surface X by studying modularity of a certain partition function. In 2017, Tanaka-Thomas defined Vafa-Witten invariants by constructing a symmetric perfect obstruction theory on the moduli space of Higgs pairs (E,\phi) on X. The instanton contribution (\phi=0) to these invariants is the virtual Euler … Read More
Lotte Hollands (Heriot-Watt University), “Four-dimensional BPS states in the E6 theory”
–
ABSTRACT: BPS states in four-dimensional N=2 theories are enumerated by spectral networks on two-dimensional Riemann surfaces. Geometrically they correspond to special Lagrangian discs ending on the spectral networks, more formally they are (conjectured to be) generalised Donaldson-Thomas invariants for an appropriate CY3 category. In this talk I will give a particularly interesting example of these BPS state counts in the … Read More