Talks
All schedule times are in Korean Standard Time (GMT + 9 hours).
For time difference to global time zones, please look here.
For time difference to global time zones, please look here.
Cyril Closset (University of Birmingham, UK)
19:00 - 19:40 (KST), Tuesday, February 15, 2022
"Comments on BPS quivers: the view from the U-plane"
I will discuss 5d BPS quivers, which are quivers associated to Calabi-Yau threefold singularities that admit a crepant resolution, reinterpreted as the quantum mechanics of BPS particles of a 5d SCFT compactified on a circle. Using local mirror symmetry, we will discuss how to derive some BPS quivers from the Seiberg-Witten geometry of these theories. Some open questions will be left open.
Dongwook Ghim (KIAS, South Korea)
19:00 - 19:40 (KST), Wednesday, February 16, 2022
"Toric Calabi-Yau 4-folds, 2d (0,2) gauge theories and Brane Brick Models"
A special class of 2d (0,2) supersymmetric gauge theories, named as Brane Brick Models (BBM), is obtained by the low-energy limit of world-volume theories of D1 branes probing toric Calabi-Yau 4-fold along its transverse directions. This talk will pedagogically introduce the combinatorial concepts involved in BBMs and how these are connected to the physics of 2d (0,2) gauge theories. In particular, I will focus on the recent developments, called 3d printing and orbifold reduction, respectively, which systematically generate 2d (0,2) gauge theories from the data of 4d N=1 gauge theories related to dimer models and toric Calabi-Yau 3-folds. Time permitting, I will also mention about an enumerative tool of 2d gauge theories, elliptic genus, which captures the infared behavior of BBMs.
Richard Kenyon (Yale University, USA)
10:50 - 11:30 (KST), Tuesday, February 15, 2022
"Dimers and SL_n"
We consider SL_n-local systems on graphs on surfaces and show how the associated Kasteleyn matrix can be used to compute probabilities of various topological events involving the overlay of n independent dimer covers (or “n-webs”). This is joint work with Dan Douglas and Haolin Shi.
Wei Li (ITP Chinese Academy of Sciences, China)
19:50 - 20:30 (KST), Monday, February 14, 2022
"From BPS crystals to BPS algebras: constructions, representations, and applications"
The BPS sectors of supersymmetric gauge theories have underlying algebraic structures, manifesting themselves in wall-crossing phenomena, BPS/CFT correspondences, Bethe/Gauge correspondences, twisted holographies, etc. I will first explain how to construct BPS algebras for string theory on general toric Calabi-Yau threefolds, based on the crystal melting description of the BPS sectors. The resulting quiver Yangians, together with their trigonometric and elliptic versions, unify various known results and generalize them to a much larger class. I will then explain how to describe their representations using subcrystals and how they can be translated to the framings of the quivers. Time permitting, I will also discuss some applications.
Matthew Pressland (University of Glasgow, UK)
19:50 - 20:30 (KST), Tuesday, February 15, 2022
"Grassmannian twists categorified"
The Grassmannian of k-dimensional subspaces of an n-dimensional space carries a birational automorphism called the twist (or sometimes the Donaldson–Thomas transformation), defined by Berenstein–Fomin–Zelevinsky and Marsh–Scott. This automorphism respects the cluster algebra structure on the coordinate ring, being a quasi-cluster automorphism in the sense of Fraser. By work of Muller–Speyer, similar results hold for positroid strata in the Grassmannian. The cluster algebras in this picture have been categorified, by Jensen–King–Su in the case of the full Grassmannian, and by myself for more general (connected) positroid varieties. In this talk I will report on joint work with İlke Çanakçı and Alastair King, in which we describe the twist in terms of these categorifications. The key ingredient is provided by perfect matching modules, certain combinatorially defined representations for a quiver 'with faces', and I will also explain this construction.
Shlomo Razamat (Technion, Israel)
10:00 - 10:40 (KST), Monday, February 14, 2022
"Comments on Quivers and Fractons"
We will discuss certain structural analogies between supersymmetric quiver gauge theories and lattice models leading to fracton phases of matter. In particular, classes of quiver models can be viewed as lattice models having subsystem symmetries, dimensions of moduli spaces growing linearly with the size of the lattice, and having excitations with limited mobility (with “excitations” and “mobility” properly defined). The talk will be based on 2107.06465.
Ralf Schiffler (University of Connecticut, USA)
10:00 - 10:40 (KST), Tuesday, February 15, 2022
"Knot Theory and Cluster Algebras"
To every diagram K of knot (or link) we associate a quiver with potential (Q,W) cluster algebra and, hence, a cluster algebra A(Q,W) as well as a Jacobian algebra B=Jac(Q,W). The vertices of the quiver are in bijection with the segments of the knot diagram.
For every segment i of K, we construct an indecomposable B-module T(i) and let T be the direct sum of these indecomposables. Each module T(i) corresponds to an element F(i) in the cluster algebra A(Q,W), the so-called F-polynomial of the module. F(i) is a polynomial in several variables y_1,..., y_n with positive integer coefficients.
We prove that, for each segment i of K, the Alexander polynomial of K is equal to a specific specialization of F(i). For an alternating knot, this specialization is simply y_i= -t if i is even; y_i=-t^{-1} if i is odd, where we label the segments of the knot in order of appearance along the knot.
Piotr Sulkowski (University of Warsaw, Poland)
19:50 - 20:30 (KST), Wednesday, February 16, 2022
"Knots, quivers, and BPS states"
I will review a recently discovered relation between quivers and knots, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence, and it states that various invariants of a given knot are captured by characteristics of a certain quiver, which can be associated to this knot. Among others, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver quiver, it provides a new insight on knot categorification, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.
Kazushi Ueda (University of Tokyo, Japan)
10:50 - 11:30 (KST), Monday, February 14, 2022
"Noncommutative local Calabi-Yau 3-folds"
Based on joint works with Tarig Abdelgadir, Akira Ishii, Álvaro Nolla de Celis, and Shinnosuke Okawa, I will discuss generalization of the description of toric Calabi-Yau 3-folds by quivers with potentials coming from dimer models to non-toric or noncommutative cases.
David Vegh (Queen Mary London, UK)
19:00 - 19:40 (KST), Monday, February 14, 2022
"The spectral curve of segmented strings"
In this talk, I will discuss how to compute the spectral curve of ``segmented strings'' in 3d anti-de Sitter spacetime. The motion of a string in this target space is integrable and the worldsheet theory can be discretized while preserving integrability. The corresponding embeddings are segmented strings, which generalize piecewise linear strings in flat space. I will present several examples. Next, I will introduce ``brane tilings'', which are doubly-periodic planar bipartite graphs. I will show that the motion of a closed segmented string can be embedded into the mutation dynamics of a certain brane tiling. This will enable us to compute the spectral curve by taking the determinant of the dressed adjacency matrix of the tiling.
Xin Wang (KIAS, South Korea)
10:00 - 10:40 (KST), Wednesday, February 16, 2022
"Quantum Periods and Spectra in Dimer Models and Calabi-Yau Geometries"
For a given toric Calabi-Yau threefold, the quantum mirror curve from B-model describes the quantum Seiberg-Witten curve of the correspondence 5d N=1 supersymmetric gauge theory. On the other hand, this quantum curve is also the spectral curve of the integrable system that arises from the Dimer model, where the dimer model can be written down from the study of 4d N=1 quiver gauge theories. The eigenvalues of the Hamiltonians are supposed to be the quantized complex structure parameters of the quantum mirror curve. In this talk, I will review the story, and test the correspondence for genus two mirror curves.