Dongmin Gang "Vacua counting of 3d gauge theories" [Lecture-on-3D.pdf]

1. Pure Chern-Simons theories on torus/general Riemann surface

2. Supersymmetric theories on torus/general Riemann surface

Refs : 

"Remarks on the Canonical Quantization of the Chern-Simons-Witten Theory", Nucl.Phys. B326 (1989)

"Aspects of 3d N=2 Chern-Simons-Matter Theories", Arxiv : 1305.1633

"Bethe/Gauge correspondence on curved spaces", Arxiv : 1405.6046

Hee-Cheol Kim "6d Supergravity and F-theory geometry"

Seok Kim "Black holes in AdS/CFT"

Prarit Agarwal "Vanishing OPE Coefficients in 4d N=2 SCFTs" [Agarwal.pdf]

The talk will be based on my recent paper arXiv:1812.04743 with Jaewon Song and Sungjay Lee. I will explain how the Schur and Macdonald index of Argyres Douglas theories, when combined with the representation theory of 4d N=2 superconformal algebras, implies that certain OPE coefficient in these theories should vanish. I will also argue that more generally these coefficients will vanish in all N=2 theories whose central charge 'c' coincides with that of the corresponding AD theory.

Jin-Beom Bae "Sporadic Groups in Two-dimensional Conformal Field Theory"

In thisis talk, I will discuss a nontrivial relation between sporadic groups and modular forms in the context of two-dimensional rational conformal field theory(CFT). First I will provide explicit modular invariant partition functions which exhibit Monster group, baby Monster group, and Fischer group as an automorphism group. Then a bilinear relation between (twined) characters of baby Monster CFT and Ising model will be explained. In addition, I will consider a bilinear relation that involving three-state Potts model and demonstrate how the Fischer group arise.

Jean-Emile Bourgine "Algebraic realization of the topological vertex" [Bourgine.pdf]

Topological strings theory provides us with a powerful technique to compute the non-perturbative partition functions of 5D N=1 supersymmetric gauge theories. Recently, an algebraic description of topological strings amplitudes has been formulated in terms of the representation theory of quantum toroidal algebras (a deformation of the symmetry algebras of quantum integrable systems). It follows from the identification of the refined topological vertex with an intertwining operator between the so-called horizontal and vertical modules. In this talk, I will review this algebraic description, present a brief overview of recent results, and introduce the 'degenerate topological vertex' pertaining to 4D N=2 supersymmetric gauge theories.

Sunjin Choi "Large AdS4,6 black holes from CFT3,5"

We study the indices of 3d, 5d SCFTs on S2 x R, S4 x R in the large N and Cardy limit. In 3d case, we study the partition functions of BPS vortices and monopoles, in gauge theories describing N M2-branes. Monopole operators condense at the physical saddle point, giving large masses to most of the N2 elementary degrees of freedom except ∼ N3/2 of them. The resulting large N free energy statistically accounts for the entropy of large BPS black holes in AdS4 x S7. In 5d case, we study the strong coupling limits of 5d gauge theories on the D4-D8-O8 system. The large N free energy scales like N5/2, accounting for the entropy of large BPS black holes in AdS6. Instanton solitons play subtle roles to realize these deconfined degrees of freedom.

Dongmin Gang "Quantum loop on hyperbolic 3-manifolds" [DongminGang.pdf]

I will talk about how to "quantize" SL(2) loop operator on hyperbolic 3-manifolds. For cusped 3-manifold case, a classical loop operator is given as a function on an algebraic variety called "character variety". After quantization, the function becomes an operator acting on a Hilbert-space. Using consistency conditions required from the physics of 3d-3d correspondence, we fix the ordering ambiguity in the quantization for some examples. I will explain how the quantum loop operator determines an asymptotic expansion of a Colored Jones polynomial associated to the loop operator. 

Seyed Morteza Hosseini "Extremization principles from geometry" [Hosseini.pdf]

I will review recent progresses in understanding the geometric duals of extremization principles in QFT and their relation to black holes microstate counting.

Patrick Jefferson "Studying UV complete 5d N=1 QFTs using Calabi-Yau geometry"

There has been a resurgence of interest in the problem of analyzing and classifying 5d minimally supersymmetric (N=1) QFTs with non-trivial UV fixed points. In this talk, I review the geometric approach to the problem of classification, in which 5d N=1 QFTs can be realized by compactifying M-theory on local Calabi-Yau threefolds and various physical properties of the 5d theory (such as the massive BPS spectrum, weak coupling limits, and global symmetries) can be inferred from the topological properties of these threefolds. I also explain how RG flows triggered by mass deformations can be understood as topology-changing transitions between different threefolds, and how this viewpoint, which organizes 5d theories into families that ultimately originate from 6d (1,0) QFTs compactified on a circle, has led to a concrete proposal for classifying 5d N=1 QFTs by studying RG flows of their 6d progenitors.

Hyojoong Kim "Black holes with baryonic charge and I-extremization" [HyojoongKim.pdf]

I will discuss the I-extremization and its geometric dual, focusing on the seven-dimensional Sasaki-Einstein manifold M^{1,1,1}. I will show that the topologically twisted index and the black hole entropy can be obtained by extremizing the entropy functional with mesonic or baryonic fluxes, respectively.

Sung-Soo Kim "New developments in 5d SCFTs and 5-brane webs" [SungSooKim.pdf]

In this talk, we will first review 5d superconformal theories (SCFTs) and its salient feature. As geometric engineering, we then discuss how one can construct 5d SCFTs from Type II string theory or M-theory. We finally report recent developments in 5-brane web in Type II string theory including constructions of spinor representations and rank-3 antisymmetric hypermultiplets and their connection to 6d SCFTs.

Taro Kimura "Super instanton counting and localization"

We study the super instanton solution in the gauge theory with U(n+| n-) gauge group. Based on the ADHM construction generalized to the supergroup theory, we derive the instanton partition function from the super instanton moduli space through the equivariant localization. We derive the Seiberg-Witten geometry and its quantization for the supergroup gauge theory from the instanton partition function, and study the connection with classical and quantum integrable systems. We also argue the brane realization of the supergroup quiver gauge theory, and possible connection to the non-supergroup quiver gauge theories. This talk is based on https://arxiv.org/abs/1905.01513

Kanghoon Lee "Kerr-Schild double field theory and classical double copy" [KanghoonLee.pdf]

In this talk, I will present a generalization of the conventional KS formalism, which is a powerful tool for constructing exact solutions in general relativity, to double field theory (DFT) and supergravities. I will describe the generalized KS ansatz for the generalized metric in terms of a pair of null vectors and apply this ansatz to the equations of motion of DFT. I'll show that it is possible to find solutions by considering linear equations only. Based on this formalism, I'll discuss that the classical double copy structure, which represents solutions of the Einstein equation in terms of solutions of the Maxwell equation, can be extended to the entire massless string NS-NS sector.

June Nahmgoong "6d superconformal Cardy formulas" 

We study the superconformal index of 6d SCFTs from their 't Hooft anomalies. In the Cardy limit where the angular momenta on S^5 are large, we show that the leading free energy, as well as a few subleading corrections, can be computed from the 6d anomaly polynomials. Our large N free energy accounts for the entropy of supersymmetric black holes in dual AdS_7.

Satoshi Nawata "New TQFT from DAHA"

  I will talk about the relationships among 4d Coulomb branch, DAHA, and modular tensor categories. 

Matteo Poggi "Supersymmetric Wilson loops in two dimensions and duality" [Poggi.pdf]

We classify bosonic N=(2,2) supersymmetric Wilson loops on arbitrary backgrounds with vector-like R-symmetry. These can be defined on any smooth contour and come in two forms which are universal across all backgrounds. We show that these Wilson loops, thanks to their cohomological properties, are all invariant under smooth deformations of their contour. At genus zero they can always be mapped to local operators and computed exactly with supersymmetric localisation. Finally, we find the precise map, under two-dimensional Seiberg-like dualities, of correlators of supersymmetric Wilson loops.

Raffaele Savelli "SUSY enhancement from T-branes" [Savelli.pdf]

By exploiting the F-theoretic engineering of rank-one four dimensional superconformal field theories, I will provide a geometric explanation of the phenomenon of supersymmetry enhancement along the RG flow, recently observed by Maruyoshi and Song. The superpotential deformations responsible for such flows are interpreted as T-brane backgrounds and are encoded in the geometry of elliptically-fibered manifolds. I will give a simple algebraic criterion to select all supersymmetry-enhancing flows and, without any maximization process, derive the main features of the corresponding N=2 theories in the infrared.

Minwoo Suh "Uplifting supersymmetric AdS6 black holes to type II supergravity"

Employing recently proposed uplift formulae, we explicitly uplift supersymmetric AdS6 black holes from pure and matter coupled F(4) gauged supergravity to type II supergravity. We obtain supersymmetric AdS6 black holes asymptotic to the Brandhuber-Oz solutions and to the non-Abelian T-dual of the Brandhuber-Oz solutions from pure and matter coupled F(4) gauged supergravity. We discuss physics of the supersymmetric black holes of type II supergravity.

Junggi Yoon "Schwarzian Theory and Chaos" [Yoon.pdf]

In this talk, I will discuss the quantum chaos of the Schwarzian theory and its quantum correction. The Schwarzian action appears as an effective action of the SYK-like models and as a boundary effective action of 2D dilaton gravity. I will explain that those can be captured by the action of coadjoint orbit, and I will discuss the contribution of the Schwarzian mode to the out-of-time-ordered correlator. Then, I will show that the stability condition of the coadjoint orbit leads to the bound of chaos. In addition, I present the semi-classical analysis of the Schwarzian theory to study Feynman diagrams of the Schwarzian mode. I will show that the quantum correction slows down the exponential growth of the out-of-time-ordered correlator.

Max Zimet  "K3 metrics from little string theory" [Zimet.pdf]

Calabi-Yau manifolds have played a central role in both string theory and mathematics for decades, but in spite of this no Ricci-flat metric on a compact non-toroidal Calabi-Yau manifold is known. I will discuss a new physically motivated approach toward the determination of such metrics for K3 surfaces. The key remaining step is the determination of the BPS spectrum of a little string theory on T^2. I will use string dualities to provide a number of mathematical reformulations of this problem. Finally, I will discuss new approximations to K3 metrics that require only minimal knowledge of this BPS spectrum.