Speaker: Hyun Kyu Kim (KIAS)
Title: Quantization of Teichmüller spaces, and 2d conformal field theory
Abstract: The Teichmüller space of a real 2d oriented surface S is the space of all complex structures on S up to pullback by diffeomorphisms isotopic to identity. The Teichmuller space has the Weil-Petersson Poisson structure, along which one considers a deformation quantization. Namely, we replace functions on the Teichmuller space by suitable self-adjoint operators on a Hilbert space. As a result, we obtain a representation on a Hilbert space of the mapping class group of S, which is the discrete symmetry group of S. On the other hand, mapping class group representations are one of the basic ingredients of the modular functor formulation of 2d conformal field theory. Teschner claimed that the representations from quantum Teichmüller theory do satisfy the axioms for a (modified) modular functor. I will review some basics of quantum Teichmüller theory, the concept of a modular functor, and Teschner's claim.

Speaker: Uhi Rinn Suh (Seoul National University)
Title: Operator product formulas in vertex algebras theory
Abstract: A vertex algebra, invented by Richard Borcherds in 1986, is an underlying algebraic structure in the 2-dimensional conformal field theory (CFT). There are several equivalent definitions of vertex algebras and each of these is used in different view points. In the first part of this talk, I will introduce definitions of a quantum field and a vertex algebra which allow us to see connections between vertex algebras and the CFT.  In the second part of this talk, I will explain commutator formulas and operator product formulas (OPE) via $n$-th products and normally ordered products between quantum fields. If time allows, I will introduce the state-field correspondence so that one can rigorously understand OPEs in physics literatures.

Speaker: Jinwon Choi (Sookmyung Women's University)
Title: Introduction to Schottky problem
Abstract: Schottky problem is the problem of characterizing Jacobians of curves among principally polarized abelian varieties. In this talk, I will introduce basic notions related to this problem. This talk is very elementary and aims at graduate students.

Speaker: Insong Choe (KonKuk University)
Title: Moduli of vector bundles over a curve and generalized theta divisors
Abstract: In the first talk, I'll briefly explain the construction of the moduli of vector bundles over a curve. In the second talk, I'll give a definition of the generalized theta divisors and discuss the base-freeness of the associated linear system.

Speaker: Martijn Kool (Utrecht)
Title: Calculation of DT invariants: vertex operators, Hall algebra, and cosection localisation
Abstract: In these three mutually independent talks, I give examples of calculations of generating functions of Donaldson-Thomas type invariants of a threefold X. Talk 1: When X is elliptically fibred, a mix of cut-paste methods and torus localisation can be used to reduce to calculations on Fock space (joint with Jim Bryan). Talk 2: I give a higher rank analog of a Hall algebra calculation by Stoppa-Thomas in order to compute topological Euler characteristics of Quot schemes of reflexive sheaves on X (no assumption on X, joint with Amin Gholampour). Talk 3: When X admits a holomorphic 2-form, I use Kiem-Li cosection localization and compare to results by Maulik-Pandharipande and Kiem-Li on the Gromov-Witten side (joint with Richard Thomas).

Speaker: Nam-Gyu Kang (KIAS)
Title: Gaussian Free Field, Conformal Field Theory, and Schramm-Loewner Evolution
Abstract: I will present an elementary introduction to conformal field theory in the context of complex analysis and probability theory. Introducing Ward functional as an insertion operator under which the correlation functions are transformed into their Lie derivatives, I will explain several formulas in conformal field theory including Ward's equations. This presentation will also include relations between conformal field theory and Schramm-Loewner evolutions.

Speaker: Sang-Bum Yoo (POSTECH)
Title: An introduction to the space of conformal blocks
Abstract: The space of conformal blocks has been used to study various moduli spaces in several perspectives. It can be interpreted as the space of generalized theta functions over the moduli space of bundles and over the moduli space of parabolic bundles on a smooth curve. It can be also applied to study the birational geometry of the moduli space of parabolic bundles and the moduli space of curves. In this lecture we will introduce basics on the space of conformal blocks, such as the definition and the fusion rule, and study the Verlinde formula for the dimension of the space of conformal blocks.