Personal Webpage of Lutian Zhao

Fall 2020 (Join with Zoom link )

Date Speaker Title Reference
12/09/20 I will introduce basic notions of what derived schemes and stacks are, along with some motivations. I will review ideas from the subject of infinity category theory (so this talk should mostly be independent of last week’s talk). If time permits, we will see how these ideas can be used to define shifted symplectic structures.
Nachiketa Adhikari Derived schemes and stacks Reference I
12/02/20 Derived algebraic geometry is useful, among other things, for understanding "higher homotopies" of schemes. Notions in derived AG are often stated in the language of infinity categories. I will introduce some ideas from model categories and infinity categories, with examples. If time permits, I will also talk about derived schemes.
Nachiketa Adhikari Infinity Categories 101
11/18/20 In this talk, I will review the Kontsevich-Soibelman’s wall crossing formula. I will define the structure of wall crossing for Bridgeland stability, and continue the talk last time on the definition of scattering diagram. The final goal of this talk is to understand the algorithm constructed by Pierrick for computation of Betti number for moduli of sheaves.
Lutian Zhao Scattering Diagram and wall crossing, II Reference I
11/11/20 In this talk, I will describe the main theorem of Bousseau on the scattering diagram of P2. This diagram is a combinatorial way of arranging the wall crossing structure for semistable coherent sheaves. There is an explicit description for this diagram in the case of P2. Moreover, as an application, one can calculate the DT invariant for P2 by an algorithm with this diagram.
Lutian Zhao Scattering Diagram and wall crossing
11/04/20 After reviewing some definitions, I will discuss integration map, which allows one to extract smaller ring from the big hall algebras. I will also discuss the results of Joyce and Song, which shows that the Behrend function is an example of this integration map in the motivic Hall algebra setting, giving the DT invariants. This will provide one of the missing parts of DT/PT correspondence that I discussed last week.
Sungwoo Nam Hall algebras and Integration maps
10/28/20 I will describe an interconnection among hall algebras, generalized DT invariants, and quiver representations. As a goal and an application, I will try to get to the Toda’s proof of euler characteristic version of DT/PT correspondence, and discuss its relation to other proofs of Bridgeland and Stoppa-Thomas.
Sungwoo Nam Hall algebras and DT invariants
10/21/20 I will talk about moduli space of (semi) stable sheaves on surfaces, especially projective plane and Hirzebruch surfaces. Their topological invariants, having Gottsche’s formula as the simplest example, are studied intensively in the literature. I will explain how they are related to the study of BPS invariants coming either from local Calabi-Yau 3-fold given by total space of canonical bundles of the surface or 4-dimensional super Yang-Mills theory on the surface. I’ll also discuss how to compute them, based on the work of Manschot(using blowup formula) and Kool(torus localization) using moduli of sheaves(instanton approach), and compare that with the work of Gholampour and Sheshmani, using sheaves on 3-fold(DT theory, IIA approach).
Sungwoo Nam Moduli of sheaves on P^2 and BPS invariants
10/14/20 In this talk, I introduce the definition of orientation data structure on moduli stack of coherent sheaves on Calabi-Yau threefold. The orientation data is important for the construction of Donaldson-Thomas invariants, and a canonical orientation data will proves to be useful in enumerative geometry. I will define what it means to be canonical and state a rough idea of the proof by Joyce-Upmeier.
Lutian Zhao Orientation Data on moduli space of coherent sheaves Reference I
10/07/20 “Classical” mirror symmetry is a statement about the equality of correlation functions on a pair of Calabi-Yau threefolds called the “mirror pair”; equivalently, about the local isomorphism between complex deformations of one and Kahler deformations of the other. This will be an expository talk consisting of my attempt at understanding this statement.
Nachiketa Adhikari Mirror Symmetry 101
09/30/20 The local Gromov Witten invariants of a Del Pezzo surface has long been studied, via local mirror symmetry. There is another invariants associated to the same setting, which is log GW invariants and there is a conjectural correspondence between log invariants and local invariants, which was proposed by Takahashi back in 90s. In this talk, I will define (only in genus 0) both log and local Gromov-Witten invariants associated to a smooth projective surface and a smooth nef divisor, and then discuss log-local principle by van Garrel-Graber-Ruddat.
Sungwoo Nam The log-local correspondence Reference I
09/09/20 In this talk, I review the notions of d-critical loci, orientations, and motivic DT invariants following Joyce and collaborators. I construct a d-critical locus structure on Hilb^n of local P^2 and provide it with an orientation using ideas of Davidson and Shi. The deduced motivic invariants are shown to agree with those which were defined by Behrend, Bryan, and Szendroi before a more general theory existed. As a consequence, the generating function of motivic DT invariants of Hilb^n of local P^2 is computed. This talk is based on joint work with Yun Shi, which should appear on the arXiv soon.
Sheldon Katz D-critical locus on Hilb^n of local P^2
09/02/20 In this talk, I will describe tropical plane curves from scratch. Over tropical numbers, plane curves over the complex numbers have analogues and they are piecewise linear curves. There is a connection between these curves via Mikhalkin’s correspondence theorem, which says that tropical curve counting coincides with the plane curve counting over complex numbers, which can be calculated by the famous Kontsevich formula.
Sungwoo Nam Tropical curves and counting plane curves Reference I

Spring 2020 (Moved Online after Mar.4th due to COVID-19)

Date Speaker Title Reference
08/06/20 The quantum cohomology of a variety is a ring whose structure constants are 3-point Gromov-Witten invariants and contain enumerative information about the variety. I will introduce these ideas and demonstrate the use of localization to compute the quantum cup product on a toric variety.
Nachiketa Adhikari Quantum products on toric varieties
07/30/20 I’ll continue focusing on ring structure of the cohomology. Boundary divisor of the Hilbert schemes, Virasoro algebra, and its relation to Nakajima operators will be discussed together with its geometric interpretation and application on chern classes of tautological sheaves.
Sungwoo Nam Cohomology of Hilbert schemes of points on a surface, II Reference I
07/23/20 In this talk, I’ll describe various theorems concerning geometric/topological structures of Hilbert schemes of points on a surface. That would include basic properties of Hilbert schemes, Gottsche’s formula, Nakajima’s creation and annihilation operator and Heisenberg algebra action on the cohomology, and associated Virasoro algebra.
Sungwoo Nam Cohomology of Hilbert schemes of points on a surface Reference I
07/16/20 In this talk, I will review the paper of Manschot and Mozgovoy on the Poincare polynomial of intersection cohomology of moduli of vector bundles. They computed the explicit generating function for motivic invariant of these intersection cohomology. In this talk, I will go over their proof and the result in rank 2 and 3 of ruled surface, where we have explicit calculation of the DT invariant.
Lutian Zhao Intersection Cohomology for Moduli of Sheaves on Surfaces Reference I
07/01/20 I will describe the Gromov-Witten calculation of the minimal resolution of $A_n$ surface singularities. Their minimal resolutions are an example of noncompact holomorphic symplectic variety admitting a reduced obstruction theory and at the same time has a torus action. Using equivariant theory, one could reduce the calculation to $A_1$ case and can identify all GW invariants in a closed form. If time permits, I will discuss its relation to threefold geometry of $A_n\times P^1.$
Sungwoo Nam Gromov-Witten theory of $A_n$ resolutions Reference I
06/17/20 In this talk, I will go over the definition of higher discriminant in Migliorini-Shende’s paper. The higer discruminant is a generalization of discriminant that deals with the decomposition theorem of perverse sheaves. I will also apply this to the relative compactified Jacobian and relative Hilbert scheme and see that the \delta-constant strata plays a crucial rule in the calculation.
Lutian Zhao Higher Discriminant Reference I, II
06/10/20 Gottsche’s conjecture says that for any smooth surface $S$, the number of $\delta$-nodal curve in a certain linear system can be expressed as a polynomial of topological invariants, such as certain intersection numbers involving canonical bundle and topological Euler characteristic. Moreover, that polynomial is universal in the sense that all surfaces have the same polynomial dependence. In this talk, I will explain a proof of this conjecture, using PT invariants.
Sungwoo Nam Counting nodal curves inside a linear system on a surface Reference I
06/03/20 In this talk, I will go over the paper of Fantechi-Goettsche-van Straten. I will define the delta-invariant of a singular curve and state the relation of Jacobian with it. Moreover, I will use the definition of delta-regular stratum to calculate the Euler characteristic of compactified Jacobian.
Lutian Zhao Euler Number of Compactified Jacobian Reference I
05/20/20 I will continue from the point that I ended last time, which was computing invariants on an abelian surface with some point insertions. The key point is the application of the degeneration formula and some exact evaluation of Hodge integral with some relative conditions, which has been already exploited in the computation of GW theory of K3 surfaces by Maulik-Pandharipande-Thomas. Time permits, I will describe the calculation of genus 3 invariants and conjectures for the abelian threefolds.
Sungwoo Nam Curves counting on Abelian surfaces and threefolds, II Reference I, II
05/13/20 In this talk, I will discuss the problem of counting curves on abelian varieties of dimension 2 and 3. In addition to the existence of holomorphic symplectic forms, it has group action by itself, and has odd cohomology. These make it more intricate to study than K3 surfaces. In this talk, based on BOPY paper I will discuss some calculations from the Gromov-Witten perspective, and I will, in a later talk, about its connection to curve counting on K3xP^1.
Sungwoo Nam Curves counting on Abelian surfaces and threefolds Reference I
05/06/20 In this talk, I will give a conjectural definition of Toda on the Gopakumar-Vafa invariant that is independent of the choice of stability condition. As an application, we will deduce the flop transformation for GV invariant.
Lutian Zhao Gopakumar-Vafa Invariant and wall crossing Reference I, II
04/29/20 In this talk, I will describe its generalization of the period and the Torelli theorem to higher dimensional Hyperkahler manifolds. The crucial ingredients, unlike in the case of K3 surfaces are the notions of parallel transport and monodromy operator. After discussing these notions, I'll review the results on the monodromy group for the known deformation type of Hyperkahler manifolds with its applications.
Sungwoo Nam The period of Hyperkahler manifolds and monodromy Reference I
04/22/20 In this talk, I’ll give the real definition of Joyce’s d-critical locus and the natural perfect obstruction theory on it. At the very end, I’ll explain how the Lagrangian intersection inherit a natural d-critical structure and how we can make use of it as in the computation of Donaldson-Thomas invariants.
Lutian Zhao D critical loci and symmetric obstruction theory Reference I
04/15/20 Based on my and Lutian’s earlier talk, I will describe how to use decomposition theorem and support theorem to compute Hodge structure of hyperkahler manifolds of OG 10 type. The idea is to use nongeneric Lagrangian fibration arising from singular moduli space of sheaves on a K3 surface, where support of the pushforward, what they call Ngo strings, can be explicitly determined with the help of the knowledge of cohomology of the Hilbert scheme of points on a K3 surface.
Sungwoo Nam The Hodge Numbers of O'Grady 10 Reference I
04/08/20 Sheldon Katz Motivic Stable Pair of K3 Surface Reference I
04/01/20 The Ngo support theorem is the key part for Ngo’s proof of his fundamental lemma. This is a theorem of possible summands inside the decomposition theorem of abelian fibration. In this talk, I will be discussing the statement of the theorem and idea of the proof. As an application, I will give a statement of de Cataldo-Rapagnetta-Sacca’s statement of what they call the Ngo’s String theorem.
Lutian Zhao The Ngo support theorem Reference I
03/25/20 The main character of this talk will be hyperkahler manifolds of OG10 type, which are 10-dimensional hyperkahler manifolds arising from singular moduli spaces of sheaves on a K3 surface. It’s Euler number is computed back in 2006 in the thesis of S. Mozgovyy, and recently by K. Hulek, R. Laza, and G. Sacca. Moreover, its Hodge numbers are computed by M. A. de Cataldo, A. Rapagnetta and G. Sacca. This talk will have a mild goal of understanding basic properties of OG10 type manifolds, and its geometry from the specific projective model, the famous Beauville-Mukai integrable system.
Sungwoo Nam The Euler number of O'Grady 10 Reference I II
03/04/20 In this talk, I’ll introduce the d critical locus and the natural perverse sheaf on the d critical locus. I’ll use this definition to recover a perfect obstruction theory on a Lagrangian intersection.
Lutian Zhao D-critical locus and orientation data Reference I, II
02/26/20 Vanishing cycle functors are measuring the change in topology for fiber of a function. In this talk, I’ll introduce the perverse sheaf of vanishing cycle and will calculate some of the basic examples. This will be a first talk of a series relating to d-critical locus.
Lutian Zhao Vanishing cycles in perverse sheaves Reference I

Seminars start late due to HCM Program Perverse Sheaves in Enumerative Geometry

Fall 2019

Date Speaker Title Reference
12/11/19 I will discuss one application of Gromov-Witten theory to a very general K3^{[2]} type varieties, which will tell us when there is a uniruled divisor swept by rational curves.
Sungwoo Nam Rational Curves of Holomorphic Symplectic varieties Reference I, II
12/04/19 In their paper "Gromov-Witten and Donaldson-Thomas theory I", Maulik, Nekrasov, Okounkov and Pandharipande used localization to compute DT invariants of toric threefolds. I will talk about some of these ideas.
Nachiketa Adhikari Localization and DT invariants Reference
11/20/19 In this talk, we will consider Hodge integrals, in the context of Gromov-Witten theory. I will introduce basic definitions of Hodge/descendent integrals and Mumford’s Grothendieck-Riemann-Roch calculations on moduli of stable curves and stable maps. Then we will discuss how the relations among Hodge integrals can be obtained from classical curve theory. If time permits, we would discuss its application, the multiple cover formula for Gromov-Witten invariants.
Sungwoo Nam Relations among Hodge integrals Reference I, II
11/13/19 : In this talk, I will define the Donaldson-Thomas invariant for moduli of quiver representations. Assuming that the superpotential is zero we will compare this invariant with the intersection cohomology of the locus of semistable representations. I will then state the integrability conjecture for Donaldson-Thomas invariant in this situation.
Lutian Zhao Donaldson-Thomas invariant and Intersection Cohomology Reference
11/06/19 In this talk, I will introduce the motivic theory and the related definition for Donaldson-Thomas theory. I will mainly work on the case of Hilbert scheme of C^3 where an explicit computation for the generating function is possible. This is a preparation for the relation between a more general setup, where we have a correspondence between DT theory and intersection cohomology.
Lutian Zhao Donaldson-Thomas Theory for C^3 Reference I, II
10/30/19 : I will give a high-level overview of the physical notions of string compactifications, supersymmetry, charge lattices, and dualities, interspersing physical intuition with mathematical definitions. The main focus will be on CHL models. One way to describe CHL models is by compactifying Type II string theory on certain Calabi-Yau quotients X of S x E, where S is a K3 surface and E is an elliptic curve. A dual description is the compactification of heterotic string theory on a corresponding quotient of a real 6-torus, which is more amenable to explicit computation (which will not be done in the talk). I will work towards describing the physics of a CHL model, and relating it to the mathematical theory of stable pair invariants (PT invariants) on X.
Sheldon Katz The physics of CHL models Reference
10/23/19 I’ll continue the last talk, and discuss the problem of computing fiber Gromov-Witten invariant of Enriques Calabi-Yau. After recall some notion of degeneration formula, I will describe the definition of Enriques Calabi-Yau threefolds. Then we will see that their fiber Gromov-Witten invariants can be reduced to some Hodge integral on Enriques surfaces. Finally, we see how it fits with the physical calculation, deduced from heterotic string theory.
Sungwoo Nam Enriques surface and Enriques Calabi-Yau, II Reference I, II
10/16/19 : In 1990, Bondal proved his remarkable theorem on the derived Morita equivalence and turn the study of derived category D^b(X) of variety X to the study of its tilting object, especially the one created by exceptional collections. On the other hand, several paper by Aspinwall-Fidkowski, Apsinwall-Katz, Bergmanp-Proudfoot etc studied the type II string theory compactified at X with BPS D-branes. The computation of the corelation function leads to the A-infinity structure which is encoded in the superpotential. In this talk, I will give a mathematical description of the superpotential and state the meaning of computaion in Aspinwall-Katz's oaoer. If time permitted, I'll state how its critical locus defines the moduli space of Donaldson-Thomas theory, which will be useful for later talk on motivic Donaldson-Thomas invariants.
Lutian Zhao Computing the D-brane superpotential Reference I, II
10/09/19 This talk will be a brief introduction to the geometry of Enriques surfaces, starting from their definition with emphasis on linear system on them. After Enriques surface, I will introduce Enriques Calabi-Yau threefold, and discuss topological string theory on them.
Sungwoo Nam Enriques surface and Enriques Calabi-Yau Reference I
10/02/19 In this talk, I will describe the coloring of the HOMFLY polynomial. The final goal is to give the statement of the conjecture by Diaconescu-Hua-Soibelman and give some idea of Maulik’s proof of the conjecture.
Lutian Zhao Colored HOMFLY polynomial from Skein model Reference I, II
09/25/19 In this talk I will review the compactified Jacobian and Hilbert scheme of unibranched plane curve singularity. I will introduce the theory of link and state the interesting conjecture by Oblomkov-Shende, where these two objects are mutually related by the calculation of HOMFLY polynomial.
Lutian Zhao Hilbert scheme of plane curve singularity and HOMFLY polynomial Reference I, II
09/18/19 I will continue my talk, explaining how to actually calculate unweighted DT generating function, using topological vertex. Especially, we will see how to get $\mathbb{C}^3$-action although our 3-fold is not toric.
Sungwoo Nam DT invariants of local elliptic surfaces, II Reference I, II
09/13/19 In this talk, I will discuss the problem of computing unweighted DT invariants of local elliptic surfaces. Main tools for this computation will be localization, motivic methods and the topological vertex. In this talk, I will introduce definitions, especially the notion of partition thickened comb curve with points(PCP curves), and show that their moduli space gives DT invariants. The moduli space of PCP curves also provide stratification which makes us use the topological vertex.
Sungwoo Nam DT invariants of local elliptic surfaces Reference I, II
08/21/19 In this talk, I will describe the Hitchin integrable system in terms of the Seiberg-Witten differential introduced last time. Then I will show the construction of a family of Calabi-Yau threefold that gives the desired correspondence.
Lutian Zhao Hitchin integrable system and Calabi-Yau integrable system, III Reference I, II
08/14/19 In this talk, I’ll explain the abstract Seiberg-Witten differential by Florian Beck for tackling the integrable system problem. I will then define the differential for both Hitchin and Calabi-Yau integrable system. The main goal is to fill in the gap and some details for the first talk.
Lutian Zhao Hitchin integrable system and Calabi-Yau integrable system, II Reference
08/07/19 The correspondence between Hitchin integrable system and Calabi-Yau integrable system was first observed in the case of G=SU(2) by Diaconascu-Dijkgraaf-Donagi-Hofman-Pantev, and later generalized to and simple group of type ADE by Diaconascu-Donagi-Pantev and more general simple group by work of Florian Beck. In this talk I’ll review the basic theorems and try to explain the detail. If time permitted, I’ll explain the compact Calabi-Yau case, where the theory of T-brane is coming in.
Lutian Zhao Hitchin integrable system and Calabi-Yau integrable system Reference
Spring 2019

Date Speaker Title Reference
04/19/19 Virtual fundamental classes are playing essential roles in modern enumerative geometry including Gromov-Witten and Stable pair invariants. In their paper, Kiem and Li introduced the notion of cosection and used it to construct a localized virtual fundamental class in algebraic geometry. It turns out it enjoys many properties as a usual virtual class including localization and wall crossing. In this talk, we will see their construction of localized virtual cycle. As a byproduct, we will see how to construct a reduced virtual fundamental class for Gromov-Witten invariants of K3 and abelian surfaces.
Sungwoo Nam Cosection localization and reduced virtual fundamental class Reference
04/12/19 In this talk I’ll start from the basic of perverse sheaves and explain some basic examples. Then I’ll explain the structure theorem of hyperkahler manifold allowing Larangian fibration given by Junliang Shen and Qizhen Ying.
Lutian Zhao The P=W Conjecture and Topology of Lagrangian fibrations Reference
04/05/19 The P=W conjecture stems from the attempt to understand the nonabelian Hodge correspondence and its related topology. In this talk, I’ll give a description of this conjecture and explain the basic idea: the weight filtration associated to the Betti moduli space should coincide with the perverse filtration associated to the Dolbeault moduli space. As a final application, I’ll explain how this conjecture gives rise to a calculation of BPS invariants.
Lutian Zhao The P=W Conjecture Reference I, II
03/29/19 Compact hyperkäher manifolds are one of the building blocks of compact Ricci-flat manifolds. It is also a target space for nonlinear sigma model which gives N=4 SCFT. In this talk, I’ll introduce motivations and definitions for compact hyperkähler manifolds. Then I’ll introduce examples and their basic properties. If time permits, I’ll describe a quadratic form on second cohomology group, called Beauville-Bogomolov-Fujiki form and use it to prove local torelli theorem for hyperkähler manifolds.
Sungwoo Nam Rudiments of compact hyperkähler manifolds Reference I, II
03/08/19 In this talk, I’ll review Bridgeland’s definition of BPS structures. In some sense the Kontsevich-Soibelman wall crossing formula determines a Riemann-Hilbert problem. I’ll explain Bridgeland’s solution of this problem and see some examples of this problem.
Lutian Zhao Riemann-Hilbert Problem for BPS Structure Reference
02/15/19 I’ll review the concept of the heart of a t-structure for K3 surfaces, which is part of the definition of Bridgeland stability condition on K3 surfaces. Then I’ll discuss how much geometric information it contains, especially its relation to derived equivalences.
Sungwoo Nam Heart of t-structures for K3 surfaces Reference I, II
02/08/19 Which Chern class can be realized by slope semistable vector bundles? The Bogomolov’s inequality gives a necessary condition. In this talk, I’ll explain the proof of this inequality. As an application, I’ll do the construction of Bridgeland stability condition for a surface.
Lutian Zhao The Bogomolov-Gieseker Inequality Reference I,II
01/25/19 I’ll present one application of Bridgeland stability condition on a classcial problem in birational geometry. I’ll start by classical Brill-Noether theory and Lazarsfeld’s result on a general curve in a K3 surface, and then I’ll describe its proof via stability condition on a K3 surface, using wall crossing argument.
Sungwoo Nam Brill-Noether from Wall Crossing Reference

Fall 2018 (You can see abstract when you hover your mouse over the date)

Date Speaker Title Reference
12/14/18 I'll described period map for family of projective varieties and complete the proof of the theorem that Calabi-Yau integrable system is analytically completely integrable.
Sungwoo Nam The Cubic Condition for Integrable Systems, III Reference I, II
11/29/18 Building on Matej's talk, I'll introduce the notion of Calabi-Yau integrable systems and explain how they connect to abelian, Lagrangian fibration(which is also complete integrable system), Matej was talking about last week. Along the way, I'll introduce some notions from Hodge theory such as intermediate Jacobian as a tool connecting two things.
Sungwoo Nam The Cubic Condition for Integrable Systems, II Reference
11/08/18 This is the first in a 2-part talk with Sungwoo on the paper https://arxiv.org/abs/alg-geom/9408004 . I will focus on section 1 where the cubic condition is introduced to answer an interesting and natural question: Which families of abelian varieties have the structure of a completely integrable systems? It turns out the answer is equivalent to the existence of a field of cubics on the tangent bundle of the base. I will explain this result more precisely, and give an idea of the proof and how it will be used in part 2 of the talk by Sungwoo.
Matej Penciak The Cubic Condition for Integrable Systems, I Reference
11/02/18 Sheldon Katz Mirror Symmetry for Toric Varieties Reference I, II
10/19/18 I’ll give a description of the toric hypersurface by polytopes and produce a calculation of the cohomology. Then we’ll describe Batyrev’s construction of mirror manifold and try to prove the coincidence of Kahler moduli of original Calabi-Yau family and the complex moduli of mirror family.
Lutian Zhao Batyrev's Construction, II Reference I, II
10/12/18 I’ll try to construct the mirror manifold out of Batyrev’s construction, assuming the knowledge from Joseph’s talk before.
Lutian Zhao Batyrev's Construction, I Reference
10/05/18 Joseph Pruitt Introduction to Toric Varieties Reference
09/28/18 Sheldon Katz Organizational Meeting and An introduction to mirror symmetry Reference

Spring 2018

No seminar due to MSRI program Enumerative Geometry Beyond Numbers

Fall 2017

Date Speaker Title Reference
11/15/17 Sheldon Katz Gromov-Witten Theory
11/01/17 Hao Sun Gromov-Witten theory, Hurwitz numbers, and Matrix models, II Reference
10/25/17 Hao Sun Gromov-Witten theory, Hurwitz numbers, and Matrix models, I Reference
10/18/17 Sungwoo Nam The Crepant Resolution Conjecture Reference
10/11/17 Yun Shi Introduction to stable pair theory Reference
10/04/17 Lutian Zhao Introduction in Topological String Theory on Calabi-Yau manifolds, III Reference
09/27/17 Sungwoo Nam The local Gromov-Witten theory of curves Reference I, II
09/20/17 Lutian Zhao Introduction in Topological String Theory on Calabi-Yau manifolds, II Reference
08/30/17 Lutian Zhao Introduction in Topological String Theory on Calabi-Yau manifolds, I Reference

Spring 2017

Date Speaker Title Reference
07/12/17 Michel van Garrel (KIAS) Rational curves in log K3 surfaces Reference I, II
07/05/17 Sungwoo Nam Relations on moduli spaces of curves Reference I, II
06/28/17 Joseph Pruitt Batyrev's relations in quantum cohomology Reference
06/21/17 Mi Young Jang A Mathematical Theory of Quantum Sheaf Cohomology Reference
06/07/17 Lutian Zhao Gopakumar-Vafa invariants via vanishing cycles Reference
05/31/17 Sungwoo Nam Localization of virtual classes Reference
05/24/17 Becca Tramel Examples of wall-crossing in Bridgeland stability.
05/10/17 Lutian Zhao Categorification of Donaldson-Thomas invariants via Perverse Sheaves Reference
05/03/17 Yun Shi The intrinsic normal cone Reference
04/26/17 Becca Tramel Bridgeland stability for the quintic threefold
04/19/17 Sheldon Katz Mirror Symmetry
04/12/17 Lutian Zhao Kontsevich-Soibelman Wall-Crossing Formula Reference I, II
04/05/17 Yun Shi Flops and Derived Categories Reference
03/29/17 Mi Young Jang Stable Maps And Quantum Cohomology Reference
03/15/17 Becca Tramel Derived Categories and Zero-Brane Stability Reference
03/08/17 Lutian Zhao Wall Crossing of BPS states by split attractor flows Reference I, II
03/01/17 Joseph Pruitt Enumeration of rational curves via torus actions Reference
02/22/17 Mi Young Jang Localization
02/15/17 Lutian Zhao BPS State Counting Reference I, II
02/01/17 Becca Tramel Bridgeland Stability
01/25/17 Yun Shi Gromov-Witten theory and Donaldson-Thomas theory Reference
01/18/17 Sheldon Katz Overview of Enumerative Geometry Reference