Sheldon’s Student Seminar

A student seminar on enumerative geometry run at the University of Illinois at Urbana–Champaign from 2017 to 2020, organised around Sheldon Katz and his students. Over three years it worked through mirror symmetry, Gromov–Witten and Donaldson–Thomas theory, stability conditions and wall-crossing, and the perverse-sheaf approach to BPS invariants.

94 talks across 7 semesters. Click any talk to read its abstract; reference links point to the original sources. The seminar met Wednesdays, latterly on Zoom.

Fall 2020 12 talks

• 12/09/20Derived schemes and stacksNachiketa Adhikari

  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.

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• 12/02/20Infinity Categories 101Nachiketa Adhikari

  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.

• 11/18/20Scattering Diagram and wall crossing, IILutian Zhao

  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.

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• 11/11/20Scattering Diagram and wall crossingLutian Zhao

  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.

• 11/04/20Hall algebras and Integration mapsSungwoo Nam

  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.

• 10/28/20Hall algebras and DT invariantsSungwoo Nam

  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.

• 10/21/20Moduli of sheaves on P^2 and BPS invariantsSungwoo Nam

  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).

• 10/14/20Orientation Data on moduli space of coherent sheavesLutian Zhao

  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.

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• 10/07/20Mirror Symmetry 101Nachiketa Adhikari

  “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.

• 09/30/20The log-local correspondenceSungwoo Nam

  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.

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• 09/09/20D-critical locus on Hilb^n of local P^2Sheldon Katz

  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.

• 09/02/20Tropical curves and counting plane curvesSungwoo Nam

  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.

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Spring 2020 19 talks

• 08/06/20Quantum products on toric varietiesNachiketa Adhikari

  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.

• 07/30/20Cohomology of Hilbert schemes of points on a surface, IISungwoo Nam

  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.

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• 07/23/20Cohomology of Hilbert schemes of points on a surfaceSungwoo Nam

  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.

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• 07/16/20Intersection Cohomology for Moduli of Sheaves on SurfacesLutian Zhao

  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.

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• 07/01/20Gromov-Witten theory of $A_n$ resolutionsSungwoo Nam

  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 $A_n\times P^1.$

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• 06/17/20Higher DiscriminantLutian Zhao

  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.

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• 06/10/20Counting nodal curves inside a linear system on a surfaceSungwoo Nam

  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.

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• 06/03/20Euler Number of Compactified JacobianLutian Zhao

  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.

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• 05/20/20Curves counting on Abelian surfaces and threefolds, IISungwoo Nam

  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.

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• 05/13/20Curves counting on Abelian surfaces and threefoldsSungwoo Nam

  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.

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• 05/06/20Gopakumar-Vafa Invariant and wall crossingLutian Zhao

  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.

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• 04/29/20The period of Hyperkahler manifolds and monodromySungwoo Nam

  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.

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• 04/22/20D critical loci and symmetric obstruction theoryLutian Zhao

  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.

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• 04/15/20The Hodge Numbers of O'Grady 10Sungwoo Nam

  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.

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• 04/08/20Motivic Stable Pair of K3 SurfaceSheldon Katz

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• 04/01/20The Ngo support theoremLutian Zhao

  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.

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• 03/25/20The Euler number of O'Grady 10Sungwoo Nam

  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.

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• 03/04/20D-critical locus and orientation dataLutian Zhao

  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.

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• 02/26/20Vanishing cycles in perverse sheavesLutian Zhao

  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.

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Fall 2019 16 talks

• 12/11/19Rational Curves of Holomorphic Symplectic varietiesSungwoo Nam

  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.

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• 12/04/19Localization and DT invariantsNachiketa Adhikari

  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.

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• 11/20/19Relations among Hodge integralsSungwoo Nam

  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.

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• 11/13/19Donaldson-Thomas invariant and Intersection CohomologyLutian Zhao

  : 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.

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• 11/06/19Donaldson-Thomas Theory for C^3Lutian Zhao

  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.

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• 10/30/19The physics of CHL modelsSheldon Katz

  : 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.

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• 10/23/19Enriques surface and Enriques Calabi-Yau, IISungwoo Nam

  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.

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• 10/16/19Computing the D-brane superpotentialLutian Zhao

  : 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.

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• 10/09/19Enriques surface and Enriques Calabi-YauSungwoo Nam

  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.

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• 10/02/19Colored HOMFLY polynomial from Skein modelLutian Zhao

  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.

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• 09/25/19Hilbert scheme of plane curve singularity and HOMFLY polynomialLutian Zhao

  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.

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• 09/18/19DT invariants of local elliptic surfaces, IISungwoo Nam

  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.

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• 09/13/19DT invariants of local elliptic surfacesSungwoo Nam

  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.

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• 08/21/19Hitchin integrable system and Calabi-Yau integrable system, IIILutian Zhao

  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.

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• 08/14/19Hitchin integrable system and Calabi-Yau integrable system, IILutian Zhao

  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.

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• 08/07/19Hitchin integrable system and Calabi-Yau integrable systemLutian Zhao

  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.

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Spring 2019 8 talks

• 04/19/19Cosection localization and reduced virtual fundamental classSungwoo Nam

  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.

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• 04/12/19The P=W Conjecture and Topology of Lagrangian fibrationsLutian Zhao

  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.

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• 04/05/19The P=W ConjectureLutian Zhao

  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.

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• 03/29/19Rudiments of compact hyperkähler manifoldsSungwoo Nam

  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.

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• 03/08/19Riemann-Hilbert Problem for BPS StructureLutian Zhao

  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.

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• 02/15/19Heart of t-structures for K3 surfacesSungwoo Nam

  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.

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• 02/08/19The Bogomolov-Gieseker InequalityLutian Zhao

  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.

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• 01/25/19Brill-Noether from Wall CrossingSungwoo Nam

  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.

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Fall 2018 8 talks

• 12/14/18The Cubic Condition for Integrable Systems, IIISungwoo Nam

  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.

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• 11/29/18The Cubic Condition for Integrable Systems, IISungwoo Nam

  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.

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• 11/08/18The Cubic Condition for Integrable Systems, IMatej Penciak

  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.

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• 11/02/18Mirror Symmetry for Toric VarietiesSheldon Katz

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• 10/19/18Batyrev's Construction, IILutian Zhao

  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.

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• 10/12/18Batyrev's Construction, ILutian Zhao

  I’ll try to construct the mirror manifold out of Batyrev’s construction, assuming the knowledge from Joseph’s talk before.

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• 10/05/18Introduction to Toric VarietiesJoseph Pruitt

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• 09/28/18Organizational Meeting and An introduction to mirror symmetrySheldon Katz

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Fall 2017 9 talks

• 11/15/17Gromov-Witten TheorySheldon Katz
• 11/01/17Gromov-Witten theory, Hurwitz numbers, and Matrix models, IIHao Sun

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• 10/25/17Gromov-Witten theory, Hurwitz numbers, and Matrix models, IHao Sun

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• 10/18/17The Crepant Resolution ConjectureSungwoo Nam

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• 10/11/17Introduction to stable pair theoryYun Shi

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• 10/04/17Introduction in Topological String Theory on Calabi-Yau manifolds, IIILutian Zhao

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• 09/27/17The local Gromov-Witten theory of curvesSungwoo Nam

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• 09/20/17Introduction in Topological String Theory on Calabi-Yau manifolds, IILutian Zhao

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• 08/30/17Introduction in Topological String Theory on Calabi-Yau manifolds, ILutian Zhao

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Spring 2017 22 talks

• 07/12/17Rational curves in log K3 surfacesMichel van Garrel (KIAS)

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• 07/05/17Relations on moduli spaces of curvesSungwoo Nam

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• 06/28/17Batyrev's relations in quantum cohomologyJoseph Pruitt

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• 06/21/17A Mathematical Theory of Quantum Sheaf CohomologyMi Young Jang

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• 06/07/17Gopakumar-Vafa invariants via vanishing cyclesLutian Zhao

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• 05/31/17Localization of virtual classesSungwoo Nam

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• 05/24/17Examples of wall-crossing in Bridgeland stability.Becca Tramel
• 05/10/17Categorification of Donaldson-Thomas invariants via Perverse SheavesLutian Zhao

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• 05/03/17The intrinsic normal coneYun Shi

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• 04/26/17Bridgeland stability for the quintic threefoldBecca Tramel
• 04/19/17Mirror SymmetrySheldon Katz
• 04/12/17Kontsevich-Soibelman Wall-Crossing FormulaLutian Zhao

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• 04/05/17Flops and Derived CategoriesYun Shi

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• 03/29/17Stable Maps And Quantum CohomologyMi Young Jang

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• 03/15/17Derived Categories and Zero-Brane StabilityBecca Tramel

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• 03/08/17Wall Crossing of BPS states by split attractor flowsLutian Zhao

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• 03/01/17Enumeration of rational curves via torus actionsJoseph Pruitt

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• 02/22/17LocalizationMi Young Jang
• 02/15/17BPS State CountingLutian Zhao

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• 02/01/17Bridgeland StabilityBecca Tramel
• 01/25/17Gromov-Witten theory and Donaldson-Thomas theoryYun Shi

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• 01/18/17Overview of Enumerative GeometrySheldon Katz

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Reconstructed from the original seminar page, which is preserved in the Internet Archive.