
Speaker: ChaoMing LinTitle: On the convexity of general inverse $\sigma_k$ equations and some applicationsVenue: CMSA Room G10Algebraic Geometry in String Theory Seminar Speaker: ChaoMing Lin (University of California, Irvine) Title: On the convexity of general inverse $\sigma_k$ equations and some applications Abstract: In this talk, I will show my recent work on general inverse $\sigma_k$ equations and the deformed HermitianYangMills equation (hereinafter the dHYM equation). First, I will show my recent results. This result states that if a level set of a general inverse $\sigma_k$ equation (after translation if needed) is contained in the positive orthant, then this level set is convex. As an application, this result justifies the convexity of the MongeAmpère equation, the Jequation, the dHYM equation, the special Lagrangian equation, etc. Second, I will introduce some semialgebraic sets and a special… 

Speaker: Ahsan KhanTitle: Categories and the Massive d AModelVenue: CMSA Room G10Algebraic Geometry in String Theory Seminar Speaker: Ahsan Khan, IAS Title: 2Categories and the Massive 3d AModel Abstract: I will outline the construction of a 2category associated to a hyperKahler moment map. The construction is based on partial differential equations in one, two, and three dimensions combined with a threedimensional version of the GaiottoMooreWitten web formalism. 

Speaker: Nicolo PiazzalungaTitle: The index of MtheoryVenue: CMSA Room G10Algebraic Geometry in String Theory Seminar Speaker: Nicolo Piazzalunga, Rutgers Title: The index of Mtheory Abstract: I’ll introduce the higherrank DonaldsonThomas theory for toric CalabiYau threefolds, within the setting of equivariant Ktheory. I’ll present a factorization conjecture motivated by Physics. As a byproduct, I’ll discuss some novel properties of equivariant volumes, as well as their generalizations to the genuszero GromovWitten theory of noncompact toric varieties. 

Speaker: Daniel PomerleanoTitle: Singularities of the quantum connection on a Fano varietyVenue: CMSA Room G10Algebraic Geometry in String Theory Seminar Speaker: Daniel Pomerleano, UMass Boston Title: Singularities of the quantum connection on a Fano variety Abstract: The small quantum connection on a Fano variety is one of the simplest objects in enumerative geometry. Nevertheless, it is the subject of farreaching conjectures known as the Dubrovin/Gamma conjectures. Traditionally, these conjectures are made for manifolds with semisimple quantum cohomology or more generally for Fano manifolds whose quantum connection is of unramified exponential type at q=\infty. I will explain a program, joint with Paul Seidel, to show that this unramified exponential type property holds for all Fano manifolds M carrying a smooth anticanonical divisor D. The basic idea of our argument is to view these structures through… 

Speaker: Sam BardwellEvansTitle: Scattering Diagrams from Holomorphic Discs in Log CalabiYau SurfacesVenue: CMSA Room G10Algebraic Geometry in String Theory Seminar Speaker: Sam BardwellEvans, Boston University Title: Scattering Diagrams from Holomorphic Discs in Log CalabiYau Surfaces Abstract: In this talk, we construct special Lagrangian fibrations for log CalabiYau surfaces and scattering diagrams from Lagrangian Floer theory of the fibers. These scattering diagrams recover the algebrogeometric scattering diagrams of GrossPandharipandeSiebert and GrossHackingKeel. The argument relies on a holomorphic/tropical disc correspondence to control the behavior of holomorphic discs, allowing us to relate open GromovWitten invariants to log GromovWitten invariants. This talk is based on joint work with ManWai Mandy Cheung, Hansol Hong, and YuShen Lin. 

Speaker: Mauricio RomoTitle: GLSM, Homological projective duality and nc resolutionsVenue: CMSA Room G10Algebraic Geometry in String Theory Seminar Speaker: Mauricio Romo, Tsinghua University Title: GLSM, Homological projective duality and nc resolutions Abstract: Kuznetsov’s Homological projective duality (HPD) in algebraic geometry is a powerful theorem that allows to extract information about semiorthogonal decompositions of derived categories of certain varieties. I will give a GLSMs perspective based on categories of Bbranes. I will focus mostly on the case of Fano (hypersurfaces) manifolds. In general, for such cases the HPD can be interpreted as a noncommutative (nc) resolution of a compact variety. I will give a physical interpretation of this fact and present some conjectures. 

Speaker: Yan ZhouTitle: Modularity of mirror families of log CalabiYau surfacesVenue: virtualAbstract: In “Mirror symmetry for log Calabi–Yau surfaces I,” given a smooth log Calabi–Yau surface pair (Y,D), Gross–Hacking–Keel constructed its mirror family as the spectrum of an explicit algebra whose structure coefficients are determined by the enumerative geometry of (Y,D). As a followup of the work of Gross–Hacking–Keel, when (Y,D) is positive, we prove the modularity of the mirror family as the universal family of log CalabiYau surface pairs deformation equivalent to (Y,D) with at worst du Val singularities. As a corollary, we show that the ring of regular functions of a smooth affine log Calabi–Yau surface has a canonical basis of theta functions. The key step towards the proof of the main theorem is the application of… 

Speaker: Ming ZhangTitle: Equivariant Verlinde algebra and quantum Ktheory of the moduli space of vorticesVenue: VirtualAbstract: In studying complex ChernSimons theory on a Seifert manifold, GukovPei proposed an equivariant Verlinde formula, a oneparameter deformation of the celebrated Verlinde formula. It computes, among many things, the graded dimension of the space of holomorphic sections of (powers of) a natural determinant line bundle over the Hitchin moduli space. GukovPei conjectured that the equivariant Verlinde numbers are equal to the equivariant quantum Kinvariants of a noncompact (Kahler) quotient space studied by HananyTong. In this talk, I will explain the setup of this conjecture and its proof via wallcrossing of moduli spaces of (parabolic) BradlowHiggs triples. It is based on work in progress with Wei Gu and Du Pei. 

Speaker: Aron HeleodoroTitle: Applications of Higher Determinant MapVenue: VirtualAbstract: In this talk I will explain the construction of a determinant map for Tate objects and two applications: (i) to construct central extensions of iterated loop groups and (ii) to produce a determinant theory on certain indschemes. For that I will introduce some aspects of the theory of Tate objects in a couple of contexts. 

Speaker: Jie Zhou, Tsinghua UniversityTitle: Regularized integrals on Riemann surfaces and correlations functions in d chiral CFTsVenue: virtualAbstract: I will report a recent approach of regularizing divergent integrals on configuration spaces of Riemann surfaces, introduced by Si Li and myself in arXiv:2008.07503, with an emphasis on genus one cases where modular forms arise naturally. I will then talk about some applications in studying correlation functions in 2d chiral CFTs, holomorphic anomaly equations, etc. If time permits, I will also mention a more algebraic formulation of this notion of regularized integrals in terms of mixed Hodge structures. The talk is partially based on joint works with Si Li. 

Speaker: Benjamin Gammage, Harvard UniversityTitle: categorical d mirror symmetryVenue: virtualAbstract: It is by now wellknown that mirror symmetry may be expressed as an equivalence between categories associated to dual Kahler manifolds. Following a proposal of Teleman, we inaugurate a program to understand 3d mirror symmetry as an equivalence between 2categories associated to dual holomorphic symplectic stacks. We consider here the abelian case, where our theorem expresses the 2category of spherical functors as a 2category of coherent sheaves of categories. Applications include categorifications of hypertoric category O and of many related constructions in representation theory. This is joint work with Justin Hilburn and Aaron MazelGee. 

Speaker: Dhyan Vas Aranha, SISSATitle: Virtual localization for Artin stacksVenue: virtualAbstract: This is a report about work in progress with: Adeel Khan, Aloysha Latyntsev, Hyeonjun Park and Charanya Ravi. We will describe a virtual AtiyahBott formula for Artin stacks. In the DeligneMumford case our methods allow us to remove the global resolution hypothesis for the virtual normal bundle. 

Speaker: Konstantin Aleshkin, Columbia UniversityTitle: HiggsCoulomb correspondence in abelian GLSMVenue: virtualAbstract: We construct a certain type of Gauged Linear Sigma Model quasimap invariants that generalize the original ones and are easier to compute. HiggsCoulomb correspondence provides identification of generating functions of our invariants with certain analytic functions that can be represented as generalized inverse Mellin transforms. Analytic continuation of these functions provides wallcrossing results for GLSM and generalizes Landau Ginzburg/CalabiYau correspondence. The talk is based on a joint work in progress with Melissa Liu. 

Speaker: Zijun Zhou, Kavli IPMUTitle: Virtual Coulomb branch and quantum KtheoryVenue: virtualAbstract: In this talk, I will introduce a virtual variant of the quantized Coulomb branch constructed by BravermanFinkelbergNakajima, where the convolution product is modified by a virtual intersection. The resulting virtual Coulomb branch acts on the moduli space of quasimaps into the holomorphic symplectic quotient T^*N//G. When G is abelian, over the torus fixed points, this representation is a Verma module. The vertex function, a Ktheoretic enumerative invariant introduced by A. Okounkov, can be expressed as a Whittaker function of the algebra. The construction also provides a description of the quantum qdifference module. As an application, this gives a proof of the invariance of the quantum qdifference module under variation of GIT. 

Speaker: Carl LianTitle: Curvecounting with fixed domain (“Tevelev degrees”)Venue: VirtualAbstract: We will consider the following problem: if (C,x_1,…,x_n) is a fixed general pointed curve, and X is a fixed target variety with general points y_1,…,y_n, then how many maps f:C > X in a given homology class are there, such that f(x_i)=y_i? When considered virtually in GromovWitten theory, the answer may be expressed in terms of the quantum cohomology of X, leading to explicit formulas in some cases (BuchPandharipande). The geometric question is more subtle, though in the presence of sufficient positivity, it is expected that the virtual answers are enumerative. I will give an overview of recent progress on various aspects of this problem, including joint work with Farkas, Pandharipande, and Cela, as well as work of other authors. 

Speaker: YuShen Lin, Boston UniversityTitle: SYZ Conjecture beyond Mirror SymmetryVenue: virtualAbstract: StromingerYauZaslow conjecture is one of the guiding principles in mirror symmetry, which not only predicts the geometric structures of CalabiYau manifolds but also provides a recipe for mirror construction. Besides mirror symmetry, the SYZ conjecture itself is the holy grail in geometrical analysis and closely related to the behavior of the Ricciflat metrics. In this talk, we will explain how SYZ fibrations on log CalabiYau surfaces detect the nonstandard semiflat metric which generalized the semiflat metrics of GreeneShapereVafaYau. Furthermore, we will use the SYZ fibration on log CalabiYau surfaces to prove the Torelli theorem of gravitational instantons of type ALH^*. This is based on the joint works with T. Collins and A. Jacob. 

Speaker: Xingyang YuTitle: d N=(,) gauge theories, Spin() orientifolds and trialityVenue: Virtual 


Speaker: Dori BejleriTitle: Wall crossing for moduli of stable log varietiesVenue: Virtual 

Speaker: Pierrick BousseauTitle: GromovWitten theory of complete intersectionsVenue: VirtualAbstract: I will describe an inductive algorithm computing GromovWitten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. The main idea is to show that invariants with insertions of primitive cohomology classes are controlled by their monodromy and by invariants defined without primitive insertions but with imposed nodes in the domain curve. To compute these nodal GromovWitten invariants, we introduce the new notion of nodal relative GromovWitten invariants. This is joint work with Hülya Argüz, Rahul Pandharipande, and Dimitri Zvonkine (arxiv:2109.13323). 