
Speaker: Thorsten SchimannekTitle: Mtheory on nodal CalabiYau 3folds and torsion refined GVinvariantsVenue: CMSA Room G10Algebraic Geometry in String Theory Seminar Speaker: Thorsten Schimannek (Utrecht University) Title: Mtheory on nodal CalabiYau 3folds and torsion refined GVinvariants Abstract: The physics of Mtheory and Type IIA strings on a projective nodal CY 3folds is determined by the geometry of a small resolution, even if the latter is not Kähler. We will demonstrate this explicitly in the context of a family of CalabiYau double covers of P^3. Using conifold transitions, we prove that the exceptional curves in any small resolution are torsion while Mtheory develops a discrete gauge symmetry.This leads to a torsion refinement of the ordinary GopakumarVafa invariants, that is associated to the singular CalabiYau and captures the enumerative geometry of the nonKähler resolutions. We further argue that… 

Speaker: Maksym FedorchukTitle: CMminimizers and standard models of Fano fibrations over curvesVenue: CMSA Room G10Algebraic Geometry in String Theory Seminar Speaker: Maksym Fedorchuk (Boston College) Title: CMminimizers and standard models of Fano fibrations over curves Abstract: A recent achievement in Kstability of Fano varieties is an algebrogeometric construction of a projective moduli space of Kpolystable Fanos. The ample line bundle on this moduli space is the CM line bundle of Tian. One of the consequences of the general theory is that given a family of Kstable Fanos over a punctured curve, the polystable filling is the one that minimizes the degree of the CM line bundle after every finite base change. A natural question is to ask what are the CMminimizers without base change. In answering this question, we arrive at a… 

Speaker: An HuangTitle: A padic Laplacian on the Tate curveVenue: CMSA Room G10Algebraic Geometry in String Theory Seminar Speaker: An Huang (Brandeis) Pretalk Speaker: TBA: 10:0010:30 am Title: A padic Laplacian on the Tate curve Abstract: We shall first explain the relation between a family of deformations of genus zero padic string worldsheet action and Tate’s thesis. We then propose a genus one padic string worldsheet action. The key is the definition of a padic Laplacian operator on the Tate curve. We show that the genus one padic Green’s function exists, is unique under some obvious constraints, is locally constant off diagonal, and has a reflection symmetry. It can also be numerically computed exactly off the diagonal, thanks to some simplifications due to the padic setup. Numerics suggest that at… 

Speaker: Sheldon KatzTitle: Stacky small resolutions of determinantal octic double solids and noncommutative GopakumarVafa invariantsVenue: CMSA Room G10Algebraic Geometry in String Theory Seminar Speaker: Sheldon Katz, UIUC Title: Stacky small resolutions of determinantal octic double solids and noncommutative GopakumarVafa invariants Abstract: A determinantal octic double solid is the double cover X of P^3 branched along the degree 8 determinant of a symmetric matrix of homogeneous forms on P^3. These X are nodal CY threefolds which do not admit a projective small resolution. Bmodel techniques can be applied to compute GV invariants up to g \le 32. This raises the question: what is the geometric meaning of these invariants? Evidence suggests that these enumerative invariants are associated with moduli stacks of coherent sheaves of modules over a sheaf B of noncommutative algebras on X constructed by… 

Speaker: Andrew HarderTitle: Deformations of LandauGinzburg models and their fibersVenue: CMSA Room G10Algebraic Geometry in String Theory Seminar Speaker: Andrew Harder, Lehigh University Pretalk Speaker: TBA: 10:0010:30 am Title: Deformations of LandauGinzburg models and their fibers Abstract: In mirror symmetry, the dual object to a Fano variety is a LandauGinzburg model. Broadly, a LandauGinzburg model is quasiprojective variety Y with a superpotential function w, but not all such pairs correspond to Fano varieties under mirror symmetry, so a very natural question to ask is: Which LandauGinzburg models are mirror to Fano varieties? In this talk, I will discuss a cohomological characterization of mirrors of (semi)Fano varieties, focusing on the case of threefolds. I’ll discuss how this characterization relates to the deformation and Hodge theory of (Y,w), and in particular, how the… 

Speaker: David FaveroTitle: Gauged Linear Sigma Models and Cohomological Field TheoriesVenue: CMSA Room G10Algebraic Geometry in String Theory Seminar Speaker: David Favero, University of Minnesota Title: Gauged Linear Sigma Models and Cohomological Field Theories Abstract: This talk is dedicated to the memory of my friend and collaborator Bumsig Kim and based on joint work with CiocanFontanineGuereKimShoemaker. Gauged Linear Sigma Models (GLSMs) serve as a means of interpolating between Kahler geometry and singularity theory. In enumerative geometry, they should specialize to both GromovWitten and FanJarvisRuanWitten theory. In joint work with Bumsig Kim (see arXiv:2006.12182), we constructed such enumerative invariants for GLSMs. Furthermore, we proved that these invariants form a Cohomological Field Theory. In this lecture, I will describe GLSMs and Cohomological Field Theories, review the history of their development in enumerative geometry, and discuss… 

Speaker: Dori BejleriTitle: Moduli of boundary polarized CalabiYau pairsVenue: CMSA Room G10Algebraic Geometry in String Theory Seminar Pretalk Speaker: Rosie Shen (Harvard): 10:0010:30 am Pretalk Title: Introduction to the singularities of the MMP Speaker: Dori Bejleri (Harvard Math & CMSA) Title: Moduli of boundary polarized CalabiYau pairs Abstract: The theories of KSBA stability and Kstability furnish compact moduli spaces of general type pairs and Fano pairs respectively. However, much less is known about the moduli theory of CalabiYau pairs. In this talk I will present an approach to constructing a moduli space of CalabiYau pairs which should interpolate between KSBA and Kstable moduli via wallcrossing. I will explain how this approach can be used to construct projective moduli spaces of plane curve pairs. This is based on joint work… 

Speaker: Kai XuTitle: Motivic decomposition of moduli space from brane dynamicsVenue: CMSA Room G10Algebraic Geometry in String Theory Seminar Pretalk Speaker: Kai Xu (CMSA): 10:0010:30 am Speaker: Kai Xu (CMSA) Title: Motivic decomposition of moduli space from brane dynamics Abstract: Supersymmetric gauge theories encode deep structures in algebraic geometry, and geometric engineering gives a powerful way to understand the underlying structures by string/M theory. In this talk we will see how the dynamics of M5 branes tell us about the motivic and semiorthogonal decompositions of moduli of bundles on curves. 

Speaker: Damian van de HeisteegTitle: Species Scale across String Moduli SpacesVenue: CMSA Room G10Algebraic Geometry in String Theory Seminar Pretalk Speaker: David Wu (Harvard Physics): 10:0010:30 am Speaker: Damian van de Heisteeg, CMSA Title: Species Scale across String Moduli Spaces Abstract: String theories feature a wide array of moduli spaces. We propose that the energy cutoff scale of these theories – the socalled species scale – can be determined through highercurvature corrections. This species scale varies with the moduli; we use it both asymptotically to bound the diameter of the field space, as well as in the interior to determine a “desert point” where it is maximized. 

Speaker: Oliver SchlottererTitle: Modular graph forms and iterated integrals in string amplitudesVenue: CMSA Room G10Algebraic Geometry in String Theory Seminar Speaker: Oliver Schlotterer (Uppsala University) Title: Modular graph forms and iterated integrals in string amplitudes Abstract: I will discuss string amplitudes as a laboratory for special functions and period integrals that drive fruitful crosstalk with particle physicists and mathematicians. At genus zero, integration over punctures on a disk or sphere worldsheet generates multiple zeta values in the lowenergy expansion of open and closedstring amplitudes. At genus one, closedstring amplitudes introduce infinite families of nonholomorphic modular forms through the integration over torus punctures known as modular graph forms. The latter inspired Francis Brown’s alternative construction of nonholomorphic modular forms in the mathematics literature via iterated integrals, and I will report on recent progress… 

Speaker: ChungMing PanTitle: KählerEinstein metrics on families of Fano varietiesVenue: CMSA Room G02Algebraic Geometry in String Theory Seminar Speaker: ChungMing Pan, Institut de Mathématiques de Toulouse Title: KählerEinstein metrics on families of Fano varieties Abstract: This talk aims to introduce a pluripotential approach to study uniform a priori estimates of KählerEinstein (KE) metrics on families of Fano varieties. I will first recall basic tools in the pluripotential theory and the variational approach to complex MongeAmpère equations. I will then define a notion of convergence of quasiplurisubharmonic functions in families of normal varieties and extend several classical properties under this context. Last, I will explain how these elements help to obtain a purely analytic proof of the openness of existing singular KE metrics and a uniform $L^\infty$ estimate of KE potentials. This… 

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: 2Categories and the Massive 3d 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 Calabi–Yau 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. 