Abstract: 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 follow-up of the work of Gross–Hacking–Keel, when (Y,D) is positive, we prove the […]
Algebraic 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 B-branes. I will focus mostly on the case of Fano […]
Algebraic Geometry in String Theory Seminar Speaker: Sam Bardwell-Evans, Boston University Title: Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces Abstract: In this talk, we construct special Lagrangian fibrations for log Calabi-Yau surfaces and scattering diagrams from Lagrangian Floer theory of the fibers. These scattering diagrams recover the algebro-geometric scattering diagrams of Gross-Pandharipande-Siebert and […]
Algebraic 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 far-reaching conjectures known as the Dubrovin/Gamma conjectures. Traditionally, these conjectures are […]
Algebraic Geometry in String Theory Seminar Speaker: Nicolo Piazzalunga, Rutgers Title: The index of M-theory Abstract: I’ll introduce the higher-rank Donaldson-Thomas theory for toric Calabi-Yau threefolds, within the setting of equivariant K-theory. 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 […]
Algebraic Geometry in String Theory Seminar Speaker: Ahsan Khan, IAS Title: 2-Categories and the Massive 3d A-Model Abstract: I will outline the construction of a 2-category associated to a hyperKahler moment map. The construction is based on partial differential equations in one, two, and three dimensions combined with a three-dimensional version of the Gaiotto-Moore-Witten web formalism. […]
Algebraic Geometry in String Theory Seminar Speaker: Chao-Ming 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 Hermitian-Yang-Mills equation (hereinafter the dHYM equation). First, I will show my recent […]
Algebraic Geometry in String Theory Seminar Speaker: Chung-Ming Pan, Institut de Mathématiques de Toulouse Title: Kähler-Einstein metrics on families of Fano varieties Abstract: This talk aims to introduce a pluripotential approach to study uniform a priori estimates of Kähler-Einstein (KE) metrics on families of Fano varieties. I will first recall basic tools in the pluripotential theory […]
Algebraic 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 cross-talk with particle physicists and mathematicians. At genus zero, integration over punctures on a disk or […]
Algebraic Geometry in String Theory Seminar Speaker: Andrew Harder, Lehigh University Title: Deformations of Landau-Ginzburg models and their fibers Abstract: In mirror symmetry, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w, but not all such pairs correspond to Fano varieties […]
Algebraic Geometry in String Theory Seminar Speaker: Sheldon Katz, UIUC Title: Stacky small resolutions of determinantal octic double solids and noncommutative Gopakumar-Vafa 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 […]
Algebraic Geometry in String Theory Seminar Speaker: Maksym Fedorchuk (Boston College) Title: CM-minimizers and standard models of Fano fibrations over curves Abstract: A recent achievement in K-stability of Fano varieties is an algebro-geometric construction of a projective moduli space of K-polystable Fanos. The ample line bundle on this moduli space is the CM line bundle […]