During the 2023–24 academic year, the CMSA will be hosting a seminar on Algebraic Geometry in String Theory, organized by Chuck Doran and Iacopo Brivio. During Spring 2024, this seminar will take place on Thursdays from 10:30–11:30 am (Eastern Time). There will be a pre-seminar from 10:00–10:30 am. The meetings will take place in Room G10 at the CMSA, 20 Garden Street, Cambridge MA 02138, and some meetings will take place virtually on Zoom or be held in hybrid formats. To join the Algebraic Geometry in String Theory Listserv, please visit this LINK. The schedule will be updated as talks are confirmed.

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  • December 11, 2023 10:30 AM
Speaker: Thorsten Schimannek
Title: M-theory on nodal Calabi-Yau 3-folds and torsion refined GV-invariants
Venue: CMSA Room G10

Algebraic Geometry in String Theory Seminar Speaker: Thorsten Schimannek (Utrecht University) Title: M-theory on nodal Calabi-Yau 3-folds and torsion refined GV-invariants Abstract: The physics of M-theory and Type IIA strings on a projective nodal CY 3-folds 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 Calabi-Yau double covers of P^3. Using conifold transitions, we prove that the exceptional curves in any small resolution are torsion while M-theory develops a discrete gauge symmetry.This leads to a torsion refinement of the ordinary Gopakumar-Vafa invariants, that is associated to the singular Calabi-Yau and captures the enumerative geometry of the non-Kähler resolutions. We further argue that…

  • December 04, 2023 10:30 AM
Speaker: Maksym Fedorchuk
Title: CM-minimizers and standard models of Fano fibrations over curves
Venue: CMSA Room G10

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 of Tian. One of the consequences of the general theory is that given a family of K-stable 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 CM-minimizers without base change. In answering this question, we arrive at a…

  • November 27, 2023 10:30 AM
Speaker: An Huang
Title: A p-adic Laplacian on the Tate curve
Venue: CMSA Room G10

Algebraic Geometry in String Theory Seminar Speaker: An Huang (Brandeis) Pre-talk Speaker: TBA: 10:00-10:30 am Title: A p-adic Laplacian on the Tate curve Abstract: We shall first explain the relation between a family of deformations of genus zero p-adic string worldsheet action and Tate’s thesis. We then propose a genus one p-adic string worldsheet action. The key is the definition of a p-adic Laplacian operator on the Tate curve. We show that the genus one p-adic 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 p-adic setup. Numerics suggest that at…

  • November 13, 2023 10:30 AM
Speaker: Sheldon Katz
Title: Stacky small resolutions of determinantal octic double solids and noncommutative Gopakumar-Vafa invariants
Venue: CMSA Room G10

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 CY threefolds which do not admit a projective small resolution.  B-model 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…

  • November 06, 2023 10:30 AM
Speaker: Andrew Harder
Title: Deformations of Landau-Ginzburg models and their fibers
Venue: CMSA Room G10

Algebraic Geometry in String Theory Seminar Speaker: Andrew Harder, Lehigh University Pre-talk Speaker: TBA: 10:00-10:30 am 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 under mirror symmetry, so a very natural question to ask is: Which Landau-Ginzburg 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…

  • October 23, 2023 10:30 AM
Speaker: David Favero
Title: Gauged Linear Sigma Models and Cohomological Field Theories
Venue: CMSA Room G10

Algebraic 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 Ciocan-Fontanine-Guere-Kim-Shoemaker.  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 Gromov-Witten and Fan-Jarvis-Ruan-Witten 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…

  • October 16, 2023 10:00 AM
Speaker: Dori Bejleri
Title: Moduli of boundary polarized Calabi-Yau pairs
Venue: CMSA Room G10

Algebraic Geometry in String Theory Seminar Pre-talk Speaker: Rosie Shen (Harvard): 10:00-10:30 am Pre-talk Title: Introduction to the singularities of the MMP Speaker: Dori Bejleri (Harvard Math & CMSA) Title: Moduli of boundary polarized Calabi-Yau pairs Abstract: The theories of KSBA stability and K-stability furnish compact moduli spaces of general type pairs and Fano pairs respectively. However, much less is known about the moduli theory of Calabi-Yau pairs. In this talk I will present an approach to constructing a moduli space of Calabi-Yau pairs which should interpolate between KSBA and K-stable moduli via wall-crossing.  I will explain how this approach can be used to construct projective moduli spaces of plane curve pairs. This is based on joint work…

  • October 02, 2023 10:30 AM
Speaker: Kai Xu
Title: Motivic decomposition of moduli space from brane dynamics
Venue: CMSA Room G10

Algebraic Geometry in String Theory Seminar Pre-talk Speaker: Kai Xu (CMSA): 10:00-10:30 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.

  • September 25, 2023 10:00 AM
Speaker: Damian van de Heisteeg
Title: Species Scale across String Moduli Spaces
Venue: CMSA Room G10

Algebraic Geometry in String Theory Seminar Pre-talk Speaker: David Wu (Harvard Physics): 10:00-10:30 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 so-called species scale – can be determined through higher-curvature 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.

  • April 07, 2023 12:00 PM
Speaker: Oliver Schlotterer
Title: Modular graph forms and iterated integrals in string amplitudes
Venue: CMSA Room G10

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 sphere worldsheet generates multiple zeta values in the low-energy expansion of open- and closed-string amplitudes. At genus one, closed-string amplitudes introduce infinite families of non-holomorphic modular forms through the integration over torus punctures known as modular graph forms. The latter inspired Francis Brown’s alternative construction of non-holomorphic modular forms in the mathematics literature via iterated integrals, and I will report on recent progress…

  • April 03, 2023 10:00 AM
Speaker: Chung-Ming Pan
Title: Kähler-Einstein metrics on families of Fano varieties
Venue: CMSA Room G02

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 and the variational approach to complex Monge-Ampère equations. I will then define a notion of convergence of quasi-plurisubharmonic 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…

  • February 24, 2023 09:00 AM
Speaker: Chao-Ming Lin
Title: On the convexity of general inverse $\sigma_k$ equations and some applications
Venue: CMSA Room G10

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 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 Monge-Ampère equation, the J-equation, the dHYM equation, the special Lagrangian equation, etc. Second, I will introduce some semialgebraic sets and a special…

  • October 28, 2022 09:30 AM
Speaker: Ahsan Khan
Title: 2-Categories and the Massive 3d A-Model
Venue: CMSA Room G10

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.  

  • October 21, 2022 09:30 AM
Speaker: Nicolo Piazzalunga
Title: The index of M-theory
Venue: CMSA Room G10

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 genus-zero Gromov-Witten theory of non-compact toric varieties.

  • October 14, 2022 09:30 AM
Speaker: Daniel Pomerleano
Title: Singularities of the quantum connection on a Fano variety
Venue: CMSA Room G10

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 made for manifolds with semi-simple 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…

  • October 07, 2022 09:30 AM
Speaker: Sam Bardwell-Evans
Title: Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces
Venue: CMSA Room G10

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 Gross-Hacking-Keel. The argument relies on a holomorphic/tropical disc correspondence to control the behavior of holomorphic discs, allowing us to relate open Gromov-Witten invariants to log Gromov-Witten invariants. This talk is based on joint work with Man-Wai Mandy Cheung, Hansol Hong, and Yu-Shen Lin.

  • September 30, 2022 09:30 AM
Speaker: Mauricio Romo
Title: GLSM, Homological projective duality and nc resolutions
Venue: CMSA Room G10

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 (hypersurfaces) manifolds. In general, for such cases the HPD can be interpreted as a non-commutative (nc) resolution of a compact variety. I will give a physical interpretation of this fact and present some conjectures.

  • April 26, 2022 09:30 AM
Speaker: Yan Zhou
Title: Modularity of mirror families of log Calabi–Yau surfaces
Venue: virtual

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 modularity of the mirror family as the universal family of log Calabi-Yau 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…

  • April 19, 2022 09:30 AM
Speaker: Ming Zhang
Title: Equivariant Verlinde algebra and quantum K-theory of the moduli space of vortices
Venue: Virtual

Abstract:  In studying complex Chern-Simons theory on a Seifert manifold, Gukov-Pei proposed an equivariant Verlinde formula, a one-parameter 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. Gukov-Pei conjectured that the equivariant Verlinde numbers are equal to the equivariant quantum K-invariants of a non-compact (Kahler) quotient space studied by Hanany-Tong. In this talk, I will explain the setup of this conjecture and its proof via wall-crossing of moduli spaces of (parabolic) Bradlow-Higgs triples. It is based on work in progress with Wei Gu and Du Pei.

  • April 12, 2022 11:58 AM
Speaker: Aron Heleodoro
Title: Applications of Higher Determinant Map
Venue: Virtual

Abstract: 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 ind-schemes. For that I will introduce some aspects of the theory of Tate objects in a couple of contexts.