Cyril Closset, Line and surface defects and Schubert varieties in partial flag manifolds

• Cyril Closset

Room: 02.430 After reviewing aspects of the 3d A-model, I will discuss recent results on the quantum K-theory of partial flag manifolds from the perspective of the 3d GLSM/QK correspondence. We define Schubert line defects that are defect line operators obtained by coupling appropriate 1d degrees of freedom to the 3d GLSM bulk fields, so that they flow in the infrared to Schubert classes in the QK ring. I will also discuss extensions of this approach to 4d GLSMs and elliptic quantum cohomology.

Ilka Brunner, TBA

• Ilka Brunner

Room: 02.430

Thorsten Schimmanek, Almost generic Calabi-Yau threefolds and GLSM

• Thorsten Schimmanek

Room: 02.430 In general, a projective Calabi-Yau threefold with nodal singularities does not admit a Kaehler small resolution. This happens in particular if the exceptional curves are torsion in homology. However, the presence of torsion also leads to the possibility of turning on a flat but topologically non-trivial B-field that stabilizes the singularities. After briefly introducing some of the relevant geometric ideas, we discuss how GLSMs can be used to study strings that propagate on examples of such backgrounds. We will then describe geometric examples for which a GLSM description is currently unknown and speculate on potential directions for their construction.

Albrecht Klemm, Fibering out Calabi-Yau motives, the asymptotic of higher genus invariants and black hole physics

• Albrecht Klemm

Room: 02.430 Mirror symmetry implies that the higher genus Gromov-Witten (GW), Pandharipande-Thomas (PT) and certain Donaldson-Thomas (DT) invariants on the A-model side are encoded in generating functions which are related to analytic sections of line bundles over the complex moduli space on the B-model side constructed from the periods. This relates the asymptotic behaviour of the invariants as extracted at the point of maximal unipotent monodromy to the behaviour of these sections near the closest singularities, typically a conifold. Here the relevant analytic information is encoded in closed and open modular period integrals over the modular domain of $\Gamma_0(N)$. The latter structures are determined by properties of the degenerate Calabi-Yau motive in the conifold fibre, which have been proven by the fibering out technique with B\"onisch and Golyshev. We comment on the implications of the asymptotic behaviour of the symplectic invariants for the estimates of the microscopic entropy of supersymmetric black holes and black rings as investigated recently with Alexandrov and Pioline.

Ed Segal, A few results on B-brane transport in GL_2 GLSMs

• Ed Segal

Room: 02.430 Very little is know about the general problem of B-brane transport in non-abelian GLSMs. I'll survey a few recent projects that address different aspects of this problem in specific examples where the gauge group is GL_2.

Pyry Kuusela, Physics Applications of Hodge Theory and Arithmetic Geometry

• Pyry Kuusela

Room: 02.430 This talk is an overview of recent progress in applying techniques from arithmetic geometry to physics. Many interesting physics constructions in various theories, such as CFTs and SUGRAs, can be related to non-trivial Hodge theoretic problems. Some number theoretic results and conjectures, generalising the celebrated modularity theorem in various directions, imply that these problems can be solved by using arithmetic geometry. After reviewing these connections, I give a quick overview of techniques I have developed together with collaborators to efficiently compute arithmetic geometry data, and give various examples of applications to physics. Time permitting, I will give some comments on recent work, questions, and speculation on how the correspondence between arithmetic geometry and physics can be taken beyond the context of Hodge theory.

Yann Proto, Phases of linear sigma models with torsion

• Yann Proto

Room: 02.430 I will describe joint work with D. Israël and I. Melnikov on (0,2) gauged linear sigma models relevant for heterotic flux compactifications. An important class of flux backgrounds is realized as a torus fibration over K3 with a stable holomorphic vector bundle. I will present torsional GLSMs whose large radius phase describes such a geometry with a trivial gauge bundle, and which admit a Landau–Ginzburg orbifold phase. I will also discuss related (0,2) constructions for Calabi–Yau compactifications with line bundles.

Xiaohan Yan, Quantum K-theory of GIT quotients

• Xiaohan Yan

Room: 02.430 The K-theoretic Gromov-Witten (KGW) invariants are deformation invariants of a complex variety defined by counting curves, generalizing the more familiar Gromov-Witten invariants. In this talk, I discuss my work on the generating function of the genus-zero KGW invariants of type-A flag varieties, a computation motivated by the 3D mirror symmetry. The method is based on the idea of abelian/non-abelian correspondence. I also discuss further applications of this method in studying the KGW invariants of GIT quotients and their associated q-difference equations.

YP Lee, Quantum elliptic cohomology: a progress report

• YP Lee

Room: 02.430 Among the generalized cohomology theories associated with 1-dimensional groups are ordinary cohomology (additive group), complex K-theory (multiplicative group), and elliptic cohomology (elliptic curve). In the late 1980s and early 1990s, physicists initiated quantum cohomology (Gromov-Witten theory) as the enumerative geometry associated with ordinary cohomology. A decade later, A. Givental and I introduced quantum K-theory. In this joint work with E. Bouaziz and I. Huq-Kuruvilla, I will report on recent progress toward establishing a mathematical framework for quantum elliptic cohomology.

Kentaro Hori, Grade Restriction Rule In Non-Abelian Gauged Linear Sigma Models: The Latest Update

• Kentaro Hori

Room: 02.430 I will report on the latest progress in a work on the grade restriction rule for D-brane transport in a class of non-Abelian gauged linear sigma models, represented by the Rodland model for the Pfaffian/Grassmannian correspondence. The focus will be the new method to determine the rule and the low energy behaviour of D-branes in the strongly coupled phase. Based on a joint work with Richard Eager, Johanna Knapp and Mauricio Romo.

Jirui Guo, Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double β-Grothendieck polynomials

• Jirui Guo

Room: 02.430 The GL(N) asymmetric five vertex model is an integrable system that generalizes the spin-1/2 five vertex model. In this talk, I will explain why the Bethe ansatz equations of this model encode the ring relations of the equivariant quantum cohomology and K-theory ring of partial flag varieties, which are the OPE rings of the 2D and 3D quiver GLSMs. I will also show how the Bethe ansatz states of the integrable model generate the double β-Grothendieck polynomials interpolating the double Schubert polynomials and the double Grothendieck polynomials, which are representatives of the Schubert classes.

Tyler Kelly, On Open Enumerative Geometry for Landau-Ginzburg Models

• Tyler Kelly

Room: 02.430 I will describe an open enumerative theory for certain Landau-Ginzburg models. Its intersection numbers are constructed by taking certain multivariate integrals of a multisection of an open analogue of Witten’s bundle over a moduli space of orbidisks. This so-called open FJRW theory satisfies mirror symmetry. If time permits, I will explain the B-model. This is joint work with Mark Gross and Ran Tessler.

Chiu-Chu Melissa Liu, Extended Landau-Ginzburg/Calabi-Yau correspondence and open/closed correspondence for the quintic threefold

• Melissa Liu

Room: 02.430 Chiodo-Ruan proved genus-zero Landau-Ginzburg/Calabi-Yau (LG/CY) correspondence for the quintic Calabi-Yau threefold, which relates genus-zero Fan-Jarvis-Ruan-Witten (FJRW) invariants of the Fermat quintic polynomial in five variables and genus-zero Gromov-Witten (GW) invariants of the quintic Calabi-Yau threefold. This correspondence can be viewed as an example of GIT wall-crossing in a gauged linear sigma model (GLSM). I will explain results and conjectures on (1) extending this correspondence to genus-zero open FJRW invariants and genus-zero open GW invariants of the quintic Calabi-Yau threefold, and (2) open/closed correspondence relating the above genus-zero open GW (resp. FJRW) invariants and closed GLSM invariants of a specific GLSM, the extended quintic GLSM, in the positive (resp. negative) phase. This is based on joint work with Konstantin Aleshkin.

Emanuel Scheidegger, TBA

• Emanuel Scheidegger

Room: 02.430

Ilarion Melnikov, The spectral flow operator in (2,2) Calabi-Yau GLSMs

• Ilarion Melnikov

Room: 02.430 The (2,2) GLSM Lagrangian allows for a simple presentation of a number of deformations of the IR SCFT obtained as the endpoint of the RG flow defined by the gauge theory path integral. Typically, this only covers a subset of the deformations. In this talk I will review some work on describing the missing, so-called “non-toric” and “non-polynomial”, deformations as operators in the chiral algebra of the Lagrangian theory, and I will explain the key challenge through a construction, found together with Ronen Plesser, of a special holomorphic operator—the chiral spectral flow operator—in terms of the GLSM fields.