# Mathematical Physics Seminar, Mondays

#### Beginning immediately, until at least April 30, all seminars will take place virtually, through Zoom. A link to attend can be found in the schedule below.

The seminar on mathematical physics will be held on Mondays from 12 – 1pm virtually. Please email the seminar organizers to obtain a link. This year’s Seminar will be organized by Bogdan Stoica and Tsung-ju Lee.

The list of speakers for the upcoming academic year will be posted below and updated as details are confirmed. Titles and abstracts for the talks will be added as they are received.

To learn how to attend this seminar, please fill out this form

Date Speaker Title/Abstract

1/27/2020

Lawrence Barrott (Boston College)

Abstract: A classical question in algebraic geometry asks to count the number of plane curves of degree d meeting a smooth elliptic curve in a single point tangent to order 3d. This question is best reformulated in terms of log Gromov–Witten invariants which I will introduce. By considering the degeneration of the elliptic curve to the toric boundary Navid Nabijou and I provide a localisation formalism to count these curves. We uncover a refined set of enumerative invariants which we believe are related to certain scattering diagram calculations. If time permits I will explain what happens in higher dimension.

2/3/2020

Ignacio Barros (Northeastern University)

Abstract: For a moduli space $M$ of stable sheaves over a K3 surface $X$, we propose a series of conjectural identities in the Chow rings $CH_\star (M \times X^\ell),\, \ell \geq 1,$ generalizing the classic Beauville–Voisin identity for a K3 surface. We emphasize consequences of the conjecture for the structure of the tautological subring $R_\star (M) \subset CH_\star (M).$ We prove the proposed identities when $M$ is the Hilbert scheme of points on a K3 surface. This is based on joint work with L. Flapan, A. Marian and R. Silversmith.

2/10/2020

Dan Mangoubi

(Einstein Institute of Mathematics)

Abstract: A celebrated theorem of C.L. Siegel from 1929 shows that the multiplicity of eigenvalues for the Laplace eigenfunctions on the unit disk is at most two. We study the fourth order clamped plate problem, showing that the multiplicity of eigenvalues is uniformly bounded. Our method is based on new recursion formulas and Siegel–Shidlovskii theory. If time permits, we discuss possible applications also to nodal geometry. The talk is based on a joint work with Yuri Lvovsky.

2/17/2020

President’s Day

2/24/2020

Yingdi Qin (Harvard)

Abstract: Homological mirror symmetry (HMS) asserts that the Fukaya category of a symplectic manifold is derived equivalent to the category of coherent sheaves on the mirror complex manifold. Without suitable enlargement (split closure) of the Fukaya category, certain objects of it are missing to prevent HMS from being true. Kapustin and Orlov conjecture that coisotropic branes should be included into the Fukaya category from a physics view point. In this talk, I will construct for linear symplectic tori a version of the Fukaya category including coisotropic branes and show that the usual Fukaya category embeds fully faithfully into it. I will also explain the motivation of the construction through the perspective of Homological mirror symmetry.

3/2/2020

Mauricio Romo (Tsinghua University)

Video

Abstract: I will define and review the basics of exponential networks associated to CY 3-folds described by conic bundles. I will focus mostly on the mathematical aspects and general ideas behind this construction as well as its conjectural connection with generalized Donaldson–Thomas invariants. This is based on joint work with S. Banerjee and P. Longhi.

3/9/2020

Laure Flapan (MIT)

Abstract: For any polarized hyperkahler manifold of K3 type whose dimension is divisible by 8, we produce a Lagrangian submanifold which is Fano arising as a connected component of the fixed locus of an involution on the hyperkahler manifold. This is an ongoing joint work with E. Macrì, K. O’Grady, and G. Saccà.

3/16/2020

Spring Break

3/23/2020

Bogdan Stoica (CMSA)

This meeting will be taking place virtually on Zoom.

Title: Bit Threads: Understanding Gravitation from Quantum Entanglement

Abstract: The AdS/CFT correspondence stipulates that gravitational evolution in a bulk spacetime is dual to a boundary description that has no gravity. In the AdS/CFT picture the bulk spacetime evolves gravitationally against an anti-de Sitter space background, and the boundary dual theory is a conformal gauge theory in a spacetime of one dimension less. Recent insights by Ryu and Takayanagi have conjectured that quantum entangled boundary states quantitatively give rise to geometry in the bulk. They do so by explicitly referring to “minimal surfaces” in the bulk, connecting them to the entropy of a related area in the boundary. I will present a conceptually and technically powerful complementary holographic entanglement picture, reformulating Ryu–Takayanagi to no longer refer to minimal surfaces, and suggesting a new way to think about the holographic principle and the connection between spacetime gravitation and information. I will introduce the idea of bit threads, and show how they can be used for fun and profit.

3/30/2020

11:00am

Timothy Large (MIT)

This meeting will be taking place virtually on Zoom.

Title: Floer K-theory and exotic Liouville manifolds

Abstract: In this talk, I will discuss how to define the (wrapped) Fukaya category of an exact symplectic manifold with coefficients in extraordinary cohomology theories, following the ideas of Cohen–Jones–Segal. I will then explain how to construct an exotic symplectic ball, which has vanishing ordinary symplectic homology, but can be distinguished from the standard ball by using Floer homology with coefficients in complex K-theory.

4/6/2020

3:00pm

Daniel Harlow (MIT)

This meeting will be taking place virtually on Zoom.

Title: What does it mean to classify ‘t Hooft anomalies?

Abstract: Recent discussions of topological phases of matter have sometimes been phrased in the language of classifying anomalies.  In this talk I will review what is really meant by an ‘t Hooft anomaly, and then point out that this is not what is actually classified in most of these discussions.  I also will discuss some progress towards filling this gap. Based on work with Hirosi Ooguri (see section 2.7 of https://arxiv.org/abs/1810.05338).

4/13/2020

Video

This meeting will be taking place virtually on Zoom.

Abstract: The goal of this talk is to precisely describe how certain operator properties of continuum QFT (e.g. operator product expansions, current algebras, vertex operator algebras) emerge from an underlying lattice theory.  The main lesson will be that a “continuum limit” must always involve two or more cutoffs being taken to zero in a specific order.  In other words, the naive statement that continuum theories are obtained from lattice ones by letting a “lattice spacing” go to zero is never sufficient to describe the lattice-continuum correspondence.  Using these insights, I will show in detail how the Kac-Moody algebra arises from a nonperturbatively well defined, fully regularized model of free fermions, and I will comment on generalizations and applications to bosonization.  Time permitting, I will describe more intricate examples involving scalar fields, and I will discuss several open questions.

4/20/2020

Kuan-Wen Lai (UMass Amherst)

This meeting will be taking place virtually on Zoom

Title: Fourier–Mukai equivalences arising from Cremona transformations I: K3 surfaces

Abstract: The derived equivalences of K3 surfaces and the K3 categories of certain cubic fourfolds are known to be realizable as Hodge isometries, i.e. lattice isometries preserving Hodge structures. On the other hand, Hodge isometries are also known to appear when one factorizes a birational map between varieties and tracks the actions on the middle cohomologies. When does a Hodge isometry induced from the derived equivalence of K3 surfaces/categories arise from a birational map? This is the first of two related talks discussing this question. In this talk, I will exhibit such examples for general K3 surfaces of degree 12. As a corollary, I will introduce how the construction gives an interesting relation in the Grothendieck ring of algebraic varieties. This is joint work with Brendan Hassett.

4/27/2020

Yu-Wei Fan (UC Berkeley)

Video

This meeting will be taking place virtually on Zoom.

Abstract: It is conjectured that two cubic fourfolds are birational if their associated K3 categories are equivalent. We prove this conjecture for very general cubic fourfolds of discriminant 20, where the birational maps are produced via certain Cremona transformations defined by Veronese surfaces. Using these birational maps, we find new rational cubic fourfolds. Joint work with Kuan-Wen Lai.

5/4/2020

10:30-11:30am

John Alexander Cruz Morales (Universidad Nacional de Colombia)

This meeting will be taking place virtually on Zoom.

Abstract: We will revisit the computations of Stokes matrices for tt*-structures done by Cecotti and Vafa in the 90’s in the context of Frobenius manifolds and the so-called monodromy identity. We will argue that those cases provide examples of non-commutative Hodge structures of exponential type in the sense of Katzarkov, Kontsevich and Pantev.

5/15/2020

James Sully (University of British Columbia)

Video

This meeting will be taking place virtually on Zoom.

Abstract: It has long been believed that progress in understanding the black hole information paradox would require coming to terms with microscopic details of quantum gravity, beyond the reach of semiclassical effective field theory. In that light, one of the most surprising discoveries of the last year has been that signature features of the unitary evaporation of black holes can already be seen within effective field theory, albeit with the inclusion of ‘euclidean wormholes’. However, these novel contributions are best understood when the gravitational theory is not a single microscopic theory, but an average over many different theories. To save unitarity must we then simultaneously throw it away? I will explain how the same story can be recovered within a single microscopic theory by thinking carefully about the right effective theory for finite-lifetime observers.