Mathematical Physics Seminar, Mondays

The seminar on mathematical physics will be held on select Mondays and Wednesdays from 12 – 1pm in CMSA Building, 20 Garden Street, Room G10. 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. 

Date Speaker Title/Abstract
9/9/2019 Daniel Pomerleano (UMass Boston) 

Title: Intrinsic mirror symmetry via symplectic topology

Abstract: Given a maximally degenerate log Calabi–Yau variety $X$, I will describe how one can recover the birational class of the mirror manifold from a Floer theoretic invariant of $X$ (symplectic cohomology). I will then explain how this result relates to recent constructions in mirror symmetry due to Gross–Hacking–Keel and Gross–Siebert.

9/16/2019 Eirik Eik Svanes (King’s College London and ICTP)

Title: On coupled moduli problems and effective topological theories

Abstract: I will discuss recent developments in understanding coupled moduli spaces for geometries which appear naturally in string theory. Focusing on heterotic geometries and $SU(3)$ and $G2$ structure compactifications in particular, which also come equipped with a gauge sector, I will describe how the moduli are captured by effective quasi-topological theories derived from the heterotic supergravity. In the case of $SU(3)$ structure compactifications the topological theory in question is a natural generalization of holomorphic Chern–Simons theory or Donaldson–Thomas theory. In the case of heterotic $G2$ structures we will see that the moduli problem is a lot more coupled, and the moduli space has no intrinsic fibration structure in general.

9/25/2019
Wednesday
Fenglong You (University of Alberta)

Title: Gluing Periods for DHT Mirrors

Abstract: Let $X$ be a Calabi–Yau manifold that admits a Tyurin degeneration to a union of two quasi-Fano varieties $X_1$ and $X_2$ intersecting along a smooth anticanonical divisor $D$. Doran–Harder–Thompson conjectured that the Landau–Ginzburg mirrors of $(X_1,D)$ and $(X_2,D)$ can be glued to obtain the mirror of $X$. In this talk, I will explain how periods on the mirrors of $(X_1,D)$ and $(X_2,D)$ are related to periods on the mirror of $X$. The relation among periods relates different Gromov–Witten invariants via their respective mirror maps. This is joint work with Charles Doran and Jordan Kostiuk.

9/30/2019 Dmitry Tonkonog (Harvard)

Title: Floer theory and rigid subsets of symplectic manifolds

Abstract: Suppose we are given a symplectic manifold. What general things can we say about the dynamics of its symplectomorphisms? A classical way to explore this question is to find rigid subsets: subsets that cannot be displaced from themselves by any symplectomorphism. This has inspired many developments in Floer theory, including recent ones. I will survey the topic, and prove that Lagrangian skeleta of divisor complements of Calabi–Yau manifolds are rigid. This partially reports on joint work with Umut Varolgunes, as well as other things I learned from him.

10/7/2019 Xiao Zheng (Boston University)
 
Abstract: In this talk, I will introduce an equivariant mirror construction using a Morse model of equivariant Lagrangian Floer theory, formulated in a joint work with Kim and Lau. In case of semi-Fano toric manifold, our construction recovers the $T$-equivariant Landau–Ginzburg mirror found by Givental. For toric Calabi–Yau manifold, the equivariant disc potentials of certain immersed Lagrangians are closely related to the open Gromov–Witten invaraints of Aganagic–Vafa branes, which were studied by Katz–Liu, Graber–Zaslow, Fang–Liu–Zong and many others using localization techniques. The later result is a work in progress joint with Hong, Kim and Lau.
10/14/2019 Columbus Day  

10/21/2019

12:10pm

Man-Wai Cheung (Harvard)

Title: Compactification for cluster varieties without frozen variables of finite type

Abstract: Cluster varieties are blow up of toric varieties. They come in pairs $(A,X)$, with $A$ and $X$ built from dual tori. Compactifications of $A$, studied by Gross, Hacking, Keel, and Kontsevich, generalize the polytope construction of toric varieties while the compactifications of X, studied by Fock and Goncharov, generalize the fan construction. The conjecture is that the $A$ and the $X$ cluster varieties are mirrors to each other. Together with Tim Magee, we have shown that there exists a positive polytope for the type $A$ cluster varieties which give us a hint to the Batyrev–Borisov construction.

10/28/2019

G02

Max Zimet 

(BHI)

Title: K3 metrics from little string theory

 

Abstract: Calabi–Yau manifolds have played a central role in both string theory and mathematics for decades, but in spite of this no Ricci-flat metric on a compact non-toroidal Calabi–Yau manifold is known. I will discuss a new physically motivated approach toward the determination of such metrics for K3 surfaces. The key remaining step is the determination of a BPS spectrum of a heterotic little string theory on $T^2$. I will use string dualities to provide a number of mathematical reformulations of this problem, ranging from open string reduced Gromov–Witten theory for the mirror K3 surface (in accordance with the SYZ conjecture) to Donaldson–Thomas theory for auxiliary Calabi–Yau threefolds. Finally, I will discuss new approximations to K3 metrics near the semi-flat limit that require only a minimal knowledge of this BPS spectrum.

11/4/2019 Elana Kalashnikov  (Harvard)
Abstract: I will discuss joint work with Chiodo investigating the mirror symmetry of Calabi–Yau hypersurfaces in weighted projective spaces. I will show how given such a hypersurface endowed with a finite order automorphism of a specific type, the traditional cohomological mirror statement can be both specialised and broadened to take into account the weights of the action of the automorphism and the cohomology of its fixed locus. The main tool is Berglund–Hubsch–Krawitz duality. When the automorphism is an involution, this allows us to construct generalisations of Borcea–Voisin orbifolds in any dimension and with any number of factors (joint work with Chiodo and Veniani). For odd prime order automorphisms and dimension 2 orbifolds, this implies mirror symmetry for the associated lattice polarised K3 surfaces.
11/13/2019 Cancelled  
11/18/2019 Lampros Lamprou (MIT)  TBA
11/25/2019 David Svoboda (Perimeter Institute) Title: Topological and supersymmetric sigma models from para-Hermitian geometry

Abstract: In recent years, para-Hermitian geometry has been used to describe T-duality covariant spacetimes for string theory. In my talk, I will present applications of para-Hermitian geometry to 2D (2,2) SUSY sigma models and show that this geometry gives rise to a new, yet unexplored, notion of mirror symmetry.

12/2/2019 W. A. Zuniga-Galindo (CINVESTAV)

Title: Strings and Quantum Fields Over p-Adic Spacetimes

Abstract: I will discuss some recent results on the connections between local zeta functions with the regularization of p-adic Koba-Nielsen string amplitudes, and with the construction of quantum fields over p-adic spacetimes. The theory of local zeta functions was started in the 50s by Gel’fand and Weil. In the 70s Igusa developed a uniform theory of local zeta functions over local fields of characteristic zero. In the last years the theory has suffered a tremendous expansion due to the introduction of the motivic Igusa zeta functions by Denef and Loeser. By using the theory of local zeta functions is possible to establish (in rigorous way) the regularization of Koba-Nielsen amplitudes on R, C or Q_{p}. There is empirical evidence that in the limit p approaches to one, the p-adic strings are related with the ordinary ones. The theory of local zeta functions allows to define rigorously the limit p tends to one of p-adic Koba-Nielsen amplitudes. Since the 50s is known that the existence of fundamental solutions (Green functions) is consequence of the existence of meromorphic continuation for the Archimedean local zeta functions. This fact is also true in the p-adic case, for this reason the p-adic local zeta functions play a central role in the construction of quantum fields over p-adic spacetimes.

12/9/2019 Jie-qiang Wu (MIT) TBA
For a listing of previous Mathematical Physics Seminars, please click here.

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