Departement Mathematik

Talks in mathematical physics

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Frühjahrssemester 2022

Datum / Zeit Referent:in Titel Ort
24. Februar 2022
15:15-16:15 		Michele Del Zotto
Uppsala University, Sweden
Details

Talks in Mathematical Physics

Titel Remarks on geometric engineering and correspondences
Referent:in, Affiliation Michele Del Zotto, Uppsala University, Sweden
Datum, Zeit 24. Februar 2022, 15:15-16:15
Ort HG G 43
Abstract Over the past decade we have witnessed the emergence of a plethora of correspondences between QFTs in various dimensions arising from higher dimensional theories (famous examples include the AGT correspondence, the so called BPS/CFT correspondence, the 3d/3d correspondence, and others). In this talk I will overview another strategy to obtain correspondences building upon geometric engineering techniques in string theory. Several applications and examples will be presented, involving supersymmetric theories in different dimensions. In particular, we will comment on recent results about the higher Donaldson-Thomas theory for Calabi-Yau three-folds, generalizations of level/rank dualities, and the evidence for an algebra organizing instantons on G(2) manifolds.
Remarks on geometric engineering and correspondencesread_more
HG G 43
3. März 2022
15:15-16:15 		Elba Garcia-Failde
Sorbonne Université
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Talks in Mathematical Physics

Titel Witten’s r-spin conjecture and its negative counterpart
Referent:in, Affiliation Elba Garcia-Failde, Sorbonne Université
Datum, Zeit 3. März 2022, 15:15-16:15
Ort HG G 43
Abstract In 1990, Witten conjectured that the generating series of intersection numbers of psi classes is a tau function of the KdV hierarchy. This was first proved by Kontsevich. In 2017, Norbury conjectured that the generating series of intersection numbers of psi classes with a negative square root of the canonical bundle is also a tau function of the KdV hierarchy. In ongoing work with N. Chidambaram and A. Giacchetto, we prove Norbury’s conjecture and obtain polynomial relations among kappa classes which were recently conjectured by Kazarian--Norbury. We also extend the conjecture to (negative) r-th roots (previously r=2) and prove that the corresponding intersection numbers can also be computed recursively using topological recursion (which I will briefly introduce) and W-constraints. The strategy draws inspiration from our proof, together with S. Charbonnier, of Witten’s r-spin conjecture from 1993 (Faber—Shadrin—Zvonkine’s theorem from 2010), which corresponds to the positive side of the story. We also obtain tautological relations in the (negative) analogous way to Pandharipande--Pixton--Zvonkine. The talk will be an overview of these four topics (r=2/>2; positive/negative) and their connections.
Witten’s r-spin conjecture and its negative counterpartread_more
HG G 43
10. März 2022
15:15-16:15 		Donald Youmans
University of Bern
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Talks in Mathematical Physics

Titel Darboux coordinates for hyperbolic Virasoro coadjoint orbits
Referent:in, Affiliation Donald Youmans, University of Bern
Datum, Zeit 10. März 2022, 15:15-16:15
Ort HG G 43
Abstract In this talk, we define Darboux coordinates for hyperbolic Virasoro coadjoint orbits with constant representative. These coordinates allow for many explicit computations, such as the partition function and several time-ordered and out-of-time ordered correlation functions, in the so-called Schwarzian theory which, in recent years, has gotten a lot of attention in both, mathematics and physics. This talk is based on joint work with Anton Alekseev and Olga Chekeres.
Darboux coordinates for hyperbolic Virasoro coadjoint orbitsread_more
HG G 43
31. März 2022
15:15-16:15 		Miquel Cueca
Georg-August-Universität, Göttingen
Details

Talks in Mathematical Physics

Titel Dimensional reduction of Courant sigma models
Referent:in, Affiliation Miquel Cueca, Georg-August-Universität, Göttingen
Datum, Zeit 31. März 2022, 15:15-16:15
Ort HG G 43
Abstract I will show that the 2d Poisson sigma model with target a Poisson groupoid arises as an effective theory of the 3d Courant sigma model associated to the double of the corresponding Lie bialgebroid. This is joint work with Alejandro Cabrera.
Dimensional reduction of Courant sigma modelsread_more
HG G 43
7. April 2022
15:15-16:15 		Fridrich Valach
Imperial College
Details

Talks in Mathematical Physics

Titel Higher Poisson-Lie T-dualities
Referent:in, Affiliation Fridrich Valach, Imperial College
Datum, Zeit 7. April 2022, 15:15-16:15
Ort HG G 43
Abstract I will describe a general BV framework for studying dualities of Poisson-Lie type. This puts on the same footing the ordinary Poisson-Lie T-duality and the electric-magnetic duality, and leads to a new family of dualities of higher gauge theories. An important role will be played by (a "baby" version of) the derived intersection of Lagrangians of Pantev-Toën-Vaquié-Vezzosi. This is a joint work with Ján Pulmann and Pavol Ševera (arXiv:1909.06151).
Higher Poisson-Lie T-dualitiesread_more
HG G 43
12. Mai 2022
15:15-16:15 		Dr. Danica Kosanović
ETH Zurich, Switzerland
Details

Talks in Mathematical Physics

Titel Graph complexes in knot theory
Referent:in, Affiliation Dr. Danica Kosanović, ETH Zurich, Switzerland
Datum, Zeit 12. Mai 2022, 15:15-16:15
Ort HG G 43
Abstract Quantum link invariants of Reshetikhin and Turaev can be factored through certain universal link invariants whose target is a certain algebra of graphs. In this talk I will explain what these graphs have to do with configuration spaces and operads, and why they offer a computable approach for the study of embedding spaces.
Graph complexes in knot theoryread_more (ABGESAGT)
HG G 43
19. Mai 2022
15:15-16:15 		Simone Noja
Ruprecht-Karls-Universität Heidelberg
Details

Talks in Mathematical Physics

Titel The de Rham / Spencer double complex and the geometry of forms on supermanifolds
Referent:in, Affiliation Simone Noja, Ruprecht-Karls-Universität Heidelberg
Datum, Zeit 19. Mai 2022, 15:15-16:15
Ort HG G 43
Abstract Integral forms are characteristic supergeometric objects that allow to define a meaningful notion of integration on supermanifolds. In this talk I will introduce a double complex of non-commutative sheaves which related integral forms to the more customary notion of differential forms. I will then discuss how this framework specializes to the so-called cotangent bundle supermanifolds, which are relevant to odd symplectic geometry and BV theory. If time permits, I will explain how the geometry of forms is related to the problem of splitting a complex supermanifold in this particular setting.
The de Rham / Spencer double complex and the geometry of forms on supermanifoldsread_more
HG G 43
26. Mai 2022
15:15-16:15 		Ivan Contreras
Amherst College
Details

Talks in Mathematical Physics

Titel Frobenius objects in the category of spans and the symplectic category
Referent:in, Affiliation Ivan Contreras, Amherst College
Datum, Zeit 26. Mai 2022, 15:15-16:15
Ort HG G 43
Abstract It is well known that Frobenius algebras are in correspondence with 2-dimensional TQFT. In this talk, we introduce Frobenius objects in any monoidal category and in particular, in the category where objects are sets and morphisms are spans of sets. We prove the existence of a simplicial set that encodes the data of the Frobenius structure in this category. This serves as a (simplicial) toy model of the Wehrheim-Woodward construction for the symplectic category. This is part of a program that intends to describe, in terms of category theory, the relationship between symplectic groupoids and topological field theory, via the Poisson sigma model. Based on joint work with Rajan Mehta and Molly Keller (arXiv:2106.14743), and ongoing work with Rajan Mehta and Walker Stern.
Frobenius objects in the category of spans and the symplectic categoryread_more
HG G 43
2. Juni 2022
15:15-16:15 		Eugene Rabinovich
Notre Dame University
Details

Talks in Mathematical Physics

Titel Classical Bulk-Boundary Correspondences via Factorization Algebras
Referent:in, Affiliation Eugene Rabinovich, Notre Dame University
Datum, Zeit 2. Juni 2022, 15:15-16:15
Ort HG G 43
Abstract A factorization algebra is a cosheaf-like local-to-global object which is meant to model the structure present in the observables of classical and quantum field theories. In the Batalin-Vilkovisky (BV) formalism, one finds that a factorization algebra of classical observables possesses, in addition to its factorization-algebraic structure, a compatible Poisson bracket of cohomological degree +1. Given a ``sufficiently nice'' such factorization algebra on a manifold $N$, one may associate to it a factorization algebra on $N\times \mathbb{R}_{\geq 0}$. The aim of the talk is to explain the sense in which the latter factorization algebra ``knows all the classical data'' of the former. This is the bulk-boundary correspondence of the title. Time permitting, we will describe how such a correspondence appears in the deformation quantization of Poisson manifolds.
Classical Bulk-Boundary Correspondences via Factorization Algebrasread_more
HG G 43
6. Juli 2022
14:00-15:00 		Domenico Fiorenza
Sapienza Università di Roma
Details

Talks in Mathematical Physics

Titel String bordism invariants in dimension 3 from U(1)-valued TQFTs
Referent:in, Affiliation Domenico Fiorenza, Sapienza Università di Roma
Datum, Zeit 6. Juli 2022, 14:00-15:00
Ort HG G 19.1
Abstract The third string bordism group is known to be Z/24Z. Using Waldorf's notion of a geometric string structure on a manifold, Bunke--Naumann and Redden have exhibited integral formulas involving the Chern-Weil form representative of the first Pontryagin class and the canonical 3-form of a geometric string structure that realize the isomorphism Bord3String to Z/24Z (these formulas have been recently rediscovered by Gaiotto--Johnson-Freyd--Witten). In the talk I will show how these formulas naturally emerge when one considers the U(1)-valued 3d TQFTs associated with the classifying stacks of Spin bundles with connection and of String bundles with geometric structure. Based on joint work with Eugenio Landi (in preparation).
String bordism invariants in dimension 3 from U(1)-valued TQFTsread_more
HG G 19.1

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