Mathematical physics seminar
Date: Tuesdays 11:15-12:45 Uhr
Venue: 1.023 (BMS Room, Haus 1, ground floor), Rudower Chaussee 25, Adlershof, 12489 Berlin
Organiser: Gaëtan Borot
To be in the mailing list, please write to Kristina Schulze (schulze@hu-berlin.de).
For HU students in Maths, or Physics P27 or P28, this is 2SWS and you can get credits by regular attendance (>50%) and writing at least one report on a talk of your choice during the term -- the Antrag must be submitted to the Prüfungsbüro. If you intend to do so, please contact me at the beginning of the semester.
Wintersemester 24/25
22. Oktober 2024
No seminar (KMPB Doctoral school)
29. Oktober 2024
Bernadette Lessel (Bonn Universität)
On the early history of quantum gravity
Quantum gravity, in the sense of a formal quantization of general relativity, had a first beginning in the year 1930. That year, the Belgian physicist Léon Rosenfeld published a seminal paper called "Zur Quantelung der Wellenfelder" in which he developed Heisenberg and Pauli's recently constructed method to quantize the electromagnetic field in order to apply it to the tetrad formulation of general relativity. In my talk, I aim to shed light on a perhaps surprising crucial historical influence that made this piece of intellectual work possible: that of unified field theory. A purely classical program, most prominently pursued by Albert Einstein and Hermann Weyl, to formally reduce the (classical) electromagnetic field to the gravitational field as described by general relativity.
5. November 2024
Guilherme Feitosa de Almeida (Hannover Universität)
1D Landau-Ginzburg superpotential of big quantum cohomology of CP2
Using the inverse period map of the Gauss-Manin connection associated with QH∗(CP2) and the Dubrovin construction of Landau-Ginzburg superpotential for Dubrovin Frobenius manifolds, we construct a one-dimensional Landau-Ginzburg superpotential for the quantum cohomology of CP2. In the case of small quantum cohomology, the Landau-Ginzburg superpotential is expressed in terms of the cubic root of the j-invariant function. For big quantum cohomology, the one-dimensional Landau-Ginzburg superpotential is given by Taylor series expansions whose coefficients are expressed in terms of quasi-modular forms. Furthermore, we express the Landau-Ginzburg superpotential for both small and big quantum cohomology of QH∗(CP2) in closed form as the composition of the Weierstrass ℘-function and the universal coverings of C \ (Z ⊕ jZ) and C \ (Z ⊕ zZ) respectively. This seminar is based on the results of
arXiv/2402.09574.
12. November 2024
Gernot Akemann (Bielefeld Universität)
Three universality classes in non-Hermitian random matrices
Non-Hermitian random matrices with complex eigenvalues have important applications, for example in open quantum systems in their chaotic regime. It has been conjectured that amongst all 38 symmetry classes of non-Hermitian random matrices only 3 different local bulk statistics exist. This conjecture has been based on numerically generated nearest-neighbour spacing distributions between complex eigenvalues so far. In this talk I will present first analytic evidence for this conjecture. It is based on expectation values of characteristic polynomials in the three simplest representatives for these statistics: the well-known Ginibre ensemble of complex normal matrices, complex symmetric and complex self-dual random matrices. After giving a basic introduction into the complex eigenvalue statistics of the Ginibre ensemble, I will present results for all three ensembles for finite matrix size N as well as in various large-N limits. These are expected to be universal, that is valid beyond ensembles with Gaussian distribution of matrix elements.
This paper is based on joint work with Noah Aygün, Mario Kieburg and Patricia Päßler in arXiv/2410.21032
19. November 2024
Guillaume Baverez (Aix-Marseille Université)
Uniqueness of Malliavin-Kontsevich-Suhov measures
About 20 years ago, Kontsevich & Suhov conjectured the existence and uniqueness of a family of measures on the set of Jordan curves, characterised by conformal invariance and another property called "conformal restriction". This conjecture was motivated by (seemingly unrelated) works of Schramm, Lawler & Werner on stochastic Loewner evolutions (SLE), and Malliavin, Airault & Thalmaier on "unitarising measures". The existence of this family was settled by works of Werner-Kemppainen and Zhan, using a loop version of SLE. The uniqueness was recently obtained in a joint work with Jego. I will start by reviewing the different notions involved before giving some ideas of our proof of uniqueness: in a nutshell, we construct a family of "orthogonal polynomials" which completely characterise the measure. In the remaining time, I will discuss the broader context in which our construction fits, namely the conformal field theory associated with SLE.
26. November 2024 (Unusual room : IRIS 1.207; hybrid format)
Rob Klabbers (HU Berlin)
Elliptic long-range quantum integrable systems
There are at least two seemingly distinct realms of quantum integrability. The first domain is formed by the (short-range) Heisenberg spin chains, connected to the quantum inverse scattering method, which play a role in many different contexts both in physics and mathematics. The second domain is formed by the Calogero-Sutherland models and their deformations, which are families of differential or difference operators associated to root systems, with close ties to harmonic analysis, orthogonal Jack and Macdonald polynomials, and Knizhnik-Zamolodchikov equations. Their integrability follows from a connection to affine Hecke algebras.
Understanding how these two realms are connected goes through the elliptic CS models and their generalisations, which are also interesting in their own right. I will discuss in what way this bridge between worlds is formed and how far we are in building it. Along the way I will try to point out connections to different research areas.
3. Dezember 2024
Niklas Martensen, Jan Pulmann (HU Berlin)
Moduli spaces of flat connections as Kähler spaces, part I
Moduli spaces of flat connections on surfaces appear in physics and geometry. Consequently, they themselves carry various geometric structures. We will recall the constructions of Poisson and complex structures on these moduli spaces, as well as the non-abelian Hodge correspondence. This talk will be mainly a literature review; our goal for the second part is to discuss the problem of inventing "quasi" generalizations of Kähler structures.
10. Dezember 2024
Niklas Martensen, Jan Pulmann (HU Berlin)
Moduli spaces of flat connections as Kähler spaces, part II
Building on the introduction of the various moduli spaces in part I, we will sketch the proof of the non-abelian Hodge correspondence for flat bundles on compact Kähler manifolds, which provides a homeomorphism between the moduli space of (semisimple) flat connections and of (certain) Higgs bundles. Moreover, we will propose the existence of an approach to obtain Kähler structures on the moduli spaces analogous to the quasi-Hamiltonian reduction.
17. Dezember 2024
1. Jan Pulmann (HU Berlin)
Moduli spaces of flat connections as Kähler spaces, part III
Building on earlier sessions, we will propose the existence of an approach to obtain Kähler structures on the moduli spaces analogous to the quasi-Hamiltonian reduction.
2. Silvia Ragni (University of Padua/HU Berlin)
Teleman reconstruction of CohFTs
7. Januar 2025
Seminar cancelled
14. Januar 2025
Türkü Özlüm Çelik (MPI of Molecular Cell Biology and Genetics, Dresden)
Algebraic curves and Grassmannians via the KP Hierarchy
Algebraic curves are fundamental objects in the mathematical sciences. Integrable systems, particularly the Kadomtsev-Petviashvili hierarchy, provide an example of a such phenomenon, and also reaffirm the significance of the Grassmannians. In this talk we will examine connections between algebraic curves and Grassmannians guided by the hierarchy. We will explore these connections within the transcendental, real, and combinatorial algebraic geometry from a computational perspective.
21. Januar 2025
Olivier Marchal (Univ. St-Etienne)
Isomonodromic deformations, quantization and exact WKB
28. Januar 2025
Daniel Roggenkamp (MiS Leipzig)
Rozansky-Witten models as extended defect TQFTs
Very few examples of extended topological quantum field theories are known explicitly. In this talk I will discuss a very explicit construction of the extended TQFTs associated to Rozanksy-Witten models with affine target spaces. I will furthermore explain how to incorporate defects into the extended TQFTs. This can be used for instance to derive the Hilbert spaces of affine Rozansky-Witten models associated to surfaces with arbitrary insertions of defect networks.
4. Februar 2025
Raffaele Vitolo (University of Salento)
Bi-Hamiltonian geometry of WDVV equations: general results
It is known (work by Ferapontov and Mokhov) that a system of N-dimensional WDVV equations can be written as a pair of N-2 commuting quasilinear systems (first-order WDVV systems). In recent years, particular examples of such systems were shown to possess two compatible Hamiltonian operators, of the first and third order. It was also shown that all $3$-dimensional first-order WDVV systems possess such bi-Hamiltonian formalism. We prove that, for arbitrary N, if one first-order WDVV system has the above bi-Hamiltonian formalism, than all other commuting systems do. The proof needs some interesting results on the structure of the WDVV equations that will be discussed as well. (Joint work with S. Opanasenko).
11. Februar 2025
Mikhail Gorskii (Hamburg Universität)
Counting in Calabi-Yau categories
I will discuss a replacement of the notion of homotopy cardinality in the setting of even-dimensional Calabi--Yau categories and their relative generalizations. This includes cases where the usual definition does not apply, such as Z/2-graded dg categories. As a first application, this allows us to define a version of Hall algebras for odd-dimensional Calabi-Yau categories. I will explain its relation to some previously known constructions of Hall algebras. If time permits, I will also discuss another application in the context of invariants of smooth and graded Legendrian links, where we prove a conjecture of Ng-Rutherford-Shende-Sivek relating ruling polynomials with augmentation categories. The talk is based on joint work with Fabian Haiden, arxiv:2409.10154.