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
Wintersemester 2025-26
21. Oktober 2025
Matijn Francois (University of Geneva)
On the open topological strings/spectral theory correspondence
The topological string/spectral theory correspondence establishes a precise, non-perturbative duality between topological strings on local Calabi–Yau threefolds and the spectral theory of quantized mirror curves. This duality has been rigorously formulated for the closed string sector, but the open string sector is less understood. In this talk, I will explain how one can use open-string partition functions to construct true eigenfunctions for the quantized mirror curve of local F₀. We will then discuss the four-dimensional limit, underlining the implications of the topological string/spectral theory correspondence for spectral problems relating four-dimensional supersymmetric gauge theories to the quantization of their Seiberg–Witten curves.
28. Oktober 2025
Lasse Merkens (HU)
Renormalization group flows from defects in N = 1 minimal models
Leveraging the structure of non-invertible symmetries, we construct a family of
renormalization group flows connecting N = 1 superconformal minimal models:
SM(p, kp + I) → SM(p, kp − I). The triggering operator is G−1/2ϕ(1,2k+1). A key ele-
ment of our argument is that the topological defect lines of the bosonic coset theory
persist in the fermionic case. These flows represent a supersymmetric generalization
of the Virasoro flows discovered by Tanaka and Nakayama and include the previ-
ously known unitary flows (Pogossyan, k = 1, I = 2) as a special case. Furthermore,
we demonstrate the completeness of this family; any flow between models SM(p, q)
and SM(p, q′) can be obtained by composing these fundamental flows.
4. November 2025
Xavier Blot (Unversiteit van Amsterdam)
On the DR-DZ equivalence, and beyond
Witten’s conjecture, proved by Kontsevich, predicted that the Gromov–Witten invariants of a point are governed by the KdV hierarchy. In this talk, I will explain how the DR–DZ equivalence extends this result by constructing the Dubrovin–Zhang (DZ) hierarchy, which governs the Gromov–Witten invariants of any smooth projective variety (and more generally, any cohomological field theory). I will also discuss the equivalence between the DZ and Double Ramification (DR) hierarchies, and, if time allows, their equivalence to new hierarchies associated with the Chiodo class.
This is based on joint works with Danilo Lewanski, Adrien Sauvaget and Sergey Shadrin.
11. November 2025
Taro Kimura (Université Bourgogne Europe)
Non-perturbative Schwinger-Dyson equation for DT/PT vertices
Non-perturbative Schwinger-Dyson (SD) equation is a discrete analog of the loop equation appearing in matrix models and related models. It was initially discussed for the gauge theory partition function and, as in the case of the matrix models, it has a close relation to the underlying infinite-dimensional symmetry of the system. In this talk, I'd like to discuss the non-perturbative SD equation for the higher-dimensional gauge theory partition function, interpreted as the generating function of the DT and PT invariants (DT/PT vertices) for CY3 and CY4 varieties, and address its underlying quantum algebraic structure, which is a consequence of geometric representation theory of the corresponding algebra.
18. November 2025
Piotr Sulkowski (Warsaw University)
Wall-crossing, Schur indices and symmetric quivers
I will show that symmetric quivers encode various
observables of 4d N=2 theories related to wall-crossing phenomena. The
observables in question include (wild) Donaldson-Thomas invariants, as
well as Schur indices, which at the same time are known to reproduce
characters of 2d conformal field theories. Furthermore, symmetric
quivers of our interest encode 3d N=2 theories, therefore all these
relations can be interpreted as a web of dualities between 2d, 3d, and
4d systems.
25. November 2025
Gaëtan Borot (HU Berlin) - (date could be moved!)
Panorama of matrix models and topological recursion I
This is crash course which aims at explaning various aspects of: random matrix ensembles and Coulomb gases, loop equations, spectral curves, topological recursion, maps, free probability, how they fit together and pose some open problems.
2. Dezember 2025
Nikolay Barashkov (MiS Leipzig)
Small deviations of Gaussian multiplicative chaos and the free energy of
the two-dimensional massless Sinh-Gordon model
We derive a bound on the probability that the total mass of Gaussian multiplicative
chaos measure obtained from a Gaussian field with zero spatial average, is small. We also give the probabilistic path integral formulation of the massless Sinh-Gordon model on a torus of side length R, and study its partition function R tends to infinity. We apply the small deviation bounds for Gaussian multiplicative chaos to obtain lower and upper bounds for the logarithm of the partition function, leading to the existence of a non-zero and finite subsequential infinite volume limit for the free energy.
9. Dezember 2025
Gaëtan Borot (HU Berlin) - (date could be moved!)
Panorama of matrix models and topological recursion II
This is crash course which aims at explaning various aspects of: random matrix ensembles and Coulomb gases, loop equations, spectral curves, topological recursion, maps, free probability, how they fit together and pose some open problems.
16. Dezember 2025
Dang Dang (HU Berlin)
Koszul duality in twisted QFTs
This talk gives an introduction to twisting procedures in supersymmetric field theories, with an emphasis on their modern mathematical formulation. We will then review the notion of Koszul duality, explaining how it captures dual descriptions of local operators and boundary conditions in twisted quantum field theories. Finally, we illustrate these ideas in the case of the B-twist of a two-dimensional N=(2,2) theory, where the resulting topological model leads to a familiar differential graded algebra of polyvector fields and its Koszul dual.
6. Januar 2026
Gaëtan Borot (HU Berlin) - (date could be moved!)
Panorama of matrix models and topological recursion III
This is crash course which aims at explaning various aspects of: random matrix ensembles and Coulomb gases, loop equations, spectral curves, topological recursion, maps, free probability, how they fit together and pose some open problems.
13. Januar 2026
Kein Seminar
20. Januar 2026
Cancelled
27. Januar 2026
Maciej Dolega (Institute of Mathematics, Polish Academy of Sciences)
Discrete N-particle systems at high temperature through Jack generating functions
We discuss random discrete N-particle systems with the deformation (inverse temperature) parameter θ. We find necessary and sufficient conditions for the Law of Large Numbers as their size N tends to infinity simultaneously with the inverse temperature going to zero. We apply the general framework to obtain the LLN for a large class of Markov chains of N nonintersecting particles with interaction of log-gas type, and the LLN for the multiplication of Jack polynomials, as the inverse temperature tends to zero. We express the answer in terms of novel one-parameter deformations of cumulants and discuss their relation to quantized free probability and continuous log-gas systems. If time permits, we will discuss a crystallization phenomenon observed in this regime and describe it in terms of the real-rootedness of certain special functions. Based on joint work with Cesar Cuenca.
3. Februar 2026
Cancelled
10. Februar 2026
Andrea Brini (Sheffield University)
On the conifold gap for the local projective plane
The conifold gap conjecture asserts that the polar part of the Gromov-Witten potential of a Calabi-Yau threefold near its conifold locus has a universal expression described by the logarithm of the Barnes G-function. In this talk I will describe a proof of the conifold gap conjecture for the local projective plane, whereby the higher genus conifold Gromov-Witten generating series of local P2 are related to the thermodynamics of a certain statistical mechanical ensemble of repulsive particles on the positive half-line. As a corollary, this establishes the all-genus mirror principle for local P2 through the direct integration of the BCOV holomorphic anomaly equations.
Semesterpause
Sommersemester 2026
21. April 2026 (SPECIAL TIME : 12-13Uhr)
Pierrick Bousseau (Oxford University)
Boomerangs, elliptic curves and del Pezzo surfaces
We study boomerangs in the derived category of an elliptic curve C. These are filtrations of the zero object whose factors are polystable objects with strictly increasing phase. The numerical invariants of a boomerang are given by the Chern characters of the direct summands of these factors, which together determine a lattice polygon. When this polygon is a T-polygon, we show that the moduli space of boomerangs with a fixed collection of polystable factors is the complement of an anti-canonical embedding of C in a del Pezzo surface Z. The proof uses exceptional collections on Z, and the result has applications to the theory of q-Painlevé equations. This is joint work in progress with Tom Bridgeland and Luca Giovenzana.
28. April 2026
Demian Goos (HU Berlin)
Analysis of the mathematical content of recently discovered letters from Dedekind to Cantor
The correspondence between Georg Cantor and Richard Dedekind plays a pivotal role in the understanding of the emergence of set theory. It is in this exchange that the foundational concepts and key results have been developed. Until recently, only Cantor's letters in Dedekind's Nachlass were available for research. However, in the past months Dedekind's side of the correspondence has been discovered.
In this seminar the main mathematical results of Dedekind's letters will be analyzed. Particular attention will be paid to the letters from November 30 and December 26, both 1873. This analysis will then open the room for a discussion concerning the authorship of Cantor's seminal 1874 paper that kicked off set theory, as the letters reveal that a part of the paper were, in fact, results obtained by Dedekind.
5. Mai 2026
Damien Simon (Sorbonne Universite)
Operadic structure of spatial Markov processes
The study of Markov chains intertwins probability theory and classical linear algebra, as a consequence of the 1D Markov property. When considering two-dimensional models of statistical mechanics, a spontaneous reflex is often to split the 2D geometry into a 1+1 geometry through the transfer matrix and reuse 1D result. In the present talk, we will consider the 2D Markov property of such models on its own and see how it invites to replace classical linear algebra by a more general operadic structure. In particular, we will focus on how new practical computations and equations emerge from this new formalism. We illustrate them on discrete-lattice Gaussian models.
12. Mai 2026
Burkhard Eden
The off-shell one and two-loop box recovered from intersection theory
We advertise intersection theory for generalised hypergeometric functions as a means of evaluating Mellin-Barnes representations. As an example, we study two-parameter representations of the off-shell one- and two-loop box graphs in exactly four-dimensional configuration space. Closing the integration contours for the MB parameters we transform these into double sums. Polygamma functions in the MB representation of the double box and the occurrence of higher poles are taken into account by parametric differentiation. Summing over any one of the counters results into a p+1Fp that we replace by its Euler integral representation. The process can be repeated a second time and results in a two- or four-parameter Euler integral, respectively. We use intersection theory to derive Pfaffian systems of equations on related sets of master integrals and solve for the box and double box integrals reproducing the known expressions. Finally, we use a trick to re-derive the double box from a two-parameter Euler integral. This second computation requires only very little computing resources.
19. Mai 2026
Sara Perletti (SISSA)
On the integrability of non-diagonalisable systems of hydrodynamic type
Building on the interplay between geometry and the theory of integrable systems, we will explain how Tsarev’s seminal work on diagonalisable systems of hydrodynamic type can be extended to the non-diagonalisable setting. By employing the F-manifold framework, which expands the theory of Dubrovin-Frobenius manifolds, we will formulate a generalised hodograph method for non-diagonalisable systems of hydrodynamic type, leading to the uncovering of the Darboux-Tsarev class. Time permitting, we will discuss semi-Hamiltonian properties of these systems and present
explicit examples.
26. Mai 2026
No seminar
2. Juni 2026
Nikolai Kuchumov (Abo Akademi)
Limit shapes and harmonic tricks
The talk will be on the tangent plane method — a novel method for analysys of limit shapes of the dimer model. It will consist of three parts. In the first part, we will briefly introduce the dimer model and the necessary concepts including the associated variational problem. The second part will focus on the underlying geometry using harmonic parametrization. In the third part, we will consider two specific examples of limit shape parametrized by a modular parameter: the Aztec diamond with a hole, and a hexagon with a hexagonal hole. The talk is based on arXiv/2603.21255
9. Juni 2026
Lasse Merkens (HU Berlin)
A bijective derivation of topological recursion for maps
We will discuss the combinatorics of maps, which is known to be solved by topological recursion. The usual derivation relies on analytical methods, leaving the combinatorial meaning of the recursion open. To obtain such a meaning, we aim to find a procedure of excising a pair of pants from a given map. This will be achieved by iteratively applying Tutte's procedure until we change topology. The resulting combinatorial identity is equivalent to Eynard-Orantin topological recursion, where the recursion kernel counts the excised pairs of pants. We extend the analysis to maps with self-avoiding loops and stuffed maps, where we give a combinatorial interpretation of the appearing blobs in the latter.
16. Juni 2026
Bertrand Eynard (IPhT CEA Saclay)
An approach to CFT from topological recursion and integrable systems
Conformal field theories (CFT) can be defined by a set of axioms (bootstrap axioms) and a challenge is to find mathematical objects satifying the axioms. Topological recursion (TR) is a procedure that, to a spectral curve (a complex curve immersed in a cotangent space) associates a sequence of meromorphic differentials. Using this sequence one can produce formal series that satisfy the axioms of CFT. Moreover this establishes a link with integrable systems.
23. Juni 2026
Anna Hartkopf (FU Berlin, MIP.labor)
Art as a medium in science communication of mathematics: research and practice
Mathematics is a highly abstract science with its own language and notation that are not easily accessible. Nevertheless, the culture and fascination of mathematics can be experienced in other ways. An important medium for this is art, which facilitates access and understanding on different levels.
In my work and research on science communication in mathematics, artistic elements serve both as an important component of communication -- for example, in the form of design -- and as an opportunity for participation through artistic activity.
In my talk, I will present how I expand the concept of citizen science to include an artistic dimension, and I would like to illustrate this using the case study of Polytopia. In this project, participants can “adopt” a polyhedron by giving it a name. Each polyhedron has a unique net that can be printed out and assembled.
At the MIP.labor experimental lab, which is based at Freie Universität Berlin and funded by the Klaus Tschira Foundation, we develop innovative formats for science communication. We develop these formats using our own toolkit: We incorporate current and established research in science communication, integrate elements of design thinking, and continually adapt to new insights. In addition, we provide scientific guidance throughout the format development process and conduct detailed evaluations of individual formats.
30. Juni 2026
Kein Seminar, sondern Institutskolloqium, 15-16Uhr, RUD 25 1.013
Pascal Hubert (Universite Aix-Marseille, CIRM)
Complexity of polygonal billiards
Given a polygon in the plane, one can code a billiard trajectory by the sequence of sides its intersects. The complexity is the number of words of a given length we get this way starting from any point with any initial direction. It is a measure of the disorder of the dynamical system. Katok considered this problem as one of the most resistant one in dynamics. For rational polygons, following results of Howard Masur, one can get cubic lower and upper bounds. I will explain recent results obtained with Athreya and Troubetzkoy. For regular polygons, we get a cubic asymptotic behavior for this quantity. With Athreya, Forni and Matheus, we find an error term for this counting.
7. Juli 2026
Alexander Alexandrov (IBS Pohang)
KP integrability of topological recursion
Topological recursion is a powerful tool in mathematical physics with applications to various problems in enumerative geometry, including intersection theory on moduli spaces and Hurwitz numbers. In this talk, I will discuss the KP integrability of topological recursion, which arises naturally in the context of the x-y swap relation. I will explain how this KP integrability can be described via certain integral transforms, leading to Kontsevich-type matrix models.
14. Juli 2026
Motohico Mulase (UC Davis)
TBA