Name: Geometries and Special Functions for Physics and Mathematics
Start: 2023-03-20T09:00:00+01:00
End: 2023-03-24T16:00:00+01:00
Location: Bethe Center for Theoretical Physics

Geometries and Special Functions for Physics and Mathematics

from Monday, 20 March 2023 (09:00) to Friday, 24 March 2023 (16:00)

Monday, 20 March 2023

10:00 Registration & Coffee
Registration & Coffee
10:00 - 11:00
Room: Seminar Room
11:00 Period geometry of Calabi-Yau n-folds for Feynman integrals - Albrecht Klemm
Period geometry of Calabi-Yau n-folds for Feynman integrals
- Albrecht Klemm
11:00 - 12:00
Room: Seminar Room This introduction aims at the pragmatic understanding of those differential and analytic properties of periods -- and chain integrals on Calabi-Yau n-folds that facilitate the evaluation of parametric higher loop Feynman integrals. In particular we exhibit the application of the Riemann bilinear relations, the Griffiths transversality, the Griffith reduction method, the Gauss Manin connection of GKZ systems as well as some aspects of mixed Hodge Structures and monodromy properties to the evaluation of simple classes of parametric higher loop Feynman integrals and amplitudes.
12:00 Lunch break
Lunch break
12:00 - 13:30
13:30 Geometries, Iterated Period Integrals and Feynman Integrals - Christoph Nega
Geometries, Iterated Period Integrals and Feynman Integrals
- Christoph Nega
13:30 - 14:30
Room: Seminar Room
14:30 Coffee Break
Coffee Break
14:30 - 15:30
Room: Seminar Room
15:30 Calabi-Yau operators and p-adic zeta function - Masha Vlasenko
Calabi-Yau operators and p-adic zeta function
- Masha Vlasenko
15:30 - 16:30
Room: Seminar Room
17:00 Reception
Reception
17:00 - 19:00
Room: Seminar Room
Tuesday, 21 March 2023
09:30 Mould theory and the elliptic associator - Leila Schneps
Mould theory and the elliptic associator
- Leila Schneps
09:30 - 10:30
Room: Seminar Room
10:30 Coffee Break
Coffee Break
10:30 - 11:00
Room: Seminar Room
11:00 Single-valued polylogarithms and modular forms from zeta generators - Oliver Schlotterer
Single-valued polylogarithms and modular forms from zeta generators
- Oliver Schlotterer
11:00 - 12:00
Room: Seminar Room
12:00 Lunch Break
Lunch Break
12:00 - 13:30
13:30 The algebra of elliptic hyperlogarithms - Federico Zerbini
The algebra of elliptic hyperlogarithms
- Federico Zerbini
13:30 - 14:30
Room: Seminar Room
14:30 Coffee Break
Coffee Break
14:30 - 15:30
Room: Seminar Room

15:30 My Favorite Problem Session: Brödel & Pögel
My Favorite Problem Session: Brödel & Pögel
15:30 - 16:30
Room: Seminar Room Johannes Brödel: "What does it need for general amplitude recursions?" Sebastian Pögel: "Automorphic forms for Calabi—Yau Feynman Integrals"
Wednesday, 22 March 2023
09:30 Calabi-Yau Operators: geometry and arithmetic - Duco van Straten
Calabi-Yau Operators: geometry and arithmetic
- Duco van Straten
09:30 - 10:30
Room: Seminar Room
10:30 Coffee Break
Coffee Break
10:30 - 11:00
Room: Seminar Room

11:00 My Favorite Problem Session: Tancredi & von Hippel
My Favorite Problem Session: Tancredi & von Hippel
11:00 - 12:00
Room: Seminar Room Lorenzo Tancredi: "Leading Singularities and canonical bases beyond d-log forms" Matt von Hippel: "Alphabets for all n and L: what are we asking for?"

12:00 Lunch Break
Lunch Break
12:00 - 13:30

13:30 My Favorite Problem Session: Charlton & Zickert
My Favorite Problem Session: Charlton & Zickert
13:30 - 14:30
Room: Seminar Room Steven Charlton: tba Christian Zickert: "Holomorphic 1-forms, motivic complexes, and hyperbolic 5-manifolds"

14:30 Coffee Break
Coffee Break
14:30 - 15:30
Room: Seminar Room
15:30 Cluster polylogarithms (Virtual) - Daniil Rudenko
Cluster polylogarithms (Virtual)
- Daniil Rudenko
15:30 - 16:30
Room: Seminar Room I will start with a brief introduction to polylogarithms and the Goncharov Program. Next, I will define cluster polylogarithms associated with an arbitrary cluster algebra and describe their classification in type A. Then I will explain, how cluster polylogarithms can be used to prove an "unobstructed" part of the Goncharov depth conjecture.
18:30 Dinner at the restaurant "Gasthaus im Stiefel"
Dinner at the restaurant "Gasthaus im Stiefel"
18:30 - 21:30
Thursday, 23 March 2023
09:30 Cluster adjacency for amplitudes from Gröbner fans - James Drummond
Cluster adjacency for amplitudes from Gröbner fans
- James Drummond
09:30 - 10:30
Room: Seminar Room
10:30 Coffee Break
Coffee Break
10:30 - 11:00
Room: Seminar Room
11:00 Grassmannian Cluster Algebras and Their Symmetries - Dani Kaufman
Grassmannian Cluster Algebras and Their Symmetries
- Dani Kaufman
11:00 - 12:00
Room: Seminar Room
12:00 Lunch Break
Lunch Break
12:00 - 13:30

13:30 My Favorite Problem Session: Greenberg & Gürdogan
My Favorite Problem Session: Greenberg & Gürdogan
13:30 - 14:30
Room: Seminar Room Zachary Greenberg: “Polylogarithm Relations in Finite Type Cluster Algebras” Ömer Gürdoğan: "Cosmic Galois properties of q functions"

15:30 Coffee and Cake
Coffee and Cake
15:30 - 16:10
Room: Seminar Room
16:15 Bethe Colloquium: Cluster integrable systems and the tame symbol - Vladimir Fock
Bethe Colloquium: Cluster integrable systems and the tame symbol
- Vladimir Fock
16:15 - 17:15
Room: Seminar Room Cluster integrable systems discovered by Goncharov and Kenyon is an approach to a large class of integrable systems starting with the Poncelet porism discovered 200 years ago to modern spinning tops, Toda lattices and in its quantum versions, which are not yet very well understood, lattice models, Hofstadter's butterfly and many others. The cluster approach to those systems interprets their phase spaces either as the space of configurations of flags in an infinite dimensional space or as the space of pairs (spectral curve, line bundle on it). This dual approach allows to study the systems in detail and of course to find their classical solutions. However, the quantization of these systems does not go as smoothly as its classical part. We will suggest a quasi-classical approach to those systems using a tool borrowed from number theory namely the tame symbol. In its simplest incarnation, tame symbol is a multiplicative analogue of the residue. We use it to formulate the Bohr-Sommerfeld condition on the Lagrangian subvarieties for the integrable systems, thus giving the quasi-classical spectrum with the wave function expressed in terms of the dilogarithm. If time permits we will speak about some elementary applications of the tame symbol.
Friday, 24 March 2023
09:30 Motivic Galois theory for Feynman integrals via twisted cohomology (Virtual) - Clément Dupont
Motivic Galois theory for Feynman integrals via twisted cohomology (Virtual)
- Clément Dupont
09:30 - 10:30
Room: Seminar Room I will report on ongoing joint work with Francis Brown, Javier Fresán, and Matija Tapušković, in which we prove that dimensionally regularized Feynman integrals are closed under the action of the motivic Galois group, termwise in the epsilon expansion. This fits into a larger framework of motivic Galois theory for algebraic Mellin transforms, where the main protagonists are formal versions of « twisted » cohomology groups for algebraic varieties.
10:30 Coffee Break
Coffee Break
10:30 - 11:00
Room: Seminar Room
11:00 Symmetries and twisted cohomology - Stefan Weinzierl
Symmetries and twisted cohomology
- Stefan Weinzierl
11:00 - 12:00
Room: Seminar Room
12:00 The End
The End
12:00 - 12:20
Room: Seminar Room