Geometries and Special Functions for Physics and Mathematics

20 Mar 2023, 09:00 → 24 Mar 2023, 16:00 Europe/Berlin

Seminar Room (Bethe Center for Theoretical Physics)

1_Gruppenkarte.pdf

GeometriesFoto.jpg

GeometriesFoto_Klein.jpg

Menu Stiefel english.pdf

Poster_GeometriesAndSpecialFunctions.jpg

Poster_GeometriesAndSpecialFunctions.pdf

ScheduleBetheForum.pdf

Monday 20 March

10:00 Registration & Coffee

1 Period geometry of Calabi-Yau n-folds for Feynman integrals

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.

Speaker: Albrecht Klemm

KlemmBonn.pdf

12:00 Lunch break

2 Geometries, Iterated Period Integrals and Feynman Integrals

Speaker: Christoph Nega

NegaBonn.pdf

14:30 Coffee Break

3 Calabi-Yau operators and p-adic zeta function

Speaker: Masha Vlasenko

VlasenkoBonn.pdf

17:00 Reception

Tuesday 21 March

4 Mould theory and the elliptic associator

Speaker: Leila Schneps

SchnepsBonn.pdf

10:30 Coffee Break

5 Single-valued polylogarithms and modular forms from zeta generators

Speaker: Oliver Schlotterer

SchlottererBonn.pdf

12:00 Lunch Break

6 The algebra of elliptic hyperlogarithms

Speaker: Federico Zerbini

14:30 Coffee Break

7 My Favorite Problem Session: Brödel & Pögel

Johannes Brödel: "What does it need for general amplitude recursions?"

Sebastian Pögel: "Automorphic forms for Calabi—Yau Feynman Integrals"

PögelBonn.pdf

Wednesday 22 March

8 Calabi-Yau Operators: geometry and arithmetic

Speaker: Duco van Straten

VanStratenBonn.pdf

10:30 Coffee Break

9 My Favorite Problem Session: Tancredi & von Hippel

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?"

TancrediBonn.pdf

12:00 Lunch Break

10 My Favorite Problem Session: Charlton & Zickert

Steven Charlton: tba

Christian Zickert: "Holomorphic 1-forms, motivic complexes, and hyperbolic 5-manifolds"

CharltonBonn.pdf

14:30 Coffee Break

11 Cluster polylogarithms (Virtual)

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.

Speaker: Daniil Rudenko

18:30 Dinner at the restaurant "Gasthaus im Stiefel"

Thursday 23 March

12 Cluster adjacency for amplitudes from Gröbner fans

Speaker: James Drummond

10:30 Coffee Break

13 Grassmannian Cluster Algebras and Their Symmetries

Speaker: Dani Kaufman

KaufmanBonn.pdf

12:00 Lunch Break

14 My Favorite Problem Session: Greenberg & Gürdogan

Zachary Greenberg: “Polylogarithm Relations in Finite Type Cluster Algebras”

Ömer Gürdoğan: "Cosmic Galois properties of q functions"

15:30 Coffee and Cake

15 Bethe Colloquium: Cluster integrable systems and the tame symbol

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.

Speaker: Vladimir Fock

Friday 24 March

16 Motivic Galois theory for Feynman integrals via twisted cohomology (Virtual)

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.

Speaker: Clément Dupont

DupontBonn.pdf

10:30 Coffee Break

17 Symmetries and twisted cohomology

Speaker: Stefan Weinzierl

WeinzierlBonn.pdf

12:00 The End