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

• Albrecht Klemm

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.

Geometries, Iterated Period Integrals and Feynman Integrals

• Christoph Nega

Room: Seminar Room

Calabi-Yau operators and p-adic zeta function

• Masha Vlasenko

Room: Seminar Room

Mould theory and the elliptic associator

• Leila Schneps

Room: Seminar Room

Single-valued polylogarithms and modular forms from zeta generators

• Oliver Schlotterer

Room: Seminar Room

The algebra of elliptic hyperlogarithms

• Federico Zerbini

Room: Seminar Room

My Favorite Problem Session: Brödel & Pögel Room: Seminar Room Johannes Brödel: "What does it need for general amplitude recursions?" Sebastian Pögel: "Automorphic forms for Calabi—Yau Feynman Integrals"

Calabi-Yau Operators: geometry and arithmetic

• Duco van Straten

Room: Seminar Room

My Favorite Problem Session: Tancredi & von Hippel 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?"

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

Cluster polylogarithms (Virtual)

• Daniil Rudenko

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.

Cluster adjacency for amplitudes from Gröbner fans

• James Drummond

Room: Seminar Room

Grassmannian Cluster Algebras and Their Symmetries

• Dani Kaufman

Room: Seminar Room

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

Bethe Colloquium: Cluster integrable systems and the tame symbol

• Vladimir Fock

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.

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

• Clément Dupont

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.

Symmetries and twisted cohomology

• Stefan Weinzierl

Room: Seminar Room