Flavors of Amplitudes

mercredi 28 janv. 2026, 13:30 → 17:30 Europe/Paris

Salle Yvette Cauchois (IHP - Bâtiment Perrin)

The Seed seminar of mathematics and physics is a seminar series that aims to foster interactions between mathematicians and theoretical physicists, especially among young researchers. It is structured into three-month thematic periods, the winter 2026 one being on Flavors of Amplitudes.

We open this thematic trimester with an in-person kick-off event at the Institut Henri Poincaré with contributions from Julio Parra-Martinez, Eric Pichon-Pharabod and Roberta Angius.

Registration for attending the event in person is free but mandatory, see Registration in the indico menu.

If you cannot attend the event in person but are interested in following the talks online, please subscribe here to the Seed seminar mailing list, on which Zoom links will be shared for this event and future ones.

13:30 → 14:30 Feynman Periods in Classical and Quantum Field Theory

In this talk I will review the appearance of periods as Feynman integral associated to classical and quantum scattering.
Using some specific examples, I will give a brief survey of the state of the art of the subject and describe in which physical quantities they arise.

Orateur: Julio PARRA-MARTINEZ (IHES)

14:30 → 15:00 Coffee break

15:00 → 16:00 Numerical computations of periods and monodromy representations

The period matrix of a smooth complex projective variety encodes the isomorphism between its singular homology and its algebraic De Rham cohomology. Numerical approximations with sufficient precision of the entries of the period matrix allow to recover some algebraic invariants of the variety. Such approximations can be obtained from an effective description of the homology of the variety, which itself can be obtained from the monodromy representation associated to a generic fibration. I will describe these methods to several hundred digits, and showcase implementations and applications, in particular to computation of the Picard rank of certain K3 surfaces.

Orateur: Eric PICHON-PHARABOD (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany)

Seed_seminar.pdf

16:00 → 16:30 Coffee break

16:30 → 17:30 Thimble decomposition and Wall Crossing Structure for Physical Integrals

A growing body of evidence suggests that the complexity of physical integrals is most naturally understood through geometry. Recent mathematical developments by Kontsevich and Soibelman [arXiv:2402.07343] have illuminated the role of exponential integrals as periods of twisted de Rham cocycles over Betti cycles, offering a structured approach to address this problem in a wide range of settings. In this talk, I will first introduce the key tools underlying this structure and then apply them to show how families of physically relevant integrals, ranging from holomorphic exponentials to logarithmic multivalued functions, can be reformulated within this language. For holomorphic exponents, I will present an explicit decomposition of a family of integrals into thimbles expansion together with a detailed analysis of the wall-crossing structure behind the analytic continuation of its relevant parameter. Finally, I will discuss the generalization to multivalued functions, which provides the appropriate framework for describing Feynman integrals in special representations.
In this context, the thimble decomposition is expected to match the decomposition into Master Integrals, while the study of the wall-crossing structure yields a precise count of independent Master Integrals (or periods), circumventing complications arising from Stokes phenomena

Orateur: Roberta ANGIUS (Institute for Theoretical Physics, University of Hamburg, Germany)

Angius_Seed.pdf