Date/Time
29 August 2027 - 3 September 2027
Organized by
Damien Calaque (U. of Montpellier), Clément Dupont (U. of Montpellier), and Erik Panzer (U. of Oxford)
Event page & registration
https://indico.global/event/16596/
Description
Integrals associated with graphs appear in many areas of mathematics and physics. In particle physics, Feynman integrals encode the interactions of elementary particles but also reveal rich algebraic and geometric structures. In geometry and topology, graph integrals play a central role in deformation quantization, homotopy theory, and the study of graph complexes. Despite arising from different motivations, these integrals share strikingly similar features and often point to the same underlying phenomena.
Recent years have seen remarkable progress in uncovering the hidden structure of these objects. Feynman integrals can be interpreted as periods of algebraic varieties, bringing in tools from Hodge theory, motives, and Galois theory. Combinatorial approaches have produced discrete invariants and new computational methods. Meanwhile, geometric and homotopical perspectives have linked graph integrals to configuration spaces, operads, and the Grothendieck–Teichmüller Lie algebra, revealing unexpected connections with number theory and arithmetic geometry.
This conference will explore these diverse yet deeply related viewpoints, with the goal of highlighting the common geometric thread that runs through them. By bringing together researchers from particle physics, algebraic and arithmetic geometry, topology, homotopy theory, and combinatorics, the event aims to foster new interactions and identify unifying principles. The study of graph integrals thus serves as a meeting point where ideas from multiple disciplines converge, offering fresh insight into both mathematics and physics.
Location
SwissMAP Research Station, Les Diablerets, Switzerland
