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Events
Positive Geometry in Particle Physics and Cosmology

conference

12/02/2024 16/02/2024

Positive Geometry in Particle Physics and Cosmology

MPI für Mathematik in den Naturwissenschaften Leipzig

E1 05 (Leibniz-Saal)

This is the kick-off workshop for the ERC-synergy project with the same title which starts in June 2024. Lectures and discussions will explore novel mathematical structures in fundamental physics, ranging from elementary particles to the Big Bang, and revealing hidden principles beyond quantum mechanics and spacetime. We will focus on positive geometries, such as amplituhedron, and their recent applications to scattering amplitudes and cosmology. The program of the week will begin with plenary presentations by international experts, and it will conclude with shorter research talks, informal discussions, and intense working groups. To foster interactions with Leipzig University, Daniel Baumann (University of Amsterdam) will give the Physics Colloquium on Tuesday, and Nima Arkani-Hamed (IAS Princeton) will give the Felix-Klein Colloquium on Wednesday.

Limited travel funding can be provided for early-career participants such as postdoctoral researchers and PhD students. Applicants are expected to submit a brief academic CV and a motivation letter. The application for funding is included in the registration form.

The deadline for registering will be December 15, 2023.

Speakers

Nima Arkani-Hamed

IAS Princeton

Daniel Baumann

University of Amsterdam

Hofie Hannesdottir

IAS Princeton

Pierre Lairez

INRIA Paris

Pierpaolo Mastrolia

University of Padua

Saiei-Jaeyeong Matsubara-Heo

Kumamoto University

Scott Melville

Queen Mary University of London

Sebastian Mizera

IAS Princeton

Enrico Pajer

University of Cambridge

Matteo Parisi

Harvard University / IAS Princeton

Guilherme Pimentel

Scuola Normale Pisa

Giulio Salvatori

MPI for Physics, Munich

Anna-Laura Sattelberger

KTH Royal Institute of Technology

Oliver Schlotterer

Uppsala University

Carsten Schneider

RISC, Johannes Kepler University, Linz

Melissa Sherman-Bennett

Massachusetts Institute of Technology / UC Davis

Marcus Spradlin

Harvard / Brown University

Ran Tessler

Weizmann Institute of Science

Jaroslav Trnka

UC Davis

Feb 12, 2024
09:00	Johannes Henn (Max Planck Institute for Physics, Munich, Munich), Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences, Leipzig) Opening remarks
09:30	Marcus Spradlin (Harvard / Brown University) Some aspects of positive particle physics I will review (and highlight open problems concerning) several aspects of the still rather mysterious appearance of positive geometries in quantum field theory scattering amplitudes, including connections between cluster algebras, symbol alphabets, and the amplituhedron.
10:30	Coffee break
11:00	Ran Tessler (Weizmann Institute of Science) Positivity in open Gromov-Witten theory
12:00	Hofie Hannesdottir (IAS Princeton) The geometry of infrared divergences
13:00	Lunch
14:00	Working groups
15:30	Coffee break
16:00	Pierre Lairez (INRIA Paris) The 22 periods of a quartic surface A smooth complex quartic surface in the projective 3-space defines 22 complex numbers called periods. The integer relations between them describe the algebraic curves lying on this surface, in the form of the Néron-Severi group. I will explain how to compute numerically the periods with thousands of digits of precision and recover heuristically the lattice of integer relations. This provides an insight on the Néron-Severi group that purely algebraic methods fail to provide. This is joint work with Eric Pichon-Pharabod (Inria), Emre Sertöz (Leiden University) and Pierre Vanhove (CEA).
17:00	Matteo Parisi (Harvard University / IAS Princeton) Combinatorics of amplituhedra - scattering amplitudes and cluster algebras
Feb 13, 2024
09:00	Scott Melville (Queen Mary University of London) Positive phenomenology in cosmology
10:00	Giulio Salvatori (MPI for Physics, Munich) A positive path from Teichmüller spaces to scattering amplitudes
11:00	Coffee break
11:30	Melissa Sherman-Bennett (Massachusetts Institute of Technology / UC Davis) Cluster algebras and tilings of amplituhedra
12:30	Lunch
13:30	Carsten Schneider (RISC, Johannes Kepler University, Linz) Computer algebra and Feynman integrals
14:30	Guilherme Pimentel (Scuola Normale Pisa) An invitation to cosmological correlators and differential equations I will give a general and gentle introduction to cosmological correlation functions — their usage as a tool to understand the beginning of the universe, and their connection to particle physics and scattering amplitudes. Then I will show in a toy model of cosmology a beautiful mathematical structure of differential equations that control the strength of the correlations as a function of distances in the sky. In this setup, time evolution emerges as a solution to these static differential equations.
16:30	Physics Colloquium: Daniel Baumann (University of Amsterdam) Positive geometry in cosmology: University of Leipzig, Hörsaal für Theoretische Physik, Linnéstraße 5
18:30	Conference dinner
Feb 14, 2024
09:00	Sebastian Mizera (IAS Princeton) Modeling mathematical language
10:00	Anna-Laura Sattelberger (KTH Royal Institute of Technology) Shift relations among Feynman integrals from parametric annihilators Feynman integrals are Mellin integrals: they are the Mellin transform of the graph polynomial of the Feynman diagram taken to the power -d/2, if d denotes the dimension of Minkowski spacetime. It is important to construct relations among Feynman integrals in different dimensions of spacetime. One way to construct such relations is via integration by parts techniques. These IBP relations can be explained via cohomological theories. Also techniques from the theory of D-modules help to construct shift relations, namely by means of Bernstein-Sato operators and s-parametric annihilators, which I explain in this talk. This talk is based on the joint work arXiv:2208.08967 with D. Agostini, C. Fevola, and S. Telen, as well as on ongoing work.
11:00	Coffee break
11:30	Pierpaolo Mastrolia (University of Padua) Intersection numbers and fundamental interactions
12:30	Lunch
13:30	Saiei-Jaeyeong Matsubara-Heo (Kumamoto University) Hypergeometric study of Feynman integrals
14:30	Jaroslav Trnka (UC Davis) Grassmannians and non-planar graphs
16:30	Felix-Klein-Kolloquium: Nima Arkani-Hamed (IAS Princeton) Spacetime, quantum mechanics and positive geometry: University of Leipzig, Felix-Klein-Hörsaal, Paulinum, Augustusplatz 10
Feb 15, 2024
09:00	Short talks
11:00	Coffee break
11:30	Enrico Pajer (University of Cambridge) A timeless history of time
12:30	Lunch break
14:30	Oliver Schlotterer (Uppsala University) Iterated integrals on Riemann surfaces of different genus The multitude of integrals encountered in perturbative quantum field theory and string theory calls for systematic studies of function spaces that close under taking primitives. For integrations on the sphere — Riemann surfaces of genus zero — this is accomplished by multiple polylogarithms which had huge impact on Feynman integrals and string amplitudes. The more challenging iterated integrals on genus-one surfaces seen in various physics contexts were recently harnessed by means of elliptic polylogarithms. After reviewing the Brown-Levin formulation of elliptic polylogarithms, I will present a generalization to Riemann surfaces of arbitrary genus. The construction of higher-genus polylogarithms in this talk is based on a flat connection built from convolutions of Arakelov Green functions on the surface.
15:30	Coffee break
16:00	Working groups
Feb 16, 2024
09:00	Short talks
11:00	Working groups

Positive Geometry in Particle Physics and Cosmology

Speakers

Nima Arkani-Hamed

Daniel Baumann

Hofie Hannesdottir

Pierre Lairez

Pierpaolo Mastrolia

Saiei-Jaeyeong Matsubara-Heo

Scott Melville

Sebastian Mizera

Enrico Pajer

Matteo Parisi

Guilherme Pimentel

Giulio Salvatori

Anna-Laura Sattelberger

Oliver Schlotterer

Carsten Schneider

Melissa Sherman-Bennett

Marcus Spradlin

Ran Tessler

Jaroslav Trnka

Scientific Organizers

Johannes Henn

Bernd Sturmfels

Administrative Contact

Mirke Olschewski