13.05.24 17.05.24

Combinatorial Algebraic Geometry from Physics

This one-week course offers an introduction to recent advances in combinatorics and algebraic geometry that were inspired by particle physics. How can quantum field theory help with enumerating graphs? How does scattering of elementary particles lead to the study of semialgebraic subsets of configuration spaces? We will learn about these questions and more in the following two lecture series.

Michael Borinsky: Counting graphs using quantum field theory

Quantum field theory is surprisingly effective at describing various interesting algebraic-geometric and topological invariants. In this lecture series, we will examine this fascinating connection between physics and mathematics by focusing on simple topologies: graphs. The quantum field theory framework allows us to solve numerous interesting graph counting problems, many inaccessible using traditional methods. I will introduce this elegant combinatorial framework focusing on asymptotic graph enumeration. We will discuss applications in topology and, if time permits, statistical mechanics and complex networks.

Thomas Lam: Moduli spaces in positive geometry

Recent developments in the physics of scattering amplitudes has led to the new field of positive geometry. We will discuss positive geometries appearing in projective space, Grassmannians, moduli spaces of rational curves, and various configuration spaces. The focus of the lecture series will be on the algebro-geometric aspects of positive geometries, together with hints of the relations to phi^3-amplitudes, super Yang-Mills amplitudes, and string theory amplitudes.

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.

Registration is closed.


Michael Borinsky

ETH Zürich Homepage

Thomas Lam

University of Michigan Homepage


09:30 - 10:30 Michael Borinsky (ETH Zürich)
10:30 - 11:00
11:00 - 12:00 Michael Borinsky (ETH Zürich)
12:00 - 14:00
14:00 - 15:00 Thomas Lam (University of Michigan)
15:00 - 15:30
15:30 - 16:30 Thomas Lam (University of Michigan)
16:30 - 18:00


Daniele Agostini

University of Tübingen

Eugenia Akhmedova

Weizmann Institute of Science

Melda Akyazi

University of Vienna

Rigers Aliaj

DESY/Uni Hamburg

George Balla

Technische Universität Berlin

Zaineb Bel-Afia

University of Oxford

Daniel Bermudez

University of Bonn/ MPIm Bonn

Michael Borinsky

ETH Zürich

Viktoriia Borovik

Osnabrück Universität

Alessio Borzì

MPI MiS, Leipzig

Lara Bossinger


Matthieu Bouyer

Ecole Polytechnique Paris

Victor Carmona


Oliver Clarke

University of Edinburgh

Shelby Cox

University of Michigan, Ann Arbor

Karel Devriendt

Max Planck Institute for Mathematics in the Sciences

Gabriele Dian

DESY Hamburg

Nick Early

Max Planck Institute for Mathematics in the Sciences


RWTH Aachen University

Jonah Epstein

University of Bonn

Claudia Fevola


Hannah Friedman

UC Berkeley

Angel Garcia Chung

Tec de Monterrey

Sofía Garzón Mora

Freie Universität Berlin

Marcos Emmanuel Gonzalez Laffitte

Leipzig University

Paul Görlach

OvGU Magdeburg

Kyle Huang

Freie Universität Berlin

Claudio Iuliano


Abel Jansma


Samuel Johnston

Imperial College London

Enno Keßler

Max-Planck-Institut für Mathematik in den Naturwissenschaften

Joris Koefler

MPI Mathematics in the Sciences

Andreas Kretschmer

MPI MiS Leipzig

Arne Kuhrs

Goethe University Frankfurt

Thomas Lam

University of Michigan

Yucong Lei

University of Michigan

Diana López-Falcón

MPI MPP München

Felix Lotter

MPI MiS Leipzig

Elia Mazzucchelli

Max Planck Institut für Physik

Chiara Meroni

ETH Institute for Theoretical Studies

Florentin Münch

MPI MiS Leipzig

Elke Neuhaus

MPI MiS, Leipzig

Michael Oren Perlstein

Weizmann Institute of Science

William Pannell

King's College London

Niharika Paul

Max Planck Institute for Mathematics in the Sciences

Dmitrii Pavlov

Max Planck Institute for Mathematics in the Sciences

Anaëlle Pfister


Eric Pichon-Pharabod

Inria Saclay

Irem Portakal


Jean-Luc Portner

University of Oxford

Rosa Preiß

MPI MiS Leipzig

David Prinz

Max Planck Institute for Mathematics

Lakshmi Ramesh

RPTU Kaiserslautern

Carlos Rodriguez

University of Uppsala

Anna-Laura Sattelberger

KTH Royal Institute of Technology

Leonard Schmitz

U Greifswald

Sebastian Seemann

KU Leuven

Dawei Shen

University of Michigan - Ann Arbor

Rob Silversmith

University of Warwick

Peter Spacek

TU Chemnitz

Avi Steiner

TU Chemnitz

Bernd Sturmfels

Max Planck Institute for Mathematics in the Sciences

Svala Sverrisdottir

UC Berkeley

Máté László Telek

University of Copenhagen

Simon Telen

Max Planck Institute for Mathematics in the Sciences

Simon Theil

Friedrich-Alexander-Universität Erlangen-Nürnberg

Hannah Tillmann-Morris

University College London

Francesca Tombari

MPI Leipzig

Tuyen Truong

Leipzig University

Julian Weigert

University of Konstanz

Maximilian Wiesmann

MPI MiS Leipzig

Daniel Windisch

MPI MiS Leipzig

Qinglin Yang

Institute of Theoretical Physics, Chinese Academy of Sciences

Bailee Zacovic

University of Michigan

Francesca Zaffalon

KU Leuven

Scientific Organizers

Dmitrii Pavlov

Max Planck Institute for Mathematics in the Sciences

Bernd Sturmfels

Max Planck Institute for Mathematics in the Sciences

Simon Telen

Max Planck Institute for Mathematics in the Sciences

Administrative Contact

Mirke Olschewski

Max Planck Institute for Mathematics in the Sciences Contact via Mail