Special Year on Algebraic and Geometric Combinatorics

During the 2024-25 academic year the School will have a special program on Algebraic and Geometric Combinatorics. June Huh from Princeton University will be the Distinguished Visiting Professor.

Mathematical objects often have a combinatorial structure, sometimes overtly and other times in a concealed way. The special year will focus on those research that uncovers and exploit such a structure in algebra and geometry. The program will bring together active researchers from various fields, including tropical geometry, matroid theory, computational algebraic geometry, representation theory, toric geometry, Schubert geometry, and "algebra and geometry over the field of one element." Many recent breakthroughs in these areas have come from teams of mathematicians with various backgrounds spanning the above disciplines, a trend that is likely to continue. We will make a concerted effort to foster the formation of such teams throughout the year. Experimental methods using computational tools will be actively explored.

Confirmed participants: Dave Anderson, Federico Ardila, Shiyue Li, Lucia Lopez de Medrano, Oliver Lorscheid, Mateusz Michalek, Leonardo Mihalcea, Igor Pak, Greta Panova, Sam Payne, Cecilia Salgado, Alan Stapledon and Liz Vivas.

Workshops:

The 'Geometry of Matroids' workshop is scheduled for October 21-25, 2024, at the Institute for Advanced Study in Princeton. Organized by Matt Baker, Chris Eur, June Huh, Oliver Lorscheid, and Felipe Rincon, this event aims to bring together leading researchers in different areas of combinatorial geometry. This workshop is a part of the special year Algebraic and Geometric Combinatorics.

See the Fall Workshop website for more information.

The 'Combinatorics of Fundamental Physics' workshop is scheduled for November 18-22, 2024, at the Institute for Advanced Study in Princeton.

Organized by Nima Arkani-Hamed, June Huh, Thomas Lam, and Bernd Sturmfels, this event aims to foster collaboration between mathematicians and physicists. The focus will be on the intersection of combinatorial geometry and fundamental physics, covering topics like scattering and string amplitudes, positive geometry, Euler integrals, and tropical moduli spaces. This workshop is a part of the special year Algebraic and Geometric Combinatorics.

See the workshop website for more information.
 

The 'Combinatorics of Enumerative Geometry' workshop is scheduled for February 3-7, 2025, at the Institute for Advanced Study in Princeton.

Organized by Paolo Aluffi, Dave Anderson, June Huh, and Leonardo Mihalcea, this workshop is dedicated to the exploration of the combinatorial dimensions of intersection theory and enumerative geometry, broadly interpreted. Topics include characteristic classes of matroids and Schubert varieties, classical and quantum intersection rings of flag manifolds, and applications of tropical geometry. This workshop is a part of the special year Algebraic and Geometric Combinatorics.

See the Spring Workshop website for more information.

Please email the organizers with questions.