Apply for funding
for this workshop

The geometry of polynomials in combinatorics and sampling

March 3 to March 7, 2025

at the

American Institute of Mathematics, Pasadena, California

organized by

Nima Anari, Petter Branden, Jacob Matherne, and Cynthia Vinzant

This workshop, sponsored by AIM and the NSF, will focus on the geometry of polynomials. One aim of this field is to study negative dependence properties of discrete probability distributions via analytic and functional properties of their multivariate generating polynomials. This brings together research in analysis, combinatorics, optimization, and computer science. Two special classes have proved to be exceptionally useful in this regard, namely stable polynomials and Lorentzian polynomials. This conference aims to bring together researchers in a broad range of fields to discuss structural questions about these spaces of polynomials and their applications in combinatorics and theoretical computer science.

The main topics for the workshop are

  • Negative correlation and real rooted-ness in matroids
  • Generalizations of Lorentzian polynomials
  • Applications to approximate counting and approximate sampling
  • Applications in algebraic combinatorics

This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than November 1, 2024. Applications are open to all, and we especially encourage women, underrepresented minorities, junior mathematicians, and researchers from primarily undergraduate institutions to apply.

Before submitting an application, please read the description of the AIM style of workshop.

For more information email

Plain text announcement or brief announcement.