Mathematics Research Communities


MRC Week 1b: May 30 – June 5, 2021

Combinatorial Applications of Computational Geometry and Algebraic Topology

Organizers:

  • Stephen Melczer, University of Pennsylvania
  • Marni Mishna, Simon Fraser University
  • Robin Pemantle, University of Pennsylvania

The new and rapidly expanding area of Analytic Combinatorics in Several Variables (ACSV) concerns enumeration problems in such areas as lattice walks, statistical mechanical models, quantum walks and other exactly solvable models where asymptotic estimation of coefficients of a bivariate or multivariate generating function is required. The multivariate setting incorporates a wider swath of mathematics. including singularity theory, algebraic topology, and computational algebra. Participants in this MRC will be introduced to problems from these areas of mathematics whose solutions have direct applications to ACSV. These problems are not hard to state in the language of disciplines such as Morse theory, harmonic analysis, or commutative algebra, but they ask questions not typical in those fields. A long-term goal is to advance and automate this work, so that its benefits can be used by other researchers in mathematics and the natural sciences through implementations in computer algebra packages. Problems for this MRC will be arranged around five central topics: effective computer algebra methods, algorithms using computational topology, multivariate asymptotic phase transitions, singular transforms for degenerate saddle-point integrals, and applications of harmonic analysis and singularity theory. Researchers with knowledge in any one of these areas are encouraged to apply to this MRC.

In addition to interacting with the organizers throughout the summer conference week, participants will also have the opportunity to work with advisors Professors Yuliy Baryshnikov (University of Illinois, Urbana-Champaign) and Mark Wilson (University of Auckland/University of Massachusetts). 

Please see the article “Combinatorial Adventures in Analysis, Algebra, and Topology” by the organizers in the February 2020 issue of Notices.

Applications closed on February 15, 2020, and the admission process is complete.

For questions about the application process, please contact Kim Kuda at the AMS.