Algebraic and Enumerative Combinatorics
January 13 - April 30, 2020
This program is devoted to Algebraic Combinatorics with a special focus on enumeration, random processes and zeros of polynomials. There have been several interactions between the three themes.
For example techniques from enumerative combinatorics are frequently used in problems arising in statistical physics, techniques using zeros of polynomials have been used to analyze the behavior of certain Markov processes, and the zeros of polynomials appearing in enumerative combinatorics have been studied frequently. Tools from algebraic combinatorics are often used to attack problems in the theme areas. We believe that research in the themes would benefit from further interactions.
Examples of topics among the themes of the proposed program are:
Algebraic combinatorics. Combinatorics of Coxeter groups, Grassmannians, Schubert polynomials and Macdonald polynomials, representation theory of the symmetric group, algebraic aspects of matroid theory, symmetric functions.
Analytic techniques. Asymptotics of combinatorial sequences and arrays, stable polynomials, real-rootedness, log-concavity, Interlacing families.
Random processes. Particle models, tilings, random maps, random surfaces, limit shapes, correlation inequalities.
Enumerative combinatorics. Combinatorial descriptions of stationary distributions of Markov processes, combinatorics of the symmetric group, unimodality, bijections, generating functions.
During the program, there will be three workshops with thematically focused talks:
- Combinatorics and Random Processes, January 27 – 31 Schedule
- Unimodality, Log-concavity and beyond, March 16 – 20 Schedule
- Algebraic Combinatorics, April 20 – 24 Schedule
Participation in the program is by invitation only.