Research Programs


Algebraic and Enumerative Combinatorics

13 January - 30 April 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.


Participation in the program is by invitation only.

Sara Billey
University of Washington
Petter Brändén
KTH Royal Institute of Technology
Sylvie Corteel
Université Paris Diderot, Paris 7
Svante Linusson
KTH Royal Institute of Technology


Svante Linusson


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