Summer School of Algebraic Combinatorics

Abstract: Organizers/ Organisatrices:

Véronique Bazier-Matte, Souheila Hassoun et Nancy Wallace

Courses and lecturers - Cours et professeures

Cluster Categories and Related Topics by Pr. Gordana Todorov

Introduction to Cluster Algebras and Combinatorics of Friezes by Pr. Khrystyna Serhiyenko

Schubert calculus and symmetric functions by Pr. Maria Gillespie

Tamari Lattices and Posets by Pr. Emily Barnard

The aim of this school is to advance the participants knowledge and enthusiasm towards algebraic combinatorics. Through high-level presentations, the students will learn multiple combinatorial aspects linked to representation theory. Every day, a postdoctoral researcher will introduce a research topic tied to the introductory classes. Schubert calculus, symmetric functions, cluster algebra, Tamari lattices, frieze combinatorics and cluster categories are not only ways to study representation theory, but have many links between them. On one hand, cluster algebras, introduced by Sergey Fomin and Andrei Zelevinsky, can be studied using the combinatorics of friezes, on the other hand, they can be studied algebraically using cluster categories. Moreover, they have a correspondence with double Bruhat cells. In the case of Flag varieties and grassmanians, the decomposition into Bruhat cells gives way to decomposition into Schubert cells. These can be obtained using Schubert calculus. Schubbert polynomials are a generalization of Schur functions, which are symmetric functions. Using sub-word complexes, Schubert varieties are tied to the study of Tamari Lattices. These lattices correspond to exchange graphs of some cluster algebra. Finally, our goal is to promote the visibility and accomplishment of women in mathematics. Even though the school is open to people of all genders, only women were invited to give lectures and talks. It seems important to us to give the occasion to students to interact accomplished women in mathematics, since they are underrepresented among teachers in mathematics in universities.

combinatoricscategory theoryrepresentation theory

Audience: researchers in the topic

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The TRAC Seminar - Théorie de Représentations et ses Applications et Connections

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