COVID 19 : This school has been postponed to 2021
The aim of this school is to develop the participants knowledge and enthusiasm towards algebraic combinatorics. Through high-level presentations, the students will learn multiple combinatorial aspects linked to representation theory. They will also have the opportunity to try out what they have learned in exercise periods. Every day, a postdoctoral researcher will introduce a research topic tied to the introductory classes. In addition, introduction to programming in Python and Sage, very useful tool for coding problems in algebraic combinatorics, will take place at the end of the day.
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. Therefore, at the end of the school, participants will be able to reflect on many representation theory problems using multiple aspects.
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.
- Emily Barnard, assistant professor at DePaul University (Chicago), will give the lecture: Tamari Lattice and Posets.
- Jennifer Morse, professor at l the University of Virginia, will give the lecture: Schubert Calculus and Symmetric Functions.
- Khrystyna Serhiyenko, assistant professor at the University of Kentucky, will give the lecture: Introduction to Cluster Algebras and Combinatorics of Friezes.
- Gordana Todorov, professor at Northeastern University (Boston), will give the lecture: Cluster categories.
We also invited the following postdoctoral researchers:
- Emily Gunawan at the University of Connecticut.
- Nadia Lafrenière at Dartmouth College (Hannover).
- Rebecca Patrias at the University of Michigan.
- Emine Yıldırım at Queen’s University (Kingston).
For more information please contact one of the organizers.