Informal seminar on combinatorics and representation theory
This is an informal seminar on combinatorics and representation theory.
In Winter 2021
discussed the combinatorics of q,tCatalan numbers and Shuffle conjecture,
as well as their geometric counterparts:
affine Springer fibers and positroid varieties.
In Spring 2021 we will discuss combinatorics related to affine Schubert calculus.
Organizers: Erik Carlsson ,
Eugene Gorsky,
Anne Schilling,
Monica Vazirani .
The seminar meets on Mondays at 11am.
Notes from past quarters: Fall 2020 .
Program
1/4 Organizational meeting. Notes
1/11 Erik: A combinatorial formula for the nabla operator
1/18 MLK Day
1/25 Erik continues
2/1 Erik continues
2/8 Joseph (recap from last quarter )
notes
2/15 Presidents Day
2/22 Joseph continues
notes
3/1 Eugene: sections 23 of [KLS]
notes
3/8 Eugene: sections 45 of [KLS]
notes
3/15, 3/22: Spring break
3/29 Eugene: section 7 of [KLS]
notes
4/5 Anne: intro to affine Schubert calculus
notes
4/12 Jianping on https://arxiv.org/abs/2103.09551
notes
4/19 Jianping continued
notes
4/26 Yue Zhao
notes
5/3 Emi Brawley
notes , Josh Petrack
notes
5/10 Milo Bechtloff Weising
References:

[CM] E. Carlsson, A. Mellit. A combinatorial formula for the nabla operator. arXiv:2012.01627

[KLS] A. Knutson, T. Lam, D. Speyer. Positroid Varieties: Juggling and Geometry. arXiv:1111.3660

[GL] P. Galashin, T. Lam. Positroids, knots, and q,tCatalan numbers.arXiv:2012.09745