| winter 2025 schedule | |
| when | wednesdays from 12:30 to 14:00 |
| where | pk-4323, uqam |
| fall 2024 schedule | |
| when | (most) tuesdays 13:00 to 14:30 |
| where | pk-4323, uqam |
The winter seminar is divided in two types of meetings : a learning seminar and a research seminar. The objective of learning seminars is to learn about cluster algebras and monoidal categorifications in general while research seminars are oriented towards open problems. You can find each meeting's type in their header.
This winter seminar is coorganized with Théo Pinet.
Monoidal categorification of cluster algebras : what? where? why? how? Notes available here.
Théo Pinet
Representation theory of shifted quantum groups : the $\mathfrak{sl}_2$ case (part 1) mostly based on section 5 of [h25], formulas can be found in [cp95] and [hz24]
Alexis Leroux-Lapierre
Introduction to cluster algebras (based on Théo's notes in [o23]) Notes available here.
Théo Pinet
Representation theory of shifted quantum groups : the $\mathfrak{sl}_2$ case (part 2)
Alexis Leroux-Lapierre
Cluster algebras with coefficients, $c$-vectors and $F$-polynomials based on [fz], [fwz], [k12] and [m10]. Jonathan's notes available here.
Jonathan Boretsky
Cluster structures on $\mathbb{C}[G/\hspace{-0.3em}/N]$ (part 1)
Joel Kamnitzer
Cluster structures on $\mathbb{C}[G/\hspace{-0.3em}/N]$ (part 2)
Joel Kamnitzer
No meetings during the reading week.
Scattering diagrams based on [r18] and [ghk13]
Aleksandr Trufanov
The MV basis and cluster monomials in $\mathbb{C}[N]$
Pierre Baumann
Fusion of MV cycles and tensor products tensor products of modules over shifted Yangians (part 1)
Joel Kamnitzer
No meeting.
Fusion of MV cycles and tensor products tensor products of modules over shifted Yangians (part 2)
Joel Kamnitzer
Based cluster algebras of infinite rank and their applications to Lie theory
We introduce based cluster algebras of infinite rank. By extending cluster algebras arising from double Bott-Samelson cells to the infinite rank setting, we recover certain infinite rank cluster algebras connected to monoidal categories of representations of (shifted) quantum affine algebras. This allows us to calculate standard bases on quantum double Bott-Samelson cells via braid group actions. Several conjectures also follow as consequences.
Fan Qin
Exceptionally, this meeting will take place at 12:00 via Zoom.
topic tba
speaker tba
What is categorification? The nilCoxeter algebra and a weak categorification of the polynomial representation of the Weyl algebra. The presentation was based on chapter 3 of the notes by Alistair Savage Introduction to categorification which can be found here. Alexis Leroux-Lapierre
Basics : from categorification of linear maps to 2-categories (Chapter 2 of [m12]) Aleksandr Trufanov
Basics: 2-representations of finitary 2-categories (Chapter 3 from [m12]) Antoine Labelle
Basics: 2-representations of finitary 2-categories (end of chapter 3 from [m12]) Antoine Labelle
Category $\mathcal{O}$: definitions (beginning of chapter 4 from [m12]) Philippe Petit
Translation functors, wall-crossing functors and projective objects of $\mathcal{O}$ (based on [h21] and [m12]) Alexis Leroux-Lapierre
Tilting modules, shuffling functors and parabolic category $\mathcal{O}$ Alexis Leroux-Lapierre
Soergel's $\mathbb{V}$ functor and the struktursatz (Théo's notes available here) Théo Pinet
winter 2025
fall 2024