categorification seminar

schedule

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

log

winter 2025

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.

meeting 1, january 15th 2025 (intro seminar)

Monoidal categorification of cluster algebras : what? where? why? how?
Notes available here.

Théo Pinet

meeting 2, january 22nd 2025 (research seminar)

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

meeting 3, january 29th 2025 (learning seminar)

Introduction to cluster algebras (based on Théo's notes in [o23])
Notes available here.

Théo Pinet

meeting 4, febuary 5th 2025 (research seminar)

Representation theory of shifted quantum groups : the $\mathfrak{sl}_2$ case (part 2)

Alexis Leroux-Lapierre

meeting 5, febuary 12th 2025 (learning seminar)

Cluster algebras with coefficients, $c$-vectors and $F$-polynomials
based on [fz], [fwz], [k12] and [m10]. Jonathan's notes available here.

Jonathan Boretsky

meeting 6, febuary 19th 2025 (research seminar)

Cluster structures on $\mathbb{C}[G/\hspace{-0.3em}/N]$ (part 1)

Joel Kamnitzer

meeting 7, febuary 26th 2025 (research seminar)

Cluster structures on $\mathbb{C}[G/\hspace{-0.3em}/N]$ (part 2)

Joel Kamnitzer

reading week, march 3rd to march 7th

No meetings during the reading week.

meeting 8, march 12th 2025 (learning seminar)

topic tba

Aleksandr Trufanov

meeting 9, march 2025 (research seminar)

topic tba

speaker tba

fall 2024

meeting 1, september 3rd 2024

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

meeting 2, september 24th 2024

Basics : from categorification of linear maps to 2-categories (Chapter 2 of [m12])
Aleksandr Trufanov

meeting 3, october 8th 2024

Basics: 2-representations of finitary 2-categories (Chapter 3 from [m12])
Antoine Labelle

meeting 4, october 22nd 2024

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

meeting 5, november 5th 2024

Translation functors, wall-crossing functors and projective objects of $\mathcal{O}$ (based on [h21] and [m12])
Alexis Leroux-Lapierre

meeting 6, november 19th 2024

Tilting modules, shuffling functors and parabolic category $\mathcal{O}$
Alexis Leroux-Lapierre

meeting 7, december 10th 2024

Soergel's $\mathbb{V}$ functor and the struktursatz (Théo's notes available here)
Théo Pinet

references

winter 2025

[cp95] Chari, V., & Pressley, A. N. (1995). A guide to quantum groups.
[cw19] Cautis, S., & Williams, H. (2019). Cluster theory of the coherent Satake category. arXiv link
[cw23] Cautis, S., & Williams, H. (2023). Canonical bases for Coulomb Branches of 4d $\mathcal{N}= 2$ gauge theories. arXiv link
[c10] Chan, M. (2010). A survey of cluster algebras. link
[f24] Fujita, R. (2024). Singularities of normalized R-matrices and E-invariants for Dynkin quivers. arXiv link
[fwz] Fomin, S., Williams L. & Zelevinsky A. (2016-2024). Introduction to cluster algebras.
Chapters 1-3, Chapters 4-5, Chapters 6, Chapters 7,
[fz] Fomin, S. & Zelevinsky, A. (2001-2006). Cluster algebras.
I. Foundations, II. Finite type classification, III. Upper bounds and double Bruhat cells (joint with Berenstein, A.), IV. Coefficients,
[ghl24] Geiss, C., Hernandez, D., Leclerc, B. (2024). Representations of shifted quantum affine algebras and cluster algebras I. arXiv link
[hl10] Hernandez, D., & Leclerc, B. (2010). Cluster algebras and quantum affine algebras. arXiv link
[h25] Hernandez, D. (2025). Symmetries of Grothendieck rings in representation theory. arXiv link
[hz24] Hernandez, D., & Zhang, H. (2024). Shifted Yangians and polynomial $R$-matrices. arXiv link
[k12] Keller, B. (2012). Cluster algebras and derived categories. arXiv link
[kkko18] Kang, S. J., Kashiwara, M., Kim, M., & Oh, S. J. (2018). Monoidal categorification of cluster algebras. arXiv link
[kq14] Kimura, Y., & Qin, F. (2014). Graded quiver varieties, quantum cluster algebras and dual canonical basis. arXiv link
[n11] Nakajima, H. (2011). Quiver varieties and cluster algebras. arXiv link
[o23] Oberwolfach report, arbeitsgemeinschaft: Cluster Algebras. link

fall 2024

[h21] Humphreys, J. E. (2021). Representations of semisimple Lie algebras in the BGG category $\mathcal{O}$.
[m12] Mazorchuk, V. (2012). Lectures on algebraic categorification. arXiv link
[s14] Savage, A. (2014). Introduction to categorification. arXiv link