Past subjects

Mini-course on p-KL combinatorics April 17-21 2023

For more information on the Ghent University doctoral schools mini-course on p-KL combinatorics, please navigate to    https://sites.google.com/view/kleine-seminar-mini-course. You can also navigate to this webpage for relay of information.

Current topic of the seminar: Soergel bimodules

We will begin the study of the book Introduction to Soergel Bimodules by Elias, Makisumi, Thiel, Williamson and the many contributors.

Next meeting: Thursday 14:00 30 March 2023, Leslokaal 3.2 S8, on Chapter 12 by Michiel Smet

Michiel will close the seminar with Chapter 27.

Winter 2023 schedule

Ch. 8 Frobenius extensions and the one-color calculus Jari Desmet 07/02/2023
Ch. 9 The dihedral cathedral Sigiswald Barbier 16/02/2023
Ch. 10 Generators and relations for BS bimodules I Sam Claerebout 23/02/2023
Ch. 10 Generators and relations for BS bimodules II Sam Claerebout 02/03/2023
Ch. 11 The Soergel categorification Theorem part I Marcelo De Martino 09/03/2023
Ch. 11 The Soergel categorification Theorem part II Marcelo De Martino 16/03/2023
Ch. 12 How to draw Soergel bimodules Alexis Langlois-Rémillard 23/03/2023
Ch. 27 The p-canonical basis Michiel Smet 30/03/2023

Fall 2022 schedule

Coxeter groups and reflection groups Marcelo De Martino 18/11/2022
Hecke algebra and KL polynomial Michiel Smet 25/11/2022
Soergel bimodules Sam Claerebout 02/12/2022
Classical theory of Soergel bimodules Sigiswald Barbier 09/12/2022
Diagrammatic Alexis Langlois-Rémillard 16/12/2022
Remaining? - Next year?

Meetings minutes

You can find here the note of the meeting if provided by the speaker.

Past meetings in the Summer 2022 semester

  • 2022-09-13 Chapter 8 by Sam Claerebout
  • 2022-09-05 Chapter 7 by Sigiswald Barbier
  • 2022-08-30 Chapter 6 by Asmus Bisbo
  • 2022-08-23 Chapter 5 by Michiel Smet
  • 2022-08-16 Chapter 4 by Marcelo De Martino
  • 2022-07-12 Chapter 3 by Jari Desmet
  • 2022-07-05 Chapter 2 by Alexis Langlois-Rémillard
    •

    Winter 2022 seminar

    Past meetings in the Winter 2022 semester

  • 24-05-2022: Recap of the book by Gert Vercleyen
  • 04-04-2022: Chapter 9 part III by Marcelo De Martino
  • 28-03-2022: Chapter 9 part II by Marcelo De Martino
  • 21-03-2022: Chapter 9 part I by Jari Desmet
  • 07-03-2022: Chapter 8 part III by Sam Claerebout
  • 28-02-2022: Chapter 8 part II by Michiel Smet
  • 21-02-2022: Chapter 8 part I by Alexis Langlois-Rémillard
  • 14-02-2022: Recap of last semester by Gert Vercleyen
  • 31-01-2022: Chapter 7 part III by Marcelo De Martino
    •

    Past meetings in the Fall 2021 semester

  • 16-12-2021: Chapter 7 part II by Marcelo De Martino
  • 10-12-2021: Chapter 7 part I by Sigiswald Barbier
  • 03-12-2021: Chapter 6 by Michiel Smet
  • 26-11-2021: Chapter 5 part II by Hadewijch De Clercq
  • 19-11-2021: Chapter 5 part I by Alexis Langlois-Rémillard
  • 12-11-2021: Chapter 4 part II by Jari Desmet
  • 05-11-2021: Chapter 4 part I by Sam Claerebout
  • 29-10-2021: Chapter 3 by Gert Vercleyen
  • 22-10-2021: Chapter 2 by Kieran Calvert
  • 15-10-2021: Chapter 1 by Kieran Calvert
  • 28-09-2021: Organisational session
    •

    Fall 2022 schedule

    Review Ch.1, and Ch.2 Kieran Calvert 15/10/2021, 22/10/2021
    Chapter 3 Gert Vercleyen 29/10/2021
    Chapter 4 Sam Claerabout and Jari Desmet 05/11/2021, 12/11/2021
    Chapter 5 Hadewijch De Clercq and Alexis Langlois-Rémillard 19/11/2021, 26/11/2021
    Chapter 6 Michiel Smet 03/12/2021
    Chapter 7 Sigiswald Barbier and Marcelo De Martino 10/12/2021, 17/12/2021
    Chapter 8 to see next semester Spring 2022?
    Chapter 9 to see next semester Spring 2022?

    Fall 2021 and Spring 2021

    Resources for the seminar

    Etingof, Gelaki, Nikshych and Ostrik have written recently a book on tensor categories (see https://pages.uoregon.edu/vostrik/ and navigate to the book). In the preface, they outline a possible one-semester course that we could do to cover this exciting material. Here is it with minor touch:

    Chapter 1Homework and brief recap (1.1 to 1.9)
    Chapter 22.1 to 2.10
    Chapter 3Skip unless needed
    Chapter 44.1 to 4.9
    Chapter 55.1 to 5.6, more if wanted
    Chapter 66.1 to 6.3
    Chapter 77.1 to 7.12
    Chapter 88.1 to 8.14
    Chapter 99.1 to 9.9 with 9.12
    Do not hesitate to use other sources such as Deligne's work, Mac Lane, Etingof and Ostrik, Joyal or Drinfeld etc.

    Winter 2022 schedule

    Review of previous meetings Gert Vercleyen 14/02/2022
    Chapter 8 part I (8,1--8.5) Alexis Langlois-Rémillard 21/02/2022
    Chapter 8 part II (8.6--8.9) Michiel Smet 28/02/2022
    Chapter 8 part III (8.10--8.14) Sam Claerebout 07/03/2022
    Chapter 9 part I (9.1--9.5) Jari Desmet 21/03/2022
    Chapter 9 part II (9.6--9.9) Marcelo De Martino 28/03/—04/04/2022
    Chapter 9 part III (9.12) Sigiswald Barbier 18?/04/2022
    Talks about "applications" Gert Vercleyen, Laurens Lootens and Jacob Bridgeman —/04/2022

    Winter 2021

    Category $\mathcal{O}$

    The third semester was on the book Representations of Semisimple Lie algebras in the BGG category $\mathcal{O}$ by Humphreys. The members were:

  • Sigiswald Barbier, Postdoc UGent;
  • Asmus Bisbo, PhD candidate UGent;
  • Sam Claerebout, PhD candidate UGent;
  • Hadewijch De Clercq, PhD candidate UGent;
  • Marcelo De Martino, Postdoc UGent, Oxford;
  • Tom De Medts, Prof UGent;
  • Alexis Langlois-Rémillard, PhD candidate UGent;
  • Roy Oste, Postdoc UGent;
  • Wouter van de Vijver, PhD candidate UGent.
    •

    Meeting in the Winter 2021 semester

  • 14-01-2021: Organisational session
  • 21-01-2021: Chapter 0 A short review of Semisimple Lie algebras by Roy Oste. Notes of the meeting
  • 26-01-2021: Chapter 1 Basics of category O, Part I by Alexis Langlois-Rémillard. Notes of the meeting
  • 02-02-2021: Chapter 1 Basics of category O, Part II by Alexis Langlois-Rémillard. Notes of the meeting
  • 09-02-2021: Chapter 1 Basics of category O, Part III by Alexis Langlois-Rémillard. Notes of the meeting
  • 16-02-2021: Chapter 2 Finite-dimensional case Asmus's notes and Chapter 3: Methods of category O part I by Sam Claerebout. Notes of the meeting
  • 23-02-2021: Chapter 3 Mathods of category O Part II by Sam Claerebout. Notes of the meeting
  • 02-03-2021: Chapter 3 Mathods of category O Part III by Sam Claerebout. Notes of the meeting
  • 09-03-2021: Chapter 3 Mathods of category O Part IV by Sam Claerebout. Notes of the meeting
  • 16-03-2021: Chapter 4 Highest weight modules I Part I by Asmus Bisbo. Notes of the meeting
  • 23-03-2021: Chapter 4 Highest weight modules I Part II by Asmus Bisbo. Notes of the meeting (include 30-03)
  • 30-03-2021: Chapter 4 Highest weight modules I Part III by Asmus Bisbo. Notes of the meeting (include (23-03)
  • 20-04-2021: Chapter 5 Highest weight modules II Part I by Hadewijch De Clercq. Notes of the meetings
  • 27-04-2021: Chapter 5 Highest weight modules II Part II by Hadewijch De Clercq. Notes of the meetings
  • 04-05-2021: Chapter 5 Highest weight modules II Part III by Hadewijch De Clercq. Notes of the meetings
  • 11-05-2021: Chapter 6 Extensions and resolutions Part I by Marcelo De Martino. Notes of the meetings
  • 18-05-2021: Chapter 6 Extensions and resolutions Part II by Marcelo De Martino. Notes of the meetings
  • 25-05-2021: Chapter 6 Extensions and resolutions Part III by Marcelo De Martino. Notes of the meetings
  • 01-06-2021: Chapter 7 Translation functors Part I by Sigiswald Barbier Notes of the meeting
  • 08-06-2021: Chapter 7 Translation functors Part II by Sigiswald Barbier Notes of the meeting
  • 15-06-2021: Chapter 7 Translation functors Part III by Sigiswald Barbier Notes of the meeting
    •

    Winter 2020 and Fall 2020

    Categorification

    The second semester of the Kleine seminar was dedicated to categorification. We took a hiatus due to Covid-19 and returned online in Fall 2020. The members who partipated at least once during this strange double semester were:

  • Sigiswald Barbier, Postdoc UGent;
  • Asmus Bisbo, PhD candidate UGent;
  • Sam Claerebout, PhD candidate UGent;
  • Hadewijch De Clercq, PhD candidate UGent;
  • Ali Guzmán Adán, Postdoc UGent;
  • Paulien Jansen, PhD candidate UGent;
  • Alexis Langlois-Rémillard, PhD candidate UGent;
  • Roy Oste, Postdoc UGent;
  • Wouter van de Vijver, PhD candidate UGent.
    •

    Meetings in the Winter and Fall 2020 semester

  • 15-12-2020 The categorification of $U_q(\mathfrak{sl}_2) part III by Hadewijch De Clercq Notes of the meeting
  • 08-12-2020 The categorification of $U_q(\mathfrak{sl}_2) part II by Hadewijch De Clercq Notes of the meeting
  • 01-12-2020 The categorification of $U_q(\mathfrak{sl}_2) part I by Hadewijch De Clercq Notes of the meeting
  • 24-11-2020 $S_n$ categorification by Alexis Langlois-Rémillard Notes of the meeting
  • 17-11-2020 Category $\mathcal{O}$ basis for $S_n$ categorification by Alexis Langlois-Rémillard Notes of the meeting
  • 03-11-2020 Strong categorification by Sigiswald Barbier Notes of the meeting
  • 27-10-2020 Strong categorification by Sigiswald Barbier Notes of the meeting
  • 20-10-2020 Fock space representation of the Heisenberg algebra by Sigiswald Barbier. Notes of the meeting
  • 13-10-2020 Getting back in categorical shape by Alexis Langlois-Rémillard. Notes of the meeting
  • 11-03-2020 Trace decategorication by Sam Claerebout.
  • 10-03-2020 Grothendieck rings and weak categorification by Paulien Jansen.
  • 19-02-2020 Pivotal categories and string diagrams by Asmus Kjær Bisbo.
  • 12-02-2020 Wouter van der Vijver on monoidal categories and string diagrams.
    •

    Fall 2019-January 2020

    Hecke algebras and double affine Hecke algebras

    This semester was the first one of the Kleine seminar. The members participating were:

  • Sigiswald Barbier, Postdoc UGent;
  • Asmus Bisbo, PhD candidate UGent;
  • Sam Claerebout, PhD candidate UGent;
  • Hadewijch De Clercq, PhD candidate UGent;
  • Alexis Langlois-Rémillard, PhD candidate UGent;
  • Roy Oste, Postdoc UGent;
  • Wouter van de Vijver, PhD candidate UGent.
    •

    This semester topic was on Hecke algebras with a view toward double affine Hecke algebras (DAHA). The reference we were following is the book Iwahori-Hecke Algebra and Schur Algebras of the Symmetric Group by Andrew Mathas and Pavel Etingof's course notes on DAHA. Some more references are in the shared files, only available for UGent members. We completed in Mathas chapters 1 to 3 completely, part of chapter 4 and added some material on DAHA after.

    Past meetings

  • Tuesday January 21st, Hadewijch De Clercq finished the construction and justification of DAHA, closing the Fall seminar.
  • Wednesday January 15th, Hadewijch De Clercq presented preliminaries on affine root systems and gave the construction of AHA.
  • Thursday January 09th, Roy Oste presented the construction of DAHA and introduced all the in between construction pertaining to this.
  • Tuesday December 10th, Asmus Bisbo reviewed some of the interesting results in the fourth chapter of Mathas.
  • Wednesday December 4th, Wouter van de Vijver finished section 3.4 giving a characterization of simple standard modules of the Iwahori-Hecke algebra.
  • Tuesday November 26th, Sam Claerabout finished section 3.3 by proving the orthogonality of the basis elements and Wouter van de Vijver returned to an example of irreducible modules via the Murphy basis
  • Tuesday November 19th, Sam Claerabout presented the Specht modules for the Hecke algebra in section 3.3
  • Tuesday November 12th, Sigiswald Barbier presented the Murphy basis theorem of section 3.2 and related lemmas.
  • Tuesday November 05th, Sigiswald Barbier presented the theorem of Ehresmann of section 3.1 and related lemmas.
  • Tuesday October 22th, Alexis Langlois-Rémillard presented the last part of the second chapter of Mathas. Proof of lemmas 2.18, 2.9 and of theorem 2.20 were given. Sigiswald Barbier then started the study of chapter 3 with the beginning of section 1. Reaching Corollary 3.4.
  • Tuesday October 8th, Alexis Langlois-Rémillard presented the second part of the second chapter of Mathas. We reached theorem 2.20, skipping lemmas 2.18 and 2.19
  • Friday October 4th, Alexis Langlois-Rémillard presented the first part of the second chapter of Mathas on Cellular algebra. We reached the statement of theorem 2.16 on a complete list of non-equivalent simple modules in a cellular algebras (Theorem 2.16)
  • Thursday September 19th, Asmus Bisbo presented the first chapter of Mathas on introduction to Hecke algebras and some preliminary results on the symmetric group
    •

    Meetings minutes

    You can find here the (uncompleted) notes of the meeting. The material has probably a higher chance of being error-filled here, but the margins content some hastily scribbled snippets of the discussion we had in the seminar and might prove interesting!

    Contact

    If you have inquiries about the Kleine seminar, the easiest would be to contact me with the information below, but contacting any other member is also a valid strategy!