# Schedule of the Winter School

Please note that there are small presentations during the poster sessions on Tuesday and Wednesday. You can find a time schedule for that here.

## Monday, November 20

10:15 - 10:50 |
Registration & Welcome coffee |

10:50 - 11:00 |
Opening remarks |

11:00 - 12:00 |
Volodymyr Mazorchuk - Introduction to 2-representation theory (part I) |

12:00 - 13:50 |
Lunch break |

13:50 - 14:50 |
Andrew Mathas - Cyclotomic KLR algebras (part I) - slides |

15:00 - 16:00 |
Eugene Gorsky - Hilbert schemes and knot homology (part I) |

16:00 - 16:30 |
Tea and cake |

16:30 - 17:30 |
Volodymyr Mazorchuk - Introduction to 2-representation theory (part II) |

17:30 - |
Reception |

## Tuesday, November 21

09:30 - 10:30 |
Catharina Stroppel - Springer fibres and generalised KLR algebras (part I) |

10:30 - 11:00 |
Group photo and coffee break |

11:00 - 12:00 |
Yankı Lekili - Fukaya categories and their appearance in representation theory (part I) |

12:00 - 13:30 |
Lunch break |

13:30 - 15:00 |
Poster session - part I New: Time schedule for mini presentations |

15:00 - 16:00 |
Yankı Lekili - Fukaya categories and their appearance in representation theory (part II) |

16:00 - 16:30 |
Tea and cake |

16:30 - 17:30 |
Eugene Gorsky - Hilbert schemes and knot homology (part II) |

## Wednesday, November 22

09:30 - 10:30 |
Volodymyr Mazorchuk - Introduction to 2-representation theory (part III) |

10:30 - 11:00 |
Coffee break |

11:00 - 12:00 |
Catharina Stroppel - Springer fibres and generalised KLR algebras (part II) |

12:00 - 13:30 |
Lunch break |

13:30 - 15:00 |
Poster session - part II New: Time schedule for mini presentations |

15:00 - 16:00 |
Andrew Mathas - Cyclotomic KLR algebras (part II) |

16:00 - 16:30 |
Tea and cake |

16:30 - 17:30 |
Eugene Gorsky - Hilbert schemes and knot homology (part III) |

## Thursday, November 23

09:30 - 10:30 |
Andrew Mathas - Cyclotomic KLR algebras (part III) |

10:30 - 11:00 |
Coffee break |

11:00 - 12:00 |
Yankı Lekili - Fukaya categories and their appearance in representation theory (part III) |

12:00 - 13:30 |
Lunch break |

13:30 - 15:00 |
Poster session - part III |

15:00 - 16:00 |
Yankı Lekili - Fukaya categories and their appearance in representation theory (part IV) |

16:00 - 16:30 |
Tea and cake |

16:30 - 17:30 |
Catharina Stroppel - Springer fibres and generalised KLR algebras (part III) |

## Friday, November 24

09:30 - 10:30 |
Eugene Gorsky - Hilbert schemes and knot homology (part IV) |

10:30 - 11:00 |
Coffee break |

11:00 - 12:00 |
Catharina Stroppel - Springer fibres and generalised KLR algebras (part IV) |

12:00 - 13:50 |
Lunch break |

13:50 - 14:50 |
Andrew Mathas - Cyclotomic KLR algebras (part IV) |

15:00 - 16:00 |
Volodymyr Mazorchuk - Introduction to 2-representation theory (part IV) |

16:00 - 16:30 |
Tea and cake and Farewell |

## Eugene Gorsky: Hilbert schemes and knot homology

Khovanov and Rozansky introduced a knot homology theory which categorifies the HOMFLY polynomial. This homology has a lot of interesting properties, but it is notoriously hard to compute. I will introduce HOMFLY homology and discuss its conjectural relation to algebraic geometry of the Hilbert scheme of points on the plane. For torus links, this conjecture was recently confirmed by Elias, Hogancamp and Mellit. I will also outline a possible strategy of the proof using the recent work of Elias and Hogancamp on categorical diagonalization. All notions will be introduced in lectures, no preliminary knowledge is assumed.

Lecture I: Introduction to HOMFLY homology

Lecture II: Introduction to Hilbert schemes

Lecture III: Categorical diagonalization

Lecture IV: From braids to sheaves on Hilbert scheme

## Yankı Lekili: Fukaya categories and their appearance in representation theory

TBA

## Andrew Mathas: Cyclotomic KLR algebras

The cyclotomic KLR algebras are certain quotients of the quiver Hecke algebras, or Khovanov–Lauda–Rouquier algebras. These algebras are important because they categorify the highest weight representations of the corresponding quantum group. We will start by discussing these algebras in arbitrary type, where surprisingly little is known. We then focus on type A where Brundan and Kleshchev’s graded isomorphism theorem tells us that these algebras are isomorphic to the cyclotomic Hecke algebras of type A, which are a family of deformation algebras that include as special cases the group algebras of the symmetric groups and their Iwahori–Hecke algebras. The main aim of my lectures is to understand the Ariki–Brundan–Kleshchev categorification theorem in terms of the representation of the cyclotomic KLR algebras of type A.

## Volodymyr Mazorchuk: Introduction to 2-representation theory

The aim of this series of lectures is to introduce the audience to the general area of 2-representation theory of finitary 2-categories. The main emphasis will be made on structural properties of finitary 2-categories and study of classification problems of various classes of 2- representations, in particular, that of simple transitive 2-representations. Both less advanced and more advanced methods will be discussed. The 2-category of projective bimodules over a finite dimensional algebra will be used as a running example.

## Catharina Stroppel: Springer fibres and generalised KLR algebras

TBA