# Winter school: Categorification, representation theory and symplectic geometry

## News

YouTube videos of the talks can be found here.

Slides for Mathas' talks: first, second, third, last.

The first talk of Mazorchuk's lectures was sadly not recorded properly. However, here are Mathas' lectures notes (for all four lectures): click.

The posters can be found here.

Some slides for the minitalks: González, Jensen, Koppensteiner, Lenzen, Naisse, Zhang, Zhu.

The group photo can be found here.

## Related programs

There is an additional workshop, see here and here

The winter school and the workshop are part of the Junior Hausdorff Trimester Program “Symplectic Geometry and Representation Theory” of the Hausdorff Research Institute.

Also part of the program is the “Workshop: Quantum geometric and algebraic representation theory” organized by Sam Gunningham and Travis Schedler, see here, and the “Workshop $A_\infty$-structures in geometry and representation theory” organized by Gustavo Jasso and Julian Külshammer, see here

## List of speakers giving a lecture series

• Eugene Gorski (University of California Davis); Title: Hilbert schemes and knot homology
• Yankı Lekili (King's College London); Title: Fukaya categories and their appearance in representation theory
• Andrew Mathas (University of Sydney); Title: Cyclotomic KLR algebras
• Volodymyr Mazorchuk (Uppsala University); Title: Introduction to $2$-representation theory
• Catharina Stroppel (Universität Bonn); Title: Springer fibres and generalised KLR algebras
Abstracts can be found here.

## Poster session

There will be a poster session where PhD students and postdocs can present their work. If you want to present a poster please let us know via email. (You have to be registered to present a poster, see below.)

There are also minitalks by some of the authors of the posters. Here is the schedule: here.

Some slides and the poster are linked above.

## Program

The program can be found here.

## Participants

A list of participants can be found here.

## General information

### Some introductory words

There is a fruitful interplay between categorification, representation theory and symplectic geometry, and our intention is to highlight some of it in detail.
To understand the deep interplay of these fields is a far-fetched goal, but we hope to organize the winter school and the workshop such that at least some interactions become clear.

### Aim and scope of the winter school

The winter school is indented to present a biased choice of topics concerning “categorification, representation theory and symplectic geometry”. We hope to bring together researchers as well as students who want to learn more about the various presented aspects of these broad fields.

### Structure of the lectures

The main speakers will give a series of introductory lectures on various aspects of modern mathematics as e.g.:
• Khovanov and HOMFLY-PT homology and its relation to geometry and representation theory
• Fukaya categories and their appearance in topology
• Graded representation theory of the symmetric group via KL-R algebras and related questions
• Representation theory of $2$-categories a.k.a. “higher” representation theory
• Lie theoretic aspects of categorification
Each lecture is a 60 minutes talk (plus time for questions), and the lectures will be held in the Lecture hall of the Hausdorff Research Institute of the University of Bonn. There will be 4-5 lectures per speaker which hopefully gives enough time for a deeper understanding of the topics above.

## Registration

The seat limit of the lecture hall has been reached, and THE REGISTRATION IS NOW CLOSED. If you still want to attend the winter school, then please contact the organizers and you will be put on waiting list. If there is any cancelation, then you will be contacted.

If you are interested in participating, please complete the online application form click

Make sure that you register if you want to participate due to seats constraints.

## Support

Financial support for PhD students and postdocs is available. Please complete the online application form click

## Local Information

### Venue

The lectures will take place in the Lecture hall of the Hausdorff Research Institute. Here is the address:

Lecture Hall
Hausdorff Research Institute for Mathematics
Poppelsdorfer Allee 45
53115 Bonn
Germany

Here is how you can find the the HIM and the Institute (called Math Center on the map):

To go to the HIM:
It is a five minute walk from the main train station to the HIM. Leave the station with your back facing towards the city. Turn left and walk approximately 100 meters until you hit a cross street called Poppelsdorfer Allee. You will see Schloss Poppelsdorf at the end of this street. The HIM can be found at the left-hand side of this street, Number 45, the HIM administration on the right-hand side, Number 82. (Both seen while facing Schloss Poppelsdorf.)

To go to the institute:
The bus stop Kaufmannstraße is located right in front of the Mathematik-Zentrum, Endenicher Allee 60. Lines 604, 605, 606, 607 (from and to the main train station Bonn Hbf), line 631 and night bus line N2 (after midnight) stop here.

### Some useful maps

Here a pdf with some hopefully useful maps: click
Some places to eat close to the HIM and the Institute can be found here
But there are also several good restaurants in the main part of the city.

### WiFi

There is eduroam available which works at the HIM and the whole institute. If you do not have eduroam, then it is also possible to get a guest account.

### Accommodation

We will take care of booking a hotel for registered participants.
All other participants are asked to make their own hotel reservation.
Here are some hotels close to the institute:
• Hotel Krug, walking distance to the institute: 15 Minutes, walking distance to the main station and the city: 15 minutes
• Hotel Mozart, walking distance to the institute: 10 Minutes, walking distance to the main station and the city: 5 minutes
• Hotel Kurfürstenhof, walking distance to the institute: 10 Minutes, walking distance to the main station and the city: 5 minutes
All of these are in a medium price range (50-75 Euros per night). There are also cheaper options.

### How to get to Bonn via airplane

Nearest airport: Cologne Bonn Airport
There is a bus (SB60) going directly from the airport to Bonn Hbf (train station) every 30 min.
Airports which are also close by (and easy to reach via train): Flughafen Düsseldorf or Frankfurt Airport

### How to get to Bonn via train

Nearest train station: Bonn Hauptbahnhof (Hbf)
The page of the German railway company can be found here (you can easily buy tickets online)

### How to get to Bonn via train

Nearest train station: Bonn Hauptbahnhof (Hbf)
The page of the German railway company can be found here (you can easily buy tickets online)

### Information that you hopefully will not need

In case of an emergency: click
English speaking doctors: click

## Organizers

Anne-Laure Thiel email
Daniel Tubbenhauer email

Pictures' credits: left picture; right picture