SFB Summer School: Discrete Random Structures

7-12 September 2025

Hotel Dermuth, Pörtschach an Wörthersee

Hauptstraße 178
9210 Pörtschach am Wörthersee

The summer school  lectures will take place at the picturesque Grüner Salon of Villa Wörth, a few minutes walk from Hotel Dermuth. 

For directions between Hotel Dermuth and Villa Wörth, please see googlemaps.

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The aim of the first summer school is to connect our SFB members and network of researchers to present and discuss latest research achievements and findings on aspects related to the SFB, e.g.: random graphs, dimers, planar maps, plane partitions and alternating sign matrices.

The summer school will feature minicourses from Guillaume Chapuy (CNRS) and Fabio Toninelli (TU Wien). Exercise classes will round off the program.

The program will start on Monday, September 8 in the morning and finish on Friday, 12 September in the afternoon. Participants are expected to arrive on Sunday, September 7.

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Program

The minicourse speakers will be Guillaume Chapuy (CNRS) and Fabio Toninelli (TU Wien).   The speaker of the third minicourse will be announced in due course.

REGISTRATION

Registration is now closed.

Invited applicants have been contacted.

ABSTRACTS MINICOURSES

Minicourse by Guillaume Chapuy

INTRODUCTON TO PLANAR MAPS (RANDOMNESS AND ENUMERATION)

Abstract: We will introduce the basic techniques and concepts about enumeration of planar maps:

- Equations with catalytic variables, Tutte's formulas, Bousquet-Mélou Jehanne stategy.
- Bijective techniques, map-to-tree bijections.
- We will explore basic results about large random planar maps, via analytic combinatorics and via scaling limits of trees.
Exercise sessions will take the time to manipulate the basic concepts from the lectured. They will also propose a few more advanced problems for students wanting to explore some other topics: maps on other surfaces, maps and the symmetric group, maps and computer algebra.

Minicourse by Fabio Toninelli

MARKOV CHAIN MIXING: AN INTRODUCTION

Abstract: How fast can one sample a random instance from a very large discrete set? I will give an introduction to the theory of (total variation) mixing for Markov chains, with special emphasis on Markov chains on large discrete combinatorial structures, such as dimer and spin models.

Getting there

By plane:
The nearest airport is Klagenfurt Airport. Shuttle service can be arranged to the hotel, please contact the hotel. Estimated costs €50.

By train:
Pörtschach is conntected directly by international trains. Alternatively change at Villach or Klagenfurt to continue with Schnellbahn S1. From Klagenfurt the journey time with S1 is 14 minutes.

Please check your journey at ÖBB Scotty.

Hotel Dermuth is a short distance of approx. 300m from Pörtschach trainstation.


This event is supported by the Austrian Science Fund FWF under grant 10.55776/F1002.