Fall School “Phase Transition in Random Discrete Structures”

September 02 - 20, 2013, Graz University of Technology, Austria


The phase transition is a phenomenon observed in mathematics and natural sciences in many different contexts. It deals with a sudden change in the properties of a large structure caused by altering a critical parameter. The phase transition in random discrete structures (e.g. random graphs, random graph processes, random satisfiability problems, Ising/Potts model, percolation) has captured the attention of many scientists in recent years.

The goal of the fall school is to provide advanced master students, PhD students, and early stage postdocs, who are interested in random discrete structures and related fields, the opportunities

  • to learn the state of the art results in the study of the phase transition in various random discrete structures, in particular, in random constraint satisfaction problems and random graphs;
  • to understand modern proof techniques that have successfully been applied to the study of phase transition and its critical behaviour;
  • to meet fellow colleagues in their early research career, which possibly results in their future collaboration.

Amin Coja-Oghlan and Konstantinos Panagiotou have recently developed a new Survey Propagation and a new asymmetric second moment method for random CSP problems. They have verified the statistical mechanics conjecture for a special case of random satisfiability problems. In the fall school they will deliver a series of lectures, starting with an overview of the field and a gentle introduction to statistical physics and continuing with classical and new results on k-SAT and k-NAESAT thresholds as well as k-colorability threshold.

In addition to lectures, there will be a one-day mini-workshop on Phase Transition in Random Graphs. The plenary speaker is Oliver Riordan, and the invited speakers include Oliver Cooley and Charilaos Efthymiou.

On top of scientific and educational achievements, young participants can experience the research environment of TU Graz as a candidate place for their future research, and establish contacts with other participants for their future collaboration. The language of the school is English.

The fall school is supported by the Austrian Science Fund (FWF) within the Doctoral Programme “Discrete Mathematics” at TU Graz and by the European Science Foundation (ESF) within the Research Networking Programme “Random Geometry of Large Interacting Systems and Statistical Physics (RGLIS)”.


The lectures of the fall school will be given by the two experts in the field:


The course is addressed to advanced master students, PhD students, and early stage postdocs, who are interested in random discrete structures and related fields. The total number of participants is limited to 35.

There will be a limited amount of scholarships (of max. 500 Euro each) available for PhD students or for advanced Master students in a field related to the topics of the school. The scholarship is designed to cover accommodation costs for the whole duration of stay.

There is no registration fee.


  • Applications for participation only, with a short curriculum vitae and scientific background, should be sent by 5 July 2013 to:
  • Applications for scholarship and participation, with curriculum vitae, a short research statement, and a letter of recommendation (sent directly by a thesis advisor or a renowned mathematician in the field), should be sent by 5 July 2013 to:

Applicants will be notified by 15 July 2013.


The whole programme of the fall school consists of lectures, exercise sessions and a one-day mini-workshop and will take place from the 2nd of September to the 20th of September 2013. Lectures will be given in the morning, and discussion and exercise sessions in the afternoon. Exercises will be solved individually and then discussed and solved together in small groups. The solutions of exercises will be presented by participants in exercise sessions.

Typical Day Schedule
10:00-10:50 Lecture 1
11:00-11:50 Lecture 2
12:00-14:00 Lunch Break
14:00-16:00 Individual Problem Solving Session
16:00-18:00 Group Discussion and Exercise Session

2-6 September: 10 Lectures by Amin Coja-Oghlan

  • Overview + Statistical Physics
  • Classical 2nd Moment for k-NAESAT and k-COL
  • New results in k-COL

9-13 September & 18-19 September: 14 Lectures by Konstantinos Panagiotou

  • Classical 2nd Moment for SAT
  • New results for k-SAT and k-NAESAT
  • k-XORSAT and Orientability
  • Application Cuckoo Hashing

20 September: Mini-Workshop on Phase Transition in Random Graphs

  • Plenary Speaker: Oliver Riordan (University of Oxford)
  • Invited Speakers include:
    • Oliver Cooley (Graz University of Technology)
    • Charilaos Efthymiou (University of Frankfurt)

For details visit the website of the mini-workshop

Venue and Accommodation

All lectures, discussions and exercise sessions as well as Mini-Workshop will take place at the Mathematics Building of TU Graz, Steyrergasse 30, 8010 Graz, Austria.

Participants will have to arrange and pay for accommodation and travel themselves.

The nearest accommodation with a good price is Pension Stadthalle Johannes, Münzgrabenstrasse 48, 8010 Graz, which has both regular single rooms and furnished apartments. Another possibility is to rent a regular furnished appartment with a group of people.

The following links should help you to find accommodation.


The fall school is organized as part of scientific activities of the Doctoral Programme (DK) “Discrete Mathematics” by local committee members:

  • Mihyun Kang
  • Philipp Sprüssel
  • Tamas Makai
  • Wilfried Huss (DK coordinator)

For further information contact:
Tamas Makai

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