Université de Fribourg, Switzerland

Proseminar SA-SP, 2016 -2017: Expander graphs

The aim of this Proseminar is to read the book by Giuliana Davidoff, Peter Sarnak and Alain Valette entitled ``Elementary Number Theory, Group Theory and Ramanujan Graphs''. The book is meant for undergraduate students and is self-contained, the prerequisites being only linear algebra, elementary algebra, analysis and combinatorics.

Roughly speaking, expander graphs are highly connected sparse finite graphs, our goal being to study and understand this notion and to give explicit constructions. Expanders play an important role in computer science as basic building blocks for network constructions, error correcting codes, algorithms and more. They also play a significant role in pure mathematics like number theory, group theory, geometry and more.

For the Spring semester the Proseminar is part of the Free seminar http://commonweb.unifr.ch/math/seminars/SeminaireLibre.html
The presence for the Proseminar (for the Spring semester) is counted as a presence for the Free seminar!


  • Dr. Ciobotaru Corina,  Reinhard Basil
  • Contact : Ciobotaru Corina (office 1.108, Math I, corina.ciobotaru@unifr.ch), Reinhard Basil (office 0.106, Math II, basil.reinhard@unifr.ch)

Practical information

  • Announcement, list of talks and hints for a good talk
  • Time - Place SA 2016: Tuesdays, 15:15-17:00, auditoire 2.52, Bâtiment de Physiques
  • Main reference : Giuliana Davidoff, Peter Sarnak and Alain Valette, Elementary Number Theory, Group Theory and Ramanujan Graphs.
  • This Proseminar is compulsory for third year students in Mathematics.

Validation conditions

  • To participate regularly and actively in almost all the seminars
  • To give one talk of 90 min (without reading the handout or the book)
  • To provide a LaTeX manuscript of about 4-5 pages (without copying down the book) containing a summary of your talk and the solutions of some of the exercises at the end of the corresponding section of the book 
  • To solve at least two exercises related to the talk (more are welcome!)


If you want to register for a talk, please contact Corina Ciobotaru!

Date Speaker Theme Responsible
27.09.2016 STAUDT Denis The adjacency matrix of a graph and its spectrum, Cayley graphs CC
04.10.2016 ZIMMERMANN Sèverine Inequalities of the spectral gap CC
11.10.2016 SCHUHMACHER Rahel Asymptotic behaviour of eigenvalues in families of expanders
18.10.2016 VOGT Christian Proof of the asymptotic behaviour CC
25.10.2016 GRAND-GUILLAUME-PERRENOUD Davina Independence number and chromatic number, Large girth and large chromatic number
08.11.2016 COPPEX Jeannine Sums of two squares
16.11.2016 SCHALLER Vinzenz Theodor Quadratic reciprocity, Sums of 4 squares
22.11.2016 RANIOLO Julie Quaternions, The arithmetic of integer quaternions
23.11.2016 FRONTINI Magali Some finite groups, Simplicity
29.11.2016 PRIVITERA Aurelio Structure of subgroups, and the summary
30.11.2016 SKOPA Eugene,
Representation theory of finite groups
06.12.2016 Di BERNARDO Emmanuel Degrees of representations of PSL(2,q)
13.12.2016 LIEBERMANN Clelia Construction of X^{p,q}
15.12.2016 ROSSET Julien
Spectral estimates
20.12.2016 KARLEN Matthieu 4-regular graphs with large girth
24.02.2017 WEY Jan  Free groups I
24.02.2017 BAKIU Vjosa  Free groups II CC
03.03.2017 VÖHRINGER Eliane  Free groups III
03.03.2017 GENDRE Gwenael  The group SL(2,R) CC
10.03.2017 SIMONET Johanne  The p-adic numbers CC