Université de Fribourg, Switzerland
Proseminar SASP, 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 selfcontained, 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.
The presence for the Proseminar (for the Spring semester) is counted as a presence for the Free seminar!
Responsible
 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, 15:1517:00, 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 45 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!)
Talks
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 
CC  
18.10.2016  VOGT Christian  Proof of the asymptotic behaviour  CC  
25.10.2016  GRANDGUILLAUMEPERRENOUD Davina  Independence
number and chromatic number, Large girth and large chromatic
number 
CC 

08.11.2016  COPPEX Jeannine  Sums of
two squares 
CC 

16.11.2016  SCHALLER Vinzenz Theodor  Quadratic
reciprocity, Sums of 4 squares 
RB 

22.11.2016  RANIOLO Julie  Quaternions,
The arithmetic of integer quaternions 
RB 

23.11.2016  FRONTINI Magali  Some
finite groups, Simplicity 
CC 

29.11.2016  PRIVITERA Aurelio  Structure
of subgroups, and the summary 
CC 

30.11.2016  SKOPA Eugene, 
Representation
theory of finite groups 
CC  
06.12.2016  Di BERNARDO Emmanuel  Degrees
of representations of PSL(2,q) 
CC 

13.12.2016  LIEBERMANN Clelia  Construction of X^{p,q} 
CC  
15.12.2016  ROSSET Julien 
Spectral
estimates 
CC  
20.12.2016  KARLEN Matthieu  4regular
graphs with large girth 
CC  
24.02.2017  WEY Jan  Free
groups I 
CC  
24.02.2017  BAKIU Vjosa  Free groups II  CC  
03.03.2017  VÖHRINGER Eliane  Free
groups III 
CC  
03.03.2017  GENDRE Gwenael  The group SL(2,R)  CC  
10.03.2017  SIMONET Johanne  The padic numbers  CC 