Automorphic Forms, Group Theory and Graph Expansion

February 9 - 13, 2004

Schedule

All times in this Schedule are Pacific Time (PT)

Monday, February 9, 2004

Morning Session
8:00 - 9:00 Check-In/Breakfast (Hosted by IPAM)
9:00 - 9:50
Avi Wigderson (Institute for Advanced Studies, Princeton)

Expander graphs - where Combinatorics and Algebra compete and cooperate.
Presentation (PowerPoint File)
9:50 - 10:20 Break
10:20 - 10:50
Roy Meshulam (Technion, Haifa, Israel)

Laplacians, Homology and Hypergraph Matching
PDF Presentation
10:50 - 11:20 Break
11:20 - 11:50
Igor Pak (Massachusetts Institute of Technology)

The Product Replacement Algorithm: an Update

11:50 - 12:20
Joel Friedman (University of British Columbia, Vancouver)

A Proof of the Alon Second Eigenvalue Conjecture
PDF Presentation
12:30 - 2:00 Lunch (on your own)

Afternoon Session
2:00 - 2:50
3:00 - 3:50
Wen-Ching Li (Pennsylvania State University)

Automorphic forms and Ramanujan hypergraphs
PDF Presentation
3:50 - 4:10 Break
4:10 - 4:40
Cristina Ballantine (Holy Cross)

Ramanujan Type Graphs and Bigraphs
PDF Presentation
4:40 - 6:00 Wine/Cheese Reception (Hosted by IPAM)

Tuesday, February 10, 2004

Morning Session
8:00 - 9:00 Check-In/Breakfast (Hosted by IPAM)
9:00 - 9:50
Donald Cartwright (University of Sydney)

Ãn groups and their applications
PDF Presentation
9:50 - 10:20 Break
10:20 - 10:50
Beth Samuels (Yale University)

Ramanujan Complexes of Type Ãd
PDF Presentation
10:50 - 11:20 Break
11:20 - 11:50
11:50 - 12:20
Yair Glasner (University of Illinois)

On Ramanujan graphs and their girth

12:30 - 2:00 Lunch (on your own)

Afternoon Session
2:00 - 2:50
Alexander Lubotzky (Hebrew University, Jerusalem, Israel)

Property 'tau' I : Applications to Discrete Mathematics

3:00 - 3:50
Audrey Terras (University of California at San Diego)

Fun with Zeta and L-Functions of Graphs
PDF Presentation
3:50 - 4:10 Break
4:10 - 4:40
Nathan (Nati) Linial (Hebrew University, Jerusalem, Israel)

Lifts, discrepancy and nearly optimal spectral gaps


Wednesday, February 11, 2004

Morning Session
8:00 - 9:00 Check-In/Breakfast (Hosted by IPAM)
9:00 - 9:50
Alexander Lubotzky (Hebrew University, Jerusalem, Israel)

Property 'tau' II : Applications to Hyperbolic Geometry

9:50 - 10:20 Break
10:20 - 11:10
Ron Livne (Hebrew University, Jerusalem, Israel)

Mumford's 2-dimensional complex and generalizations
PDF Presentation
11:10 - 11:30 Break
11:30 - 12:00
12:00 - 2:00 Lunch (on your own)

Afternoon Session
2:00 - 2:50
David Zuckerman (University of Texas, Austin)

Some Successes and Failures of Algebra in Constructing Extractors
PDF Presentation
3:00 - 3:50
3:50 - 4:10 Break
4:10 - 5:00
Avi Wigderson (Institute for Advanced Study)

Some explicit constructions we don't yet have

5:00 - 7:00 Dinner (Hosted by IPAM)

Thursday, February 12, 2004

Morning Session
8:00 - 9:00 Check-In/Breakfast (Hosted by IPAM)
9:00 - 9:50
Anton Deitmar (Exeter University)

A discrete Lefschetz Formula
PDF Presentation
9:50 - 10:20 Break
10:20 - 10:50
Eyal Rozenman (Hebrew University, Jerusalem, Israel)

A New Explicit Construction of Constant-Degree Expander Cayley Graphs (?)
Presentation (PowerPoint File)
10:50 - 11:20 Break
11:20 - 11:50
Andrzej Zuk (University of Chicago)

Spectra of buildings

11:50 - 12:20
Tatiana Smirnova-Nagnibeda (University of Geneva)

Random walks on trees and Ramanujan graphs
PDF Presentation
12:30 - 2:00 Lunch (on your own)

Afternoon Session
2:00 - 2:50
Shahar Mozes (Hebrew University, Jerusalem, Israel)

Irreducible lattices in products of trees

3:00 - 3:30
3:30 - 3:50 Break
3:50 - 4:40
Peter Sarnak (Princeton University)

The generalized Ramanujan Conjectures I


Friday, February 13, 2004

Morning Session
8:00 - 9:00 Check-In/Breakfast (Hosted by IPAM)
9:00 - 9:30
Bruce Jordan (Baruch College, New York)

Ramanujan graphs and the Weil Conjectures
PDF Presentation
9:30 - 10:00 Break
10:00 - 10:30

To Be Announced
10:30 - 11:00 Break
11:00 - 11:50
Peter Sarnak (Princeton University)

The generalized Ramanujan Conjectures II

11:50 - 12:20

To Be Announced
12:30 - 2:00 Lunch (on your own)

Afternoon Session
2:00 - 3:30
Avi Wigderson (Institute for Advanced Study)
Joint with Alex Lubotzky (Hebrew University)

Future Directions and Open Problems