Automorphic Forms, Group Theory and Graph Expansion - IPAM

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

08:00-09:00
Check-In/Light Breakfast (Hosted by IPAM)
09:00-9:50
Avi Wigderson (Institute for Advanced Study)
Expander graphs - where Combinatorics and Algebra compete and cooperate.
09:50-10:20
Break
10:20-10:50
Roy Meshulam (Technion - Israel Institute of Technology)
Laplacians, Homology and Hypergraph Matching
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

Afternoon Session

12:30-14:00
Lunch (on your own)
14:00-14:50
Jon Rogawski (UCLA)
Background on Automorphic Representations and the Ramanujan Conjecture
15:00-15:50
Wen-Ching Li (Pennsylvania State University)
Automorphic forms and Ramanujan hypergraphs
15:50-16:10
Break
16:10-16:40
Cristina Ballantine (College of the Holy Cross)
Ramanujan Type Graphs and Bigraphs
16:40-18:00
Wine/Cheese Reception (Hosted by IPAM)

Tuesday, February 10, 2004

Morning Session

08:00-09:00
Check-In/Light Breakfast (Hosted by IPAM)
09:00-9:50
Donald Cartwright (University of Sydney)
<i>Ã<sub>n</sub></i> groups and their applications
09:50-10:20
Break
10:20-10:50
Beth Samuels (Yale University)
Ramanujan Complexes of Type <i>Ã<sub>d</sub></i>
10:50-11:20
Break
11:20-11:50
Uzi Vishne (Bar-Ilan University)
Ramanujan complexes of type Ãd and isospectrality
11:50-12:20
Yair Glasner (University of Illinois)
On Ramanujan graphs and their girth

Afternoon Session

12:30-14:00
Lunch (on your own)
14:00-14:50
Alexander Lubotzky (Hebrew University)
Property 'tau' I : Applications to Discrete Mathematics
15:00-15:50
Audrey Terras (University of California, San Diego (UCSD))
Fun with Zeta and L-Functions of Graphs
15:50-16:10
Break
16:10-16:40
Nathan (Nati) Linial (Hebrew University)
Lifts, discrepancy and nearly optimal spectral gaps

Wednesday, February 11, 2004

Morning Session

08:00-09:00
Check-In/Light Breakfast (Hosted by IPAM)
09:00-9:50
Alexander Lubotzky (Hebrew University)
Property 'tau' II : Applications to Hyperbolic Geometry
09:50-10:20
Break
10:20-11:10
Ron Livne (Hebrew University, Jerusalem, Israel)
Mumford's 2-dimensional complex and generalizations
11:10-11:30
Break
11:30-12:00
Tim Steger (UNISS, Italy)
Tempered Irreducible Unitary Representations of the Free group

Afternoon Session

12:00-14:00
Lunch (on your own)
14:00-14:50
David Zuckerman (University of Texas at Austin)
Some Successes and Failures of Algebra in Constructing Extractors
15:00-15:50
Salil Vadhan (Harvard University)
The Zig-Zag Product and Expansion Close to the Degree
15:50-16:10
Break
16:10-17:00
Avi Wigderson (Institute for Advanced Study)
Some explicit constructions we don't yet have
17:00-19:00
Dinner (Hosted by IPAM)

Thursday, February 12, 2004

Morning Session

08:00-09:00
Check-In/Light Breakfast (Hosted by IPAM)
09:00-9:50
Anton Deitmar (Exeter University)
A discrete Lefschetz Formula
09:50-10:20
Break
10:20-10:50
Eyal Rozenman (Technion - Israel Institute of Technology)
A New Explicit Construction of Constant-Degree Expander Cayley Graphs (?)
10:50-11:20
Break
11:20-11:50
Andrzej Zuk (University of Chicago)
Spectra of buildings
11:50-12:20
Tatiana Smirnova-Nagnibeda (Université de Genève)
Random walks on trees and Ramanujan graphs

Afternoon Session

12:30-14:00
Lunch (on your own)
14:00-14:50
Shahar Mozes (Hebrew University, Jerusalem, Israel)
Irreducible lattices in products of trees
15:00-15:30
Alexander Gamburd (Stanford University)
Uniform expansion and diameter bounds for some families of Cayley graphs
15:30-15:50
Break
15:50-16:40
Peter Sarnak (Princeton University)
The generalized Ramanujan Conjectures I

Friday, February 13, 2004

Morning Session

08:00-09:00
Check-In/Light Breakfast (Hosted by IPAM)
09:00-09:30
Bruce Jordan (Baruch College, New York)
Ramanujan graphs and the Weil Conjectures
09:30-10:00
Break
10:00-10:30
()
Title not available
10:30-11:00
Break
11:00-11:50
Peter Sarnak (Princeton University)
The generalized Ramanujan Conjectures II
11:50-12:20
()
Title not available

Afternoon Session

12:30-14:00
Lunch (on your own)
14:00-15:30
Avi Wigderson (Institute for Advanced Study)
Future Directions and Open Problems
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