Monday, February 09, 2004
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Morning Session
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8:00 - 9:00
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Check-In/Breakfast (Hosted by IPAM)
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9:00 - 9:50
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Avi Wigderson (Institute for Advanced Studies, Princeton)
"Expander graphs - where Combinatorics and Algebra compete and cooperate."
Presentation (PowerPoint File)
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9:50 - 10:20
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Break
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10:20 - 10:50
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Roy Meshulam (Technion, Haifa, Israel)
"Laplacians, Homology and Hypergraph Matching"
Presentation (PDF File)
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10:50 - 11:20
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Break
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11:20 - 11:50
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Igor Pak (Massachusetts Institute of Technology)
"The Product Replacement Algorithm: an Update"
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11:50 - 12:20
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Joel Friedman (University of British Columbia, Vancouver)
"A Proof of the Alon Second Eigenvalue Conjecture"
Presentation (PDF File)
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12:30 - 2:00
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Lunch (on your own)
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Afternoon Session
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2:00 - 2:50
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Jon Rogawski (UCLA)
"Background on Automorphic Representations and the Ramanujan Conjecture"
Presentation (PDF File)
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3:00 - 3:50
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Wen-Ching Li (Pennsylvania State University)
"Automorphic forms and Ramanujan hypergraphs"
Presentation (PDF File)
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3:50 - 4:10
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Break
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4:10 - 4:40
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Cristina Ballantine (Holy Cross)
"Ramanujan Type Graphs and Bigraphs"
Presentation (PDF File)
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4:40 - 6:00
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Wine/Cheese Reception (Hosted by IPAM)
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Tuesday, February 10, 2004
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Morning Session
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8:00 - 9:00
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Check-In/Breakfast (Hosted by IPAM)
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9:00 - 9:50
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Donald Cartwright (University of Sydney)
"Ãn groups and their applications"
Presentation (PDF File)
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9:50 - 10:20
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Break
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10:20 - 10:50
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Beth Samuels (Yale University)
"Ramanujan Complexes of Type Ãd"
Presentation (PDF File)
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10:50 - 11:20
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Break
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11:20 - 11:50
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Uzi Vishne (Bar-Ilan University)
"Ramanujan complexes of type Ãd and isospectrality"
Presentation (PDF File)
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11:50 - 12:20
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Yair Glasner (University of Illinois)
"On Ramanujan graphs and their girth"
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12:30 - 2:00
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Lunch (on your own)
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Afternoon Session
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2:00 - 2:50
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Alexander Lubotzky (Hebrew University, Jerusalem, Israel)
"Property 'tau' I : Applications to Discrete Mathematics"
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3:00 - 3:50
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Audrey Terras (University of California at San Diego)
"Fun with Zeta and L-Functions of Graphs"
Presentation (PDF File)
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3:50 - 4:10
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Break
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4:10 - 4:40
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Nathan (Nati) Linial (Hebrew University, Jerusalem, Israel)
"Lifts, discrepancy and nearly optimal spectral gaps"
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Wednesday, February 11, 2004
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Morning Session
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8:00 - 9:00
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Check-In/Breakfast (Hosted by IPAM)
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9:00 - 9:50
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Alexander Lubotzky (Hebrew University, Jerusalem, Israel)
"Property 'tau' II : Applications to Hyperbolic Geometry"
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9:50 - 10:20
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Break
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10:20 - 11:10
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Ron Livne (Hebrew University, Jerusalem, Israel)
"Mumford's 2-dimensional complex and generalizations"
Presentation (PDF File)
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11:10 - 11:30
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Break
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11:30 - 12:00
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Tim Steger (UNISS, Italy)
"Tempered Irreducible Unitary Representations of the Free group"
Presentation (PDF File)
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12:00 - 2:00
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Lunch (on your own)
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Afternoon Session
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2:00 - 2:50
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David Zuckerman (University of Texas, Austin)
"Some Successes and Failures of Algebra in Constructing Extractors"
Presentation (PDF File)
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3:00 - 3:50
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Salil Vadhan (Harvard University)
"The Zig-Zag Product and Expansion Close to the Degree"
Presentation (PowerPoint File)
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3:50 - 4:10
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Break
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4:10 - 5:00
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Avi Wigderson (Institute for Advanced Study)
"Some explicit constructions we don't yet have"
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5:00 - 7:00
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Dinner (Hosted by IPAM)
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Thursday, February 12, 2004
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Morning Session
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8:00 - 9:00
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Check-In/Breakfast (Hosted by IPAM)
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9:00 - 9:50
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Anton Deitmar (Exeter University)
"A discrete Lefschetz Formula"
Presentation (PDF File)
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9:50 - 10:20
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Break
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10:20 - 10:50
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Eyal Rozenman (Hebrew University, Jerusalem, Israel)
"A New Explicit Construction of Constant-Degree Expander Cayley Graphs (?)"
Presentation (PowerPoint File)
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10:50 - 11:20
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Break
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11:20 - 11:50
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Andrzej Zuk (University of Chicago)
"Spectra of buildings"
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11:50 - 12:20
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Tatiana Smirnova-Nagnibeda (University of Geneva)
"Random walks on trees and Ramanujan graphs"
Presentation (PDF File)
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12:30 - 2:00
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Lunch (on your own)
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Afternoon Session
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2:00 - 2:50
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Shahar Mozes (Hebrew University, Jerusalem, Israel)
"Irreducible lattices in products of trees"
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3:00 - 3:30
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Alexander Gamburd (Stanford University)
"Uniform expansion and diameter bounds for some families of Cayley graphs"
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3:30 - 3:50
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Break
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3:50 - 4:40
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Peter Sarnak (Princeton University)
"The generalized Ramanujan Conjectures I"
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Friday, February 13, 2004
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Morning Session
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8:00 - 9:00
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Check-In/Breakfast (Hosted by IPAM)
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9:00 - 9:30
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Bruce Jordan (Baruch College, New York)
"Ramanujan graphs and the Weil Conjectures"
Presentation (PDF File)
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9:30 - 10:00
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Break
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10:00 - 10:30
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To Be Announced
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10:30 - 11:00
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Break
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11:00 - 11:50
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Peter Sarnak (Princeton University)
"The generalized Ramanujan Conjectures II"
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11:50 - 12:20
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To Be Announced
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12:30 - 2:00
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Lunch (on your own)
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Afternoon Session
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2:00 - 3:30
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Avi Wigderson (Institute for Advanced Study)
Joint with Alex Lubotzky (Hebrew University)
"Future Directions and Open Problems"
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