Hebrew University of Jerusalem
Institute of Mathematics,
Givat-Ram, Jerusalem 91904, Israel
Telephone numbers: Office (972)2-6584729, Home (972)2-6536301,
kalai at math.huji.ac.il,
Telephone number: Office 203-4321238
e-mail (There is automatic farwarding between the two adresses)
kalai at cs.yale.edu
Assignement for the Course "Combinatorics"
The assinments, and the
instructions, and the
picture of the tree for II-1
An article (in Hebrew)
How to prevent the NEXT strike
Popular article: (Hebrew):
Nati Linial and Gil Kalai,
Ten Landmarks in the Story of Mathematics ,
to appear in "Galileo".
Main areas of interest: Combinatorics and convexity.
Papers and lectures:
Papers and writings: Recent items:
(with Jeff Kahn)
Functions without influential coalitions. and
Sharp Thresholds for Monotone Non Boolean Functions
and Social Choice Theory.
How quantum computers fail: Quantum codes, correlations in
physical systems, and noise accumulation.
When noise accumulates.
Slides from a related lecture at IQI.
The work of Daniel A. Spielman.
With E. Friedgut, N. Keller, and N. Nisan,
A quantitative version of the Gibbard-Satterthwaite
theorem for three alternatives.
with R. Meshulam,
Leray numbers of projections and a topological Helly-type theorem.
With S. Shelah, An example related to the Sauer-Shelah theorem.
Is the universe noise sensitive?
A power point
presentation (HU-hep seminar, April 2007).
With A. Wigderson, Neighborly embedded manifolds.
with J. Kahn,
Thresholds and expectation thresholds
Science, beliefs and knowledge:
a personal reflection on Robert J. Aumann's approach.
and chaos in social choice theory. And a power point
presentation (HU-center of rationality, June, 2007).
with M. Safra, Threshold phenomena and
Slides of lectures
homepages of some past graduate classes
Fall 2004 - Course at Yale: Boolean functions
Kalle Karu proved the nonnegativity of
toric h-vectors for general polytopes.
The seminar (Fall 2003 HU, with David Kazhdan)
Convex polytopes and Toric Varieties
was devoted to studying parts of this proof and related issues.
(with Avi Wigderson) Mathematical problems in computer science
Fall 2006, Yale University:
Topic in discrete mathematics: Mathematical problems arising from
theoretical computer science.
MW 11:30-12:45, AKW 400.
Fall 2005, Yale University - Topic in discrete mathematics:
Convexity and Linear Programming
Fall 2004, Yale University - Topic in discrete mathematics:
Analysis of Boolean function
Spring 2004, Yale University - Topic in discrete mathematics:
Past special semesters, Conferences, workshops and season-schools.
Special Semester in Jerusalem:
Combinatorics of Polytopes and Complexes: Relations with Topology and Algebra
1 March 2007- 31 August 2007
Toric varieties, polytope duality, mirror symmetry
and Kozsul duality day, Sunday, 18 March. Speakers: Tom Braden,
Sasha Zvonkin, Victor Batyrev.
Valuations day: (organizer: Semyon Alesker), Wednesday, April 11, 2007,
speakers: Semyon Alesker, Gil Kalai, Andreas Bernig.
Spring School in
Polytopes, Graphs and Convexity, 6-11 May, 2007.
Convexity, Random polytopes,
random complexes, random spaces: (co-organizer: Chris Hoffman)
June 14,15 and 18, 2007.
Combinatorics and Topology: (co-organizer: Rade Zivaljevic)
June, 18 - June 21, 2007
Workshop on Graph Rigidity, Monday, July 9, 10:30. Main speaker, Bob Connelly.
Thursday August 2 2007,
Lectures by Henry Cohn and Igor Pak.
WORLSHOP ON BOOLEAN FUNCTIONS: Spet 27-29 2004.
Spring School 2003 PROGRAM
Past and Available computer projects
Math problems, Math news, Non-math problems (under construction)
Graduate students and post-docs.
My Own Supervisor was
Micha A. Perles (Both for M.Sc and Ph. D).
My host for Post-Doctoral studies was
Face numbers and related invariants of polytopes
of the simplex algorithm
Influences, threshold phenomena
and random graphs
Ph. D. Students:
(with Micha A. Perles),
(with Micha A. Perles and (unofficially) Janos Pach),
Hagit Last, Romina Zigdon,
Nathan Keller, Noa Nitzan (with Micha A. Perles).
M. Sc Students:
Yonathan Samet, Eyal Novinsky,
Ilan Nehama, Moti Novick, Aviv Sheyn, Uri Leder, Yannai Gonczarowski, and Yuval Peled.
Hein van der Holst,
Elad Dokow, Mark Kozdoba .
Coauthors and collaborators
Gunter M. Ziegler,
Saharon Shelah, Avi Wigderson, Irit Dinur, Noam Nisan, Imre Barany,
Nathan Keller, Moshe Tennelholtz, Uri Feige, Reshef Meir.
Other frequent collaborators: (definition: on more than one occasion we
were seriously working on a project with the potential of leading to a
joint research paper.)
Pictures (before 2005).
Top right: lecturing in a discrete geometry meeting
Ascona , 1999 (taken by: Emo Welzl), left: with Mazi, Lior, Neta and Hagai,
Below: With Itai Benjamini and Oded Schramm,
Beit Belgia, Dec 2004 (Tselil Schramm).
Below: Listening with Michael Ben-Or and Sergiu Hart to
Elchanan Ben-Porath, 2002 (Yaakov Bergman). Below: the joint class with Avi,
lecture on evasiveness, 2003 (Boas Barak).
Below: right, with Shahar Mozes 2001 (Dror Bar-Natan),
left, 24th CCCC (Cambridge Combinatorics and Coffee Club) 2004,
with Yisrael Aumann, 2002 (Yaakov Bergman),
left: with Jirka Matousek, 1999 (Emo Welzl).