(with Elchanan
Mossel)
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.
and
A presentation
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?
and
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.
Noise sensitivity
and chaos in social choice theory. And a power point
presentation (HU-center of rationality, June, 2007).
with M. Safra, Threshold phenomena and
influences.
###

Slides of lectures
## 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
Richard Stanley
.

###
M. Sc Students:
Graduated:
Oded Schramm
,
Eran London,
Yuri Rabinovich
,
Alex Samorodnitsky
,
Yuval Roichman
,
Isabella Novik,
Moshe Litvin,
Akiva Kadari,
Yoav Kirsch,
Shachar Lovett,
,
Eran Nevo,
Yuval Salant,
Yonathan Samet, Eyal Novinsky,
Ilan Nehama, Moti Novick, Aviv Sheyn, Uri Leder, Yannai Gonczarowski, and Yuval Peled. Currently: Michael Simkin.

###
Post-doctorate researchers:
Helena Jorge,
David Garbiner,
Hein van der Holst,
Guy Kindler
,
Mathieu Detour,
Frank Valentin
,
Uli Wagner,
Shakhar Smorodinsky,
Elad Dokow, Mark Kozdoba, Currently: Karim Adiprasito.

## Coauthors and collaborators

### Coauthors:
Michael Maschler,
Guillermo Owen,
Noga Alon,
Shmuel Friedland,
Anders Bjorner,
Peter Frankl,
Zoltan Furedi,
Jeff Kahn,
Nati Linial,
Jean Bourgain,
Yitzhak Katznelson,
Daniel Kleitman,
Motty Ricklin,
Larry Stockmayer,
Ehud Friedgut,
Jirka Matousek,
Itai Benjamini,
Oded Schramm,
Branden McKay,
Maya Bar-Hillel,
Dror Bar-Natan,
Gunter Meisinger,
Peter Kleinschmidt,
Roy Meshulam,
Ariel Rubinstein,
Ran Spiegler,
Assaf Naor,
Muli Safra,
Helene Barcelo,
Gunter M. Ziegler,
Amnon Shashua,
Lior Wolf,
Anat Levin,
Elchanan Mossel,
Olle Haggstrom,
Greg Friedman,
Saharon Shelah, Avi Wigderson, Irit Dinur, Noam Nisan, Imre Barany,
Nathan Keller, Moshe Tennelholtz, Uri Feige, Reshef Meir, Maria Chudnovsky, Eran Nevo, Isabella Novik, Paul Seymour,
Greg Kuperberg,
Guy Kindler.

### Other frequent collaborators:

(definition: Not from the above lists, on more than one occasion we
were seriously working on a project with the potential of leading to a
joint research paper.)
###
Micha Perles,
Richard Stanley,
Mike Saks,
Lou Billera,
Karanbir Sarkaria,
Yuval Peres,
Alex Lubotzky,
Eric Babson,
Sergiu Hart,
Laci Lovasz,
Ravi Kannan,
Janos Pach,
Doron Zeilberger,
Leonard Schulman,
Yishay Mansour,
Aviad Rubinshtein.

## homepages of some past graduate classes

###

### 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.

### Spring 2003:

(with Avi Wigderson) Mathematical problems in computer science
### Classes 2006/2007

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:
Combinaorics.
##
Past special semesters, Conferences, workshops and season-schools.

###
___s_p_r_i_n_g______2_0_0_7___________J_e_r_u_s_a_l_e_m____________________

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.

###
Midrasha
Matematicae:
Spring School in
Jerusalem:
Polytopes, Graphs and Convexity, 6-11 May, 2007.

Back-to-back mini-workshops:

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,
Metric DAY,
Lectures by Henry Cohn and Igor Pak.

___s_p_r_i_n_g______2_0_0_7___________J_e_r_u_s_a_l_e_m____________________

###
Fall 2004

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)

Face numbers and related invariants of polytopes
and complexes
The combinatorics
of the simplex algorithm
Influences, threshold phenomena
and random graphs
### Pictures (before 2005).

Top right: lecturing in a discrete geometry meeting
Ascona , 1999 (taken by: Emo Welzl), left: with Mazi, Lior, Neta and Hagai,
Jerusalem 2005,
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,
Below right:
with Yisrael Aumann, 2002 (Yaakov Bergman),
left: with Jirka Matousek, 1999 (Emo Welzl).