The academic year starts today. As usual it is very hectic and it is wonderful to see the ever younger and younger students. Being a TelAvivian in residence in the last few years, I plan this year to split my time between HUJI and TAU.

Let me tell you about a special year taking place at the Israeli Institute of Advanced Science at Jerusalem on Geometric, Topological and Computational Aspects of High-Dimensional Combinatorics, the opening workshop of this conference at Sde boker, and my course on Helly-type theorems.

## Geometric, Topological and Computational Aspects of High-Dimensional Combinatorics

organized by Alexander Lubotzky and Tali Kaufman

The web page of the semester is here. And the summary of its activity is:

Combinatorics in general and the theory of expander graphs, in particular, have been fruitful areas of interaction of pure and applied mathematics. In recent years a “high dimensional” theory has emerged. This theory, aside from its intellectual interest, also has great potential for various applications in mathematics and computer science. This theory calls for a collaboration of experts in combinatorics, topology, geometry, group theory and computer science. We propose to organize a program that will bring together people from these areas in order to create a community of scholars who can collaborate on these new challenges.

Starting tomorrow there will be a full day of activities every Monday with some additional activities on Sunday and Thursday.

### Monday Program

9:00 – 11:00 – “High Dimensional Expanders and Group Stability”, a course by Alex Lubotzky

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11:00 – 12:30 – Combinatorics research seminar

(this is the usual combinatorics seminar, which takes place in the IIAS this year instead of in the computer science building)

Organizer: Karim Adiprasito (karim.adiprasito@mail.huji.ac.il)

Upcoming talk (Oct. 23): “Counting lattice points inside a d-dimensional polytope via Fourier analysis”, Quang Nhat Le

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14:00 – 16:00 – “Afternoon learning seminar on high dimensional combinatorics”, talks and series of talks by various lecturers, intended for studying various topics together

Upcoming talk (Oct. 23): “High-dimensional permutations”, Nati Linial

On Thursdays at 11 I will give a course on Helly-type theorems which is with some relations to the special year. (Time may change.)

Next week there will be an opening workshop at Sde Boker

## Lecturers and Topics for Sde Boker 29.10 to 2.11 2017

Great topics!

Alex’ lecture reviewed the “group stability” part of the lecture. This is very fascinating, related to many deep notions and can be seen as “property testing theory for groups”. At the end of the road (or one road) comes one of the most outrageous conjectures in mathematics asserting that all groups are sofic and it is related to the congruence subgroup problem, to Kazhdan property T and Garland’s method and many other things.

Here is a link for slides for a lecture by Nati Linial on the fascinating topic of high-dimensional permutation

The talk by Quang Nhat Le was about integer points in polytopes. He started with mentioning Gauss’ circle problem: that of determining how many integer lattice points there are in a circle centered at the origin and with radius r. Then he moved to talk about polytopes, Ehrhart polynomials and Fourier methods to study them.

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