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The 26th *Amitsur Memorial Symposium *will be held at the Einstein Institute of Mathematics, the Hebrew University of Jerusalem.

Coordinators: Avinoam Mann, Aner Shalev

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**Programme**

9:30 - Gathering

10:00 - Marcel Herzog (Tel-Aviv University): *On the orders of elements in finite and periodic groups*

11:00 - Zlil Sela (The Hebrew University): *Basic conjectures and preliminary results in non-commutativealgebraic geometry*

12:00 - Lunch break

14:00 - Gili Golan (Ben Gurion University):

*Divergence functions of Thompson groups*

15:00 - Coffee break

15:30 - Chen Meiri (The Technion):

*First order rigidity of higher-rank arithmetic groups*.

16:30 - Shifra Reif (Bar-Ilan University):

*Denominator identities for periplectic Lie superalgebras*

18:00 - Dinner at Cafit, in the botanical garden near the campus.

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**Abstracts**

**Gili Golan:** **Divergence functions of Thompson groups**.

The divergence function of a group generated by a finite set X is the smallest function f(n) such that for every n any pair of elements of length n can be connected in the Cayley graph (corresponding to X) by a path of length at most f(n) avoiding the ball of radius n=4 around the identity element. We prove that R. Thompson groups F, T, and V have linear divergence functions. Therefore the asymptotic cones of these groups do not have cut points. This is joint work with Mark Sapir.

**Marcel Herzog: On the orders of elements in nite and periodic groups.**

Part A of the talk will deal with problems related to the spectrum of periodic groups, which denotes the set of element orders in such groups.

Part B of the talk will deal with problems related to the multisets of all element orders in finite groups, in particular the sums of these orders.

**Chen Meiri: First order rigidity of higher-rank arithmetic groups.**

In many contexts, there is a dichotomy between lattices in Lie groups of rank one and lattices in Lie groups of higher-rank. I will talk about a manifestation of this dichotomy in Model Theory.

Based on joint works with Nir Avni and Alex Lubotzky.

**Shifra Reif: Denominator identities for periplectic Lie superalgebras.**

Identities involving symmetric functions often have a deep meaning in representation theory, as in case of the Amitsur–Levitzky identity and Macdonald’s identities.

The latter are in fact denominator identities for affine Lie algebras, that is they are obtained by applying the Kac–Weyl character formula for the trivial representation.

In this talk I will present polynomial identities which are denominator identities of the periplectic Lie superalgebra p(n). We shall discuss their origin and homological meaning.

Joint work with Crystal Hoyt and Mee Seong Im.

**Zlil Sela: Basic conjectures and preliminary results in non-commutative algebraic geometry.**

Algebraic geometry studies the structure of sets of solutions (varieties) over fields and commutative rings. Starting in the early 1960’s ring theorists (Cohn, Bergman, Amitsur and others) have tried to study the structure of varieties over non-commutative rings (notably free associative algebras). The lack of unique factorization that they tackled and studied in detail, and the pathologies that they were aware of, prevented any attempt to prove or even speculate what can be the properties of such varieties.

Using techniques and concepts from geometric group theory and from low dimensional topology, we formulate concrete conjectures on the structure of these varieties, and prove preliminary results in the direction of these conjectures.

The *Amitsur Memorial Symposium* is an annual conference in memory of Prof. Shimshon Avraham Amitsur, hosted primarily by The Einstein Institute of Mathematics of the Hebrew University.