# Amitsur Algebra

The Amitsur Algebra seminar meets on Thursdyas at 12:00 at room 70 in the Ross Building.
2018 Jun 26

# Amitsur Symposium: Lev Glebsky - "Approximations of groups by finite and linear groups"

4:30pm to 5:30pm

## Location:

Manchester House, Lecture Hall 2
The sofic groups and hyperlinear groups are groups approximable by finite symmetric
and by unitary groups, respectively. I recall their definitions and discuss why those classes of groups are interesting. Then I consider approximations by other classes of groups and review some results, including rather recent ones by N. Nikolov, J. Schneider, A.Thom, https://arxiv.org/abs/1703.06092 .
If time permits I'll speak about stability and its relations with approximability.
2018 Jun 26

# Amitsur Symposium: Arye Juhasz - "On the center of Artin groups"

2:00pm to 3:00pm

## Location:

Manchester House, Lecture Hall 2
Let A be an Artin group. It is known that if A is spherical (of finite type) and irreducible (not a direct sum), then it has infinite cyclic center.
It is conjectured that all other irreducible Artin groups have trivial center. I prove this conjecture under a stronger assumption that not being spherical namely, if there is a standard generator which is not contained in any 3-generated spherical standard parabolic subgroup. The main tool is relative presentations of Artin groups.
2018 Jun 27

# Amitsur Symposium: Yael Algom-Kfir - "The metric completion of an asymmetric metric space"

4:30pm to 5:30pm

## Location:

Manchester House, Lecture Hall 2
The Teichmuller space with the Thurston metric and Outer Space with the Lipschitz metric are two examples of spaces with an asymmetric metric i.e. d(x,y)
eq d(y,x). The latter case is also incomplete: There exist Cauchy sequences that do not have a limit. We develop the theory of the completion of an asymmetric space and give lots of examples. Time permitting we will describe the case of Outer Space.
2018 Jun 26

# Amitsur Symposium: Alex Lubotzky - "First order rigidity of high-rank arithmetic groups"

10:00am to 11:00am

## Location:

Manchester House, Lecture Hall 2
The family of high rank arithmetic groups is a class of groups playing an important role in various areas of mathematics.
It includes SL(n,Z), for n>2 , SL(n, Z[1/p] ) for n>1, their finite index subgroups and many more.
A number of remarkable results about them have been proven including; Mostow rigidity, Margulis Super rigidity and the Quasi-isometric rigidity.
2018 Jun 27

# Amitsur Symposium: Chloe Perin - "Forking independence in the free group"

2:00pm to 3:00pm

## Location:

Manchester House, Lecture Hall 2
Model theorists define, in structures whose first-order theory is "stable" (i.e. suitably nice), a notion of independence between elements. This notion coincides for example with linear independence when the structure considered is a vector space, and with algebraic independence when it is an algebraically closed field. Sela showed that the theory of the free group is stable. In a joint work with Rizos Sklinos, we give an interpretation of this model theoretic notion of independence in the free group using Grushko and JSJ decompositions.
2018 Jun 27

# Amitsur Symposium: Elyiahu Rips - "Free Engel groups" (joint work with Arye Juhasz)

10:00am to 11:00am

## Location:

Manchester House, Lecture Hall 2
A free n-Engel group is the relatively free group of the variety of groups with the identical relation [x, y, y,...,y (n times)]=1. Let n>=20. We show that the free Engel group on at least two generators is not locally nilpotent. Our approach to Engel groups combines
2018 Jun 26

# Amitsur Symposium: Aner Shalev - "The length and depth of finite groups, algebraic groups and Lie groups"

3:00pm to 4:00pm

## Location:

Manchester House, Lecture Hall 2
The length of a finite group G is defined to be the maximal length of an unrefinable chain of subgroups going from G to 1. This notion was studied by many authors since the 1940s.
Recently there is growing interest also in the depth of G, which is the minimal length of such a chain. Moreover, similar notions were defined and studied for important families of infinite groups, such as connected algebraic groups and connected Lie groups.
2018 Jun 26

# Amitsur Symposium: Malka Schaps - "Symmetric Kashivara crystals of type A in low rank"

11:30am to 12:30pm

## Location:

Manchester House, Lecture Hall 2
The basis of elements of the highest weight representations of affine Lie algebra of type A can be labeled in three different ways, my multipartitions, by piecewise linear paths in the weight space, and by canonical basis elements. The entire infinite basis is recursively generated from the highest weight vector of operators f_i from the Chevalley basis of the affine Lie algebra, and organized into a crystal called a Kashiwara crystal. We describe cases where one can move between the different labelings in a non-recursive fashion, particularly when the crystal has some symmetry.
2018 Jun 27

# Amitsur Symposium: Tsachik Gelander - "Local rigidity of uniform lattices"

3:00pm to 4:00pm

## Location:

Manchester House, Lecture Hall 2
We establish topological local rigidity for uniform lattices in compactly generated groups, extending the result of Weil from the realm of Lie groups. We generalize the classical local rigidity theorem of Selberg, Calabi and Weil to irreducible uniform lattices in Isom(X) where X is a proper CAT(0) space with no Euclidian factors, not isometric to the hyperbolic plane. We deduce an analog of Wang’s finiteness theorem for certain non-positively curved metric spaces.
This is a joint work with Arie Levit.
2018 Jun 27

# Amitsur Symposium: Amiram Braun - "The polynomial question in modular invariant theory, old and new"

11:30am to 12:30pm

## Location:

Manchester House, Lecture Hall 2
Let G be a finite group, V a finite dimensional G- module over a field F, and S(V) the symmetric algebra of V. The above problem seeks to determine when is the ring of invariants S(V)^G , a polynomial ring. In the non-modular case (i.e. char(F) being prime to order(G)), this was settled in the Shephard-Todd-Chevalley theorem. The modular case (i.e. char(F) divides order (G) ), is still wide open. I shall discuss some older results due to Serre, Nakajima , Kemper-Malle and explain some new results, mostly in dimension 3.
2016 Jun 09

# Joint Amitsur Algebra&NT Seminar: Shai Haran (Technion), "New foundations for geometry"

12:00pm to 1:15pm

## Location:

Manchester Building (Ross 63), Jerusalem, Israel
*** Please note the LOCATION ***
We shall give a simple generalization of commutative rings. The
category GR of such generalized rings contains ordinary commutative
rings (fully, faithfully), but also the "integers" and the "residue
field" at a real or complex place of a number field ; the "field with
one element" F1 (the initial object of GR) ; the "Arithmetical
Surface" (the categorical sum of the integers Z with them self). We
shall show this geometry sees the real and complex places of a number
2016 Apr 21

# Amitsur Algebra: Konstantin Golubev (HU)

12:00pm to 1:15pm

## Location:

Manchester Building (room 209), Jerusalem, Israel
Title: Spectral approach to the chromatic number of a simplicial complex
Abstract: In this talk, we'll summarize results obtained in recent years in a pursuit for spectral bounds for the chromatic number of a simplicial complex. As the principal application, we'll show that Ramanujan complexes serve as family of explicitly constructed complexes with large girth and large chromatic number. We'll also present other results, such as a bound on the expansion and a bound on the mixing of a complex, and refer to open questions.
2016 Jan 07

# Amitsur Algebra: Gili Schul (Hebrew U): Rapid expansion in finite simple groups

12:00pm to 1:15pm

## Location:

Manchester Building (room 209), Jerusalem, Israel
Title: Rapid expansion in finite simple groups
Abstract: We show that small normal subsets $A$ of finite simple groups expand
very rapidly -- namely, $|A^2| \ge |A|^{2-\epsilon}$, where $\epsilon >0$ is
arbitrarily small.
Joint work with M. W. Liebeck and A. Shalev
2016 Jun 16

# Amitsur Algebra: Gili Golan, "The generation problem in Thompson group F"

12:00pm to 1:15pm

## Location:

Manchester Building (room 209), Jerusalem, Israel
We show that the generation problem in Thompson group F is decidable, i.e., there is an algorithm which decides if a finite set of elements of F generates the whole F. The algorithm makes use of the Stallings 2-core of subgroups of F, which can be defined in an analogue way to the Stallings core of subgroups of a free group. An application of the algorithm shows that F is a cyclic extension of a group K which has a maximal elementary amenable subgroup B. The group B is a copy of a subgroup of F constructed by Brin.
2016 Apr 07

# Amitsur Algebra: Ayala Byron (HUJI), "Definable fields in the free group"

12:00pm to 1:15pm

## Location:

Manchester Building (room 209), Jerusalem, Israel
Abstract: In the early 2000s Sela proved that all non-abelian free groups share a common first-order theory. Together with R. Sklinos, we use tools developed in his work to show that no infinite field is definable in this theory. In this talk we will survey the line of proof for a formal solution theorem for a simple sort of definable sets, that have a structure of a hyperbolic tower, and use it to characterize definable sets that do not carry a definable structure of an abelian group.