Amitsur Algebra

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.
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 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.
2015 Dec 03

Amitsur Algebra: Boris Plotkin (Hebrew U)

12:00pm to 1:15pm

Location: 

Manchester Building (room 209), Jerusalem, Israel
Title: Algebraic Geometry in an arbitrary variety of algebras and Algebraic Logic
Abstract: I will speak about a system of notions which lead to interesting new problems for groups and algebras as well as to reinterpretation of some old ones.
2015 Dec 24

Amitsur Algebra: Michael Larsen (Indiana U)

12:00pm to 1:15pm

Location: 

Manchester Building (room 209), Jerusalem, Israel
Title: Character values on compact simple Lie groups
Abstract: This work is part of a joint project with Aner and others to find upper bounds for values of irreducible characters in two related settings: compact simple Lie groups and finite groups of Lie type. I will discuss the first case, presenting bounds of the form
$$|\chi(g)| = O(\chi(1)^\alpha),$$
2017 Dec 28

Amitsur Algebra: Ari Shnidman (Boston College), "The behavior of rational points in one-parameter families"

12:00pm to 1:00pm

Location: 

Ross 70, Math Building, Givat Ram

Title: The behavior of rational points in one-parameter families
Abstract: How often does a "random" algebraic plane curve f(x,y) = 0
have a solution with rational coordinates? In one-parameter "twist"
families of elliptic curves, Goldfeld conjectured that there should be
a rational point exactly half of the time. Recent progress towards
this conjecture makes use of Selmer groups, and I'll explain the
geometric idea underlying their construction. I'll also describe
results for families of curves of higher genus, and abelian varieties
2016 Dec 29

Amitsur Algebra: Igor Rivin, "Random integer matrices"

12:00pm to 1:00pm

Location: 

Manchester Building, Room 209
Title: Random integer matrices
Abstract: I will discuss various models of random integer matrices, and their (occasionally surprising) properties. Some of the work discussed is joint with E. Fuchs.
2016 Dec 08

Amitsur Algebra: George Glauberman (Chicago)

12:00pm to 1:15pm

Location: 

Manchester Building, Room 209
Title: Fixed points of finite groups on modules
Abstract: Suppose G is a finite group, p is a prime, S is a Sylow p-subgroup of G, and V is a G-module over a field of characteristic p. In some situations, an easy calculation shows that the fixed points of G on V are the same as the fixed points of the normalizer
of S in G. Generalizations of this result have been obtained previously to study the structure of G for p odd. We plan to describe a new generalization for p = 2. (This is part of joint work with J. Lynd that removes the classification of finite simple groups
2017 Mar 02

Amitsur Algebra: Lev Glebsky, " Almost Congruence Extension Property for subgroups of free groups"

12:00pm to 1:00pm

Location: 

Manchester Building, Room 209
Title: Almost Congruence Extension Property for subgroups of free groups.
Abstract.
The talk essentially based on: https://arxiv.org/abs/1606.02345
Let G be a group and H every normal subgroup N of H is an intersection of some normal subgroup of G with H. The CEP appears in group theory in different context.
The following question seems to be very difficult:
Which finitely generated subgroup of a free group has CEP?

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