Seminars

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 field K : the valuation sub GR of K correspond to the finite and
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. Based on joint work with S.Evra, A.Lubotzky and O.Parzanchevski.
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.

Pages