Tel Aviv University
School of Mathematical Sciences
Tel Aviv University אוניברסיטת תל אביב
בית הספר למדעי המתמטיקה

Mini-conference on Algebra and Number Theory

Friday, January 23, 2015

Held at Tel Aviv University,
Schreiber building, room 007

Organizers

Eli Aljadeff      (aljadeff@tx.technion.ac.il)
Lior Bary-Soroker      (barylior@post.tau.ac.il)
Dan Haran      (haran@post.tau.ac.il)

Speakers

Pierre Dèbes (Lille)
Eli Matzri (BGU)
Chen Meiri (Technion)

Program

9:20-9:40: Gathering and Coffee
9:40-10:30: Eli Matzri, Triple Massey products in Galois cohomology
10:30-11:00: Refreshments (breakfast+coffee)
11:00-11:50: Pierre Dèbes, A Hilbert-Malle theorem for Inverse Galois Theory
12:00-12:50: Chen Meiri, Infinite index maximal subgroups of SL(n,Z)
12:50-14:00: Lunch


Abstracts:

Eli Matzri, Triple Massey products in Galois cohomology: Fix an arbitrary prime p. Let F be a field, containing a primitive p-th root of unity, with absolute Galois group G_F. The triple Massey product (in the mod-p Galois cohomology) is a partially defined, multi-valued function <*,*,*>: H^1(G_F)^3 -> H^2(G_F). In this work we prove a conjecture made by Minac and Tan stating that any defined triple Massey product contains zero. As a result the pro-p groups constructed by Minac and Tan are excluded from being absolute Galois groups of fields F as above.
Pierre Dèbes, A Hilbert-Malle theorem for Inverse Galois Theory: The main application of Hilbert's irreducibility theorem to Inverse Galois Theory is that if E/Q(T) is a Galois extension of group G, then for infinitely many positive integers t, the specialized extension E_t/Q is Galois with the same group G. In the spirit of the Malle conjecture (on the number of Galois extensions of Q with a given group and with bounded discriminant), it is desirable to know in addition that many of these specialized extensions E_t/Q are distinct. We will present a new version of HIT that counts the different specialized extensions E_t/Q and will discuss its implications to Inverse Galois Theory.
Chen Meiri, Infinite index maximal subgroups of SL(n,Z): Margulis and Soifer proved that every finitely generated linear group which is not virtually solvable has uncountably many infinite index maximal subgroups. However, not much is known about the structure of these subgroups. We will construct infinite index maximal subgroups of SL(n,Z) whose actions on projective space have different dynamical properties and discuss some algebraic consequences of these constructions. This is joint work with Tsachik Gelander.