First Talk: 16:00-17:00
Ido Grayevsky: Quasi-isometric rigidity of lattices in semi-simple Lie groups
Abstract: in geometric group theory one associates a metric space to a group, with the aim of using the geometry of the space in order to understand the algebraic structure of the group (and vice-versa). The theme of quasi-isometric rigidity concerns with the following question: to what extent does the 'large-scale geometry of a group' determines its algebraic properties.
A class of groups for which this approach is extremely fruitful is the class of Lie groups (e.g. SL_n(R)) and their lattices (e.g. SL_n(Z)). This class of groups is highly important in various fields of mathematics, and admits rich geometric, algebraic and arithmetic structure.
In this talk I will give an introduction to the theme of 'large-scale geometry' and quasi-isometric rigidity, and present some remarkable results in the context of (lattices of) Lie groups, highlighting the geometric aspects which come into play in the course of the proofs.
I will not assume any familiarity with Lie groups or lattices.Second Talk: 17:00-18:00
Amichai Lampert: From finite fields to the complex numbers and back again.
Abstract: The celebrated Ax–Grothendieck theorem states that if
P:ℂn→ℂn is a polynomial map which is injective then it is also surjective. If ℂ is replaced by a finite field then this statement is trivial. Surprisingly, the above theorem actually follows from the easy finite field case! We will prove this and some other results of a similar spirit.
Join Zoom Meeting
Meeting ID: 879 7102 0108
Mon, 22/03/2021 - 16:00 to 18:00