__16:00-17:00__

**First Talk:****Quasi-isometric rigidity of lattices in semi-simple Lie groups**

__Ido Grayevsky:__**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.**

__Abstract:__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.

__17:00-18:00__

**Second Talk:**

**Amichai Lampert:****From finite fields to the complex numbers and back again.**

__The celebrated Ax–Grothendieck theorem states that if__

**Abstract:**P:ℂ

^{n}→ℂ

^{n}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.

Reference: https://arxiv.org/abs/0903.0517

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Join Zoom Meeting

https://huji.zoom.us/j/87971020108?pwd=d0swbUFrUDdCb3QzVGJQdVRZenZ4Zz09

Meeting ID: 879 7102 0108

Passcode: 946601

## Date:

Mon, 22/03/2021 - 16:00 to 18:00