**Speaker: Zlil Sela**

**Title: Basic conjectures and preliminary results in non-commutative algebraic geometry**

**Abstract**: Algebraic geometry studies the structure of varieties over

fields and commutative rings. Starting in the 1960's ring theorists

(Cohn, Bergman and others) have tried to study the structure of varieties

over some non-commutative rings (notably free associative algebras).

The lack of unique factorization that they tackled and studied in detail,

and the pathologies that they were aware of, prevented any attempt

to prove or even speculate what can be the properties of such varieties.

Using techniques and concepts from geometric group theory and from low

dimensional topology, we formulate concrete conjectures about the

structure of these varieties, and prove preliminary results in the

direction of these conjectures. Further (possible) applications to the

study of representations into free associative algebras will also be

discussed.

We intend to survey the relevant background from geometric group theory,

and some from low dimensional topology, including the structure of

varieties over free groups and semigroups that motivate the conjectures.

## Date:

2018-11-22 16:00 to 17:15

## Location:

Ross 70