Skip to content
# Events for 02/05/2021 from all calendars

## Seminar in Random Tensors

## Teaching Online Departmental Open Forum

## Noncommutative Geometry Seminar

## Algebra and Combinatorics Seminar

**Time: ** 11:00AM - 12:00PM

**Location: ** zoom

**Speaker: **Shachar Lovett, UCSD

**Title: ***Tensor ranks and their applications*

**Abstract: **Tensors are high-order analogs of matrices. There are several notions of "tensor rank" that extend the standard notion of matrix rank to tensors. In this talk I will describe these notions, with a focus on tensors that are formed as high tensor powers of base tensors. I will also describe some applications of tensor ranks of tensor powers, both in combinatorics and in computer science.

**Time: ** 12:00PM - 1:00PM

**Location: ** Zoom

**Speaker: **Vanessa Coffelt & Justin Cantu, Texas A&M University

**Description: **All forums will be
from 12:00 pm to 1:00 pm. The topic will be emailed to faculty the week
prior to the forum. We will use the following Meeting ID: 979 6560
9771, and will send out the password in the emails.

**Time: ** 1:00PM - 2:00PM

**Location: ** Zoom 951 5490 42

**Speaker: **Jens Hemelaer, University of Antwerp

**Title: ***Toposes in arithmetic noncommutative geometry*

**Abstract: **We give an introduction to topos theory from a geometric point of view, focusing on toposes that arise from a discrete group acting on a topological space. In particular, we will look at lattices over a global field, and see how the topos classifying them is related to the ring of finite adeles of the global field. In the case where the class group is trivial, this topos is equivalently described as a topos of presheaves on a monoid, leading to toposes that are analogous to (the underlying topos) of the Arithmetic Site of Connes and Consani. We then discuss how the different toposes are related to each other. Are there interesting geometric morphisms between them? When are these morphisms embeddings, or local homeomorphisms?
The talk is based on joint work in progress with Morgan Rogers and joint work in progress with Aurélien Sagnier.

**URL: ***Event link*

**Time: ** 3:00PM - 4:00PM

**Location: ** Zoom

**Speaker: **Jurij Volcic, TAMU

**Title: ***Freely noncommutative Hilbert's 17th problem*

**Abstract: **One of the problems on Hilbert's 1900 list asked whether every positive rational function can be written as a sum of squares of rational functions. Its affirmative resolution by Artin in 1927 was a breakthrough for real algebraic geometry. The talk addresses the analog of this problem for positive semidefinite noncommutative rational functions. More generally, a rational Positivstellensatz on matricial sets given by linear matrix inequalities will be presented; a crucial intermediate step is an extension theorem on invertible evaluations of linear matrix pencils, which has less to do with positivity and ostensibly more to do with representation theory. One of the consequences of the Positivstellensatz is an algorithm for eigenvalue optimization of noncommutative rational functions. Finally, some contrast between the polynomial and the rational Positivstellensatz in the noncommutative setting will be discussed.