## Speaker:

Adam Boocher

## Speaker Link:

## Institution:

University of San Diego

## Time:

Thursday, October 3, 2019 - 3:00pm to 4:00pm

## Host:

## Location:

RH 306

Let M be a graded module over a polynomial ring. It is natural to count the number of generators and relations of M, and these two numbers are the first in a sequence of "betti numbers" for the module. In this talk I'll describe what the betti numbers are and how they encode in a sense the complexity of M. I'll discuss conjectured lower bounds and some recent work establishing these bounds in certain cases.