# Patricio Almirón: On the quotient of Milnor and Tjurina numbers in low dimension

**Time: **
Mon 2020-06-29 15.30

**Location: **
Zoom, registration required

**Participating: **
Patricio Almirón, Complutense University of Madrid

### Abstract

In 2017, Liu gave a bound for the quotient of the Milnor and Tjurina numbers of a hypersurface singularity as a consequence of Briançon-Skoda theorem. After that, Dimca and Greuel proposed the following improvement of Liu's bound in the plane curve case: for any germ of isolated plane curve singularity, is the quotient of Milnor and Tjurina number less than 4/3?

In this talk I will present a complete answer to this question by using techniques of surface singularities. I will also focus on the algebraic and geometric aspects of this question. In addition, I will discuss a possible extension of this problem to the case of surfaces. This links the problem of studying this quotient with an old standing conjecture posed by Durfee in 1978 about a topological upper bound for the geometric genus of a surface singularity.

**Registration: **If you haven't received a link before, please email
smirnov@math.su.se
.