The meeting will be held on the 14th July 2017 in the Alan Turing Building

(directions) at the University of Manchester.
All talks take place in Frank Adams Room 1 on the first floor.

All talks take place in Frank Adams Room 1.
Further to the talks, we will have a social dinner.

We have funding to support the attendance of PhD students, please contact Johan Martens (johan.martens@ed.ac.uk).

The meeting is supported by the LMS.

### Abstracts

#### Aleksandr Pukhlikov: Birational geometry via maximal singularities

I will explain the main ideas and techniques of the method of maximal singularities by a number of examples of birationally (super)rigid higher-dimensional Fano varieties and fibre spaces.

#### Elisa Postinghel: Polyhedrality of Newton-Okounkov bodies for Mori dream spaces

Let X be a Mori Dream Space embedded in a toric variety with algebraic torus T. We construct a tropical compactification of the restriction of X to T that determines a model of X dominating all its small Q-factorial
modifications. Exploiting the combinatorial properties of such compactification, we recover a Minkowski basis for the Newton-Okounkov bodies of Cartier divisors on X and hence a set of generators of the movable cone of X. The existence of such basis allows us to prove the polyhedrality of the global Newton-Okounkov body and the existence of toric degenerations.

This is joint work with Stefano Urbinati.

#### Damiano Testa: Singular plane sections of Fermat surfaces and roots of unity

Let X be a Fermat surface in projective space. I will show how it is possible to relate plane sections with many singular points with certain linear equations in roots of unity. The analysis exploits an explicit description of the projective dual of the surface X. The ultimate goal is to determine which highly singular plane curves are contained in X.