The meeting will be held on the 28 February and 1 March in the Alan Turing Building

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

### Thursday, 28 February

### Friday, 1 March

Further to the talks, we will have a social dinner on Thursday evening.

#### Organisers:

Christopher Frei,

Daniel Loughran,

Hendrik Süß
#### Travel Expenses:

**We have funding available to cover travel and accommodation for participants, in particular PhD students and postdocs.**
Please contact Johan Martens (

johan.martens@ed.ac.uk).

The meeting is supported by the LMS.

### Abstracts

#### Yohan Brunebarbe: Algebraicity of period maps via o-minimal GAGA

We prove a conjecture of Griffiths on the quasi-projectivity of images
of period maps using algebraization results arising from o-minimal geometry (joint with Benjamin Bakker and Jacob Tsimerman).

#### Ana-Maria Castravet: Exceptional collections on moduli spaces of stable rational curves

A question of Orlov is whether the derived category of the Grothendieck--Knudsen moduli space of stable, rational curves with n markings admits a full, strong, exceptional collection that is invariant under the action of the symmetric group \(S_n\). I will present an approach towards answering this question. This is joint work with Jenia Tevelev.

#### Jesus Martinez Garcia: The moduli continuity method for log Fano pairs

The existence of a Kähler-Einstein metric on a

**Q**-Gorenstein
smoothable Fano variety is equivalent to the algebro-geometric property of
K-stability. It is natural to perturb the metric along a
pluri-anticanonical divisor, which gives rise to the equivalent property of
log K-stability for log pairs. The 'moduli continuity method' has permitted
to explicitly realise certain connected components of the moduli of
K-stable Fano varieties as GIT quotients. In this talk, we extend the
method to log pairs to study some fundamental examples, including log pairs
formed by a cubic surface and an anti-canonical divisor, and those formed
by projective space and hyperplane sections of high degree. As an
application, we show that the moduli of log pairs in these examples is
projective.

#### Vicky Hoskins: A formula for the motive of the moduli stack of vector bundles on a curve

Following Grothendieck's vision that a motive of an algebraic variety should capture many of its cohomological invariants, Voevodsky introduced a triangulated category of motives which partially realises this idea. After describing some properties of this category, I will explain how to define the motive of certain algebraic stacks. I will then state and sketch a proof for the motive of the moduli stack of vector bundles on a smooth projective curve; this formula is compatible with classical computations of invariants of this stack due to Harder, Atiyah-Bott and Behrend-Dhillon. The proof involves rigidifying this stack using Quot and Flag-Quot schemes parametrising Hecke modifications as well as a motivic version of an argument of Laumon and Heinloth on the relative cohomology of small maps. This is joint work with Simon Pepin Lehalleur.

#### Gregory Sankaran: tbc

#### Susanna Zimmermann: Quotients of plane Cremona groups

The Cremona group is the group of binational maps of the projective space. I would like to explain how to construct a quotient of the plane Cremona group if the ground field has an extension of degree 8.