# Seminars Calendar

## Tuesday May 14, 2019 - 1BC45 - 14:30 - Gianluca Occhetta (Trento)

** Manifolds with two projective bundles structures **

ABSTRACT: Having a projective bundle structure makes a variety rather special, so having two different projective bundle structure should be quite uncommon, especially if we assume that the Picard group of the variety is two-dimensional (in this case the variety is Fano). On the other hand, such varieties appear in many different - apparently unrelated - contexts, for instance in the study of dual defective varieties, flops and horospherical varieties; therefore classification results for these varieties are very interesting. In my talk I will review old and new results about this problem.

## Thursday, May 16th, 2019 - 2AB40 - 14:00 - Johannes Schmitt (ETH Zürich)

** Admissible cover cycles in the moduli space of stable curves **

ABSTRACT: Inside the moduli space of stable curves there are closed subsets defined by the condition that the curve C admits a finite cover of a second curve D with specified ramification behavior. I will show how these sets can be parametrized by nice smooth and proper moduli spaces. In many cases, this parametrization can be used to compute the fundamental class of such admissible cover loci in the cohomology group of the moduli space. This is joint work with Jason van Zelm.

## Friday, May 17th, 2019 - 1AD100 - 9:30 - Nicola Pagani (Liverpool)

** Different extensions of the double ramification cycles **

ABSTRACT: Fix natural numbers g,n and integers d1, d2, ..., dn. The moduli space Mgn of n-pointed curves of genus g contains an interesting locus that parameterises pointed curves (C, p1, ..., pn) that admit a meromorphic function f such that div(f) equals \sum di pi. There is different ways of extending this cycle to the compactification of Mgn by means of stable n-pointed curves of arithmetic genus g. One way of extending this cycle is by means of the theory of relative stable maps, and another is by pulling back the Brill-Noether class w^0_0 via a (possibly rational) section to some compactified universal Jacobian. In this talk I will explain how the first can be seen as a particular case of the second (a joint work with David Holmes and Jesse Kass). If the ramification vector is of type (1, -1, 0,...0) then this gives an (unexpected to me) relation between two tautological classes.

## Friday, May 17th, 2019 - 1AD100 - 11:00 - Dimitri Zvonkine (CNRS Versailles)

** **

Fractional quantum Hall effect and vector bundles over M_{g,n} -- the first steps

ABSTRACT: Vector bundles of Laughlin states were introduced by physicists to study the fractional quantum Hall effect and their Chern classes are related to measurable physical quantities. We will explain how they are related to the vector bundle of theta-functions over the moduli space and perform the first steps in the computation of their Chern classes. Work in progress with Semyon Klevtsov.

# Working Seminars

From Berkovich to Moduli.

October 16, 2018 - room SR701 - 10:30 - Alessandra Bertapelle - A gentle introduction to Berkovich spaces I.

October 23, 2018 - room SR701 - 10:30 - Alessandra Bertapelle - A gentle introduction to Berkovich spaces II.

November 6, 2018 - room 1A150 - 12:30 - Alessandra Bertapelle - A gentle introduction to Berkovich spaces III.

November 13, 2018 - room SR701 - 10:30 - Velibor Bojkovich - On the structure of smooth k-analytic curves.

November 20, 2018 - room SR701 - 11:00 - Stefano Urbinati - Introduction to Tropical Geometry, I.

November 27, 2018 - room SR701 - 11:30 - Carla Novelli - Introduction to Tropical Geometry, II.

December 4, 2018 - room SR701 - 10:30 - Ernesto Mistretta - Introduction to Toric Varieties.

December 11, 2018 -room SR701I - 10:30 - Stefano Urbinati - Introduction to Toric Varieties, II.

December 18, 2018 - room SR701 - 11:00 - Stefano Urbinati - Compactification of Toric Varieties.

January 15, 2019 - room SR701 - 10:30 - Orsola Tommasi - An introduction to moduli spaces in algebraic geometry.

January 22, 2019 - room 1BC45 - 10:00 - Paolo Rossi - Moduli spaces of curves.

January 29, 2019 - room 1C150 - 10:00 - Orsola Tommasi - Moduli space of tropical curves.

February 5, 2019 - room 2AB40 - 10:30 - Orsola Tommasi - Tropicalization of the moduli space curves.

February 20, 2019 - room 1BC50 - 14:00 - Orsola Tommasi - Berkovich skeleton of the moduli space of curves.

April 15, 2019 - room SR701 - 13:30 - Daniele Turchetti - ** Universal Mumford curves over $\mathbb Z$ and moduli of tropical curves.**

In the theory of algebraic curves, a prominent role is played by uniformization, i.e., the description of a curve as the quotient of an open dense subset of the projective line by the action of a Schottky group. All complex algebraic curves admit uniformization, as well as some p-adic curves, called Mumford curves. In this talk, I present a construction of universal Mumford curves, analytic spaces that parametrize both archimedean and non-archimedean uniformizable curves of a fixed genus. This construction relies on the existence of suitable moduli space for marked Schottky groups, that can be achieved using the theory of Berkovich spaces over rings of integers of number fields.

In a second part, I explain how we can derive topological properties of Schottky spaces and universal Mumford curves by comparing them with two classical objects: the Culler-Vogtmann outer space and the moduli space of tropical curves.

This is joint work with Jérôme Poineau.

May 6, 2019 - room SR701 - 14:15 - Giacomo Graziani - Tate's uniformisation: from complex to p-adic. I.

May 13, 2019 - room 2BC60 - 14:30 - Giacomo Graziani - Tate's uniformisation: from complex to p-adic. II.

Page maintained by A. Bertapelle, M. Longo