Resúmenes
Alberto Verjovsky Solá
"Some geometry, arithmetic, and dynamics on arithmetic quaternionic manifolds."
We will present some results about modular orbifolds and Hilbert-Blumental varieties over the quaternions.
This is joint work with Helena Lizarraga Collí, Otto Romero, and Adrián Zenteno
Ernesto Lupercio
"Singularity theory, zeta functions and representation theory."
In this talk I will tour the intersection of the subjects in the title for some interesting conclusions. Joint work with Enrique Becerra and Ludmil Katzarkov.
Laurent Meersseman
"The geography of Teichmüller stacks."
Given a smooth compact manifold M, the set of complex structures on M modulo isomorphisms isotopic to the identity can be turned into an analytic stack, the so-called Teichmüller stack, under a mild hypothesis. This being done, it is important to understand where and why there exist some bad points, that is points that prevent the Teichmüller stack from being a manifold/analytic space, and to analyse their geography and the local models around them. In this talk, we will discuss these questions and associate to any Teichmüller stack a simpler object - an orbifold in the case of Kähler complex structures - that captures the geometry of the locus of good points.
Mathias Zach
"Singularities in the search for automorphisms of Enriques surfaces."
Oguiso and Yu proved the existence of an Enriques surface $X$ with a specific automorphism $f \colon X \to X$ with maximal entropy. The universal covering of such a surface is a $2:1$ mapping $Y \to X$ from K3 surface $Y$. By virtue of the Torelli theorems, the automorphisms of the latter allow for a purely combinatorial description via the induced action on their integer lattices. This combinatorial fingerprint of the sought for automorphism $f$ is known. But as the Torelli theorems are highly non-constructive, it yet remains to construct an explicit K3 surface $X$, its Enriques involution, and the automorphism $f$. In this talk I will explain how we use singularity theory, intersection theory, and computer algebra systems to take on this task. This is a work in progress with Simon Brandhorst.
Thais Maria Dalbelo
"Local Euler obstruction of Isolated Determinantal Singularities."
An important invariant studied in singularity theory is the local Euler obstruction, which was defined by
MacPherson in [3] as one of the main ingredients of its proof for the Deligne and Grothendieck’s conjecture.
This conjecture concerns the existence and uniqueness of the Chern classes in the singular case.
Although it is very important, the local Euler obstruction is not easily computed using its definition,
which motivated many authors to find formulas to facilitate its computation. In [1], Brasselet, Lˆe and Seade
provided a Lefschetz type formula, therefore a topological formula, for the local Euler obstruction.
Using the formula presented by Brasselet, Lˆe and Seade and Newton polyhedra we compute the local Euler obstruction of isolated determinantal singularities.
Joint work with Anne Fruhbis-Kruger, Luiz Hartmann and Maicom Varella
Universidade Federal de Sao Carlos
thaisdalbelo@ufscar.br
References
[1] J.-P. Brasselet, D. T. Lˆe, and J. Seade. Euler obstruction and indices of vector fields. Topology, 39(6):1193–1208, 2000.
[2] R. D. MacPherson. Chern classes for singular algebraic varieties. Ann. of Math. (2), 100:423– 432, 1974.
Yenni Cherick
"Lipschitz Geometry of Complex Surface Germs."
It has been known since the work of Tadeusz Mostowski in 1985 that the set of complex surface germs up to bilipschitz equivalence is countable. By leveraging the work of Walter Neumann and Anne Pichon on the bilipschitz classification of complex surface germs, we describe how to construct an infinity of complex surface germs that have the same topological type and whose normalization to a fixed analytic type but are not pairwise bilipschitz equivalent.