1. Rudy Rosas: Curvas características de campos de vectores holomorfos.
2. Clementa Alonso: TBA
3. Christian Valqui:Twisted tensor products of K^n with K^m
Joint work with Jack Arce, Jorge Guccione and Juan José Guccione. We give a detailed description of different families of twisted tensor products of K^n with K^m. These families include the case K^n x K^2 considered by Cibils in [C] and yield a simple description in the case of reduced rank one considered in [JLNS]. This family corresponds to truncated quiver algebras with square zero radical, whereas another family corresponds to (formal) deformations of some these algebras. We also construct all twisting maps of K^3 x K^3.
4. Alvaro Rittatore: Representation theory for algebraic groups
In this talk we will present a representation theory for arbitrary algebraic groups over a algebraically closed field $\Bbbk$, generalizing the representation theory of affine algebraic groups.
A "good" representation theory must at least solve the following two key problems:
The Reconstruction Problem: can an algebraic group be described in terms of its category of representations? That is, given two algebraic groups $G,G'$ with equivalent categories of representations, then the $G$ and $G'$ are isomorphic.
The Recognition Problem: can a “category of representations” be described intrinsically? In other words, we seek to describe which categories are the representation theory of an algebraic group; if the answer is affirmative, we can say that the representation theory describe the categorie of algebraic groups in an "efficient" way.
In the case of affine group schemes, the work of Grothendieck, Saavedra and Deligne-Milne gives an affirmative answer for both problems above, in the so-called Tannaka Duality Theorem. However, up to now no representation theory has been developed. In order to do so, we consider not the algebraic group $G$, but its Chevalley's decomposition as an extension of an Abelian variety $A$ by an affine algebraic group $G_{aff}$, and "represent" such an extension by letting the group $G$ act over a homogeneous vector bundle over $A$ -- of course, we impose additional restrictions on the action. As in the affine case, where in order to solve the Recognition Problem one needs to deal with projective limits of finite type group schemes (that is, with affine group schemes) instead of affine algebraic group, in our situation
we need to deal with projective limits of \emph{finite type affine extensions} of an Abelian variety $A$.
This is a joint work in progress with Pedro Luis del Ángel (Cimat, Mexico) and Walter Ferrer Santos (Udelar, Uruguay).
5. Antonio Laface: On the Chow ring of complexity one T-varieties.
A T-variety is a normal complex variety X endowed with an effective action of an algebraic torus T.
The complexity of X is dim X − dim T. Such varieties generalize toric varieties, which have complexity zero, and can be described by means of the language of divisorial fans developed by Altmann, Hausen and Süß. The topology of toric varieties has been widely studied (see e.g. [3, 5, 6]), in particular a presentation for the Chow ring is given in terms of fan of cones [3, 4, 6]. In this talk I will discuss the Chow ring of complexity one T-varieties in terms of their divisorial fans. This is joint work in progress with A. Liendo and J. Moraga.
6. Fernando Cukierman: Stability of logarithmic foliations.
7. Elizabeth Gasparim: Geometría de superfícies y 3-variedades complejas.
Describiré superfícies y 3-variedades complejas de Calabi-Yau, sus deformaciones, moduli de fibrados, y aplicaciones a la física matemática.
8. Javier Zúñiga: Modular Operations on Semistable Ribbon Graphs
Modular Operations arise on moduli spaces of Riemann Surfaces as an "opposite" to degeneration of surfaces along geodesics. This idea can be formalized through the Quantum Master Equation. Semistable Ribbon Graphs provide a combinatorial model for these moduli spaces and thus it is possible to ask: what are the corresponding modular operations in this model? In this talk we explore the degeneration of semistable ribbon graphs in order to provide some answers to this question.
9. Arturo Fernández: Normal forms of singular Levi-flat hypersurfaces
We present normal forms for Levi-flat hypersurfaces which are defined by the vanishing of the real part of complex quasi-homogeneous polynomials with isolated singularity. Furthermore, we also present two new rigid normal forms for Levi-flat hypersurfaces which are preserved by a change of coordinates that preserves volume.
10. Richard Gonzales: K-theory of varieties with group action.