2010

14/05/10,  11:00
Dep. Álgebra,  UCM 		Mario García Fernández (MPI Bonn)
Solutions of the Strominger system via deformation
We prove that a given Calabi-Yau threefold X with a stable holomorphic vector bundle E can be deformed to a simultaneous solution of the Strominger system and the equation of motion of a heterotic string compactification provided that the second Chern class of the vector bundle equals the second Chern class of TX. The existence of such solutions has been implicitly assumed in heterotic model building based on a perturbation method developed by Witten, which gave evidence for the existence of such solutions. This is joint work with Bjorn Andreas.
09/07/10,  12:00
Sala de conferencias   		Peter Newstead (Univ. Liverpool)   
Bundles of rank 2 with 4 sections on an algebraic curve
When one fixes the rank and dimension of the space of sections of a stable or semistable vector bundle on an algebraic curve, it is an interesting question to determine the minimum degree which the bundle can have. The simplest unsolved case is for rank 2 with 4 independent sections. I will present an example which has been known for some years but has only very recently appeared on the arXiv and set this in a more general context than has been done previously. In particular, the arguments apply to any smooth curve rather than just the general curve of a given genus and give a complete answer to the problem in many cases.
08/10/10,  13:00
Sala de juntas   		Claudia Reynoso (Univ. Guanajuato & Inst. Fourier de Grenoble)   
Sobre la pendiente de fibraciones relativamente minimales en superficies racionales complejas
Sea S una superficie racional compleja y consideremos una fibración relativamente minimal f:S→P1 con fibra general C de género g. En este trabajo buscamos condiciones para que la desigualdad 6(g-1)≤Kf2 se satisfaga, donde Kf es el haz canónico relativo de f, las condiciones que damos están relacionadas con la gonalidad de C y el número de ciertos divisores excepcionales contenidos en S. Finalmente construiremos algunos ejemplos de fibraciones con las propiedades deseadas. Colaboración con Abel Castorena (UNAM, México) y Alexis Zamora (Univ. Zacatecas, México)
29/10/10,  12:00
ICMAT 		João Pedro P. dos Santos (Univ. Paris 6)   
The homotopy exact sequence for the fundamental group scheme defined via D-modules
Let X be a smooth and connected scheme over an algebraically closed field of prime characteristic. The category of OX-coherent D-modules, where D stands for the ring of differential operators defined in EGA IV-4, allows us to define, by means of Tannakian duality, an affine group scheme Π(X) which generalizes the etale fundamental group. The goal of the present work is to relate Π(X) and Π(Y), when X and Y are connected by the existence of a flat, proper and "not very singular" morphism f:X→Y. More precisely, we establish the existence of an exact sequence of affine group schemes Π(f-1(y))→Π(X)→Π(Y)→1. This is an analogue of Corollary 1.4 in exposé X of Grothendieck's Séminaire de Géométrie Algébrique. In this seminar we will start by recalling the basic equivalence between D-modules and a more soothing object for algebraic geometers, the Frobenius divided sheaves. (The latter are the replacement of local systems.) We then show how standard methods from algebraic geometry and Berthelot's theory of arithmetic D-modules can be used to tackle the problem.

2009

20/02/09,  11:00
Sala de conferencias   		Marina Logares (Univ. Porto)   
Moduli of parabolic Higgs bundles and the Atiyah algebroid
We will discuss the holomorphic Poisson geometry of the moduli space of parabolic Higgs bundles over a Riemann surface with marked points in terms of Lie algebroids. Time permitting we will also discuss the Hitchin system in this setting and show how this provides a global analogue of the Grothendieck-Springer resolution. This is joint work with Johan Martens.
27/03/09,  11:00
Sala de conferencias   		Jochen Heinloth (Univ. Amsterdam)   
Moduli spaces of torsors under twisted groups and degenerations of the affine Graßmanian
Pappas and Rapoport made a series of conjectures concerning the geometry of moduli spaces of bundles for twisted group schemes on curves. In this talk I would like to explain what these group schemes are, and why you might know some of the corresponding moduli spaces even if you have not seen the groups before. Finally I would like to explain a proof of some of the conjectures. Focusing mainly on the Picard group of the moduli spaces.
24/04/09,  11:00
Sala de conferencias   		Sergio Lukic (Imperial College London)   
Problems from extra dimensions and some numerical solutions
I will review some mathematical problems motivated from the physics of supersymmetric kaluza-klein reductions, which can be solved by using numerical methods. We use Donaldson's quantization link between infinite and finite dimensional GIT quotients as the mathematical framework to define our numerical techniques. I will discuss different algorithms, numerical implementations and some explicit examples with Calabi-Yau three-folds.
08/05/09,  11:00
Sala de conferencias   		Graham Smith (CRM, Univ. Autònoma de Barcelona)   
Flat conformal structures and constant curvature hypersurfaces
Kulkarni and Pinkall associate to every Flat Conformal Structure (excluding exceptional cases) a complete hyperbolic manifold with a single concave boundary component. The exact relationship between these manifolds and the Flat Conformal Structure remains unclear. I show how many of these hyperbolic manifolds may be foliated by hypersurfaces of constant curvature and how this reveals information about that relationship.
03/06/09,  15:30
Sala de conferencias   		Peter Newstead (Univ. Liverpool)   
ICMAT Colloquium: Clifford indices for vector bundles on Riemann surfaces

The problem of determining the possible dimensions of linear systems (in modern terms, the dimensions of the spaces of sections of holomorphic line bundles) was posed by Riemann in the mid-19th century. For a general Riemann surface, the problem was solved by classical Brill-Noether theory. The classical Clifford index is a measure of the failure of a Riemann surface to be general in this sense.

In this talk, I will review the classical theory and then discuss its extension to linear systems of higher rank (vector bundles). It turns out that there are several possible definitions of the Clifford index for vector bundles and that they are subtler invariants of the Riemann surface than the classical index. This theory is in its infancy and I will describe its birth and some pointers to its development.

This is joint work with Herbert Lange.

09/06/09,  15:00
Sala de juntas  
Contact: O. García-Prada (CSIC Madrid)    Higgs bundle Spring day
15:00 Peter Newstead (U Liverpool): Higgs bundles for genus 1
15:45 Álvaro Antón (CSIC): Higgs bundles and triality
16:30 Roberto Rubio (CSIC): Exceptional Hermitian symmetric spaces and Higgs bundles
17:15 Steven Bradlow (U Illinois, Urbana-Champaign): Hitchin maps for Sp(4,R) and SL(2,R) Higgs bundles
12/06/09,  11:00
Sala de conferencias   		Timothy Logvinenko (Univ. Liverpool)   
A derived approach to the geometric McKay correspondence
We describe a three dimensional generalization of the geometric McKay correspondence constructed by Gonzales-Sprinberg and Verdier in dimension two. More precisely, we show that the Bridgeland-King-Reid derived category equivalence induces a natural geometric correspondence between irreducible representations of G⊂SL3(C) and closed subschemes of the exceptional set of G-Hilb(C3). Applied in dimension two this produces precisely the classical McKay. For an abelian G the Fourier-Mukai computations involved turn out to be intrinsically related to the piece of toric combinatorics known as 'Reid's recipe'.
26/06/09,  11:00
Sala de conferencias   		Claudia Reynoso (Univ. Guanajuato)   
Puntos singulares y automorfismos de foliaciones holomorfas de CP2
Consideramos la acción de cambio de coordenadas del grupo de automorfismos de CP2 en el espacio de foliaciones holomorfas de grado d en CP2 y estudiamos esta acción en el sentido de la teoría de invariantes geométricos. Veremos algunas propiedades de las foliaciones inestables y semiestables relacionadas con sus puntos singulares, existencia de soluciones algebraicas, transversalidad respecto a fibraciones racionales y sus automorfismos.
16/10/09,  11:00
Serrano 119 		Study group: the geometric Langlands correspondence
WEB - http://www.icmat.es/seminarios/langlands/
12/11/09,  11:00
Serrano 121&113bis
Study group: the geometric Langlands correspondence
WEB - http://www.icmat.es/seminarios/langlands/
11/12/09,  11:00
Sala de conferencias   		Fernando Muro (Univ. Sevilla)   
A glimpse at the moduli space of triangulated categories
Kontsevich, in his ICM'94 talk, stated that his Homological Mirror Symmetry conjecture is equivalent to the concurrence of two points in the same connected component of the moduli space of triangulated categories, ``whatever it means'' (sic). The recent development of homotopical algebraic geometry allows a precise definition of such a moduli space. Without getting into technicalities we will present a description of the spaces of algebraic and classical triangulated structures over a fixed k-linear category, k a field, with a given suspension functor. We will also comment on the map relating these spaces.

2008

25/01/08 Atanas Iliev (Bulgarian Academy of Sciences)   
Fano Varieties and Integrable Systems
25/01/08 André Gama Oliveira (Univ. Porto)    Representations of surface groups in the projective general linear group
09/05/08 V.V.Nikulin (Univ. Liverpool)    On the classification of arithmetic hyperbolic reflection groups
13/05/08 Laurent Ducrohet (TIFR, Mumbai)    Frobenius and vector bundles on curves
29/05/08 S. Ramanan (Chennai Mathematical Institute)   
Coloquium: Some Mathematical Achievements in the Last 50 Years
30/05/08
Contact: O. García-Prada (CSIC Madrid)    Higgs bundle Spring day
10:00 - 11:00 Peter Newstead (Liverpool): Rank 2 coherent systems on algebraic curves
11:30 - 12:30 S. Ramanan (Chennai): Kostant's TDS and Hitchin morphism
12:45 - 13:45 Christian Pauly: Strange duality for principal G-bundles over curves

2007

19-23/02/07 German-Spanish workshop on moduli spaces of vector bundles   URL: http://www.mat.csic.es/webpages/conf/german-spanish-mod07/
11/10/07 Domingo Toledo (Univ. Utah)    Coloquio: Ecuaciones Cúbicas y Geometría Hiperbólica Compleja
26/10/07 Peter Newstead (Univ. Liverpool)    Clifford's Theorem for coherent systems
08/06/07 Maria Jesus Vazquez Gallo (Univ. Politécnica de Madrid)    Polinomios de Hodge de los espacios de móduli de triples de rango (2,2).
25/05/07 Nigel Hitchin (Univ. Oxford)    Higgs Bundles in Arbitrary Representations
25/05/07 Nigel Hitchin (Univ. Oxford)    New Aspects of Higgs Bundles (after Kapustin and Witten)
30/11/07 Alastair King (Univ. Bath)    Dimer models and Calabi-Yau algebras

2006

09/06/06 Francisco Presas (CSIC Madrid)    Construcción de variedades de contacto no rellenables
02/06/06 Julien Keller (Imperial College London)    Vortex type equations and canonical metrics
26/05/06 Oscar García-Prada (CSIC Madrid)    Involuciones del espacio de móduli de fibrados de Higgs
12/05/06 Tomas L. Gomez (CSIC Madrid)    Teorema de Torelli para fibrados de Higgs
28/04/06 Klaus Niederkrueger (Univ. Libre de Bruxelles)    Un intento de generalizar overtwisted a dimensiones superiores
20/04/06 Le Dung Trang (ICTP, Trieste)    COLOQUIO: Lefschetz method to study Algebraic Varieties
17/11/06 Alexander Schmitt (Univ. Essen)    Parabolic Principal Bundles and the Cohomology Ring of the Moduli Stack
24/03/06 Carlo Madonna (CSIC Madrid)    On some rank 3 and 4 vector bundles on quartic threefolds
17/03/06 Vicente Muñoz (CSIC Madrid)    Teorema de Torelli para espacios de móduli de conexiones
10/03/06 Tomás Gómez (CSIC Madrid)    Correspondencia de Hecke para fibrados simplécticos
24/02/06 Luis Álvarez Cónsul (CSIC Madrid)    Funciones theta generalizadas y Gromov-Witten
15/12/06 Hernan Cendra (Univ. Nacional del Sur Bahía Blanca, Argentina)    Desingularization of Implicit Differential Equations
10/11/06 Carlo Madonna (CSIC Madrid)    Fibrados vectoriale sobre superficies K3
03/11/06 Olivier Biquard (Universite Louis Pasteur, Strasbourg)    Around the Kostant-Sekiguchi-Vergne correspondence
27/01/06 Marina Logares (CSIC Madrid)    Números de Betti del espacio de móduli de fibrados de Higgs U(2,1) parabólicos

2005

30/09/05 Esther Vergara (Univ. York)    Secciones armónicas y geometría de contacto
17/06/05 Peter Newstead (Univ. Liverpool)    Coherent systems on elliptic curves
10/06/05 Francisco Presas (CSIC Madrid)    Morse-Bott contact homology
07/06/05 Lluis Acero Sistach (Univ. Politècnica de Catalunya)    Cuadrados latinos y grafos de Moore
03/06/05 Maria Calle (Courant Institute, New York)    Restricción de la codimensión de flujo de la curvatura media
27/05/05 Marina Logares (CSIC Madrid)    On the topology of the moduli of U(p,q) parabolic Higgs bundles
13/05/05 Andras Szenes (BME Budapest)    Equivariant intersection theory of moduli spaces of Higgs bundles
06/05/05 David Martín de Diego (CSIC Madrid)    Mecánica en Grupoides de Lie
26/04/05 François Labourie (Univ. Paris-Sud, Orsay)    Crossratio, curves and representations of surface groups
22/04/05 Marco Castrillón (Univ. Complutense de Madrid)    Estructuras homogéneas y variedades cuaterniónicas
13/04/05 Shoshichi Kobayashi (Univ. Berkeley)    Almost complex manifolds and hyperbolicity
13-15/04/05 Santiago Simanca (Stony Brook)    Curso sobre Métricas Extremales
08/04/05 Andrew Dancer (Univ. Oxford)    Superpotentials and the Einstein equations
01/04/05 Domingo Toledo (IHÉS)    Volume of the space of real cubic surfaces
11/03/05 Daniel Pons (Univ. Pompeu Fabra, Univ. Autónoma de Barcelona)    Metricas canónicas y no canónicas en geometría real y Kahleriana
04/03/05 Marta Aparicio (CSIC Madrid)    Clasificación de álgebras de Lie reales simples. Álgebras de Lie excepcionales
25/02/05 Marta Aparicio (CSIC Madrid)    Clasificación de álgebras de Lie complejas semisimples
18/02/05 Alexander Schmitt (Univ. Essen)    An update on singular principal bundles
14/02/05 José Figueroa-O'Farrill (Univ. Edimburgo)    ¿Qué es la supersimetría?
02/12/05 Javier Gallego (Univ. Complutense de Madrid)    Deformaciones de morfismos finitos y alisamiento de estructuras multiples
18/11/05 Christian Pauly (Univ. Montpellier)    G-fibrados principales sobre curvas y funciones theta
04/11/05 Enrique Arrondo (Univ. Complutense de Madrid)    The Picard group of subvarieties of small codimension
14/10/05 Indranil Biswas (TIFR, Mumbai)    On the stability of the tangent bundle of a hypersurface in a Fano variety
07/10/05 Arijit Dey (Institute of Mathematical Sciences, Chennai)    Parabolic bundles on algebraic surfaces: The Donaldson-Uhlenbeck compactification
28/01/05 Francisco Presas (CSIC Madrid)    La métrica de Hofer en el espacio de simplectomorfismos
21/01/05 Dan Fox (Georgia Institute of Technology, Atlanta)    Null Path Geometries
14/01/05 Ignasi Mundet (Univ. Barcelona)    Una inversa por la derecha de la aplicación de Kirwan
27-28/07/05
Contact: O. García-Prada (CSIC Madrid)    Workshop on Higgs bundles and surface group representations
Monday, 27 June
9:30 - 10:30: Marc Burger (ETH, Zurich): Symplectic Anosov Structures I
11:00 - 12:00: Oscar García-Prada (CSIC Madrid): Maximal Toledo representations and Higgs bundles
12:30 - 13:30: Vicente Muñoz (CSIC Madrid): Parabolic Higgs bundles of rank 3
16:00 - 17:00: Marina Logares (CSIC Madrid): U(p,q)-parabolic Higgs bundles
17:30 - 18:30: Bill Goldman (Maryland): Mapping class groups actions on moduli spaces
Tuesday, 28 June
9:30 - 10:30: Alessandra Iozzi (Bassel): Symplectic Anosov Structures II
11:00 - 12:00: Ignasi Mundet (UB, Barcelona): Symplectic Higgs bundles
12:30 - 13:30: Anna Wienhard (Bassel): Symplectic Anosov Structures III
16:00 - 17:00: Antony Maciocia (Edinburgh): TBA
17:30 - 18:30: Peter Newstead (Liverpool): Existence of $\alpha$-stable coherent systems
20/05/05
Contact: O. García-Prada (CSIC Madrid)    Higgs bundle Spring day
11:00: Oscar García-Prada (CSIC Madrid): Generalised Teichmüller spaces and Higgs bundles.
12:30: Steven Bradlow (Univ. Illinois, Urbana-Champaing): On some special cases, including the earliest known example of a G-Higgs bundle.
15:30: Peter Gothen (Univ. Porto): Components of of moduli of representations with maximal Toledo invariant.
17:00: S. Ramanan (Chennai Mathematical Institute): Higgs bundles and the Hitchin map.

2004

17/12/04 Szilard Szabo (Univ. Strasbourgh)    Nahm transform for Higgs bundles with singularities on the Riemann sphere
10/12/04 Francisco Presas (IMAFF-CSIC)    Pinceles de Lefschetz singulares
03/12/04 Cristina Martínez (Univ. Autónoma de Madrid)    Intersección de Q-divisores en el stack de aplicaciones estables de curvas racionales en la Grassmanniana y geometría enumerativa
26/11/04 Francisco Presas (CSIC Madrid)    Estructuras algebraicas en la homología de los espacios de lazos
19/11/04 Jaime Muñoz Masqué    Hamiltonianas covariantes que son invariantes gauge en el fibrado de conexiones de un fibrado principal
12/11/04 Francisco Presas (CSIC Madrid)    Problemas de empaquetamiento en geometría simpléctica
05/11/04 Luis Álvarez Cónsul (CSIC Madrid)    Una caracterización cohomológica de los haces semiestables
29/10/04 Tom Bridgeland (Univ. Sheffield)    Birational geometry and derived categories
22/10/04 Vicente Muñoz (CSIC Madrid)    Propiedad hard Lefschetz y formas simplécticamente armónicas
15/10/04 Francisco Presas (CSIC Madrid)    Estructuras geométricas en espacios de lazos
01/10/04 Tomás Gómez (CSIC Madrid)    Teoremas de restricción para fibrados principales
Last updated 30 Jun 2010