09/09/2015, 10:30 — 12:00 — Room P3.10, Mathematics Building
Valery Alexeev, University of Georgia
Lectures on compactification of moduli spaces of surfaces (IV)
Moduli compactifications of moduli spaces of $K3$ surfaces.
08/09/2015, 14:30 — 15:45 — Room P3.10, Mathematics Building
Valery Alexeev, University of Georgia
Lectures on compactification of moduli spaces of surfaces (III)
Compactifications of moduli spaces of surfaces of general type in several special cases.
08/09/2015, 10:30 — 11:45 — Room P3.10, Mathematics Building
Valery Alexeev, University of Georgia
Lectures on compactification of moduli spaces of surfaces (II)
Moduli of stable pairs in the toric case and its variations: abelian varieties; moduli of weighted stable hyperplane arrangements.
07/09/2015, 14:30 — 16:00 — Room P3.10, Mathematics Building
Valery Alexeev, University of Georgia
Lectures on compactification of moduli spaces of surfaces (I)
Review of the one-dimensional case. Introduction to Minimal Model Program and its applications to moduli problems.
28/06/2013, 14:30 — 15:30 — Room 1.22, Faculdade de Ciências da Universidade do Porto
Oscar García-Prada, Instituto de Ciencias Matemáticas, Madrid
Geometry of Higgs Bundles
See also
http://cmup.fc.up.pt/cmup/pbgothen/IST_lectures/
Sessions at the University of Oporto
28/06/2013, 11:30 — 12:30 — Room 1.22, Faculdade de Ciências da Universidade do Porto
Steven Bradlow, University of Illinois at Urbana-Champaign
Geometry of Higgs Bundles
See also
http://cmup.fc.up.pt/cmup/pbgothen/IST_lectures/
Sessions at the University of Oporto
27/06/2013, 16:00 — 17:00 — Room 1.22, Faculdade de Ciências da Universidade do Porto
Steven Bradlow, University of Illinois at Urbana-Champaign
Geometry of Higgs Bundles
See also
http://cmup.fc.up.pt/cmup/pbgothen/IST_lectures/
Sessions at the University of Oporto
27/06/2013, 14:30 — 15:30 — Room 1.22, Faculdade de Ciências da Universidade do Porto
Oscar García-Prada, Instituto de Ciencias Matemáticas, Madrid
Geometry of Higgs Bundles
See also
http://cmup.fc.up.pt/cmup/pbgothen/IST_lectures/
Sessions at the University of Oporto
26/06/2013, 16:00 — 17:00 — Room 1.07, Faculdade de Ciências da Universidade do Porto
Steven Bradlow, University of Illinois at Urbana-Champaign
Geometry of Higgs Bundles
See also
http://cmup.fc.up.pt/cmup/pbgothen/IST_lectures/
Sessions at the University of Oporto
26/06/2013, 14:30 — 15:30 — Room 1.07, Faculdade de Ciências da Universidade do Porto
Oscar García-Prada, Instituto de Ciencias Matemáticas, Madrid
Geometry of Higgs Bundles
See also
http://cmup.fc.up.pt/cmup/pbgothen/IST_lectures/
Sessions at the University of Oporto
25/06/2013, 16:00 — 17:00 — Room 1.07, Faculdade de Ciências da Universidade do Porto
Steven Bradlow, University of Illinois at Urbana-Champaign
Geometry of Higgs Bundles
Higgs bundles appear in several guises including (a) as solutions to gauge-theoretic equations for connections and sections of a bundle (b) as holomorphic realizations of fundamental group representations or, equivalently, local systems and (c) as special cases of principal bundles with extra structure (principal pairs). Each point of view leads to a construction of a moduli space, i.e. a geometric object whose points parametrize equivalence classes of Higgs bundles. The first part of this mini course will explain these different points of view and describe how they are related. We will then explore some key topological and geometric features of the moduli spaces. We will confine attention to Higgs bundles over closed Riemann surfaces.
See also
http://cmup.fc.up.pt/cmup/pbgothen/IST_lectures/
Sessions at the University of Oporto
25/06/2013, 14:30 — 15:30 — Room 1.07, Faculdade de Ciências da Universidade do Porto
Oscar García-Prada, Instituto de Ciencias Matemáticas, Madrid
Geometry of Higgs Bundles
Higgs bundles appear in several guises including (a) as solutions to gauge-theoretic equations for connections and sections of a bundle (b) as holomorphic realizations of fundamental group representations or, equivalently, local systems and (c) as special cases of principal bundles with extra structure (principal pairs). Each point of view leads to a construction of a moduli space, i.e. a geometric object whose points parametrize equivalence classes of Higgs bundles. The first part of this mini course will explain these different points of view and describe how they are related. We will then explore some key topological and geometric features of the moduli spaces. We will confine attention to Higgs bundles over closed Riemann surfaces.
See also
http://cmup.fc.up.pt/cmup/pbgothen/IST_lectures/
Sessions at the University of Oporto
08/09/2011, 14:00 — 15:00 — Room P3.10, Mathematics Building
Sandor Kovacs, University of Washington
Stable canonically polarized varieties (IV)
The theory of moduli of curves has been extremely successful and part of this success is due to the compactification of the moduli space of smooth projective curves by the moduli space of stable curves. A similar construction is desirable in higher dimensions but unfortunately the methods used for curves do not produce the same results in higher dimensions. In fact, even the definition of what "stable" should mean is not clear a priori. In order to construct modular compactifications of moduli spaces of higher dimensional canonically polarized varieties one must understand the possible degenerations that would produce this desired compactification that itself is a moduli space of an enlarged class of canonically polarized varieties. In this series of lectures I will start by discussing the difficulties that arise in higher dimensions and how these lead us to the definition of stable varieties and stable families. Time permitting construction of compact moduli spaces and recent relevant results will also be discussed.
08/09/2011, 11:30 — 12:30 — Room P3.10, Mathematics Building
Gavril Farkas, Humboldt Universität zu Berlin
Geometry of moduli of higher spin curves
The moduli space \(S_{g, r}\) of \(r\)-spin curves parametrize \(r\)-th order roots of the canonical bundles of curves of genus \(g\). This space is an interesting cover of the moduli space of curves. For instance it carries a highly non-trivial virtual fundmental class whose numerical properties lead to a well-known prediction of Witten. I will discuss various topics related to the birational geometry and intersection theory of these spaces, focusing both on the more classical case of theta-characteristics (\(r=2\)), as well as on the higher order analogues.
07/09/2011, 16:00 — 17:00 — Room P3.10, Mathematics Building
Sandor Kovacs, University of Washington
Stable canonically polarized varieties (III)
The theory of moduli of curves has been extremely successful and part of this success is due to the compactification of the moduli space of smooth projective curves by the moduli space of stable curves. A similar construction is desirable in higher dimensions but unfortunately the methods used for curves do not produce the same results in higher dimensions. In fact, even the definition of what "stable" should mean is not clear a priori. In order to construct modular compactifications of moduli spaces of higher dimensional canonically polarized varieties one must understand the possible degenerations that would produce this desired compactification that itself is a moduli space of an enlarged class of canonically polarized varieties. In this series of lectures I will start by discussing the difficulties that arise in higher dimensions and how these lead us to the definition of stable varieties and stable families. Time permitting construction of compact moduli spaces and recent relevant results will also be discussed.
07/09/2011, 14:00 — 15:00 — Room P3.10, Mathematics Building
Gavril Farkas, Humboldt Universität zu Berlin
Geometry of moduli of higher spin curves
The moduli space \(S_{g, r}\) of \(r\)-spin curves parametrize \(r\)-th order roots of the canonical bundles of curves of genus \(g\). This space is an interesting cover of the moduli space of curves. For instance it carries a highly non-trivial virtual fundmental class whose numerical properties lead to a well-known prediction of Witten. I will discuss various topics related to the birational geometry and intersection theory of these spaces, focusing both on the more classical case of theta-characteristics (\(r=2\)), as well as on the higher order analogues.
06/09/2011, 16:00 — 17:00 — Room P3.10, Mathematics Building
Gavril Farkas, Humboldt Universität zu Berlin
Geometry of moduli of higher spin curves
The moduli space \(S_{g, r}\) of \(r\)-spin curves parametrize \(r\)-th order roots of the canonical bundles of curves of genus \(g\). This space is an interesting cover of the moduli space of curves. For instance it carries a highly non-trivial virtual fundmental class whose numerical properties lead to a well-known prediction of Witten. I will discuss various topics related to the birational geometry and intersection theory of these spaces, focusing both on the more classical case of theta-characteristics (\(r=2\)), as well as on the higher order analogues.
06/09/2011, 14:00 — 15:00 — Room P3.10, Mathematics Building
Sandor Kovacs, University of Washington
Stable canonically polarized varieties (II)
The theory of moduli of curves has been extremely successful and part of this success is due to the compactification of the moduli space of smooth projective curves by the moduli space of stable curves. A similar construction is desirable in higher dimensions but unfortunately the methods used for curves do not produce the same results in higher dimensions. In fact, even the definition of what "stable" should mean is not clear a priori. In order to construct modular compactifications of moduli spaces of higher dimensional canonically polarized varieties one must understand the possible degenerations that would produce this desired compactification that itself is a moduli space of an enlarged class of canonically polarized varieties. In this series of lectures I will start by discussing the difficulties that arise in higher dimensions and how these lead us to the definition of stable varieties and stable families. Time permitting construction of compact moduli spaces and recent relevant results will also be discussed.
05/09/2011, 16:00 — 17:00 — Room P3.10, Mathematics Building
Sandor Kovacs, University of Washington
Stable canonically polarized varieties (I)
The theory of moduli of curves has been extremely successful and part of this success is due to the compactification of the moduli space of smooth projective curves by the moduli space of stable curves. A similar construction is desirable in higher dimensions but unfortunately the methods used for curves do not produce the same results in higher dimensions. In fact, even the definition of what "stable" should mean is not clear a priori. In order to construct modular compactifications of moduli spaces of higher dimensional canonically polarized varieties one must understand the possible degenerations that would produce this desired compactification that itself is a moduli space of an enlarged class of canonically polarized varieties. In this series of lectures I will start by discussing the difficulties that arise in higher dimensions and how these lead us to the definition of stable varieties and stable families. Time permitting construction of compact moduli spaces and recent relevant results will also be discussed.
05/09/2011, 14:00 — 15:00 — Room P3.10, Mathematics Building
Gavril Farkas, Humboldt Universität zu Berlin
Geometry of moduli of higher spin curves
The moduli space \(S_{g, r}\) of \(r\)-spin curves parametrize \(r\)-th order roots of the canonical bundles of curves of genus \(g\). This space is an interesting cover of the moduli space of curves. For instance it carries a highly non-trivial virtual fundmental class whose numerical properties lead to a well-known prediction of Witten. I will discuss various topics related to the birational geometry and intersection theory of these spaces, focusing both on the more classical case of theta-characteristics (\(r=2\)), as well as on the higher order analogues.
