Moduli spaces

Programme theme

Algebraic geometry is a key area of mathematical research of international significance. It has strong connections with many other areas of mathematics (differential geometry, topology, number theory, representation theory, etc.) and also with other disciplines (in the present context, particularly theoretical physics). Moduli theory is the study of the way in which objects in algebraic geometry (or in other areas of mathematics) vary in families and is fundamental to an understanding of the objects themselves. The theory goes back at least to Riemann in the mid-nineteenth century, but moduli spaces were first rigorously constructed in the 1960s by Mumford and others. The theory has continued to develop since then, perhaps most notably with the infusion of ideas from physics after 1980.

The programme will focus on the following topics:

Moduli of bundles and augmented bundles on algebraic curves: more specifically Higgs bundles, parabolic bundles, coherent systems, principal bundles.
Relationship of moduli spaces to topology, Teichmüller theory and hyperbolic geometry - this relationship takes place in the study of representations of a surface group in a real Lie group and involves Higgs bundle theory, bounded cohomology, Anosov systems, cluster varieties, tropical algebraic geometry; there is a very rich geometric structure and the various points of view are complementary, the relationship between them yet to be understood.
Moduli of algebraic varieties - recent work has made exciting connections with the subject of special metrics in Kähler geometry. This has led to the old unsolved question of giving an intrinsic criterion for the stability of algebraic varieties being revisited.
Moduli in derived categories - the study of moduli spaces in derived categories is a new and highly promising area of research, involving in particular new notions of stability.

We should emphasise that the topics are not independent. There are obvious links between (i) and (ii), while (iv) has already had an impact on all the other topics and we believe that this impact is likely to get stronger.

The central aims of the programme are to bring together experts in various aspects of moduli theory and related areas, to advance these topics, and to introduce research students and post-docs to the welath of ideas and problems in them. As stated above, the interdependence of the topics we have identified is crucial to the development of the theory, and a major goal is to develop these ideas further. The programme will include an instructional course and three further workshops, one of which will be held outside Cambridge.

Click here to download the programme's final scientific report

Preprints

Title	Year	Programme
Degenerate cohomological Hall algebra and quantized Donaldson-Thomas invariants for $\it m$-loop quivers Authors: Markus Reineke Download PDF	2010	MOS	21 October 2016
The class of the locus of intermediate Jacobians of cubic threefolds Authors: Klaus Hulek, S Grushevsky Download PDF	2010	MOS	21 October 2016
Stable bundles of rank 2 with 4 sections Authors: V Mercat, Peter Newstead, Ivona Grzegorczyk Download PDF	2010	MOS	21 October 2016
Compactification of the Prym map for non cyclic triple coverings Authors: Angela Ortega, Herbert Lange Download PDF	2010	MOS	21 October 2016
Igusa quartic and Steiner surfaces Authors: Shigeru Mukai Download PDF	2010	MOS	21 October 2016
Bridgeland stability conditions on threefolds I: Bogomolov-Gieseker type inequalities Authors: Arend Bayer, Emanuele Macri, Yukinobu Toda Download PDF	2010	MOS	21 October 2016
Bridgeland stability conditions on threefolds II: An application to Fujita's conjecture Authors: Emanuele Macri, Yukinobu Toda, Arend Bayer, Aaron Bertram Download PDF	2010	MOS	21 October 2016
Affine cubic surfaces and relative $SL$(2)-character varieties of compact surfaces Authors: Domingo Toledo, WM Goldman Download PDF	2010	MOS	21 October 2016
Bundles of rank 2 with small Clifford index on algebraic curves Authors: Herbert Lange, Peter Newstead Download PDF	2010	MOS	21 October 2016
Rank on Bridgeland stable moduli spaces on principally polarized Abelian surface Authors: Ciaran Meachan, Antony Maciocia Download PDF	2010	MOS	21 October 2016
Special determinants in higher rank Brill-Noether theory Authors: Brian Osserman Download PDF	2010	MOS	21 October 2016
Multiple cover formula of generalized DT invariants I: parabolic stable pairs Authors: Yukinobu Toda Download PDF	2010	MOS	21 October 2016
Multiple cover formula of generalized DT invariants II: Jacobian localizations Authors: Yukinobu Toda Download PDF	2010	MOS	21 October 2016
Coupled equations for Kähler metrics and Yang-Mills connections Authors: Oscar García-Prada, Luis Álvarez-Cónsul, Mario Garcia-Fernandez Download PDF	2010	MOS	21 October 2016
Hodge Polynomials of SL(2,C)-character varieties for curves of small genus Authors: V Munoz, Peter Newstead, Marina Logares Download PDF	2010	MOS	21 October 2016
Stability of affine $\it G$-varieties and irreducibility in reductive groups Authors: Ana Cristina Casimiro, Carlos Florentino Download PDF	2010	MOS	21 October 2016

Workshops

MOSW01

Seminars

Monday 10th January 2011
16:30 to 19:00	MOS tutorials	Room 2

Tuesday 11th January 2011
16:30 to 19:00	MOS tutorials	Room 2

Wednesday 12th January 2011
16:30 to 19:00	MOS tutorials	Room 2

Thursday 13th January 2011
16:30 to 19:00	MOS tutorials	Room 2

Friday 14th January 2011
16:30 to 19:00	MOS tutorials	Room 2

Tuesday 18th January 2011
11:30 to 12:30	Derived McKay correspondence in dimensions 4 and above	Room 1

Thursday 20th January 2011
14:00 to 15:00	Stable spectral bundles on K3 fibered 3-folds	Room 1
15:30 to 16:30	Alberto Lopez Martin Korea Institute for Advanced Study (KIAS) Relative Fourier-Mukai transforms for Weierstrass fibrations, abelian schemes and Fano fibrations	Room 1

Tuesday 25th January 2011
10:00 to 11:00	Anna Pratoussevitch University of Liverpool Moduli Spaces of Gorenstein Quasi-Homogenous Surface Singularities	Room 1
11:30 to 12:30	Young-Hoon Kiem Seoul National University Kirwan blow-ups and moduli spaces	Room 1

Thursday 27th January 2011
14:00 to 15:00	Mario Garcia-Fernandez Aarhus Universitet Coupled Equations, cscK metrics and geodesic stability	Room 1
15:30 to 16:30	Kai Behrend University of British Columbia On the Calculus underlying Donaldson-Thomas theory	Room 1

Tuesday 1st February 2011
10:00 to 11:00	Norbert Hoffmann Freie Universität Berlin Poincare families and line bundles on moduli stacks of G-bundles	Room 1
11:00 to 12:30	Vladimir Baranovsky University of California, Irvine A compactification for the moduli stack of bundles on a surface	Room 1

Thursday 3rd February 2011
14:00 to 15:00	Jeff Giansiracusa University of Bath Cell decompositions of moduli spaces and generalisations	Room 1
15:30 to 16:30	Marina Logares ICMAT Hodge polynomials of the moduli space of SL (2,C) - character varieties	Room 1

Tuesday 8th February 2011
11:30 to 12:30	Elham Izadi University of Georgia Counter-examples of high Clifford index to Prym-Torelli	Room 1

Thursday 10th February 2011
14:00 to 15:00	Klaus Hulek Leibniz Universität Hannover The locus of intermediate Jabobians of cubic threefolds	Room 1
15:30 to 16:30	Osbaldo Mata Gutierrez CIMAT (Centro de Investigación en Matemáticas), Mexico (k,l)-stability	Room 1

Tuesday 15th February 2011
10:00 to 11:00	Vikraman Balaji Chennai Mathematical Institute Parahoric bundles and parabolic bundles	Room 1
11:30 to 12:30	Olivier Serman Université des Sciences et Technologies de Lille On the singularities of moduli spaces of principal bundles	Room 1

Thursday 17th February 2011
14:00 to 15:00	The polynomial method in combinatorial incidence geometry	Room 1
15:30 to 16:30	Nitin Nitsure Tata Institute of Fundamental Research Schematic Harder Narasimhan stratification	Room 1

Tuesday 22nd February 2011
10:00 to 11:00	Olivier Guichard Université Paris Saclay Moduli of Symplectic Maximal Representations	Room 1
11:30 to 12:30	Vikraman Balaji Chennai Mathematical Institute Stable bundles and holonomy groups of smooth projective varieties.	Room 1

Thursday 24th February 2011
14:00 to 15:00	Christian Pauly Université de Montpellier 2 On the monodromy of the Hitchin connection.	Room 1
15:30 to 16:30	The $L^2$ geometry of vortex moduli spaces	Room 1

Tuesday 1st March 2011
10:00 to 11:00	Andras Szenes Observatoire Astronomique de l'Universite de Geneve Calculating Thom polynomials	Room 1
11:30 to 12:30	Higgs bundles for the non-compact dual of the unitary group	Room 1

Thursday 3rd March 2011
14:00 to 15:00	Ulrich Goertz Universität Duisburg-Essen Moduli spaces of abelian varieties with Iwahori level structure	Room 1
15:30 to 16:30	Carlos Simpson Université de Nice Sophia Antipolis Moduli of local systems on Deligne-Mumford stacks	Room 1

Tuesday 8th March 2011
10:00 to 11:00	Nan-Kuo Ho National Tsing Hua University Morse theory and the moduli space of flat connections over a nonorientable surface	Room 1
11:30 to 12:30	Florent Schaffhauser Universidad de los Andes Moduli of real and quaternionic bundles over a curve	Room 1

Thursday 10th March 2011
09:00 to 17:30	One day ITGP meeting	Room 2
14:00 to 15:00	Jochen Heinloth Universiteit van Amsterdam Introduction to a motivic point of view on the cohomology of moduli spaces of bundles on curves	Room 1
15:30 to 16:30	Tony Pantev University of Pennsylvania A set up for the cathegorical Langlands Correspondence	Room 1

Tuesday 15th March 2011
10:00 to 12:30	MOS lecture	Room 1

Thursday 24th March 2011
14:00 to 15:00	Angela Ortega Humboldt-Universität zu Berlin Prym varieties of triple coverings	Room 2
15:30 to 16:30	Gavril Farkas Humboldt-Universität zu Berlin Koszul cohomology and higher rank vector bundles on curves	Room 2

Monday 4th April 2011
14:00 to 15:00	Arend Bayer University of Connecticut Bridgeland stability conditions on threefolds and birational geometry	Room 1

Tuesday 5th April 2011
11:30 to 12:30	Quadratic differentials as stability conditions	Room 1
16:30 to 17:30	Aaron Pixton Princeton University The stable pairs theory of local curves with stationary descendents	Room 1

Wednesday 6th April 2011
11:30 to 12:30	Ed Segal Imperial College London The Pfaffian-Grassmannian correspondence via Landau-Ginzburg models	Room 1
16:30 to 17:30	Ben Davison University of Oxford The motivic Donaldson-Thomas invariants of fat points	Room 1

Thursday 7th April 2011
11:30 to 12:30	David Ploog Leibniz Universität Hannover Postnikov stability for complexes	Room 1
16:30 to 17:30	Relative spherical objects and spherical fibrations	Room 1

Friday 8th April 2011
11:30 to 12:30	Ludmil Katzarkov University of California, Irvine Spectra and Gaps as cohomological theory	Room 1
14:00 to 15:00	Ludmil Katzarkov University of California, Irvine Homological Mirror Symmetry, Gaps and Spectra	Room 1

Tuesday 19th April 2011
10:00 to 12:30	MOS lecture	Room 1

Thursday 21st April 2011
14:00 to 15:00	Herbert Lange Friedrich-Alexander-Universität Erlangen-Nürnberg Generalisation of the tetragonal construction	Room 1
15:30 to 16:30	Brian Osserman University of California, Davis Special determinants in higher-rank Brill-Noether theory	Room 1

Thursday 28th April 2011
14:00 to 15:00	Claire Voisin Institut de Mathématiques de Jussieu Abel-Jacobi map, integral Hodge classes and decomposition of the diagonal	Room 1
15:30 to 16:30	Manfred Lehn Johannes Gutenberg-Universität Mainz On symplectic hypersurfaces	Room 1

Tuesday 3rd May 2011
10:00 to 12:30	MOS lecture	Room 1

Tuesday 10th May 2011
10:00 to 12:30	MOS lecture	Room 1

Thursday 12th May 2011
10:30 to 11:30	Burt Totaro University of Cambridge Partially positive line bundles	Room 1
15:30 to 16:30	Jon Woolf University of Liverpool Metric properties of spaces of stability conditions	Room 1

Thursday 19th May 2011
14:00 to 16:00	MOS lecture	Room 1

Tuesday 24th May 2011
10:00 to 11:00	Olivier Biquard Université Pierre et Marie Curie Paris A new approach for the Toledo invariant	Room 1
11:30 to 12:30	Jun Yu ETH Zürich Vector bundles on the algebraic 5-sphere and punctured affine 3-space	Room 1
15:30 to 16:30	Ivan Cheltsov University of Edinburgh On simple finite subgroups in the Cremona group of rank 3	Room 1

Tuesday 31st May 2011
10:00 to 11:00	Indranil Biswas Tata Institute of Fundamental Research Orthogonal and symplectic parabolic bundles	Room 1
11:30 to 12:30	Aaron Bertram University of Utah Birational models of the Hilbert scheme of points on $P^2$ are moduli of Bridgeland-stable complexes	Room 1

Thursday 2nd June 2011
14:00 to 15:00	Ugo Bruzzo SISSA Uhlenbeck-Donaldson compactification for framed sheaves	Room 1
15:30 to 16:30	Nick Shepherd-Barron University of Cambridge Stable Schottky relations	Room 1

Monday 6th June 2011
15:30 to 16:30	Sean Keel Japan Atomic Energy Agency & University of Texas at Austin Mirror symmetry for affine Calabi-Yaus	Room 1

Tuesday 7th June 2011
10:00 to 11:00	Sean Keel Japan Atomic Energy Agency & University of Texas at Austin Towards a geometric compactification of moduli of polarized K3 surfaces	Room 1
11:30 to 12:30	Localization in quiver moduli spaces and the Refined GW/Kronecker correspondence	Room 1

Thursday 9th June 2011
14:00 to 15:00	Ushadevi Bhosle Tata Institute of Fundamental Research Vector bundles and coherent systems on nodal curves	Room 1
15:30 to 16:30	Ernesto Mistretta Università degli Studi di Padova Linear stability and stability of dual span bundles	Room 1

Monday 13th June 2011
17:00 to 18:00	M.S. Narasimhan Ramanujan Mathematical Society Stability and its ramifications	Room 1

Tuesday 14th June 2011
10:00 to 11:00	Luis Álvarez-Cónsul ICMAT Coupled equations for Kähler metrics and Yang-Mills connections	Room 1
11:30 to 12:30	Ivona Grzegorczyk California State University Bundles of rank 2 with 4 sections on curves	Room 1

Thursday 16th June 2011
14:00 to 15:00	Dragos Oprea University of California, San Diego Virtual classes, Quot schemes and stable quotients	Room 1
15:30 to 16:30	Andreas Ott IHES Bounded cohomology and Higgs bundles	Room 1

Friday 17th June 2011
14:00 to 15:00	Mark Gross University of California, San Diego Logarithmic Gromov-Witten invariants	Room 1

Tuesday 21st June 2011
11:30 to 12:30	Michael Thaddeus Columbia University Extensions of Grothendieck's theorem on principal bundles over the projective line	Room 2

Thursday 23rd June 2011
14:00 to 15:00	Antony Maciocia University of Edinburgh Further Examples of Bridgeland Stable Moduli Spaces	Room 2
15:30 to 16:30	Simon Donaldson Imperial College London b-stability and blow-ups	Room 1

Organisers

Leticia Brambila-Paz Centro de Investigación en Matemáticas
Oscar García-Prada Consejo Superior de Investigaciones Cientificas
Peter Newstead University of Liverpool
Richard Thomas Imperial College London

Speakers

Vikraman Balaji Chennai Mathematical Institute
Vladimir Baranovsky University of California, Irvine
Arend Bayer University of Connecticut
Kai Behrend University of British Columbia
Aaron Bertram University of Utah
Ushadevi Bhosle Tata Institute of Fundamental Research
Olivier Biquard Université Pierre et Marie Curie Paris
Indranil Biswas Tata Institute of Fundamental Research
Ugo Bruzzo SISSA
Ivan Cheltsov University of Edinburgh
Ben Davison University of Oxford
Simon Donaldson Imperial College London
Gavril Farkas Humboldt-Universität zu Berlin
Mario Garcia-Fernandez Aarhus Universitet
Jeff Giansiracusa University of Bath
Ulrich Goertz Universität Duisburg-Essen
Mark Gross University of California, San Diego
Ivona Grzegorczyk California State University
Olivier Guichard Université Paris Saclay
Jochen Heinloth Universiteit van Amsterdam
Nan-Kuo Ho National Tsing Hua University
Norbert Hoffmann Freie Universität Berlin
Klaus Hulek Leibniz Universität Hannover
Elham Izadi University of Georgia
Ludmil Katzarkov University of California, Irvine
Sean Keel Japan Atomic Energy Agency & University of Texas at Austin
Young-Hoon Kiem Seoul National University
Herbert Lange Friedrich-Alexander-Universität Erlangen-Nürnberg
Manfred Lehn Johannes Gutenberg-Universität Mainz
Marina Logares ICMAT
Alberto Lopez Martin Korea Institute for Advanced Study (KIAS)
Antony Maciocia University of Edinburgh
Osbaldo Mata Gutierrez CIMAT (Centro de Investigación en Matemáticas), Mexico
Ernesto Mistretta Università degli Studi di Padova
M.S. Narasimhan Ramanujan Mathematical Society
Nitin Nitsure Tata Institute of Fundamental Research
Dragos Oprea University of California, San Diego
Angela Ortega Humboldt-Universität zu Berlin
Brian Osserman University of California, Davis
Andreas Ott IHES
Tony Pantev University of Pennsylvania
Christian Pauly Université de Montpellier 2
Aaron Pixton Princeton University
David Ploog Leibniz Universität Hannover
Anna Pratoussevitch University of Liverpool
Florent Schaffhauser Universidad de los Andes
Ed Segal Imperial College London
Olivier Serman Université des Sciences et Technologies de Lille
Nick Shepherd-Barron University of Cambridge
Carlos Simpson Université de Nice Sophia Antipolis
Andras Szenes Observatoire Astronomique de l'Universite de Geneve
Michael Thaddeus Columbia University
Burt Totaro University of Cambridge
Claire Voisin Institut de Mathématiques de Jussieu
Jon Woolf University of Liverpool
Jun Yu ETH Zürich
Luis Álvarez-Cónsul ICMAT

Show All

Programme theme

Preprints

Degenerate cohomological Hall algebra and quantized Donaldson-Thomas invariants for $\it m$-loop quivers

The class of the locus of intermediate Jacobians of cubic threefolds

Stable bundles of rank 2 with 4 sections

Compactification of the Prym map for non cyclic triple coverings

Igusa quartic and Steiner surfaces

Bridgeland stability conditions on threefolds I: Bogomolov-Gieseker type inequalities

Bridgeland stability conditions on threefolds II: An application to Fujita's conjecture

Affine cubic surfaces and relative $SL$(2)-character varieties of compact surfaces

Bundles of rank 2 with small Clifford index on algebraic curves

Rank on Bridgeland stable moduli spaces on principally polarized Abelian surface

Special determinants in higher rank Brill-Noether theory

Multiple cover formula of generalized DT invariants I: parabolic stable pairs

Multiple cover formula of generalized DT invariants II: Jacobian localizations

Coupled equations for Kähler metrics and Yang-Mills connections

Hodge Polynomials of SL(2,C)-character varieties for curves of small genus

Stability of affine $\it G$-varieties and irreducibility in reductive groups

Workshops

School on moduli spaces

One day meeting : ITGP network meeting

Representations of surface groups and Higgs gundles

Derived categories

MOS Spitalfields day

Vector bundles and coherent systems

Closing conference

Seminars

Organisers

Speakers

Supported By

Moduli spaces

Programme theme

Preprints

Degenerate cohomological Hall algebra and quantized Donaldson-Thomas invariants for $\it m$-loop quivers

The class of the locus of intermediate Jacobians of cubic threefolds

Stable bundles of rank 2 with 4 sections

Compactification of the Prym map for non cyclic triple coverings

Igusa quartic and Steiner surfaces

Bridgeland stability conditions on threefolds I: Bogomolov-Gieseker type inequalities

Bridgeland stability conditions on threefolds II: An application to Fujita's conjecture

Affine cubic surfaces and relative $SL$(2)-character varieties of compact surfaces

Bundles of rank 2 with small Clifford index on algebraic curves

Rank on Bridgeland stable moduli spaces on principally polarized Abelian surface

Special determinants in higher rank Brill-Noether theory

Multiple cover formula of generalized DT invariants I: parabolic stable pairs

Multiple cover formula of generalized DT invariants II: Jacobian localizations

Coupled equations for Kähler metrics and Yang-Mills connections

Hodge Polynomials of SL(2,C)-character varieties for curves of small genus

Stability of affine $\it G$-varieties and irreducibility in reductive groups

Workshops

School on moduli spaces

One day meeting : ITGP network meeting

Representations of surface groups and Higgs gundles

Derived categories

MOS Spitalfields day

Vector bundles and coherent systems

Closing conference

Seminars

Organisers

Speakers

Supported By

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