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:
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
Title | Year | Programme |
---|---|---|
Degenerate cohomological Hall algebra and quantized Donaldson-Thomas invariants for $\it m$-loop quiversAuthors: Markus Reineke |
2010 | MOS |
The class of the locus of intermediate Jacobians of cubic threefoldsAuthors: S Grushevsky, Klaus Hulek |
2010 | MOS |
Stable bundles of rank 2 with 4 sectionsAuthors: Ivona Grzegorczyk, V Mercat, Peter Newstead |
2010 | MOS |
Compactification of the Prym map for non cyclic triple coveringsAuthors: Herbert Lange, Angela Ortega |
2010 | MOS |
Igusa quartic and Steiner surfacesAuthors: Shigeru Mukai |
2010 | MOS |
Bridgeland stability conditions on threefolds I: Bogomolov-Gieseker type inequalitiesAuthors: Emanuele Macri, Yukinobu Toda, Arend Bayer |
2010 | MOS |
Bridgeland stability conditions on threefolds II: An application to Fujita's conjectureAuthors: Aaron Bertram, Emanuele Macri, Yukinobu Toda, Arend Bayer |
2010 | MOS |
Affine cubic surfaces and relative $SL$(2)-character varieties of compact surfacesAuthors: Domingo Toledo, WM Goldman |
2010 | MOS |
Bundles of rank 2 with small Clifford index on algebraic curvesAuthors: Peter Newstead, Herbert Lange |
2010 | MOS |
Rank on Bridgeland stable moduli spaces on principally polarized Abelian surfaceAuthors: Ciaran Meachan, Antony Maciocia |
2010 | MOS |
Special determinants in higher rank Brill-Noether theoryAuthors: Brian Osserman |
2010 | MOS |
Multiple cover formula of generalized DT invariants I: parabolic stable pairsAuthors: Yukinobu Toda |
2010 | MOS |
Multiple cover formula of generalized DT invariants II: Jacobian localizationsAuthors: Yukinobu Toda |
2010 | MOS |
Coupled equations for Kähler metrics and Yang-Mills connectionsAuthors: Mario Garcia-Fernandez, Oscar García-Prada, Luis Álvarez-Cónsul |
2010 | MOS |
Hodge Polynomials of SL(2,C)-character varieties for curves of small genusAuthors: V Munoz, Peter Newstead, Marina Logares |
2010 | MOS |
Stability of affine $\it G$-varieties and irreducibility in reductive groupsAuthors: Ana Cristina Casimiro, Carlos Florentino |
2010 | MOS |
5 January 2011 to 14 January 2011
11 March 2011 to 11 March 2011
14 March 2011 to 18 March 2011
11 April 2011 to 15 April 2011
5 May 2011 to 5 May 2011
26 May 2011 to 26 May 2011
27 June 2011 to 1 July 2011
Monday 10th January 2011 | |||
---|---|---|---|
16:30 to 19:00 | Room 2 |
Tuesday 11th January 2011 | |||
---|---|---|---|
16:30 to 19:00 | Room 2 |
Wednesday 12th January 2011 | |||
---|---|---|---|
16:30 to 19:00 | Room 2 |
Thursday 13th January 2011 | |||
---|---|---|---|
16:30 to 19:00 | Room 2 |
Friday 14th January 2011 | |||
---|---|---|---|
16:30 to 19:00 | Room 2 |
Thursday 20th January 2011 | |||
---|---|---|---|
14:00 to 15:00 | Room 1 | |
|
15:30 to 16:30 |
Alberto Lopez Martin Korea Institute for Advanced Study (KIAS) |
Room 1 | |
Tuesday 25th January 2011 | |||
---|---|---|---|
10:00 to 11:00 |
Anna Pratoussevitch University of Liverpool |
Room 1 | |
11:30 to 12:30 |
Young-Hoon Kiem Seoul National University |
Room 1 | |
Thursday 27th January 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Mario Garcia-Fernandez Aarhus Universitet |
Room 1 | |
15:30 to 16:30 |
Kai Behrend University of British Columbia |
Room 1 | |
Tuesday 1st February 2011 | |||
---|---|---|---|
10:00 to 11:00 |
Norbert Hoffmann Freie Universität Berlin |
Room 1 | |
11:00 to 12:30 |
Vladimir Baranovsky University of California, Irvine |
Room 1 | |
Thursday 3rd February 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Jeff Giansiracusa University of Bath |
Room 1 | |
15:30 to 16:30 |
Marina Logares ICMAT |
Room 1 | |
Tuesday 8th February 2011 | |||
---|---|---|---|
11:30 to 12:30 |
Elham Izadi University of Georgia |
Room 1 | |
Thursday 10th February 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Klaus Hulek Leibniz Universität Hannover |
Room 1 | |
15:30 to 16:30 |
Osbaldo Mata Gutierrez CIMAT (Centro de Investigación en Matemáticas), Mexico |
Room 1 | |
Tuesday 15th February 2011 | |||
---|---|---|---|
10:00 to 11:00 |
Vikraman Balaji Chennai Mathematical Institute |
Room 1 | |
11:30 to 12:30 |
Olivier Serman Université des Sciences et Technologies de Lille |
Room 1 | |
Thursday 17th February 2011 | |||
---|---|---|---|
14:00 to 15:00 | Room 1 | |
|
15:30 to 16:30 |
Nitin Nitsure Tata Institute of Fundamental Research |
Room 1 | |
Tuesday 22nd February 2011 | |||
---|---|---|---|
10:00 to 11:00 |
Olivier Guichard Université Paris Saclay |
Room 1 | |
11:30 to 12:30 |
Vikraman Balaji Chennai Mathematical Institute |
Room 1 | |
Thursday 24th February 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Christian Pauly Université de Montpellier 2 |
Room 1 | |
15:30 to 16:30 | Room 1 | |
Tuesday 1st March 2011 | |||
---|---|---|---|
10:00 to 11:00 |
Andras Szenes Observatoire Astronomique de l'Universite de Geneve |
Room 1 | |
11:30 to 12:30 | Room 1 | |
Thursday 3rd March 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Ulrich Goertz Universität Duisburg-Essen |
Room 1 | |
15:30 to 16:30 |
Carlos Simpson Université de Nice Sophia Antipolis |
Room 1 | |
Tuesday 8th March 2011 | |||
---|---|---|---|
10:00 to 11:00 |
Nan-Kuo Ho National Tsing Hua University |
Room 1 | |
11:30 to 12:30 |
Florent Schaffhauser Universidad de los Andes |
Room 1 | |
Thursday 10th March 2011 | |||
---|---|---|---|
09:00 to 17:30 | Room 2 | ||
14:00 to 15:00 |
Jochen Heinloth Universiteit van Amsterdam |
Room 1 | |
15:30 to 16:30 |
Tony Pantev University of Pennsylvania |
Room 1 | |
Tuesday 15th March 2011 | |||
---|---|---|---|
10:00 to 12:30 | Room 1 |
Thursday 24th March 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Angela Ortega Humboldt-Universität zu Berlin |
Room 2 | |
15:30 to 16:30 |
Gavril Farkas Humboldt-Universität zu Berlin |
Room 2 |
Monday 4th April 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Arend Bayer University of Connecticut |
Room 1 | |
Tuesday 5th April 2011 | |||
---|---|---|---|
11:30 to 12:30 | Room 1 | |
|
16:30 to 17:30 |
Aaron Pixton Princeton University |
Room 1 | |
Wednesday 6th April 2011 | |||
---|---|---|---|
11:30 to 12:30 |
Ed Segal Imperial College London |
Room 1 | |
16:30 to 17:30 |
Ben Davison University of Oxford |
Room 1 | |
Thursday 7th April 2011 | |||
---|---|---|---|
11:30 to 12:30 |
David Ploog Leibniz Universität Hannover |
Room 1 | |
16:30 to 17:30 | Room 1 | |
Friday 8th April 2011 | |||
---|---|---|---|
11:30 to 12:30 |
Ludmil Katzarkov University of California, Irvine |
Room 1 | |
14:00 to 15:00 |
Ludmil Katzarkov University of California, Irvine |
Room 1 |
Tuesday 19th April 2011 | |||
---|---|---|---|
10:00 to 12:30 | Room 1 |
Thursday 21st April 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Herbert Lange Friedrich-Alexander-Universität Erlangen-Nürnberg |
Room 1 | |
15:30 to 16:30 |
Brian Osserman University of California, Davis |
Room 1 | |
Thursday 28th April 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Claire Voisin Institut de Mathématiques de Jussieu |
Room 1 | |
15:30 to 16:30 |
Manfred Lehn Johannes Gutenberg-Universität Mainz |
Room 1 |
Tuesday 3rd May 2011 | |||
---|---|---|---|
10:00 to 12:30 | Room 1 |
Tuesday 10th May 2011 | |||
---|---|---|---|
10:00 to 12:30 | Room 1 |
Thursday 12th May 2011 | |||
---|---|---|---|
10:30 to 11:30 |
Burt Totaro University of Cambridge |
Room 1 | |
15:30 to 16:30 |
Jon Woolf University of Liverpool |
Room 1 |
Thursday 19th May 2011 | |||
---|---|---|---|
14:00 to 16:00 | Room 1 |
Tuesday 24th May 2011 | |||
---|---|---|---|
10:00 to 11:00 |
Olivier Biquard Université Pierre et Marie Curie Paris |
Room 1 | |
11:30 to 12:30 |
Jun Yu ETH Zürich |
Room 1 | |
15:30 to 16:30 |
Ivan Cheltsov University of Edinburgh |
Room 1 | |
Tuesday 31st May 2011 | |||
---|---|---|---|
10:00 to 11:00 |
Indranil Biswas Tata Institute of Fundamental Research |
Room 1 | |
11:30 to 12:30 |
Aaron Bertram University of Utah |
Room 1 | |
Thursday 2nd June 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Ugo Bruzzo SISSA |
Room 1 | |
15:30 to 16:30 |
Nick Shepherd-Barron University of Cambridge |
Room 1 | |
Monday 6th June 2011 | |||
---|---|---|---|
15:30 to 16:30 |
Sean Keel Japan Atomic Energy Agency & University of Texas at Austin |
Room 1 | |
Tuesday 7th June 2011 | |||
---|---|---|---|
10:00 to 11:00 |
Sean Keel Japan Atomic Energy Agency & University of Texas at Austin |
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 |
Room 1 | |
15:30 to 16:30 |
Ernesto Mistretta Università degli Studi di Padova |
Room 1 | |
Monday 13th June 2011 | |||
---|---|---|---|
17:00 to 18:00 |
M.S. Narasimhan Ramanujan Mathematical Society |
Room 1 | |
Tuesday 14th June 2011 | |||
---|---|---|---|
10:00 to 11:00 |
Luis Álvarez-Cónsul ICMAT |
Room 1 | |
11:30 to 12:30 |
Ivona Grzegorczyk California State University |
Room 1 | |
Thursday 16th June 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Dragos Oprea University of California, San Diego |
Room 1 | |
15:30 to 16:30 |
Andreas Ott IHES |
Room 1 | |
Friday 17th June 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Mark Gross University of California, San Diego |
Room 1 | |
Tuesday 21st June 2011 | |||
---|---|---|---|
11:30 to 12:30 |
Michael Thaddeus Columbia University |
Room 2 | |
Thursday 23rd June 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Antony Maciocia University of Edinburgh |
Room 2 | |
15:30 to 16:30 |
Simon Donaldson Imperial College London |
Room 1 | |
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