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November 30, 2015 By GeometryAdmin

Roland Abuaf to speak in the geometry seminar 8/12/2015

Roland Abuaf (IHES Paris) will speak in the geometry seminar on 8th December, 2015. His title is Hyperkähler categories and his abstract is below. Roland’s talk will be at 2pm, in the Salle de Profs on the 9th floor of building NO. The seminar that week will be a double bill, with Ljudmila Kamenova also speaking, on Kobayashi’s pseudometric of compact complex manifolds at 3.15pm in the same room.

Along with complex tori and Calabi-Yau manifolds, compact hyper-Käahler manifolds are building blocks for the decomposition of Ricci-flat manifolds. All complex tori are “classified”, while we know how to construct a large number of different deformation classes of CY manifolds in each complex dimension (bigger than 3). The situation for compact hyper-Kähler manifolds is quite different. We have absolutely no clue on how to classify them and we only know 2 infinite series and 2 sporadic examples of such manifolds. The last new example of compact hyper-Kähler manifold has been constructed more than 15 years ago (O’Grady).

In this talk, I will introduce the notion of compact hyper-Kähler categories, study some of their invariance properties and some construction techniques. In particular, I will show that one can construct a large number of different deformation classes of compact hyper-Kähler categories in each even dimension. If time permits, I will discuss a specific modular example, whose Hochschild cohomology ring reveals some very interesting properties.

Filed Under: geometry seminar news

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Département de mathématiques
Université libre de Bruxelles CP 218
Boulevard du Triomphe, Bruxelles 1050,
Belgium

Getting here

The department of mathematics is in building NO, on the Campus de la Plaine, of the Université libre de Bruxelles. The geometry group is on the 7th floor. This page has a map of the campus as well as information on how to reach it via public transport. See the STIB website for more information on public transport in Brussels.

Image credits

Polished ammonite fossil, by Kara Stenberg, Creative Commons licence CC BY-NC 2.0.

Model of 3D projection of a 120-cell, by Edmund Harriss.

The root system of the exceptional Lie algebra E8. By Jared Tarbell, Creative Commons Licence CC BY 2.0.

Getting here

The department of mathematics is in building NO, on the Campus de la Plaine, of the Université libre de Bruxelles. The geometry group is on the 7th floor. This map shows NO, as well as the metro station Delta and entrance 2, which is right by the stop for the number 71 and 72 buses. The number 95 also stops a short walk from the department. See the STIB website for more information on public transport in Brussels.

Image credits

Polished ammonite fossil, by Kara Stenberg, Creative Commons licence CC BY-NC 2.0.

Model of 3D projection of a 120-cell, by Edmund Harriss.

The root system of the exceptional Lie algebra E8. By Jared Tarbell, Creative Commons Licence CC BY 2.0.

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