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October 3, 2017 By GeometryAdmin

Ryosuke Takahashi to speak in geometry seminar, 10th October

Ryosuke Takahashi will speak in the geometry seminar on the 10th October. The talk will take place in the Salle de Profs (9th floor, NO) at 10.30am. Ryosuke’s title is “A new parabolic flow approach to the Kähler-Einstein problem” and his abstract is below. Please note the time, which is earlier than usual! (This is to give people the possibility to attend Cédric Villani’s lecture which will take place at KULeuven, before the award of his honorary doctorate.)

We introduce the “Mabuchi flow”, a new parabolic flow of Monge-Ampère type which is designed to deform a given Kähler metric to the Kähler-Einstein one. We study the Mabuchi flow from the view point of Geometric Invariant Theory. We provide three results about the Mabuchi flow:

  1. Long-time existence and smooth convergence on the canonically polarized manifolds
  2. GIT stability relation between the self-similar solutions of the Mabuchi flow and extremal Kähler metrics
  3. Relation between the Mabuchi flow and optimal destabilizer on toric Fano manifolds

In the canonically polarized case, the large time behavior of the Mabuchi flow is similar to that of the Kähler-Ricci flow. On the other hand, the Mabuchi flow on anti-canonically polarized manifolds has a different aspect. We observe that it encodes the optimal destabilizing information about Kähler/algebro-geometric structure in a suitable sense when the manifold is toric. In addition, the Mabuchi flow has many properties similar to the Calabi flow. For instance, we can compare the GIT-stabilities for their solitons. This talk is based on a joint work with T. Collins (Harvard Univ) and T. Hisamoto (Nagoya Univ).

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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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