Shing-Tung Yau will deliver the first Łojasiewicz Lecture on Monday, 17 May 2010, at 5 p.m. On this ocassion we plan to review some of his important contributions to mathematics and physics and discuss related current research topics. The talks will be aimed at general mathematical audience. Everebody, incl. interested students and Ph.D. students, is warmly welcome.

9.00-9.45         Nuno Romão (IM UJ) Moduli spaces, moment maps and geometric structures on vector bundles        

In gauge theory, one is interested in certain moduli spaces obtained as symplectic quotients under the action of a group of gauge transformations. There is a beautiful correspondence between these spaces and another type of quotients, arising in the classification of geometric structures on complex vector bundles. My talk will give an introduction to results of this sort, which include the famous theorems on the existence of Hermitian-Einstein metrics on vector bundles over a Kähler manifold by Donaldson, Uhlenbeck and Yau.

10.00-10.45         Piotr Bizoń (IF UJ) Positive mass theorem        

I will discuss the notion of energy for isolated systems in general relativity and will sketch two different proofs of positivity of energy due to Schoen-Yau and Witten.

10.45-11.15         Coffee break

11.15-12.00         Zbigniew Błocki (IM UJ) Calabi conjecture and the complex Monge-Ampère equation        

We will present basic notions of Kähler geometry. It will be shown how to reduce the Calabi conjecture to solving nondegenerate complex Monge-Ampère equation. Basic ideas behind Yau's proof will be sketched.

12.00-13.00        Lunch break

13.00-13.45        Sławomir Dinew (IM UJ) Kähler-Einstein metrics        

A brief summary of known results regarding Kähler-Einstein metrics will be given. We shall discuss the historical contributions, state-of-the art as well as important conjectures and new techniques. While we shall describe both the theory in the compact and non-compact case, special emphasis will be given to analytic tools developed to attack the problem of existence of Kähler-Einstein metrics on compact Kähler manifolds with positive first Chern class. If time permits some connections with related problems (Hermitian-Einstein metrics, extremal metrics) will also be discussed.

14.00-14.45         Sławomir Kołodziej (IM UJ) Hamilton's Ricci flow and the Kähler-Ricci flow        

We discuss some aspects of the two geometric flows. In particular the differential Harnack inequalities, like Li-Yau estimates, and their relation to the proof of Perelman.

14.45-15.15         Coffee break

15.15-16.00         Grzegorz Kapustka (IM UJ) Manifolds with trivial first Chern class        

We will discuss the consequences in algebraic geometry of the existence of the Kähler-Einstein metric on manifolds with trivial first Chern class.

All lectures will take place in Room 1016 of the Department of Mathematics and Computer Science of Jagiellonian University (New Campus, Kraków).

Please contact Zbigniew Błocki for further details

treść:

Agnieszka Deszyńska

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Cz, 29 kwi 2010 12:50:02 +0000