Organizujemy workshop pod tytułem ,,Workshop on geometric analysis'' w dniach 1-2.06.2015.

Wszystkie wykłady odbędą się w budynku Wydziału Matematyki i Informatyki UJ, ul. prof. Stanisława Łojasiewicza 6, 30-348 Kraków

plan wykładów:

Godzina	1.06 Poniedziałek	2.06 Wtorek
10:00-10:50	pokój 1016, Jacob Sturm	pokój 0006, Tristan Collins
11:00-11:50	pokój 1016, Jian Song	pokój 0006, Ved Datar
14:00-14:50	pokój 1016, Włodzimierz Zwonek	pokój 0004, Szymon Pliś
15:00-15:50	pokój 1016, Sławomir Kołodziej	pokój 0004, Sławomir Dinew

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Referaty wygłoszą:

Tristan Collins (Uniwersytet Harvarda, USA)

Tytuł: The convergence of the J-flow on toric varieties

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Jian Song (Uniwersytet Rutgers, USA)

Tytuł: Analytic base point free theorem

Abstrakt: The abundance conjecture predicts that if the canonical bundle of a projective manifold is nef, then it is semi-ample. A special case is proved by Kawamata for big and nef canonical bundles. We give an analytic proof of Kawamata's theorem using the Ricci flow, L2 theory and degeneration of Riemannian manifolds. We further construct unique Kähler-Einstein metrics with a global Riemannian structure on canonical models. We will also discuss a more general analytic base point free theorem.

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Jacob Sturm (Uniwersytet Rutgers, USA)

Tytuł: The conical Ricci flow on S^2

Abstrakt: I will discuss the limiting properties of the conical Ricci flow in the semistable and unstable settings. This is joint work with D.H. Phong, J. Song and X. Wang.

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Ved Datar (Uniwersytet Notre Dame, USA)

Tytuł: Kähler-Einstein metrics along the smooth continuity method.

Abstrakt: I will discuss an equivariant version of the Yau-Tian-Donaldson conjecture strengthening the result of Chen-Donaldson-Sun. This potentially provides new examples of Kähler-Einstein manifolds and the methods apply equally well to Kähler-Ricci solitons. It is joint work with Gábor Székelyhidi.

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Sławomir Dinew (Uniwersytet Jagielloński)

Tytuł: Remarks on Mukai threefolds admitting C^* action

Abstrakt: We shall discuss geometrical aspects of Mukai threefolds. In particular we shall estimate log canonical thresholds and review the existence problem for Kähler-Einstein metrics on these threefolds.

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Sławomir Kołodziej (Uniwersytet Jagielloński)

Tytuł:The complex Monge-Ampère equation on compact Hermitian manifolds

Abstrakt: The existence of weak solutions and stability of the complex Monge-Ampère equation on compact Hermitian manifolds is discussed. A joint work with Cuong Ngoc Nguyen.

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Szymon Pliś (Politechnika Krakowska)

Tytuł: Plurisubharmonic functions on almost complex manifolds

Abstrakt: We will present some recent results in the theory of plurisubharmonic functions on almost complex manifolds. In particular we discuss the regularisation problem for such functions (joint results with R. Harvey and B. Lawson).

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Włodzimierz Zwonek (Uniwersytet Jagielloński)

Tytuł: Multidimensional Suita conjecture,

Abstrakt: We present the multidimensional version of the Suita conjecture which gives the lower estimate for some biholomorphic invariant involving the Bergman kernel and the volume of the indicatrix of the Azukawa metric. The discussion of the invariant on convex domains will also be presented. This is the joint work with Z. Błocki.