We are going to have a workshop on geometric analysis on 1-2.06.2015

All talks will be in the building of the faculty of Mathematics and Computer Science of the Jagiellonian University, prof. Stanisława Łojasiewicza 6 str., 30-348 Kraków, Poland

The schedule of the talks is:

Hour	1.06 Monday	2.06 Tuesday
10:00-10:50	room 1016, Jacob Sturm	room 0006, Tristan Collins
11:00-11:50	room 1016, Jian Song	room 0006, Ved Datar
14:00-14:50	room 1016, Włodzimierz Zwonek	room 0004, Szymon Pliś
15:00-15:50	room 1016, Sławomir Kołodziej	room 0004, Sławomir Dinew

The speakers will be:

Tristan Collins (Harvard)

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

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Jian Song (Rutgers)

Title: Analytic base point free theorem

Abstract: 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 (Rutgers)

Title: The conical Ricci flow on S^2

Abstract: 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 (Notre Dame)

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

Abstract: 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 (Jagiellonian University)

Title: Remarks on Mukai threefolds admitting C^* action

Abstract: 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 (Jagiellonian University)

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

Abstract: 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 (Cracow University of Technology)

Title: Plurisubharmonic functions on almost complex manifolds

Abstract: 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 (Jagiellonian University)

Title: Multidimensional Suita conjecture,

Abstract: 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.