Projekt finansowany przez:

## Witamy na stronie projektu Maestro

Nasza praca w ramach projektu omawiana jest na seminarium p.t.

,,Analiza zespolona i równania eliptyczne'' (dawniej ,,Równanie Monge'a- Ampère'a''),

które odbywa się w poniedziałki od 14:15 do 15:45 w sali 1016 budynku Wydziału

Matematyki i Informatyki UJ, ul. prof. Stanisława Łojasiewicza 6 w Krakowie oraz na platformie

Zoom. Aby brać udział w seminariach on-line prosimy skontaktować się z Żywomirem Dinewem.

Serdecznie zapraszamy na nasze posiedzenia.

30.5 Sungmin Yoo "Limit of Bergman kernels on a tower of coverings of compact Kähler manifolds" Abstrakt: A famous theorem by Kazhdan states that a tower of coverings of a compact Riemann surface converging to the universal covering is Bergman stable. Recently, Baik, Shokrieh and Wu generalized this theorem where the universal cover is replaced with any infinite Galois cover. In this talk, we prove a generalized version of this theorem, where compact Riemann surfaces are replaced with compact Kähler manifolds. We also discuss its application to the projectivity of manifolds. This is a joint work with Jihun Yum (IBS-CCG).

23.5 Rafał Czyż "A characterization of the degenerate complex Hessian equations for functions with bounded (p,m)-energy"

16.5 Marcin Sroka "Sharp uniform bound for the Monge-Ampère equation on hermitian manifolds" abstract: Based on the preprint https://arxiv.org/abs/2204.12549 "On $L^\infty$ estimates for fully nonlinear partial differential equations on Hermitian manifolds" by Bin Guo and Duong H. Phong

9.5 Zbigniew Błocki "Rearrangements and the complex Monge-Ampère equation"

25.4 Tomasz Wawak "Double EPW sextic with an A7 action" Abstrakt: During the talk we will introduce the family of hyperkähler manfiolds called double EPW sextic and construct one with an action of of the alternating group A7. Joint work with Simone Billi.

11.4 Ngoc Cuong Nguyen "Quasi-plurisubharmonic function envelope 1: Uniform estimates on Kähler manifold" na podstawie pracy V. Guedj oraz H.-C. Lu

4.4 Young-Jun Choi "Variation of Kähler-Einstein metrics and Kähler-Ricci flows" Abstrakt: In 2012, Schumacher proved that the variation of Kähler-Einstein metrics on a family of canonically polarized compact Kähler manifolds is positive definite on the total space. In his paper, he showed that the geodesic curvature, which measures the positivity of the horizontal direction, satisfies a certain elliptic PDE. Applying the maximum principle to this PDE, he obtained the positivity. In 2013, Berman proved the parabolic version of the Schumacher's result. More precisely, he proved that the geodesic curvature of a family of canonically polarized compact Kähler manifolds satisfies a parabolic equation. A parabolic maximum principle implies that the positivity of the geodesic curvature is preserved along the Kähler-Ricci flow. In this talk, we will briefly introduce the above results and discuss how to apply their methods to several families of Kähler manifolds.

28.3 Dariusz Piekarz "Smoothing q-convex functions and vanishing theorems" na podstawie pracy "Smoothing q-convex functions and vanishing theorems" autorstwa K. Diederich oraz J.E. Fornaess.

wyjątkowo we wtorek 22.3, 14:00-16:00 Duc Viet Vu ''Complex Monge-Ampère equation with solutions in finite energy classes'' Abstrakt: The notion of pluricomplex energy was introduced by U. Cegrell in 1988. Since then it has played an important role in complex Monge-Ampère equations. I present a recent joint work with Do Duc Thai in which we characterize the class of probability measures on a compact Kähler manifold such that the associated Monge-Ampère equation has a solution of finite energy. Such a characterization was previously only known in particular cases.

14.3 Sławomir Kołodziej ''On the modulus of continuity of solutions to complex Monge-Ampère equations'' na podstawie pracy Bin Guo, Duong H. Phong, Freid Tong oraz Chuwen Wang

7.3 Sławomir Kołodziej ''On the modulus of continuity of solutions to complex Monge-Ampère equations'' na podstawie pracy Bin Guo, Duong H. Phong, Freid Tong oraz Chuwen Wang

24.1 Ngoc Cuong Nguyen ''The Dirichlet problem for the Monge-Ampère equation on Hermitian manifolds with boundary'' na podstawie wspólnej pracy z Sławomirem Kołodziejem

17.1 Ngoc Cuong Nguyen ''The Dirichlet problem for the Monge-Ampère equation on Hermitian manifolds with boundary'' na podstawie wspólnej pracy z Sławomirem Kołodziejem

10.1 Sławomir Dinew ''Yamabe problem''

3.1 Sławomir Dinew ''Yamabe problem''

20.12 Sławomir Dinew ''Yamabe problem''

13.12 Szymon Myga ''Using the real Monge-Ampère equation on toric Fano manifolds'' Na podstawie pracy ''Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties'' autorstwa R.J. Berman oraz B. Berndtsson

6.12 Szymon Myga ''Using the real Monge-Ampère equation on toric Fano manifolds'' Na podstawie pracy ''Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties'' autorstwa R.J. Berman oraz B. Berndtsson

29.11 Zakarias Sjöström Dyrefelt ''Openness of stability in the Kähler cone'' Abstrakt: With respect to the Yau-Tian-Donaldson (YTD) conjecture a fundamental question is the following: If a polarized manifold is K-stable, then does it remain K-stable under small enough perturbations of the polarization? In this talk we explain why the answer is "yes" when K-stability is replaced by uniform K-stability, thus also strengthening the evidence for the uniform YTD conjecture. During the talk we will discuss in expository terms some of the main difficulties in obtaining such openness results, and finally broadly outline our recent proof. We also point out that the same approach can be applied to show openness of several other stability notions that are commonly studied in Kähler geometry. Even though the problem is phrased in algebro-geometric language, the techniques used to solve it are largely variational. As such we will explain how the result is an application of the theory of energy functionals on the space of Kähler potentials.

22.11 Szymon Myga ''Using the real Monge-Ampère equation on toric Fano manifolds'' Na podstawie pracy ''Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties'' autorstwa R.J. Berman oraz B. Berndtsson

15.11 Marcin Sroka ''On a new proof of the sharp $L^{\infty}$ estimate for the complex Monge-Ampère equation on Kähler manifolds'' Na podstawie pracy "On $L^{\infty}$ estimates for complex Monge-Ampère equations" autorstwa Bin Guo, Duong H. Phong oraz Freid Tong

8.11 Marcin Sroka ''On a new proof of the sharp $L^{\infty}$ estimate for the complex Monge-Ampère equation on Kähler manifolds'' Na podstawie pracy "On $L^{\infty}$ estimates for complex Monge-Ampère equations" autorstwa Bin Guo, Duong H. Phong oraz Freid Tong

25.10 Rafał Czyż ''On the regularity of the complex Hessian equation''

18.10 Marcin Sroka ''A new proof of the gradient estimate for the complex Monge-Ampère equation'' abstrakt: Na podstawie pracy B. Guo, D. H. Phong oraz F. Tong

11.10 Marcin Sroka ''A new proof of the gradient estimate for the complex Monge-Ampère equation'' abstrakt: Na podstawie pracy B. Guo, D. H. Phong oraz F. Tong

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14.06 Ngoc Cuong Nguyen "Analytic approximation and Monge-Ampère masses of plurisubharmonic singularities" na podstawie pracy Chi Li.

7.06 Żywomir Dinew "On a problem of Chirka" Abstrakt: We prove that subharmonic functions that are plurisubharmonic outside a set of measure zero are plurisubharmonic. This is a joint work with Sławomir Dinew.

24.05 Sławomir Dinew "Compact Kähler manifolds with positive bisectional curvature" (based on a paper of Siu and Yau)

17.05 Tomasz Wawak "Characterization of the projective spaces" Abstrakt: Based on the first part of the paper ''Characterizations of complex projective spaces and hyperquadrics'' by S. Kobayashi and T. Ochiai, we give a condition for a manifold with an ample line bundle to be a projective space depending on the first Chern class and the space of sections of the bundle.

10.05 Mihai Păun "On extension of pluricanonical forms defined on the central fiber of a Kähler family

26.04 Dariusz Piekarz "Hopf tori in S^3" Abstrakt: Using Hopf tori we prove that every compact Riemann surface of genus one can be conformally embedded in the three dimensional real unit sphere as a flat torus. I will also present a computer visualization of Hopf tori for some chosen families of closed curves in S^2. bibliografia: U. Pinkall, Hopf tori in S^3, Invent. Math. 81 (1985) 379-386

19.04 Valentino Tosatti "Higher order estimates for collapsing complex Monge-Ampère equations" Abstrakt: I will consider a family of complex Monge-Ampère equations on a compact Calabi-Yau manifold which has a fibration structure, with fiber size that is shrinking to zero, whose solutions of these equations give Ricci-flat Kähler metrics on the total space. Each equation is uniquely solvable by classical work of Yau, but understanding their asymptotic behavior as the fiber size shrinks is a very challenging problem. I will discuss very recent work with Hans-Joachim Hein where we prove a priori C^k estimates for all k, away from the singular fibers of the fibration. This is a consequence of an asymptotic expansion for the solution, which relies on a new analytic method where each additional term of the expansion arises as the obstruction to proving a uniform bound on one additional derivative of the remainder.

12.04 Robert Berman "An invitation to Kähler-Einstein metrics and random point processes" Abstrakt: While the existence of a unique Kähler-Einstein metrics on a canonically polarized manifold X was established already in the seventies there are very few explicit formulas available (even in the case of complex curves!). In this talk I will give a non-technical introduction to a probabilistic approach to Kähler-Einstein metrics, which, in particular, yields canonical approximations of the Kähler-Einstein metric on X. The approximating metrics in question are expressed as explicit period integrals and the conjectural extension to the case of a Fano variety leads to some intriguing connections to zeta functions.

29.03 Vincent Guedj "Finite entropy vs finite energy" Abstrakt: Probability measures with either finite Monge-Ampère energy or finite entropy have played a central role in recent developments in Kähler geometry. We make a systematic study of quasi-plurisubharmonic potentials whose Monge-Ampère measures have finite entropy. We show that these potentials belong to a critical finite energy class and provide examples showing that the critical exponent is sharp. Our proof relies on refined Moser-Trudinger inequalities for quasi-plurisubharmonic functions. This is joint work with E.Di Nezza and H.C.Lu

22.03 Marcin Sroka "HKT from HK metrics" Abstrakt: We present the higher order estimates for the quaternionic Monge-Ampère equation provided the initial metric is Hyperkähler. Some results in the general case will be discussed as well.

15.03 Marcin Sroka "HKT from HK metrics" Abstrakt: We present the higher order estimates for the quaternionic Monge-Ampère equation provided the initial metric is Hyperkähler. Some results in the general case will be discussed as well.

8.03 Marcin Sroka "HKT from HK metrics" Abstrakt: We present the higher order estimates for the quaternionic Monge-Ampère equation provided the initial metric is Hyperkähler. Some results in the general case will be discussed as well.

1.03 Tristan Collins "Stability of the tangent bundle through conifold transitions" Abstrakt: A conifold transition is a topology changing geometric transition between complex threefolds with trivial canonical bundle. I will discuss joint work with S. Picard and S.-T. Yau showing that the tangent bundle to a Calabi-Yau manifold admits a solution of the Hermitian-Yang-Mills equation through a conifold transition. This is motivated by connections to the Hull-Strominger system and Reid's fantasy.

25.1 Ngoc Cuong Nguyen “Hölder continuous subsolution theorems for the complex Hessian equation” na podstawie prac A. Benali i A. Zeriahi.

11.1 Guillaume Olive "Uniform estimates for complex degenerate elliptic equations comparable to the Monge-Ampère equation"

14.12 Soufian Abja "Fano manifolds with NEF tangent bundles are weakly almost Kähler-Einstein"

7.12 Sławomir Dinew "Linear uniformly elliptic equations"

30.11 Daniele Angella "On the Chern-Ricci flow on Inoue surfaces" Abstrakt: We prove that every Gauduchon metric on an Inoue-Bombieri surface admits a strongly leafwise flat form in its $\partial\overline\partial$-class. Using this result, we deduce uniform convergence of the normalized Chern-Ricci flow starting at any Gauduchon metric on all Inoue-Bombieri surfaces, as well as convergence to $S^1$ in the Gromov-Hausdorff sense.

23.11 Sławomir Dinew "Linear uniformly elliptic equations"

16.11 Jacob Sturm "Negatively curved Kähler-Einstein metrics and moduli spaces of stable varieties" Abstrakt: Let K(n,V) denote the set of pairs (X,g) such that X is an n-dimensional compact complex manifold and g is a Kähler-Einstein metric on X with volume at most V, satisfying Ric(g) = - g. We show that if (X_i,g_i) is a sequence in K(n,V), there is a subsequence that converges, in the pointed Gromov-Hausdorff topology, to a finite union of complete Kähler-Einstein metric spaces without loss of volume. Let M(n,V) be the compactified moduli space of all Kähler-Einstein varieties of dimension n and volume at most V. We show that the Weil-Petersson metric, which is a positive closed (1,1) current on the projective variety M(n,V), has continuous local potentials. We also show how one can use these ideas to give a new proof of the Deligne-Mumford stable reduction theorem. This is joint work with Jian Song and Xiaowei Wang.

9.11 Ngoc Cuong Nguyen "Geometric estimates for complex Monge-Ampere equation" na podstawie pracy Xin Fu, Bin Guo oraz Jian Song

2.11 Tamás Darvas "The closure of test configurations and algebraic singularity types" Abstrakt: Given a Kähler manifold X with an ample line bundle L, we consider the metric space of L^1 geodesic rays associated to the first Chern class of L. We characterize rays that can be approximated by ample test configurations. At the same time, we also characterize the closure of algebraic singularity types among all singularity types of quasi-plurisubharmonic functions, pointing out the very close relationship between these two seemingly unrelated problems. By Bonavero's holomorphic Morse inequalities, the arithmetic and non-pluripolar volumes of algebraic singularity types coincide. We show that in general the arithmetic volume dominates the non-pluripolar one, and equality holds exactly on the closure of algebraic singularity types. Joint work with Mingchen Xia.

26.10 1.Krzysztof Maciaszek "Polynomial Solutions of the Complex Homogeneous Monge-Ampere Equation" 2. Ngoc Cuong Nguyen “Geometric estimates for complex Monge-Ampere equation” na podstawie pracy Xin Fu, Bin Guo oraz Jian Song

19.10 Krzysztof Maciaszek "Polynomial Solutions of the Complex Homogeneous Monge-Ampere Equation"

12.10. Marcin Sroka "cscK metrics" (na podstawie cyklu prac X. X. Chen i J. Cheng)

5.10. Marcin Sroka "cscK metrics" (na podstawie cyklu prac X. X. Chen i J. Cheng)

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8.06. Marcin Sroka "cscK metrics" (na podstawie cyklu prac X. X. Chen i J. Cheng)

1.06. Marcin Sroka "cscK metrics" (na podstawie cyklu prac X. X. Chena i J. Chenga)

25.05 1. Tomasz Wawak "Duality between the pseudoeffective and the movable cone on a projective manifold" (na podstawe pracy D. W. Nyströma) 2. Daniel Fatuła "A problem of Stanisław Saks" (na podstawe pracy A. Eremenki)

18.05 Tomasz Wawak "Duality between the pseudoeffective and the movable cone on a projective manifold" (na podstawe pracy D. W. Nyströma)

11.05 Tomasz Wawak "Duality between the pseudoeffective and the movable cone on a projective manifold" (na podstawe pracy D. W. Nyströma)

4.05 Zbigniew Błocki "C^{1,1} regularity of geodesics in the space of volume forms" (na podstawie pracy Jianchun Chu)

27.04 Grzegorz Kapustka "K-STABILITY OF FANO VARIETIES" Abstrakt. We give an survey of the recent progress on the study of K-stability of Fano varieties by an algebro-geometric approach. Based on the works on Chenyang Xu.

9.03 Sławomir Dinew "Remarks on the no-sign obstacle problem"

2.03 Sławomir Dinew "Remarks on the no-sign obstacle problem"

27.1 Daniele Angella "Hermitian geometry of complex manifolds" Abstract. In the tentative to move from the Kähler to the non-Kähler setting, we consider several problems concerning Hermitian metrics on complex manifolds with special curvature properties that can be translated and attacked as analytic pdes. In this context, we study an analogue of the Yamabe problem for Hermitian manifolds: more precisely, we prove the existence of Hermitian metrics having constant scalar curvature with respect to the Chern connection when the expected curvature is non-positive, and we point out the difficulties in the positive curvature case. This problem relates also to several notions of Chern-Einstein metrics. The plural here refers to the lack of symmetries of the curvature tensor of “canonical” connections of Hermitian manifolds. To the broad subject, the Chern-Ricci flow plays an useful role: the problem of uniform convergence of the normalized Chern-Ricci flow can be dealt with on Inoue-Bombieri surfaces with Gauduchon metrics. The talk is based on joint collaborations with: Simone Calamai, Antonio Otal, Cristiano Spotti, Valentino Tosatti, Luis Ugarte, Raquel Villacampa.

20.1 Zbigniew Błocki "L^2 estimate for the Beltrami equation "

13.1 Guillaume Olive "On the weak convergence of wedge products and the div-curl lemma " Abstrakt: This will be a report on the article "On weak continuity and the Hodge decomposition" from Robbin, Rogers and Temple (1987) and on the related div-curl lemma of Murat and Tartar (1978).

16.12 Marcin Sroka "Gauduchon Conjecture" na podstawie pracy "Gauduchon metrics with prescribed volume form", autorstwa G. Szekelyhidi, V. Tosatti, B. Weinkove. W referacie będą przedstawione: Hipoteza Gauchuchona, analogon hipotezy Calabiego na rozmaitościach hermitowskich nie-Kählerowskich oraz jej dowód.

9.12 Marcin Sroka "Gauduchon Conjecture" na podstawie pracy "Gauduchon metrics with prescribed volume form", autorstwa G. Szekelyhidi, V. Tosatti, B. Weinkove. W referacie będą przedstawione: Hipoteza Gauchuchona, analogon hipotezy Calabiego na rozmaitościach hermitowskich nie-Kählerowskich oraz jej dowód.

2.12 Szymon Myga "Limit singularities of the continuity method on Fano manifolds" na podstawie pracy McCleerey'a i Tosattiego "Pluricomplex Green's functions and Fano manifolds".

25.11 Połączone spotkanie z seminarium Analiza matematyczna o 10:15

18.11 Sławomir Dinew "Analytic proof of Kawamata's base point free theorem" na podstawie pracy J. Songa "Riemannian Geometry of Kähler-Einstein currents II"

4.11 Sławomir Dinew "Analytic proof of Kawamata's base point free theorem" na podstawie pracy J. Songa "Riemannian Geometry of Kähler-Einstein currents II"

21.10 Sławomir Dinew "Analytic proof of Kawamata's base point free theorem" na podstawie pracy J. Songa "Riemannian Geometry of Kähler-Einstein currents II"

14.10 Rafał Czyż "Inequalities of Sobolev and Poincare type for m-subharmonic functions"

7.10 Rafał Czyż "Inequalities of Sobolev and Poincare type for m-subharmonic functions"

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10.06 Marcin Sroka "The C^0 estimate for the quaternionic Mange-Ampere equation"

3.06 Rafał Czyż "Inequalities of Sobolev and Poincare type for m-subharmonic functions"

27.05 Marcin Sroka "The C^0 estimate for the quaternionic Mange-Ampere equation"

20.05 Marcin Sroka "The C^0 estimate for the quaternionic Mange-Ampere equation"

13.05 Marcin Sroka "The C^0 estimate for the quaternionic Mange-Ampere equation"

6.05 Sławomir Dinew "Smooth metrics on nef line bundles"

29.04 Sławomir Dinew "Smooth metrics on nef line bundles"

15.04 Żywomir Dinew "ABP-type estimate for plurisubharmonic functions"

8.04 Sławomir Kołodziej "MORSE-TYPE INTEGRALS ON NON-Kähler MANIFOLDS" (joint work with V. Tosatti)

1.04 Ngoc Cuong Nguyen "Remarks on the local and global continuity of the extremal functions"

25.03 Szymon Myga "Pluripotential theory on toric manifolds"

18.03 Szymon Myga "Pluripotential theory on toric manifolds"

11.03 Szymon Myga "Pluripotential theory on toric manifolds"

4.03 Szymon Myga "Pluripotential theory on toric manifolds"

25.2 Szymon Pliś "Degenerate special Lagrangian equation"

14.1 Ngoc Cuong Nguyen "Equidistribution of non-pluripolar products associated with quasi-plurisubharmonic functions of finite energy"

7.1 Grzegorz Kapustka "Contractions of Hyperkähler fourfolds" Abstract: We shall describe exceptional divisors of divisorial contractions of Hyperkähler fourfolds. This is a joint work in progress with B.van Geemen.

17.12 Marcin Sroka "Quaternionic geometries"

10.12 Marcin Sroka "Quaternionic geometries"

3.12 Marcin Sroka "Quaternionic geometries"

26.11 Marcin Sroka "Quaternionic geometries"

19.11 Ngoc Cuong Nguyen "Volume-capacity inequalities and Hölder continuous solutions to complex Hessian equations (joint work with Sławomir Kołodziej)"

5.11 Marcin Sroka "Quaternionic geometries" Abstract: The aim of this talk is to discuss quaternionic geometries i.e. manifolds with some structures being a quaternionic analogue of complex structures. We will present an outline of a current level of knowledge about hypercomplex and HKT manifolds. We will provide some examples of this structures and, finally, we will discuss the construction of so called twistor space associated to any hypercomplex manifold. This is a part of a series of talks during which we will focus on quaternionic Monge-Ampere equation on HKT manifolds.

29.10 Krzysztof Maciaszek "Weighted Bergman kernel, directional Lelong number and John-Nirenberg exponent"

22.10 Krzysztof Maciaszek "Weighted Bergman kernel, directional Lelong number and John-Nirenberg exponent"

15.10 Krzysztof Maciaszek "Weighted Bergman kernel, directional Lelong number and John-Nirenberg exponent"

8.10 Sławomir Dinew "On a problem of Sadullaev"

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16.7 Pengfei Guan "Regularity estimates for scalar curvature equation " Abstract: Scalar curvature equation is a fully nonlinear PDE in differential geometry. It resembles some properties of Monge-Amp\`ere equation and exhibits other special features which are not true for higher dimensional Monge-Amp\`ere equation. The talk will concentrate on two problems: global regularity of immersed hypersurfaces in warped product spaces with nonnegative scalar curvature and interior $C^2$ estimate for immersed hypersurfaces in $R^{n+1}$ with positive scalar curvature (which is not true for $\sigma_k$ curvature equations when $k>2$ by examples of Pogorelov and Urbas). We will explain how special structures of the scalar curvature equation play the role in the estimates and discuss applications to the isometric embedding problem and notion of quasi local masses in general relativity.

11.6 Marcin Sroka "Quaternionic pluripotential theory"

28.5 Zbigniew Błocki "Monge-Ampère operator for plurisubharmonic functions with analytic singularities on Hermitian manifolds"

21.5 Constantin Schramov (Steklov Mathematical Institute and Higher School of Economics) "Fano threefolds of degree 22 with a Gm-action" ABSTRACT: It is known that the maximal possible anticanonical degree for smooth Fano threefolds of Picard rank 1 and index 1 is 22. The family of threefolds of this degree has many interesting features. In particular, it was extensively studied from the point of view of Tian's alpha-invariants and existence of Kaehler-Einstein metrics. It is known that some of them admit Kaehler-Einstein metrics, while some others do not. In some cases their existence can be deduced from a computation of alpha-invariants. In my talk I will tell about the geometry of Fano threefolds of degree 22 that admit the action of a one-dimensional torus Gm, and about their alpha-invariants. This is a joint work with Ivan Cheltsov.

14.5 Marcin Sroka "Quaternionic pluripotential theory"

7.5 Marcin Sroka "Quaternionic pluripotential theory"

23.4 DongSeon Hwang "On cascades of log del Pezzo surfaces" Abstract: There have been numerous attempts to classify log del Pezzo surfaces. In this talk, I will quickly summarize the known results to this goal and report my work on the classification of such surfaces. The result is obtained by generalizing the notion of ‘cascades’ of nonsingular del Pezzo surfaces to the singular case. This approach is turned out to be successful when the surface is toric or of Picard number one. At the end of the talk, I will also speak on the Singular Surface Database(SSDB) project which aims to realize this method.

16.4 Krzysztof Maciaszek "Cyclicity in the Dirichlet-type spaces"

9.4 Szymon Pliś "Bedford-Taylor type capacities on almost complex surfeces"

26.3 Szymon Pliś "Bedford-Taylor type capacities on almost complex surfeces"

19.3 Dominik Burek "McKay correspondence"

12.3 Sławomir Kołodziej "Hölder continuous subsolutions for the Monge-Ampère equation"

5.3 Giovanni Mongardi (Bologna) "Hilbert schemes of points and various equivalencies" Abstrakt: We will start with an introduction on irreducible symplectic (IHS) manifolds, with a particular focus on their birational geometry. Then, we analyze what happens when we take two K3 surfaces with the same derived category and their hilbert schemes of points. We will show how the birational geometry of IHS manifolds forces these schemes to be non birational in many cases. This is part of a joint work with C. Meachan and K. Yoshioka.

26.2 Żywomir Dinew "Gromov-Hausdorff limits of Kähler manifolds"

22.1 Żywomir Dinew "Gromov-Hausdorff limits of Kähler manifolds"

15.1 Marcin Sroka "Quaternionic Monge-Ampère equation IV: The Complex Attempt."

8.1 Marcin Sroka "Quaternionic Monge-Ampère equation III: Calabi Conjecture for HKT-manifolds."

18.12 Marcin Sroka "Quaternionic Monge-Ampère equation II: Quaternionic geometric structures"

11.12 Marcin Sroka "Quaternionic Monge-Ampère equation I: An introduction"

4.12 Grzegorz Kapustka "Compact Moduli spaces of del Pezzo surfaces and Kähler-Einstein metrics"

27.11 Sławomir Dinew "The $\partial\bar{\partial}$ lemma on Hermitian manifolds"

20.11 Tat Dat To "Geometric contraction of Chern-Ricci flow" Abstract: The Chern-Ricci flow is an evolution equation of Hermitian metrics by their Chern-Ricci form. It follows from previous works of Tosatti and Weinkove that the flow carries out blow-downs of exceptional curves on non-minimal surfaces. In this talk I provide more evidence that the Chern-Ricci flow is a natural evolution equation on complex manifolds and that its behavior reflects the underlying geometry.

13.11 Rafał Czyż "Extension and approximation of m-subharmonic functions"

6.11 Rafał Czyż "Extension and approximation of m-subharmonic functions"

23.10 Szymon Pliś "C^{1,1} regularity of degenerate Monge-Ampère equation"

16.10 Szymon Myga "Completion of the space of Kähler potentials"

9.10 Szymon Myga "Completion of the space of Kähler potentials"

2.10 Szymon Myga "Completion of the space of Kähler potentials"

6.9 Ngoc Cuong Nguyen "On the Hölder continuous subsolution theorem for the complex Monge-Ampère equation"

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12.6 David Witt Nyström "Complex homogeneous Monge-Ampère equations and the Hele-Shaw flow"

29.5 Szymon Myga "Minimum sets of solutions to real and complex Monge-Ampère equation"

22.5 Egmont Porten "Pseudoconcave submanifolds of complex space"

Abstrakt: Pseudoconcave CR manifolds attract particular interest since their structural properties resemble (and generalise) aspects known from complex manifolds, and also because of an abundant variety of examples originating from representation theory. In our talk, we discuss work in progress aiming at extending certain aspects of the theory, like the maximum principle and results on envelopes of holomorphy, to general real submanifolds of Cn (where CR dimension may vary with the point). A major part of this is due to joint work with Mauro Nacinovich (Rome 2).15.5 Sławomir Dinew "Compactness theorems for Kähler-Einstein manifolds in dimension 3 and up"

24.4 Xin Dong "Equality in Suita's conjecture"

10.4 Grzegorz Kapustka "HyperKähler manifolds and incident planes."

3.4 Zbigniew Błocki "Monge-Ampère operator for plurisubharmonic functions with analytic singularities"

27.3 Xin Dong "Bergman kernel and its boundary asymptotics"

20.3 Sławomir Dinew "Compactness theorems for Kähler-Einstein manifolds in dimension 3 and up"

13.3 Sławomir Dinew "Compactness theorems for Kähler-Einstein manifolds in dimension 3 and up"

6.3 Żywomir Dinew "Further developments of the Wu-Yau theorem"

27.2 Żywomir Dinew "Further developments of the Wu-Yau theorem"

23.1 Nguyen Van Thien "Entire mappings and Monge-Ampere currents"

16.1 Krzysztof Maciaszek (wyjątkowo w sali 1094) "On the Maximal Rank Problem for the Complex Homogeneous Monge-Ampere Equation"

9.1 Szymon Pliś "Remarks on holomorphic discs"

12.12 Szymon Myga "Hermitian metrics that leave the total Monge-Ampere volume invariant"

5.12 Sławomir Dinew "Remarks on the obstacle problem"

28.11 Sławomir Dinew "From the Kähler-Ricci flow to moving free boundaries and shocks"

14.11 Rafał Czyż "Moser-Trudinger type inequality in \mathcal E_{p} classes"

7.11 Żywomir Dinew "Minimum sets and differential tests for plurisubharmonic functions"

24.10 Żywomir Dinew "Minimum sets and differential tests for plurisubharmonic functions"

17.10 Szymon Myga "Singular sets of solutions to real Monge-Ampere equation"

10.10 1)Nguyen Van Thien "An inequality for beta function with application to Pluripotential theory" 2)Szymon Myga "Singular sets of solutions to real Monge-Ampere equation"

3.10 Nguyen Van Thien "Convexity of Hessian integrals and Poincare type inequalities"

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30.5 Ngoc Cuong Nguyen "The Fu-Yau equation with negative slope parameter"

16.5 Szymon Myga "Harmonic discs of solutions to Homogeneous Monge-Ampere equation - negative result"

9.5 Dan Popovici "Hodge Theory for the Second Step of Certain Spectral Sequences"

25.4 Ngoc Cuong Nguyen "Log canonical thresholds and Monge-Ampère masses"

18.4 Sławomir Dinew "Sverak theorem"

11.4 Żywomir Dinew "On minimum sets of strictly plurisubharmonic functions"

4.4 Żywomir Dinew "On minimum sets of strictly plurisubharmonic functions"

21.3 Szymon Pliś "Pluripolar sets on almost complex surfaces"

14.3 Ibrahim Djire Karamoko "Pluripolar hulls of Poletsky"

29.2 Ngoc Cuong Nguyen "The Dirichlet problem for the complex Hessian equation on non-compact Hermitian manifolds"

25.1 Ngoc Cuong Nguyen "The Dirichlet problem for the complex Hessian equation on non-compact Hermitian manifolds"

11.1 Nguyen Van Thien "On delta m-subharmonic functions"

4.1 Nguyen Van Thien "On delta m-subharmonic functions"

21.12 Ngoc Cuong Nguyen "Gauduchon metrics with prescribed volume form"

14.12 Ngoc Cuong Nguyen "Gauduchon metrics with prescribed volume form"

7.12 Szymon Myga "Construction of non-polynomial solutions to \sigma_k equation"

30.11 Sławomir Dinew "Tangents to subsolutions (paper of Harvey and Lawson)"

23.11 Ngoc Cuong Nguyen "Fully non-linear elliptic equations on compact Hermitian manifolds"

16.11 Ngoc Cuong Nguyen "Fully non-linear elliptic equations on compact Hermitian manifolds"

9.11 Żywomir Dinew "Some conjectures in Kähler geometry''

26.10 Ngoc Cuong Nguyen "Fully non-linear elliptic equations on compact Hermitian manifolds"

19.10 Ngoc Cuong Nguyen "Fully non-linear elliptic equations on compact Hermitian manifolds"

12.10 Nguyen Van Thien "The weighted pluricomplex energy class $\mathcal E_{\chi}(\Omega)"

5.10 Nguyen Van Thien "The weighted pluricomplex energy class $\mathcal E_{\chi}(\Omega)"

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15.6 Szymon Myga "Monge-Kantorovich's optimal transportation problem"

8.6 Szymon Myga "Monge-Kantorovich's optimal transportation problem"

2.6 Workshop on geometric analysis, zobacz zakładkę "workshop"

1.6 Workshop on geometric analysis, zobacz zakładkę "workshop"

25.5 1) Maria Trybuła "Bergman distance on planar domains" 2)Sławomir Dinew "Remarks on Mukai threefolds with C^{*} action"

18.5 Maria Trybuła "Bergman distance on planar domains"

4.5 Duong Hong Phong "Estimates for Hessian and Monge-Ampère equations "

Abstrakt: There has been recently a lot of progress on techniques for a priori estimates for Hessian and Monge-Ampère equations on complex manifolds. We survey some of the more recent developments, with emphasis on open problems.

13.4 Rafał Czyż "On a problem of Błocki and Zwonek"

30.3 Sławomir Dinew "Gábor Székelyhidi's paper: Remark on the Calabi flow with bounded curvature"

9.3 Sławomir Dinew "Convexity of K- energy and uniqueness of constant scalar curvature metrics"

2.3 Ngoc Cuong Nguyen "Stability and regularity of solutions of the complex Monge-Ampère equation on Hermitian manifolds"

26.1 Ngoc Cuong Nguyen "Stability and regularity of solutions of the complex Monge-Ampère equation on Hermitian manifolds"

19.1 Sławomir Dinew "Convexity of K- energy and uniqueness of constant scalar curvature metrics"

12.1 Żywomir Dinew "Canonical measures and analytic Zariski decompositions"

15.12 Żywomir Dinew "Canonical measures and analytic Zariski decompositions"

8.12 Ngoc Cuong Nguyen "Monge-Ampère type equations on Hermitian manifolds"

1.12 Ngoc Cuong Nguyen "Monge-Ampère type equations on Hermitian manifolds"

24.11 Ngoc Cuong Nguyen "Monge-Ampère type equations on Hermitian manifolds"

17.11 Ngoc Cuong Nguyen "Monge-Ampère type equations on Hermitian manifolds"

3.11 Ngoc Cuong Nguyen "Monge-Ampère type equations on Hermitian manifolds"

27.10 Grzegorz Kapustka "Hyperkähler manifolds"

20.10 Szymon Pliś "On the viscosity solution of the Dirichlet problem"

13.10 Zbigniew Błocki "Isoperimetric inequalities and symmetrization''

6.10 Ngoc Cuong Nguyen "The Kähler rank of compact complex manifolds"

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9.9 w ramach połączonego, nadzwyczajnego spotkania odbędą się następujące dwa wykłady:

13:00 - 13:50 Evgeniya Dyachenko "An algebra of pseudodifferential operators with small parameters"

14:00 -14:50 Ahmed Zeriahi "Weak solutions to degenerate complex Monge-Ampère flows"

Pani Dyachenko jest kandydatką na postdoka w IMUJ.

Oba wykłady odbędą się w sali 1016

2.6 Sławomir Dinew "Minimum sets of plurisubharmonic functins"

5.5 Grzegorz Kapustka "Kähler-Einstein metric on Fano threefolds of genus 12"

28.4 Żywomir Dinew "Demailly's approximating sequence is not decreasing"

14.4 Rafał Czyż "Singular measures"

31.3 Sławomir Dinew "Regularity results for the complex Monge-Ampère equation"

17.3 Dongwei Gu "C^{1,1} regularity for ample line bundles"

10.3 Sławomir Kołodziej "Generalized Monge-Ampère capacities"

3.3 Sławomir Dinew "Monge-Ampère equations on quasi-projective varieties"

27.1 Ngoc Cuong Nguyen "An inequality between the m-capacity and the Euclidean volume form"

20.1 Dongwei Gu "Regularity of psh upper envelopes in big cohomology class"; Ngoc Cuong Nguyen "An inequality between the m-capacity and the Euclidean volume form"

13.1 Dongwei Gu "Regularity of psh upper envelopes in big cohomology class"

16.12 Szymon Pliś "The smoothing of m-subharmonic functions"

9.12 Grzegorz Kapustka "Kähler-Einstein metrics on Fano manifolds"

2.12 Sławomir Dinew "Strong openness conjecture"

18.11 Sławomir Dinew "Berndtsson's proof of the openness conjecture"

4.11 Sławomir Dinew "J-Flow"

21.10 Żywomir Dinew "The technique of Tian-Yau-Zelditch expansion"

14.10 Żywomir Dinew "Tsuji's L^2 approach"

7.10 Spotkanie organizacyjne

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10.6 Grzegorz Kapustka "Kähler-Einstein metric on Fano manifolds"

3.6 Grzegorz Kapustka "Kähler-Einstein metric on Fano manifolds"

27.5 Żywomir Dinew "Kähler-Einstein submanifolds of the Fubini-Study projective space"

20.5 Żywomir Dinew "Kähler-Einstein submanifolds of the Fubini-Study projective space"

29.4 Żywomir Dinew "Kähler-Einstein submanifolds of the Fubini-Study projective space"

22.3 Dongwei Gu "Kähler-Einstein metrics on Fano manifolds"

15.3 Dongwei Gu "Kähler-Einstein metrics on Fano manifolds"

25.3 Dongwei Gu "Kähler-Einstein metrics on Fano manifolds"

18.3 Nguyen Ngoc Cuong "Hölder continous solutions to complex Hessian equations"

11.3 Frunza Ataev "Solutions to degenerate complex Hessian equations"

4.3 Frunza Ataev "Solutions to degenerate complex Hessian equations"

25.2 Frunza Ataev "Solutions to degenerate complex Hessian equations"

21.1 Frunza Ataev "Solutions to degenerate complex Hessian equations"

14.1 Frunza Ataev "Solutions to degenerate complex Hessian equations"

7.1 Frunza Ataev "Solutions to degenerate complex Hessian equations"

17.12 Frunza Ataev "Solutions to degenerate complex Hessian equations"

3.12 Szymon Pliś "Monge-Ampère operator for J-plurisubharmonic functions"

26.11 Szymon Pliś "Monge-Ampère operator for J-plurisubharmonic functions"

12.11 Ngoc Cuong Nguyen "The super-potential of closed positive currents and applications"

5.11 Ngoc Cuong Nguyen "The super-potential of closed positive currents and applications"

29.10 Ngoc Cuong Nguyen "The super-potential of closed positive currents and applications"

22.10 Ngoc Cuong Nguyen "The super-potential of closed positive currents and applications"

15.10 Ngoc Cuong Nguyen "The super-potential of closed positive currents and applications"

8.10 Dongwei Gu "Quaternionic Monge-Ampère equation and Calabi problem for HKT-manifolds"

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11.6 Dongwei Gu "Quaternionic Monge-Ampère equation and Calabi problem for HKT-manifolds"

4.6 Żywomir Dinew "Weak geodesics in the space of Kähler metrics"

28.5 Ngoc Cuong Nguyen "The J-flow in Kähler geometry"; Żywomir Dinew "Weak geodesics in the space of Kähler metrics"

21.5 Ngoc Cuong Nguyen "The J-flow in Kähler geometry"

7.5 Ngoc Cuong Nguyen "The J-flow in Kähler geometry"

23.4 Ngoc Cuong Nguyen "The J-flow in Kähler geometry"

16.4 Ngoc Cuong Nguyen "The J-flow in Kähler geometry"

2.4 Dongwei Gu "On the C^{2,alpha}-Regularity of the Complex Monge-Ampère Equation"

26.3 Frunza Ataev "Measures of finite pluricomplex energy"

19.3 Frunza Ataev "Measures of finite pluricomplex energy"

12.3 Frunza Ataev "Measures of finite pluricomplex energy"

5.3 Dongwei Gu "Ricci iterations on Fano manifolds"

27.2 Dongwei Gu "Ricci iterations on Fano manifolds"

26.1 Żywomir Dinew "The Ricci and scalar curvatures of the Bergman metric"

9.1 Ngoc Cuong Nguyen "Applications of the Moser-Trudinger type inequalities for complex Monge-Ampère operators"

7.1 Ngoc Cuong Nguyen "Applications of the Moser-Trudinger type inequalities for complex Monge-Ampère operators"

15.12 Ngoc Cuong Nguyen "Applications of the Moser-Trudinger type inequalities for complex Monge-Ampère operators"

12.12 Ngoc Cuong Nguyen "Applications of the Moser-Trudinger type inequalities for complex Monge-Ampère operators"

28.11 Ngoc Cuong Nguyen "Applications of the Moser-Trudinger type inequalities for complex Monge-Ampère operators"

24.11 Zbigniew Błocki "Geodesics in the space of Kähler metrics need not be C^3 (an example of Lempert and Vivas)"

17.11 Szymon Pliś "Dirichlet problem on almost complex manifolds"

7.11. Rafał Czyż "The Dirichlet problem and Dirichlet principle"; Szymon Pliś "Dirichlet problem on almost complex manifolds"

20.10 Rafał Czyż "The Dirichlet problem and Dirichlet principle"

13.10 Rafal Czyż "On Dirichlet's principle and problem"