{"id":563,"date":"2026-07-09T04:44:08","date_gmt":"2026-07-09T04:44:08","guid":{"rendered":"https:\/\/sites.rutgers.edu\/scvcgc\/?page_id=563"},"modified":"2026-07-19T15:14:53","modified_gmt":"2026-07-19T15:14:53","slug":"titles-and-abstracts","status":"publish","type":"page","link":"https:\/\/sites.rutgers.edu\/scvcgc\/titles-and-abstracts\/","title":{"rendered":"Titles and abstracts"},"content":{"rendered":"
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Speaker<\/th>\nTitle<\/th>\nAbstract<\/th>\n<\/tr>\n<\/thead>\n
J. Cao<\/strong>
\nUniversit\u00e9 C\u00f4te d’Azur, France<\/span><\/td>\n		Hodge Theory for Local Systems on Quasi-Compact K\u00e4hler Manifolds and Applications<\/td>\nIn this talk, we will present some extension theorems for local systems on quasi-compact K\u00e4hler manifolds. We will also discuss several geometric applications, including results on cohomology jumping loci and properties of local systems on special varieties. This talk is based on two joint works with Ya Deng, Christopher Hacon, and Mihai P\u0103un: arXiv:2511.06773<\/a> and arXiv:2603.14539<\/a>.<\/td>\n<\/tr>\n
S. Chanillo<\/strong>
\nRutgers University, USA<\/span><\/td>\n		Recent Progress in CR Geometry<\/td>\nWe shall present some recent progress on several problems in CR geometry related to compact CR 3-manifolds. Our results include global embedding of CR manifolds, the positive mass theorem, and results related to the Sobolev constant and the CR Yamabe problem. Lastly, we will present recent results on a CR version of Huber\u2019s theorem and the injectivity of the developing map. The classical Huber\u2019s theorem was proved in 1957 for Riemann surfaces. Time permitting, we shall link the last set of results on Huber\u2019s theorem and the developing map to the location of the first resonance of the Laplacian and the limit set of Kleinian groups and their size in the complex ball. At the heart of many of our results lies a conformally covariant fourth-order operator, the Paneitz operator. Our results have been obtained in joint work with Paul Yang.<\/td>\n<\/tr>\n
T. Collins<\/strong>
\nToronto University, Canada<\/span><\/td>\n		Boundary regularity of optimal transport maps.<\/td>\nI will discuss some new results concerning boundary regularity
\nof optimal transport maps between convex domains, and their connections
\nto degenerations of Calabi-Yau metrics. Based on joint work with Freid
\nTong.<\/td>\n<\/tr>\n
D. Coman<\/strong>
\nSyracuse University, USA<\/span><\/td>\n		Distribution of random degeneracy sets for Grassmannian embeddings<\/td>\nLet (X<\/em>, \u03c9) be a compact K\u00e4hler manifold, (L<\/em>, h<\/em>L<\/sup>) be a positive line bundle, and (E<\/em>, h<\/em>E<\/sup>) be a Hermitian holomorphic vector bundle of rank r<\/em> on X<\/em>. We show that the pullback by the Kodaira embedding associated to L<\/em>p<\/sup> \u2297 E<\/em> of the k<\/em>-th Chern form of the dual universal bundle over the Grassmannian converges as p<\/em> \u2192 \u221e to the k<\/em>-th power of the Chern form c<\/em>1<\/sub>(L<\/em>, h<\/em>L<\/sup>), for 0 \u2264 k<\/em> \u2264 r<\/em>. The degeneracy set of a k<\/em>-tuple of holomorphic sections of L<\/em>p<\/sup> \u2297 E<\/em> is the locus of points in X<\/em> where they are linearly dependent. We compute the expectation of the currents of integration along degeneracy sets of random k<\/em>-tuples of holomorphic sections of L<\/em>p<\/sup> \u2297 E<\/em>. Using these results and a sequence of suitable meromorphic transforms associated to the degeneracy sets, we prove the almost sure convergence of these currents as p<\/em> \u2192 \u221e. This talk is based on joint work with Turgay Bayraktar, Bingxiao Liu and George Marinescu.<\/td>\n<\/tr>\n
T. Darvas<\/strong>
\nUniv of Maryland, USA<\/span><\/td>\n		Sharp C1,1\u0304<\/sup> Estimates in K\u00e4hler Quantization<\/td>\nI will discuss sharp C1,1\u0304<\/sup> estimates for Bergman potentials in K\u00e4hler quantization. For a plurisubharmonic weight \u03c6, with weighted Bergman kernel K<\/em>\u03c6<\/sub>, we prove upper and positive lower bounds for i<\/em>\u2202\u2202\u0304 log K<\/em>\u03c6<\/sub> in terms of the corresponding bounds for i<\/em>\u2202\u2202\u0304\u03c6. These estimates hold both locally and on compact K\u00e4hler manifolds. I will explain the analytic ideas behind the estimates and how they lead to optimal C1,\u03b1<\/sup>-convergence of Bergman approximations for K\u00e4hler currents with bounded coefficients. Time permitting, I will also discuss applications to the quantization of non-pluripolar Radon measures. The talk is based on joint work with Zbigniew Blocki.<\/td>\n<\/tr>\n
P. Ebenfelt<\/strong>
\nUniversity of California at San Diego, USA<\/span><\/td>\n		To be announced.<\/em><\/td>\nTo be announced.<\/em><\/td>\n<\/tr>\n
X. Gong<\/strong>
\nUniversity of Wisconsin at Madison, USA<\/span><\/td>\n		Integrability of Koszul connections on complex vector bundles over domains in \u2102n<\/sup><\/td>\nWe study invertible matrix solutions A<\/em> to the equation A<\/em>\u22121<\/sup>\u2202\u0304A<\/em> = \u03c9(0,1)<\/sup> on a small open subset U<\/em> of the closure M<\/em><\/span> of a domain M<\/em> \u2282 \u2102n<\/sup>, where \u03c9(0,1)<\/sup> is a matrix of (0,1) forms on M<\/em><\/span> satisfying the formal integrable condition \u2202\u0304\u03c9(0,1)<\/sup> = \u03c9(0,1)<\/sup> \u2227 \u03c9(0,1)<\/sup>. For a C2<\/sup> domain M<\/em> that is either strongly pseudoconvex or has at least 3 negative Levi eigenvalues at a boundary point contained in U<\/em>, we obtain existence and sharp regularity of the solutions.<\/td>\n<\/tr>\n
V. Guedj<\/strong>
\nL’Universit\u00e9 Paul Sabatier, France<\/span><\/td>\n		Geometric smoothing by the K\u00e4hler-Ricci flow<\/td>\nWe study the geometric regularization of a positive closed current by the (twisted) K\u00e4hler-Ricci flow on a compact K\u00e4hler manifold. We conjecture that the local Arnold multiplicities linearly decrease to zero, while the flow produces complete K\u00e4hler metrics in the Zariski open subset of points that have zero Lelong numbers. We prove this conjecture in complex dimension 1 and provide several partial results in higher dimension. This is joint work with E. Di Nezza and H. C. Lu.<\/td>\n<\/tr>\n
B. Guo<\/strong>
\nRutgers University at Newark, USA<\/span><\/td>\n		Geometric estimates on K\u00e4hler spaces<\/td>\nWe will discuss the role of complex Monge-Amp\u00e8re equations as auxiliary equations in deriving sharp analytic and geometric estimates in K\u00e4hler geometry. By studying Green\u2019s functions, we will explore how to derive estimates for diameters and establish uniform Sobolev inequalities on K\u00e4hler manifolds, which depend only on the entropy of the volume form and are independent of the lower bound of the Ricci curvature.<\/td>\n<\/tr>\n
S. Y. Kim<\/strong>
\nInstitute of Basic Sciences, South Korea<\/span><\/td>\n		Proper holomorphic maps between bounded symmetric domains of rank p<\/em> and 2p<\/em> \u2212 1<\/td>\nBy a recent result of Kim\u2013Mok\u2013Seo, it is known that any proper holomorphic map between two irreducible bounded symmetric domains of the same type is semi-standard if rank(\u03a9\u2032) \u2264 2 rank(\u03a9) \u2212 2. On the other hand, Seo constructed examples for type-I bounded symmetric domains with rank(\u03a9\u2032) = 2 rank(\u03a9) \u2212 1, which are not semi-standard. In this talk, we classify the proper holomorphic maps between two type-I bounded symmetric domains \u03a9, \u03a9\u2032 with 5 \u2264 rank(\u03a9) and rank(\u03a9\u2032) = 2 rank(\u03a9) \u2212 1, under the assumption that the proper holomorphic maps respect the maximal invariantly geodesic subspaces. We first classify the rational proper holomorphic maps between generalized balls \u212cp,q<\/em><\/sub> and \u212c2p<\/em>\u22121,q<\/em>\u2032<\/sub> with 5 \u2264 p<\/em> \u2264 q<\/em> and 2p<\/em> \u2212 1 \u2264 q<\/em>\u2032, that are the associated moduli maps of those between the corresponding type-I domains. Then we give an explicit expression of the corresponding proper holomorphic maps between \u03a9 and \u03a9\u2032. This is joint work with Y. Gao and S.-C. Ng.<\/td>\n<\/tr>\n
T. Koike<\/strong>
\nInstitute of Pure and Applied Sciences, University of Tsukuba, Japan<\/span><\/td>\n		Recent progress on semi-positivity criteria for holomorphic line bundles<\/td>\nI will discuss geometric criteria for the semi-positivity of holomorphic line bundles on compact K\u00e4hler manifolds. Let D<\/em> be an effective nef divisor on a compact K\u00e4hler manifold X<\/em>, and assume that the numerical dimension of the line bundle [D<\/em>] associated with D<\/em> is one. I will explain a characterization of the semi-positivity of [D<\/em>] in terms of the unitary flatness of [D<\/em>] on a neighborhood of the support of D<\/em>, which leads naturally to a Levi-flat neighborhood geometry and a holomorphic foliation associated with the divisor. I will also explain the relation with Ueda theory and some related formal-principle-type questions for line bundles.<\/td>\n<\/tr>\n
\nLukasz Kosinski<\/strong>
\nJagiellonian University, Poland<\/span>\n<\/td>\n		\nExtension property and interpolation\n<\/td>\n\nThis talk concerns the interplay between Pick interpolation, holomorphic extension, the geometry of complex domains, and operator theory.<\/p>\n

The main focus is the norm-preserving extension problem. The starting point is the theorem of Agler and McCarthy characterizing extension sets in the bidisk as holomorphic retracts. We explain how this result generalizes to higher-dimensional polydisks and how the problem reduces to a distinguished family of quadratic complex surfaces. We also discuss the connections with uniqueness varieties and Lempert’s theory of invariant distances.<\/p>\n

References<\/strong>
\n[1] J. Agler and J. E. McCarthy, Norm preserving extensions of holomorphic functions from subvarieties of the bidisk<\/em>, Ann. of Math.<\/em> (2) 157 (2003), no. 1, 289–312.
\n[2] L. Kosinski and J. E. McCarthy, Totally geodesic sets and Carath\u00e9odory geometry in the polydisk<\/em>, preprint, 2026.\n<\/td>\n<\/tr>\n

Y. Kusakabe<\/strong>
\nKyushu University, Japan<\/span><\/td>\n		On pseudoconvexity of Gromov elliptic manifolds<\/td>\nIn contrast to Kobayashi hyperbolic manifolds, Gromov elliptic manifolds are defined as complex manifolds admitting a dominating holomorphic spray, that is, a holomorphic family of dominating entire maps \u2102n<\/sup> \u2192 X<\/em> parametrized by X<\/em>. By Gromov’s Oka principle, every Gromov elliptic manifold is an Oka manifold, and therefore admits sufficiently many holomorphic maps from Stein manifolds to satisfy approximation and extension properties. Geometrically, while complete Kobayashi hyperbolic manifolds are Hartogs pseudoconvex, recent developments suggest that Oka manifolds are closely related to pseudoconcavity. In this talk, however, we show that Gromov elliptic manifolds also enjoy a certain form of pseudoconvexity. As an application, we construct compact Oka manifolds that are not Gromov elliptic, thereby providing compact counterexamples to Gromov’s question.<\/td>\n<\/tr>\n
B. Lamel<\/strong>
\nUniversity of Vienna, Austria<\/span><\/td>\n		Symmetries of involutive structures<\/td>\nWe discuss some recent results on symmetries of involutive systems of PDEs and their connections to Several Complex Variables. An involutive system is given by a formally integrable subbundle of the complexified tangent bundle of a real manifold, and encodes a system of first-order linear PDEs with complex coefficients on that manifold. A particular case is given by locally integrable systems, namely those which can locally be embedded into complex Euclidean space such that part of their structure bundle is given by the (0,1) vector fields tangent to the image. Examples include CR structures, elliptic structures, and real structures. We discuss how nondegeneracy conditions for general involutive structures can naturally be introduced, and show how they imply some (ir)regularity results for infinitesimal automorphisms. This is joint work with Nicholas Braun Rodrigues from USP.<\/td>\n<\/tr>\n
S. Y. Li<\/strong>
\n University of California at Irvine, USA<\/span><\/td>\n		On Point Separation of Bergman Space on Stein Manifolds with Constant Holomorphic Sectional Curvature<\/td>\nIn this talk, we prove that the Bergman space of a Stein manifold separates points whenever its Bergman metric is well defined and has non-positive constant holomorphic sectional curvature. We construct examples of Stein manifolds whose Bergman metric is well defined and has positive constant holomorphic sectional curvature, while their Bergman spaces do not separate points. We also construct examples of Stein manifolds whose Bergman metric is well defined and has constant scalar curvature, which can be negative, zero, or positive, yet whose Bergman spaces do not separate points. Combined with previously established results, this shows that a Stein manifold cannot admit a well-defined flat Bergman metric, and that it admits a well-defined Bergman metric with negative constant holomorphic sectional curvature if and only if it is biholomorphic to the unit ball of the same dimension, possibly with a pluripolar set removed. The proof is based on Hörmander’s L2<\/sup>-estimates on ∂̄-equations; the curvature condition, together with Calabi’s rigidity and extension theorems, is used to construct the required bounded strictly plurisubharmonic functions. The construction of Stein manifolds with positive constant holomorphic sectional curvature for their Bergman metric is based on classical hyperelliptic Riemann surface theory and its higher-dimensional generalizations. This is joint work with Xiaojun Huang from Rutgers University.<\/td>\n<\/tr>\n
\nX. Ma<\/strong>
\nUniversity of Paris, France<\/span>\n<\/td>\n		\nBergman kernels on non-compact manifolds and Poincar\u00e9 series\n<\/td>\n\nWe begin by reviewing our result concerning the estimation of the exponential decay of the Bergman kernel associated with the powers of a positive line bundle on complete K\u00e4hler manifolds, within the framework of bounded geometry. As an application, we show that if a discrete group \u0393 acts on such a variety and the quotient has finite volume, then, for sufficiently large powers of the positive line bundle, the Bergman kernel on the quotient space can be expressed as the sum, over \u03b3 \u2208 \u0393, of the contributions of the Bergman kernel on the total space. In particular, we highlight new examples of relative Poincar\u00e9 series on domains in \u2102n<\/sup> and show that they do not vanish identically. This is joint work with L. Ioos, W. Lu, and G. Marinescu.\n<\/td>\n<\/tr>\n
N. Mir<\/strong>
\nTexas A&M University at Qatar, Qatar<\/span><\/td>\n		Artin approximation and CR geometry<\/td>\nWe explore the validity of Artin\u2019s approximation theorem under additional constraints arising from the CR equations of a real-analytic CR manifold. We will discuss both positive and negative results along these lines, including recent joint work with B. Lamel. Ultimately, these results highlight the crucial role played by the CR geometry of the underlying manifold.<\/td>\n<\/tr>\n
N. Mok<\/strong>
\nUniversity of Hong Kong, Hong Kong<\/span><\/td>\n		\u03c01<\/sub> of irreducible Shimura varieties of rank \u2265 2<\/td>\nLet \u03a9 be a bounded symmetric domain of rank \u2265 2 and \u0393 &subset; Aut(\u03a9) be a torsion-free irreducible lattice, so that X\u0393<\/sub> := \u03a9\/\u0393 carries a canonical structure as a quasi-projective manifold. Let (M, hM<\/sub>) be a simply connected complete K\u00e4hler-Einstein manifold of negative Ricci curvature which is moreover assumed to be Carath\u00e9odory hyperbolic, and let \u0393\u2032 &subset; Aut(M) be a torsion-free discrete subgroup such that Volume(Y\u0393\u2032<\/sub>, hY\u0393\u2032<\/sub><\/sub>) < \u221e, where Y\u0393\u2032<\/sub> := M\/\u0393\u2032 and hY\u0393\u2032<\/sub><\/sub> is the quotient metric induced from (M, hM<\/sub>). Let f: X\u0393<\/sub> \u2192 Y\u0393\u2032<\/sub> be a holomorphic map which induces an isomorphism f*<\/sub>: \u0393 \u2245 \u0393\u2032. In a recent joint article with Kwok-Kin Wong, we have proved a result called the Isomorphism Theorem, which, when adapted to the current setting, says that F: \u03a9 \u2192 M is necessarily a biholomorphism. The main object of study is the \u0393-invariant algebra \u2131 = F*<\/sup>H\u221e<\/sup>(M) of bounded holomorphic functions on \u03a9. I will explain the essential roles played by K\u00e4hler geometry, harmonic analysis, and ergodic theory in the proof of the Isomorphism Theorem.<\/td>\n<\/tr>\n
D. W. Nystrom<\/strong>
\nUniversity of Gothenburg, Sweden<\/span><\/td>\n		Extremal simply connected subdomains of Riemann surfaces and metric graphs\/tropical curves<\/td>\nGiven a compact Riemann surface S<\/em> with genus g<\/em> > 0 and with a marked point p<\/em>, there is a canonical simply connected subdomain of S<\/em> containing p<\/em>, that e.g. can be characterized in terms of its Green’s function. This follows from a classical result of Strebel, which itself built on earlier work of Teichm\u00fcller and Jenkins. This extremal subdomain is interesting because it shows how S<\/em> can be constructed from the unit disc by gluing parts of the unit circle together in a simple way, and it can thus be used to study the associated moduli space. Some time ago Fredrik Viklund and I proposed a way to find the gluing parameters for a given Riemann surface, up to some small error, by using a probabilistic model that we call interface erosion (it is closely related to another probabilistic model called competitive erosion, introduced by Propp in the early 2000s). Trying to prove that this actually works led us (now also joined by Levi Hanschmid-Sibitz) to consider some related questions for metric graphs\/tropical curves, and we then managed to prove in that setting the result analogous to that of Strebel’s. In my very non-technical talk, I will try to explain parts of this story, and time permitting maybe also discuss what might happen in higher dimensions.<\/td>\n<\/tr>\n
A. Raich<\/strong>
\nUniversity of Arkansas, USA<\/span><\/td>\n		A Generalized Bochner\u2013Martinelli Plemelj Jump Formula and Integral Kernel Methods to Solve \u2202\u0304M<\/sub><\/td>\nSolving the tangential Cauchy-Riemann equations on higher codimension CR manifolds is a relatively unexplored topic. In this talk, I have two goals. The first is to discuss a Bochner\u2013Martinelli Plemelj jump formula for smooth, embedded, and generic CR manifolds. The jump formula reduces to the standard jump formula in the case the CR manifold is a hypersurface. The second goal is to use the new jump formula and integral kernel techniques to solve the tangential Cauchy-Riemann equations on smooth, embedded q-convex CR manifolds. This work is joint with Al Boggess of Arizona State University.<\/td>\n<\/tr>\n
\nN. Savale<\/strong>
\nTrinity College, Ireland<\/span>\n<\/td>\n		\nQuantitative Weyl’s law for Toeplitz operators\n<\/td>\n\nWe prove a general estimate for the Weyl remainder of a Toeplitz operator in terms of volumes of recurrence sets for the Hamilton flow of its principal symbol. This extends classical results by Boutet de Monvel\u2013Guillemin and semiclassical results by Borthwick\u2013Paul\u2013Uribe on Toeplitz operators. It also generalizes recent work of the author in the pseudodifferential case.\n<\/td>\n<\/tr>\n
C. Schnell<\/strong>
\nState University of New York at Stony Brook, USA<\/span><\/td>\n		Meromorphic groups and their actions on compact K\u00e4hler spaces<\/td>\nI am going to review Fujiki’s theory of meromorphic groups, and then apply it to prove a new \u201cfreeness theorem\u201d for the cohomology of compact K\u00e4hler spaces with a meromorphic action by a meromorphic group. This is joint work with Mark de Cataldo and Yoonjoo Kim.<\/td>\n<\/tr>\n
Aeryeong Seo<\/strong>
\nKyungpook National University, Korea<\/span><\/td>\n		On the Pseudoconvexity and Completeness of Holomorphic Fiber Bundles<\/td>\nThis talk examines the intermediate pseudoconvexity and weakly 1-completeness of holomorphic fiber bundles. For holomorphic fiber bundles over compact K\u00e4hler manifolds with fibers given by bounded symmetric domains, we discuss the conditions under which these spaces are weakly 1-complete, particularly when the holonomy representation is reductive. Building on this, we analyze locally trivial holomorphic \u212cn<\/sup>-bundles over compact Riemann surfaces of genus greater than one. By assuming the existence of a harmonic section with a point of maximal rank, we show that these bundles are 1-convex, while their complements in the associated \u2102Pn<\/sup>-bundles exhibit n<\/em>-convexity\u2014a result derived through an analysis of the leafwise positivity of the normal bundle of the foliation induced on the boundary. This is joint work with Masanori Adachi and Seungjae Lee.<\/td>\n<\/tr>\n
Y. T. Siu<\/strong>
\nHarvard University, USA<\/span><\/td>\n		Some Problems in Several Complex Variables<\/td>\nWe will discuss the following three problems in several complex variables.<\/p>\n

(1) Finite generation problem to determine the contexts for the finite generation of the canonical ring to hold.<\/p>\n

(2) Global non-deformability problem for compact Hermitian symmetric manifolds without assuming deformation to be K\u00e4hler.<\/p>\n

(3) Differential relations derived from failure of certain conditions. For example, differential relations satisfied by Kohn’s subelliptic multipliers and Donaldson’s holomorphicity of destabilizing subsheaves for nonexistence of Hermitian-Einstein metric for vector bundles.<\/td>\n<\/tr>\n

L. Stolovitch<\/strong>
\nCNRS and Universit\u00e9 C\u00f4te d’Azur, France<\/span><\/td>\n		Recent results on equivalence of neighborhoods of embedded compact complex manifolds and higher codimension foliations<\/td>\nIn this talk, we will survey recent work done in collaboration with Xianghong Gong, Takayuki Koike, and Xiaojun Wu. We consider an embedded n<\/em>-dimensional compact complex manifold C<\/em> in (n<\/em> + d<\/em>)-dimensional complex manifolds. We are interested in the holomorphic classification of neighborhoods when the normal bundle is flat. We will give conditions ensuring that a neighborhood of C<\/em> in M<\/em> is biholomorphic to a neighborhood of the zero section of its normal bundle. We also give conditions ensuring the existence of a holomorphic foliation in a neighborhood of C<\/em> in M<\/em> having C<\/em> as a compact leaf, extending Ueda’s theory to the higher dimension and codimension cases. Both problems appear as a kind of \u201clinearization problem\u201d involving appropriate notions of resonances<\/em> and a small-divisor condition.<\/td>\n<\/tr>\n
E. Straube<\/strong>
\nTexas A&M University, USA<\/span><\/td>\n		Diederich\u2013Forn\u00e6ss index and regularity of the complex Green operator<\/td>\nLet \u03a9 be a smooth bounded pseudoconvex domain in \u2102n<\/sup>. We show that if \u03a9 satisfies a certain comparability condition on the Levi eigenvalues of its boundary, then Diederich\u2013Forn\u00e6ss index one implies regularity of the complex Green operators and the associated canonical operators on b<\/em>\u03a9. The particular comparability condition needed is relevant only in dimension n<\/em> \u2265 3, it never holds on domains in \u21022<\/sup>. (This situation is rather in contrast to that for the analogous results for the \u2202\u0304-Neumann operators: the relevant comparability condition there is relevant only in dimension n<\/em> \u2265 3 because it always holds on domains in \u21022<\/sup>.) We show that nevertheless, DF-index one implies regularity of the canonical operators on the boundary for domains in \u21022<\/sup>. This is joint work with Tanuj Gupta.<\/td>\n<\/tr>\n
D. V. Vu<\/strong>
\nCologne University, Germany<\/span><\/td>\n		Uniform estimates for singular K\u00e4hler metrics in big cohomology classes<\/td>\nWe generalize Guo-Phong-Song-Sturm’s uniform diameter estimates and local non-vanishing of volumes for K\u00e4hler metrics to the case of big cohomology classes. Main ingredients of the proof are a uniform diameter estimate for a family of smooth K\u00e4hler metrics only involving an integrability condition and stability properties of complex Monge\u2013Amp\u00e8re equations with prescribed singularities. This is a joint work with Duc-Bao Nguyen (NUS, Singapore).<\/td>\n<\/tr>\n
J. Wang<\/strong>
\nAcademia Sinica, Taiwan<\/span><\/td>\n		On Campana’s conjecture for covering of toric varieties<\/td>\nIn joint work with Ji Guo, Khoa D. Nguyen, and Chia-Liang Sun, we extend results of Corvaja\u2013Zannier, Turchet, and Capuano\u2013Turchet to establish new cases of the Lang\u2013Vojta Conjecture for varieties of log general type arising as ramified covers of algebraic tori over function fields. The main technical ingredient is a function field analogue of Vojta’s generalized abc conjecture for algebraic tori with explicitly computable exceptional sets. This is proved via a greatest common divisor theorem for multivariable polynomials evaluated at S<\/em>-unit points. I will then explain how these methods can be further developed to prove cases of Campana’s orbifold conjecture for toric varieties with sufficiently large boundary multiplicities, both over function fields and in the complex analytic setting. These results are based on joint work with Carlo Gasbarri and Ji Guo in the function field case, and with Min Ru in the complex analytic setting.<\/td>\n<\/tr>\n
M. Xiao<\/strong>
\nUniversity of California at San Diego, USA<\/span><\/td>\n		Bergman Metrics of Constant Holomorphic Sectional Curvature<\/td>\nA classical theorem of Lu states that a bounded domain with a complete Bergman metric of constant holomorphic sectional curvature must be biholomorphic to the unit ball. In this talk, we discuss some recent progress in the more general setting of complex manifolds whose Bergman metric is not necessarily complete but has constant holomorphic sectional curvature.<\/td>\n<\/tr>\n
J. Xie<\/strong>
\nBeijing University, China<\/span><\/td>\n		To be announced.<\/em><\/td>\nTo be announced.<\/em><\/td>\n<\/tr>\n
R. Zhang<\/strong>
\nUCSD, USA<\/span><\/td>\n		Collapsing Ricci flat spaces in complex geometry\u00a0<\/span><\/td>\nIn this talk, we will discuss some progress in the collapsing geometry of Calabi-Yau metrics in low and high dimensions. We will also introduce their interactions with the degenerations of complex structures.\u00a0<\/span><\/td>\n<\/tr>\n
X. Zhou<\/strong>
\nChinese Academy of Sciences, China<\/span><\/td>\n		Some Results in Several Complex Variables<\/td>\nWe’ll introduce recent advances in several complex variables and their applications in related areas, including:<\/p>\n