报告1
报告题目：The Neumann problem for nonlinear elliptic and parabolic equations
报告时间：2018年7月2日（星期一）09:00—09:45
报告地点：苏州大学本部精正楼211
报告人：Xinan Ma (University of Science and Technology of China)
报告提要：We shall study the existence of Neuamann problem for some geometry elliptic PDE, which include the Hessian equations on strict convex domain, mean curvature equation and special Lagrange equation. Then we study some parabolic corresponding results and the existence of translation solutions on strictly convex domain.
报告2
报告题目：Donaldson Question: “Tamed to Compatible”
报告时间：2018年7月2日（星期一）10:15—11:00
报告地点：苏州大学本部精正楼211
报告人：Hongyu Wang (Yangzhou University)
报告提要：In this talk, we show that on any tamed closed almost complex four-manifold (M; J) whose dimension of J-anti-invariant cohomology is equal to self-dual second Betti number minus one, there exists a new symplectic form compatible with the given almost complex structure J. In particular, if the self-dual second Betti number is one, we give an affirmative answer to Donaldson question for tamed closed almost complex four-manifolds that is a conjecture in joint paper of Tosatti, Weinkove and Yau. Our approach is along the lines used by Buchdahl to give a unified proof of the Kodaira conjecture. Thus, our main result gives an affirmative answer to the Kodaira conjecture in symplectic version.
报告3
报告题目：Shrinking Ricci solitons
报告时间：2018年7月2日（星期一）11:10—11:45
报告地点：苏州大学本部精正楼211
报告人：Lei Ni (UC Sand Diego)
报告提要：In this talk, I will discuss some classification results about gradient shrinking Ricci solitons, including joint works with Nolan Wallach, and joint work with Xiaolong Li and Kui Wang.
报告4
报告题目：Recent progress on isolated singularities
报告时间：2018年7月2日（星期一）14:00—14:45
报告地点：苏州大学本部精正楼211
报告人：Florica Cirstea (The University of Sydney)
报告提要：In this talk, we will discuss recent contributions on isolated singularities for nonlinear elliptic equations such as
(0.1) div(A(|x|)|∇u|p−2∇u) = f (x,u,∇u) in B1(0)/{0},
where p > 1 and B1(0) denotes the open unit ball in R^N. Under various assumptions on A, p and f, we fully classify the behaviour of all positive solutions of (0.1), underlining the intricate interaction of the elliptic operator and the nonlinear part f (x,u∇u) of the equation. The talk will refer to joint work with collaborators such as T.-Y. Chang, J. Ching, F. Robert and J. Vétois.
报告5
报告题目：Uniform regularity results for critical and subcritical surface energies
报告时间：2018年7月2日（星期一）14:55—15:40
报告地点：苏州大学本部精正楼211
报告人：Yann Bernard (Monash University)
报告提要：We establish regularity results for critical points to energies of immersed surfaces depending on the first and the second fundamental form exclusively. These results hold for a large class of intrinsic elliptic Lagrangians which are subcritical or critical. They are derived using uniform ε-regularity estimates which do not degenerate as the Lagrangians approach the critical regime given by the Willmore integrand. This is joint-work with Tristan Rivière.
报告6
报告题目：Homogeneous metrics with prescribed Ricci curvature
报告时间：2018年7月2日（星期一）16:10—16:55
报告地点：苏州大学本部精正楼211
报告人：Artem Pulemotov (The University of Queensland)
报告提要：We will present a new existence theorem for metrics with prescribed Ricci curvature on a homogeneous space G/H. To illustrate the application of this theorem, we will consider several special cases. Specifically, our focus will be on examples in which G/H is a generalised Wallach spaces or a generalised flag manifold.
报告7
报告题目：A boundary value problem for Monge-Ampère equations
报告时间：2018年7月2日（星期一）17:05—17:50
报告地点：苏州大学本部精正楼211
报告人：Jiakun Liu (University of Wollongong)
报告提要：In this talk, we will present a recent result on the global C^{2,α} and W^{2,p} regularity for the Monge-Ampère equation subject to a natural boundary condition arising in optimal transportation. This is a joint work with Shibing Chen and Xu-Jia Wang.