这是一个小型的研讨会。我们邀请国内外对几何偏微分方程，尤其是与调和映射的分析相关的同行一同交流。
特邀报告人：（拼音序）
其它参会人员：（拼音序）
5月12日：
| 时间 | 报告人 |
| 9:00-9:50 | 何维勇（线上） |
| 10:00-10:50 | 邱红兵 |
| 11:10-12:00 | 郭常予 |
| 14:00-14:50 | 刘磊 |
| 15:00-15:50 | 朱超娜（线上） |
| 16:10-17:00 | 朱安强 |
| 17:10-17:40 | 王子君 |
5月13日：
| 时间 | 报告人 |
| 9:00-9:50 | 王长友（线上） |
| 10:00-10:50 | 罗勇 |
| 11:10-12:00 | 林龙智（线上） |
| 14:00-14:50 | 陈优民 |
| 15:00-15:50 | 艾万君（线上） |
| 16:10-17:00 | 吴瑞军 |
| 17:10-17:40 | 汪琳 |
摘要：
The 2-dimensional discrete Minkowski problem seeks to determine the necessary and sufficient conditions for the existence of a polygon in \(R^2\) with \(n\) facets, whose outer unit normals are \(u_1,u_2,\ldots,u_n\in S^1\) and such that the facet whose outer unit normal is \(u_i\) has length \(a_i\), where \(a_1,a_2,\ldots,a_n>0\). Minkowski solved this problem in 1897 using a variational argument. In this talk, we will present a geometric constructive proof based on special reflections, which offers new insights into the problem and proposes the study of a new type of flow on 2-dimensional polygons.摘要：
In this talk, I will introduce bubbling analysis for (approximate) biharmonic maps on general Riemannian 4-manifolds. It is based on works joint with Prof. Miaomiao Zhu.摘要：
在此次报告中，我们将回顾调和映照的正则性理论及其高阶推广。特别地，我们将讨论Riviere理论和Naber-Valtorta理论，以及其对应的推广。本次报告基于与向长林教授、郑高峰教授等的近期合作。摘要：
We discuss the regularity of existence of harmonic and biharmonic almost complex structures. In particular, we prove that given a pair of homotopy classes which have the same first Chern class, there exists an energy-minimizing biharmonic almost complex structures on any compact Hermitian four manifold.摘要：
In this talk we will survey some recent results on the energy convexity for weakly harmonic and biharmonic maps and their applications. We will then introduce a conformally invariant analogue of the intrinsic biharmonic map that we call conformal-harmonic map, which is a critical point of a conformally invariant energy functional on four dimensional manifolds and satisfies a system of conformally invariant fourth order Paneitz-type PDEs. A version of energy convexity and uniqueness of conformal-harmonic maps that we showed in a recent joint work with J. Zhu will be discussed.摘要：
In this talk, we will review compactness results related to harmonic maps and Sacks-Uhlenbeck harmonic maps in dimension two. We first recall the interior case, i.e. blow up at an interior point, then talk about the free boundary case. Also, we will discuss some properties for degenerating cases. Roughly speaking, we will establish some (generalized) energy identities in these progress. This is a joint work with Prof. Juergen Jost and Miaomiao Zhu.摘要：
We talk about pinching phenomena of Legendrian submanifolds in the unit sphere. In particular, utilizing the maximum principle, we obtain a new characterization of the Calabi torus in the unit sphere which is the minimal Calabi product Legendrian immersion of a point and the totally geodesic Legendrian sphere. This is based on joint works with Prof. Linlin Sun and Prof. Jiabin Yin.摘要：
In this talk, we shall discuss rigidity results of translating solitons of the mean curvature flow. Translating solitons can be regarded as minimal submanifolds if we make a conformal change of the metric of the ambient space. This important observation is due to Ilmanen. One special class of translating solitons with higher codimension is the symplectic translating solitons, which are solutions to symplectic MCFs, we obtain a rigidity result of symplectic translating solitons via the complex phase map, which indicates that if the cosine of the Kähler angle has a positive lower bound, then any complete symplectic translating soliton with nonpositive normal curvature has to be an affine plane. In general, we study the translating solitons via the Gauss map, and we prove a Bernstein type theorem for complete translating solitons, whose images of their Gauss maps are contained in an appropriate neighborhood of the Grassmannian manifold.摘要：
For a smooth open Riemannian manifold with nonnegative Ricci curvature, we show that the space of biharmonic functions with both polynomial growth and Dirichlet energy growth of fixed rates is finite dimensional.摘要：
In this talk, I will describe a rigidity inequality of approximated harmonic maps, under the zero Neumann boundary condition, in dimension two, which aims to bound the \(L^2\)-norm of full Hessian of a map by that of tension field of the map. The main motivation for the (conditional) validity for such an inequality is to study the local or global exact controllability of the simplified Erickson-Leslie system modeling the hydrodynamic of motions of nematic liquid crystal materials, under the zero Neumann boundary condition for the director map \(d\) and the Navier-slip boundary condition for the fluid velocity field \(u\), over a two dimensional bounded, smooth region.摘要：
In this talk, we present a new proof of the regularity at the free boundary for weakly H-surfaces in Riemannian manifolds under a classical compatibility condition and derive an elliptic estimate up to the free boundary. This work is joint with Professor Miaomiao Zhu.摘要：
We study supersymmetric extensions of the harmonic map model, which are widely used in 2D susy quantum field theory. The regularity and the compactness properties of the weak solutions, together with relations to other models, will be talked about. This is a joint work with Kessler, Jost, Tolksdorf and M.Zhu.摘要：
In this report, we will give a breif introduction to the extension problem in Ricci flow. Later, we will present our work on the extension of the geometric flows.摘要：
Let \((\phi_k, \psi_k)\) be a sequence of stationary Dirac-harmonic maps from a Riemannian manifold \(M\) of dimension \(m\geq 3\) to a compact Riemannian manifold \(N\) with uniformly bounded energy. Assume that \(\|\psi_k\|_{W^{1,p}(M)}\) is uniformly bounded for some \(p>\frac{2m}{3}\), we derive a blow-up formula for such a sequence, which tells us that the weak limit is stationary if and only if the energy concentration set is a minimal submanifold.