最优输运和混合型偏微分方程是国际上两个极为重要的研究领域，在物理学、几何学和力学等领域有重要的应用。最优输运理论在计算机图形学、医学图像处理、深度学习等领域有广泛且重要的应用，其数学研究已取得重要进展；混合型偏微分方程源于跨音速流和等距嵌入等重要问题的研究，因强非线性、混合型、自由边界和退化性等本质困难，其数学理论研究一直是受到国际关注的前沿核心问题。最优输运和混合型偏微分方程的数学理论和方法不但各有侧重，而且也有交叉互融，加强这两个领域之间数学理论的深入交流有十分重要的意义。本项目旨在举办关于最优输运和混合型偏微分方程前沿问题高级研讨班，邀请国内外知名专家授课，组织国内优秀博士生、博士后以及青年研究人员参加研讨班学习、研讨。研讨班力求讲授相关领域的发展概况、最新研究进展和前沿问题，提供一个探讨新观点、新方法以及开展合作交流的平台，培养一支在该领域有创新、有潜力的年轻队伍。

The optimal transport and the partial differential equations of mixed type are two most important research fields in mathematics with extensive applications in the scientific areas such as physics, geometry, mechanics, and so on. In recent years, some important progress has been made on the theoretical analysis of optimal transport, with fruitful applications in computer graphics, medical image processing, deep learning and other scientific fields. The partial differential equations of mixed type stems from the study of important topics such as the transonic flow and equidistant embedding, and its theoretical analysis has been the key issue of the field because of the mathematical difficulties of strong nonlinearity, mixed type, free boundary, and strong degeneracy. The mathematical theories and methods of optimal transport and partial differential equations of mixed type have not only their own properties, but also have common character and cross-integration, and thus it is very important to strengthen the inter-exchange of mathematical theories in these two fields. The purpose of this project is to organize an advanced seminar on the frontier issues of optimal transport and partial differential equations of mixed type. We shall invite international well-known experts of the fields to teach minicourses on these issues in the seminars, and organize outstanding doctoral students, post-doctoral students, and young researchers to participate in the seminars. We seek to provide an overview of recent developments, important research topics and open problems in the two areas, and provide an advanced platform for young participants to explore new ideas, new approaches and collaborative exchanges in the fields.