报告题目与摘要

无限维压缩感知理论与频谱分析新技术

杨在  西安交通大学

摘要：压缩感知成功实现了高维信号在低维空间中的采样与恢复，是本世纪信息处理领域重大突破性技术之一，已推动多个学科领域的发展与变革。但传统压缩感知理论面临一项基本难题：它仅能处理有限维信号恢复，而无限维信号常常反映了问题的本质。报告具体围绕频谱分析这一信号与信息处理领域中的基本问题展开，揭示无限维压缩感知研究的必要性，并着重介绍报告人近年来在无限维压缩感知、频谱分析、阵列信号处理等课题上的原创性研究成果。

Interpolatory Curve Modeling with Feature Points Control

曹娟    厦门大学

Abstract: In curve modeling, interpolation allows users to directly control the location of curve features. While previous literatures have focused on generating interpolatory curves with properties of smoothness locality, they usually have difficulty in controlling over geometric feature points (e.g., cusps, loops, inflection points) that mark salient intrinsic features of curve shapes. In this paper, we propose an intuitive efficient method for constructing cubic curves that are curvature continuous almost-everywhere interpolate a sequence of input data points. Our method provides a good control over the location type of the geometric feature points. In particular, cusps loops only occur at specified input data points, while inflection points only occur at specified input data points joints. We refer to such feature points controlled interpolatory curves as FPC-Curves for short. To construct FPC-Curves, we focus on piecewise cubic curves, where the occurrence of loops, cusps inflection points is mutually exclusive. We also provide a simple yet efficient algorithm for real-time interactive design of cubic FPC-Curves. Various experimental results show the efficacy flexibility of our new approach for curve modeling.

基于离散微分几何和深度学习的三维人脸分析

李慧斌  西安交通大学

摘要：近年来，随着三维人脸传感技术的不断进步，三维人脸识别、三维人脸表情识别、三维人脸形状建模等技术受到了学术界和工业界的广泛关注。本报告将着重介绍离散微分几何方法在三维人脸识别和三维人脸面部表情识别方面的一些应用，内容涉及曲面微分几何、离散调和映照、计算共形几何、最优传输理论、离散法丛理论等离散微分几何方法。着力解决三维人脸关键点定位、三维人脸曲面参数化、三维人脸曲面表征、个性化表情识别等关键问题。

Simple Supermodules for Lie Superalgebras

陈志玮    厦门大学

Abstract: The problem of classification of all simple modules for Lie algebra is rather difficult. Some kind of solution exists only for the Lie algebra sl (2) due to Block’s classification theorem. A Lie superalgebra is a generalization of a Lie algebra to include a compatible Z₂-grading. We explain the connection between simple supermodules over g simple modules over the underlying Lie algebra go.

双曲面分页方法：现状和潜力

马跃  西安交通大学

摘要：在本次报告中我们将回顾双曲面分页方法（Hyperboloidal foliation method）自提出以来所取得的部分结果。随后我们将介绍该方法的一些最新应用。最后我们将简要介绍该方法的最新拓展：欧几里得-双曲分页方法（Euclidean-hyperboloidal foliation method），并对其在Einstein-正质量标量场系统的应用做简要介绍。

Symmetrization with Respect to Mixed Volumes

夏超    厦门大学

Abstract: It is well known that the Schwarz symmetrization of a function diminishes the Dirichlet integral. This is the so-called Polya-Szego Principle. similar symmetrization with respect to quermassintegral, which has been introduced by Talenti Tso, diminishes the Hessian type integral. In this talk I will introduce my recent joint work with Della Pietra Gavitone, on new symmetrization with respect to mixed volume or anisotropic curvature integral.

Fixed Subgroups in Low-dimensional Manifold Groups

张强  西安交通大学

Abstract: For a group $G$, a set of endomorphisms $\B\subset \edo(G)$, the fixed subgroup $\fix\B$ consists of elements fixed by every endomorphism $\phi\in \B$, which has many interesting properties on the intersection of subgroups. In this talk, we will introduce some progresses on the fixed subgroups of some special groups, such as free groups, surface groups, 3-manifold groups, the direct products of finitely many free surface groups.