2017年青年数学论坛

教师介绍
本讲教师： 课程介绍
2017年青年数学论坛
会议时间：2017年4月16日
会议地点：数学科学学院1518多媒体教室
8：308：40 开幕式
8：409：40
报告题目： Harmonic mappings for bounded distortion shape deformation and interpolation
报告人： 陈仁杰 德国马克斯普朗克计算机研究所
报告摘要： Harmonic mappings are extensively used in geometry processing applications to produce visually appealing deformations. We establish the sufficient and necessary conditions for a harmonic planar mapping to have bounded distortion. Our key observation is that these conditions relate solely to the boundary behavior of the mapping. This leads to an efficient and accurate algorithm that supports handlebased interactive shapeandimage deformation and is demonstrated to outperform other stateoftheart methods. The particular structure of harmonic mappings further allows efficient shape interpolation. Given the closedform expressions for the interpolants, our interpolation algorithm runs embarrassingly in parallel and is orders of magnitude faster than stateoftheart methods due to its simplicity, yet it produces mappings that are superior to those existing techniques due to guaranteed bounds on geometric distortions.
9：5010：50
报告题目： Weak approximation for 0cycles on products of varieties
报告人： 梁永祺 巴黎七大
报告摘要： We consider the sequence
for smooth projective varieties over number fields. Its exactness isconjectured by ColliotTh′en`ene{Sansuc and Kato{Saito, it means roughlythat the Brauer{Manin obstruction is the only obstruction to weak approximation for 0cycles.
We work on the compatibility of the exactness for products of varieties. Assume that (E) is exact for a rationally connected variety X (after all finite extensions of the base field). One may ask the question :For which family of varieties Y the sequence (E) is exact for X × Y ? When Y is a smooth projective curve with the finiteness of the Tate{Shafarevich group of its jacobian assumed, Harpaz and Wittenberg give a positive answer to the question (for much more general fibrations rather than only for products). We will talk about the case where Y is a smooth compactification of a homogeneous space.
11：0012：00
报告题目： The monodromy theorem for compact Kähler manifolds and smooth quasiprojective varieties
报告人： 刘永强 KU Leuven
报告摘要： Given any connected topological space X, assume that there exists an epimorphism from the fundamental group of X to the free ableian group Z. The deck transformation group Z acts on the associated infinite cyclic cover of X, hence on the homology group of the covering space with complex coefficients. This action induces a linear automorphism on the torsion part of the homology group as a module over the complex Laurent polynomial ring, which is a finite dimensional complex vector space. We study the sizes of the Jordan blocks of this linear automorphism. When X is a compact K"ahler manifold, we show that all the Jordan blocks are of size one. When X is a smooth complex quasiprojective variety, we give an upper bound on the sizes of the Jordan blocks, which is an analogue of the Monodromy Theorem for the local Milnor fibration. This is a joint work with Nero Budur and Botong Wang.
14:0015:00
报告题目： Boundary $C^{1,alpha}$ regularity of Potential functions in Optimal transportation
报告人： 陈世炳 澳洲国立大学
报告摘要： We provide a different proof for the global $C^{1,alpha}$ regularity of potential functions in optimal transport problem, which was originally proved by Caffarelli. Moreover, our method applies to a more general class of domains. This is based on a joint work with Elina Andriyanova.
15：1016：10
报告题目： Scaling Limits of Critical Inhomogeneous Random Graphs
报告人： Minmin Wang Institut HenriPoincaré and University of Bath
报告摘要： Branching processes are known to be useful tools in the study of random graphs, in particular in understanding the appearance of a phase transition in the sizes of the largest clusters of the graphs. Recently, growing interests are paid to inhomogeneous random graphs. In this talk, we look at one particular model of such graphs, called the Poisson random graph, where edges are formed with probabilities proportional to some prescribes weights on the vertices. One challenge in the study of inhomogeneous random graphs is to describe the geometry of the graphs around the critical point. In the case of Poisson random graph, we obtain a simple representation of the graph using GaltonWatson trees (genealogy trees of branching processes). Relying on this representation and previous works of Duquesne & Le Gall on the convergence of GaltonWatson trees, we prove that in the critical window, the scaling limits of the largest components of the Poisson random graphs are a collection of almosttreelike compact metric spaces, which can be constructed explicitly from the socalled Levy processes without replacement.Based on a joint work with Nicolas Broutin and Thomas Duquesne.
16：2017：20
报告题目： Computing with functions
报告人： Kuan Xu, University of Kent
报告摘要： In very recent years, the idea of computing with functions has been sparkled by the endeavor of the Chebfun project. Polynomial approximations of functions enables functional operations and operators of all kinds to be numerically approximated using fast, accurate, and robust algorithms based on these approximations, giving people the feel of symbolic computing but with the lightning speed of numerical computation. The idea of computing with functions has also extended to the solution of differential and integral equations. In this talk, the core idea of computing with functions and the underlying mathematics of Chebfun project will be discussed with the aid of handsonkeyboard demos.
4月16日 周日全天 会后讨论
主办单位：数学科学学院
中国科学技术大学

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