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 is
conjectured
by ColliotTh′en`ene{Sansuc and Kato{Saito, it means roughly
that
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.

12：0014：00

Lunch
& break

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.

17：30

Dinner

