首届三亚国际数学论坛(Inauguration Conference of TSIMF)

2010-12-23 ~ 2010-12-26 1942

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The Tsinghua International Mathematics Forum at San Ya is established to host research conferences, workshops and retreats. It is located at the beautiful resort city of San Ya of Hainan Province in Southern China. It will serve as an international hub for mathematicians and mathematical scientists to dissimilate latest results and to develop newest ideas. It will be an asset for the mathematical community worldwide.

From December 23, 2010 to December 26, 2010, an inauguration conference will take place. At this conference, there will be a series of scientific presentations. The organizers will also unveil a vision for the Forum, and invite dicussion and comments from the mathematical community on its development.

Location: Horizon Spa and Resort(三亚天域度假酒店)

If you are interested in participating in this conference, and want to know more details, please send an inquiry to the Mathematical Sciences Center of Tsinghua University (msc@math.tsinghua.edu.cn) with the subject: TIMF.

Announcement

Dear Plenary Speakers and conference participants,

Here are some last minutes information about Sanya conference:

1. The conference hotel: "Horizon Resort &Spa"(Chinese name is 天域度假酒店) Address:
Yalong Bay, Sanya, Hainan Island, 572000, P.C.China
Tel: 898-856-7888 Fax: 898-8856-7999
Website: http://horizon.u9.1358.net/en/index.php
Email: welcome@rhorizon.cn

2. Airport pick-up upon arrival:

(a) For domestic arrivals: Once you get off the STEPS of the airplaine STAIR, immediately look for the Conference sign (or perhaps your name). There will be conference staff members there to take you to meet you and take you to the bus/car and send to the conference hotel;

(b) For international arrivals: please look for the Conference sign (or perhaps your name) after you through passport/custom control and at the international arrival exit door. There will be conference staff members there to take you to meet you and take you to the bus/car and send to the conference hotel;
If you have any questions, please call cell phone number: 13976715958(Ms Huang)or 18611740501 ( Ms Yan Zhang)

ATTENTION: If you HAVE NOT emailed us your arrival/departure flight information, PLEASE DO SO As SOON AS POSSIBLE

3. Conference Registration:
Lobby of Building II, "Horizon Spa and Resort", starting from 9:00am, Dec22

4. Program Schedule: please find the program schedule of the Sanya conference at Tentative Schedule(subject to further modification).

5. Bus going to Beijing airport on Dec. 22, for those ATTENDING ICCM ONLY:
Since most people are taking either flight CA1377 or CA1345, there will be two buses going to the Beijing airport at the following times:

(i) Bus I: you can get on this bus either in the Front of Tsinghua's Main Building at 11:20am (shortly after the second morning 1-hour talk), or at the Wenjin hotel at 11:40am. The Bus will leave for the airport at 11:45am. For flight CA1377 at 14:00, you are especially advise to get on this bus.

(ii) Bus II: you can get on this bus either in the Front of Tsinghua's Main Building BEFORE 12:30am (shortly after the last morning 1-hour talk), or at the Wenjin hotel at 12:40pm. The Bus will leave for the airport at 12:45pm. For flight CA1345 at 14:55pm, this is your last chance unless you want to take a taxi to the airport by yourself.

Thank you and see you in Sanya.

Organization Committee

hing-Tung Yau
丘成桐
Harvard University
Committee
Huai-dong CAO
曹怀东
Lehigh University
Shiu-Yuen Cheng
郑绍远
Hong Kong University of Science and Technology
Yat-Sun Poon
潘日新
University of California
Jie Xiao
肖杰
Tsinghua University

Confirmed Plenary Speakers

Robbert Dijkgraaf University of Amsterdam
Bjorn Engquist University of Texas At Austin
Jean-Marc Fontaine Paris-Sud 11
Benedict Gross Harvard University
David Jonathan Gross University of California, Santa Barbara
Richard Hamilton Columbia University
Vaughan F. R. Jones University of California, Berkeley
Jun Li Stanford University
Ker-Chau Li Institute of Statistical Science Academia Sinica
Chang-Shou Lin National Chung Cheng University
Jun Liu Harvard University
Ib Madsen University of Copenhagen
Hirosi Ooguri California Institute of Technology
Wilfried Schmid Harvard University
John Tate University of Texas
Si-Jue Wu University of Michigan
Zhou-Ping Xin The Chinese University of Hong Kong


Titles And Abstracts

The Quantum Geometry of Matrix Models
Robbert Dijkgraaf

Gauge theories and string theories give rise to interesting geometrical structures that are in many ways quantum versions of classical geometries. Random matrix models form instructive examples of such structures, that relate among other things two-dimensional conformal field theories, instanton invariants of four-manifolds, and knot invariants


Multiscale methods for wave propagation
Bjorn Engquist

We will give a brief overview of multiscale modeling for wave equation problems and then focus on two techniques. One is the heterogeneous multiscale method applied to problems with oscillatory velocity fields. 
  


Factorisation of analytic functions in mixed characteristic
Jean-Marc Fontaine

I intent to describe an analog, in mixed characteristic, of the classical factorizations theorems for one variable analytic functions over an algebraically closed field complete with respect to an absolute value (joint work with Laurent Fargues).



Stable orbits in group representations and the arithmetic of elliptic curves
Benedict Gross

Manjul Bhargava has recently made a great advance in the arithmetic of elliptic curves, giving the first bounds on the average rank of the group of rational points. He shows that the average order of the 2-Selmer group is equal to 3, by studying the stable orbits of the group GL(2,Z) on the lattice of binary quartic forms. I will begin by reviewing some basic material on elliptic curves and on the classical theory of binary quadratic and cubic forms. I will then define the 2-Selmer group, and describe the stable orbits in this representation, whose invariants were determined by Hermite. If time permits, I will discuss a possible generalization to hyperelliptic curves with a rational Weierstrass point.


PHYSICS AND MATHEMATICS AT THE FRONTIER
David Gross

The relation between physics and mathematics is explored. The beauty and effectiveness of the mathematical structures that appear in fundamental physics are discussed.
  


Canonical Neighborhoods for the Ricci Flow
Richard Hamilton

Perelman proves the remarkable result that solutions to the Ricci flow on a compact 3 dimensional manifold for finite time look like ancient solutions with positive curvature. We shall discuss how to prove such a result, and ask how it might generalize to other problems. 

  


The onset of wildness.
Vaughan Jones

The free product of two groups of order two is very simple to understand whereas the



A new class of virtual cycles & applications to GW and DT invariants
Jun Li

A new class of virtual cycles using cosection localization has been constructed. This construction makes integrating virtual fundamental classes over some non-compact moduli spaces possible. Applications of this construction to GW-invariants and DT-invariants of Calabi-Yau threefolds will be discussed.


A theory of extreme p-values: how many best results are real ?
Ker-Chau Li

P-value quantifies the strength of statistical evidence against a null/uninteresting/default hypothesis- the smaller, the stronger. In data-abundant areas including high throughput genomic data analysis, researchers often encounter numerous hypothesis testing problems at a time and need to compute an array of p-values for multiple decision making. However, many fundamental questions concerning extreme p-values such as “what is the probability for the smallest p-value to come from a problem of which the null hypothesis holds?” or “among the 10 problems with most significant p-values, how many false positives are expected?” remain unanswered. In this talk, we will formulate theses problems using a semiparametric approach and present a theory of unbiased estimation.
  


Liouville System of Mean Field Equation
Chang-Shou Lin

The Liouville equation for a single equation has played an important role in many physic model of classical gauge field theory. In this lecture, I will talk about my recent joint work with Lei Zhang on a Liouville system. This system is a Euler-Lagrangian equation of certain nonlinear functional and has appeared in many physic models, e.g., magnetic self-focus systems by W.H. Bennet, also see the works by Kiessling and Lebowitz. In this lecture, we will prove the a priori bound under certain conditions. We also derive the topological degree counting formulas for this system.

Panel Discussions

Jean Pierre Bourguignon IHES
Meng-Kiat Chuah National Tsing Hua University
Tony Chan Hong Kong University of Science and Technology
Fa-Lai Chen University of Science and Technology of China
Gert-Martin Greuel Mathematical Research Institute Oberwolfach
Ari Laptev Imperial College
Ka-Sing Lau The Chinese University of Hong Kong
Wen-Ching Winnie LI National Center for Theoretical Sciences 
and Penn. State University
Yong Lin Renmin University of China
Yu-Feng Lu Dalian University of Technology
Tzon-Tzer Lu National Sun Yat-Sen University
Toshio Oshima The University of Tokyo
An-Jing Qu Northwestern University
Ramadas Ramakrishnan ICTP
Mina Teicher Bar-Ilan University
Ngo Viet Trung VAST
Yue-Fei Wang Chinese Academy of Sciences
Quan-Shui Wu FUDAN University
Guo-Xiao Yang Beijing Institute of Technology
Xi-Ping Zhu Sun Yat-Sen University

Tentative Schedule

Day One: December 23, 2010

Morning
9:00-10:30 Opening Ceremony
10:30-11:00 Tea Break

Chair: S.-T. Yau
11:00-12:00 David Gross: Physics and the Mathematics at the Frontier

Afternoon
Chair: S.-T. Yau
2:00-2:45: John Tate: Elliptic Curves in the 20th Century 
2:45-3:30: Benedict Gross: Stable Orbits in Group Representations and the Arithmetic of Elliptic Curves

3:30-4:00: Tea Break

4:00-4:45: Robbrt Dijgraaf: The Quantum Geometry of Matrix Models
4:45-5:30: Vaughan Jones: The onset of wildness

Dinner: 6:00-

Evening
8:00-10:00 Panel Discussions

Day Two: December 24, 2010

Morning
Chair: S.-Y. Cheng
9:00-9:45 Bjorn Engquist: Multiscale Methods for Wave Propagation
9:45-10:30 Zhou-Ping Xin: On Multi-Dimensional Compressible Navier-Stokes Systems

10:30-10:45 Tea Break

10:45-11:30 Hirosi Ooguri: Topological String Theory
11:30-12:15 Chang-Shou Lin: Liouville System of Mean Field Equation

12:15-2:00: Lunch Break

Afternoon
Chair: H.-D. Cao
2:00-2:45 Jean-Marc Fontaine: Factorisation of Analytic Functions in Mixed Characteristic
2:45-3:30 Ib Madsen: Moduli Spaces and Topology

3:30-4:00 Tea Break
4:00-4:45 Ker-Chau Li: A Theory of Extreme p-values: How Many Best Results Are Real ?
4:45-5:30 Jun Liu: Beyond the Naive Bayes Classifier

Evening
6:00-7:00 Reception
7:00pm- Dinner & Party

Day Three: December 25, 2010

Conference Excursion

Day Four: December 26, 2010

Morning
Chair: S.-Y. Cheng
8:30-9:15 Wilfried Schmid: Hodge Theory and Unitary Representations of Reductive Lie groups
9:15-10:00 Jun Li: A New Class of Virtual Cycles & Applications to GW and DT Invariants

10:00-10:15 Tea Break

Chair: S.-T Yau
10:15-11:00 Richard Hamilton: Canonical Neighborhoods for the Ricci Flow
11:00-11:45 Sijue Wu: Well-posedness of the Two and Three Dimensional Full Water Wave Problem