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标题: 王虹证明百年数学难题,预定了2026年菲尔兹奖? [打印本页]

作者: 酒哥    时间: 4 天前
标题: 王虹证明百年数学难题,预定了2026年菲尔兹奖?
本帖最后由 酒哥 于 2025-10-8 05:09 编辑

原创  科技大满贯  2025 年 10 月 03 日

今年大火的王虹又带来好消息了。就在昨晚,数学四大顶刊之一的《Journal of the American Mathematical Society》(JAMS ,美国数学会杂志)官网的“Articles in press(已接收待发表文章)”栏目再次更新。一篇算是等了很久的文章出现在了更新列表里,那就是今年 2 月合作宣称解决了三维挂谷猜想的王虹与 Joshua Zahl ,合作的另一篇重要文章,文章题目为“Sticky Kakeya sets and the sticky Kakeya conjecture”(粘性挂谷集与粘性挂谷猜想)。

该文预印版摘要主要讲述了:Kakeya 集是实数集 R^n 中的一个紧致子集,其包含指向所有方向的单位线段。挂谷猜想(Kakeya Conjecture)指出:此类集合的豪斯多夫维数(Hausdorff dimension)与闵可夫斯基维数(Minkowski dimension)均必为 n(空间维度)。存在一类特殊的 Kakeya 集,称为粘性 Kakeya 集(sticky Kakeya sets),其表现出近似多尺度自相似性。此类集合在 Katz、Laba 与陶哲轩于 1999 年发表的关于挂谷问题的突破性研究中发挥了关键作用。该研究提出挂谷猜想的一个特例:粘性 Kakeya 集的豪斯多夫维数与闵可夫斯基维数必为 n 。研究针对三维空间(R^3)证明了这一猜想。

相信关注王虹或关注三维挂谷问题的对这篇文章并不陌生,因为该研究早在 2022 年 10 月便上传在了预印版平台 arxiv 上了,该文挂出之后便引起了不少的关注,之前著名的《Quanta Magazine》(量子杂志)也对该研究进行过专门报道。这篇研究也被誉为王虹与 Joshua Zahl 合作证明三维挂谷猜想的“三部曲”文章的开篇之作,该研究证明了挂谷猜想没有粘性反例,扫除了横在该问题上数十年的一大障碍,强烈支持了三维挂谷猜想是真的。虽然这是该系列研究三部曲中最先做出的成果,但如今时隔 3 年文章才正式被接受(期间网络上甚至还有人质疑这篇文章);这已晚于了“三部曲”文章中的第二篇,因为“三部曲”中的第 2 篇文章(R^3 中 Kakeya 集的 Assouad 维数)已于今年 4 月底在另一本数学四大《Inventiones mathematicae》上正式在线发表;该文是 2024 年 1 月上传在 arxiv 上的,1 年 3 个月后便正式发表,进度还是明显快于本篇文章的,详见:《有望获菲尔兹的王虹与Zahl合作证明三维挂谷猜想重要进展文章正式在数学顶刊发表》。

随着王虹与 Joshua Zahl 合作证明三维挂谷猜想的“三部曲”文章中的第一篇和第二篇相继被两本数学四大期刊在线发表或正式接受,这也进一步增加了证明三维挂谷猜想的最终篇是正确的可能性(虽然已有不少“大佬”背书),应该说该文比较“稳了”,也期待最终篇能早日通过同行审议。本文两位作者目前均已受邀将在 2026 年的国际数学家大会上作 45 分钟报告,而且目前来说两位都跟我们有着密切的关系,我们再来简单回顾下两位作者。

Joshua Zahl ,他 2008 年本科毕业于美国加州理工学院,后于 2010 年和 2013 年在加州大学洛杉矶分校(UCLA)先后取得硕士和博士学位,师从著名华人数学家陶哲轩(Terence Tao)。博士毕业后他在麻省理工学院(MIT)进行博士后研究,2016 年他加入加拿大不列颠哥伦比亚大学数学系先后任助理教授和副教授。今年 6 月,Joshua Zahl 正式来到了中国,加入了南开大学陈省身数学研究所,任讲席教授,详见:《与王虹合作共同解决三维挂谷猜想的 Joshua Zahl 正式加盟南开大学任讲席教授》。Joshua Zahl 的主要研究方向为经典调和分析与组合数学等,一直以来他主要对交点几何学、限制问题和 Kakeya 问题进行研究。

王虹,1991 年生,年仅 16 岁便考入北京大学,她是大二转入北大数院的。2011 年从北京大学本科毕业后,王虹前往法国深造,并获得了巴黎综合理工学院的工程师学位和巴黎第十一大学的硕士学位;她博士则毕业于美国麻省理工学院(2019 年),师从 Larry Guth 。博士毕业后她在普林斯顿高等研究院进行博士后研究,2021 年她加入加州大学洛杉矶分校任助理教授,2023 年又加入了纽约大学库朗数学研究所。今年 9 月,王虹开始任法国高等科学研究所(IHES 的首位华人终身教授)和库朗数学研究所的双聘教授,王虹的主要研究方向为几何测度论和调和分析等,她曾获科学突破奖的玛丽安·米尔扎哈尼新前沿奖(Mirzakhani New Frontiers Prize)、ICCM 最佳论文奖和前沿科学奖(Frontier of Science Award)等荣誉。

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读者评论:

帖子在混淆视听,这篇论文和宣称证明了挂谷猜想的根本不是同一篇论文
这篇论文只是研究挂谷猜想的一个特性,和证明三维挂谷猜想没有关系


之前好像有个江苏的评论说这个挂谷证明有bug,不知真假
知乎有评价证明避开了某个关键的问题

预定不是因为挂谷猜想有多牛逼,而是因为东道主优势啊

是的,类似挂谷猜想这样的“猜想”在数学界有5千多个

她的本科教育不影响她去法国的时候要放弃数学,而且她在法国和美国的时间10年不止,你非要说本土培养,那本土那群数学系的大牛咋回事

丘成桐的徒子徒孙当初想蹭佩雷尔曼,现在又想来蹭王了吗?


除了制度外所有科学技术都抄袭还有自信心?




沁园春   神州英豪


柳工填于2025年

科学之巅,世界综观,宇宙索描。看欧洲科匠,风云叠起;美洲后秀,独誉雄枭。叹我中华,百年变局,帷幄亁坤筹远招。光阴迫,励怀精忠志,华睿争超。
微分拓扑同调,代数几何、群论范韬。嵌当今物理,当今化学,当今生物,当代科潮!符算平移,李群交换,拉密量恒惟铁条。神州唤,拓善科基础,驾驭狂飙!
註释:1、范韬一即高级范畴论。2、符算一即线性算符。3、拉密一即拉格朗日函数、密度;另即哈密顿函数、密度。4、狂飙 这里的狂飙是指当代科学代表式:θ=0E。运用这式就可以把词中所列数学基础理论应用到各个前沿科学领域。

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王虹与Joshua Zahl在世界数学中心普林斯顿数学系(和高等研究院IAS数学部)的报告


https://www.math.princeton.edu/events

October 22 Joshua Zahl
October 27 王虹

文章在线:
https://www.ams.org/cgi-bin/mstrack/accepted_papers/jams?active=press

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Journal of the American Mathematical Society
Aims and Scope

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.




作者: 酒哥    时间: 4 天前
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[ytb]BqBAi-fM6-k[/ytb]



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[ytb]c5F6X7lqqMg[/ytb]

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[ytb]ePdtSTTP45o[/ytb]




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[ytb]AtAfO_ff-G4[/ytb]

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[ytb]i0UTeQfnzfM[/ytb]





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世界数学中心普林斯顿比武擂台:Oct9- Dec18, 2025

Seminars

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09

Algebraic Topology Seminar
Ishan Levy IAS & University of Copenhagen

Trace methods beyond connective rings
1:00 PM






Oct
09

Analysis of Fluids and Related Topics
Vlad Vicol, New York University

On stable implosions
3:00 PM
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Oct
09

Discrete Mathematics Seminar
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Proper subgroup testing and non commutative error correcting codes
3:00 PM
Fine Hall 224







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09

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Jit Wu Yap, MIT

On Uniform Boundedness of Torsion Points for Abelian Varieties over Function Fields
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IAS - Simonyi Hall 101







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09

Topology Seminar
Joshua Wang, Princeton & IAS

Bott-Samelson varieties and minimal complexes
4:30 PM
Fine Hall 314







Oct
10

Joint PU/Rutgers Geometric PDEs Seminar
Fanghua Lin, Courant Institute of Math

Harmonic Map Heat Flow Into Cat(0) Space
2:30 PM
Fine Hall 214







Oct
10

Joint PU/Rutgers Geometric PDEs Seminar
Luc Nguyen, Oxford

The fully nonlinear Loewner-Nirenberg problem on manifolds: Existence and Liouville theorems
4:00 PM
Fine Hall 214







Oct
13

Joint PU/IAS Arithmetic Geometry Seminar
Dmitry Arinkin, Wisconsin

The classical limit of the geometric Langlands correspondence.
3:30 PM
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14

Joint PU/IAS Symplectic Geometry Seminar
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TBA
1:00 PM
Fine Hall 401







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16

International Polyhedral Products Seminar
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On the integral cohomology of real toric manifolds
10:30 AM






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16

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Unstable synthetic deformations
1:00 PM






Oct
20

Joint PU/IAS Analysis Seminar
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3:00 PM
Fine Hall 314







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20

Joint PU/IAS Arithmetic Geometry Seminar
Helene Esnault, Copenhagen & Harvard

TBA
3:30 PM
IAS - Simonyi Hall 101







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20

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The Khovanov stable homotopy type
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20

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A new approach to strong convergence (for non-experts)
4:30 PM
Fine Hall 214







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20

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Regularity of capillary minimizing hypersurfaces
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21

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Free Curves in Singular Varieties
3:00 PM
Fine Hall 314







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21

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3:00 PM
Fine Hall 224







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21

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Wenyuan Li, USC

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3:00 PM
IAS - Simonyi Hall 101







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21

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4:30 PM
IAS - Simonyi Hall 101







Oct
22

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Yu Yuan, University of Washington

TBA
3:00 PM
Fine Hall 314







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22

Minerva Lectures
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The Besicovitch compression phenomenon and the Kakeya set conjecture
4:30 PM
McDonnell Hall A01







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23

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Tom Bachmann, Universität Mainz

Motivic Wilson Spaces
1:00 PM






Oct
23

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3:00 PM
Fine Hall 314







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23

Discrete Mathematics Seminar
Krzysztof Choromanski, Columbia

TBA
3:00 PM
Fine Hall 224







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23

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Ben Church, Stanford

TBA
3:30 PM
IAS - Simonyi Hall 101







Oct
23

Topology Seminar
Gary Guth, Stanford

TBA
4:30 PM
Fine Hall 314







Oct
24

Minerva Lectures
Joshua Zahl, Chern Institute of Mathematics, and Nankai University

Sticky Kakeya sets
4:30 PM
Lewis Library 120







Oct
27

Analysis Seminar
Kenji Nakanishi, Kyoto University

TBA
3:00 PM
Fine Hall 314







Oct
27

Joint PU/IAS Arithmetic Geometry Seminar
Jacob Tsimerman, Toronto & IAS

TBA
3:30 PM
Fine Hall 224







Oct
27

PACM Colloquium
Steven Zucker, Yale

TBA
4:30 PM
Fine Hall 214







Oct
27

Minerva Lectures
Hong Wang, NYU Courant Institute of Mathematical Sciences and IHES

Kakeya sets in R^3
4:30 PM
McDonnell Hall A01







Oct
28

Joint PU/IAS Symplectic Geometry Seminar
Kenny Blakey, MIT

TBA
1:00 PM
Fine Hall 401







Oct
28

Algebraic Geometry Seminar
Linquan Ma, Purdue

TBA
3:00 PM
Fine Hall 314







Oct
28

Probability Seminar
Christophe Garban, Lyon

TBA
3:00 PM
Fine Hall 224







Oct
28

Joint PU/IAS Groups and Dynamics Seminar
Megan Roda, IAS

TBA
4:30 PM
Fine Hall 314







Oct
28

Mathematical Physics Seminar
Matan Harel, Northeastern

Planar percolation and the loop O(n) model
4:30 PM
Jadwin Hall A06







Oct
29

Differential Geometry & Geometric Analysis Seminar
Micah Warren, University of Oregon

TBA
3:00 PM
Fine Hall 314







Oct
29

Minerva Lectures
Hong Wang, NYU Courant Institute of Mathematical Sciences and IHES

Restriction theory and projection theorems
4:30 PM
McDonnell Hall A01







Oct
30

International Polyhedral Products Seminar
Ivan Limoncenko, Mathematical Institute of the Serbian Academy of Sciences and Arts

TBA
10:30 AM






Oct
30

Algebraic Topology Seminar
Michael Davis, Ohio State University

Exotic closed aspherical 4-manifolds
1:00 PM






Oct
30

Analysis of Fluids and Related Topics
Tarek Elgindi, Duke University

Joint Princeton-Rutgers Seminar on Analysis of Fluids
3:00 PM
Fine Hall 314







Oct
30

Joint PU/IAS Number Theory
Qiao He, Columbia

TBA
3:30 PM
Fine Hall 110







Oct
30

Topology Seminar
Elise LePage, Columbia University

TBA
4:30 PM
Fine Hall 314







Nov
03

Analysis Seminar
Ben Pineau, New York University

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3:00 PM
Fine Hall 314







Nov
03

Joint PU/IAS Arithmetic Geometry Seminar
Ferdinand Wagner, Bonn

TBA
3:30 PM
IAS - Simonyi Hall 101







Nov
03

Minerva mini-course
Robert Lipshitz, Minerva Distinguished Visitor & University of Oregon

Steenrod squares…
4:30 PM
Fine Hall 314







Nov
03

PACM Colloquium
Anna Seigal, Harvard

TBA
4:30 PM
Fine Hall 214







Nov
04

Algebraic Geometry Seminar
Zhiyuan Chen, Princeton

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3:00 PM
Fine Hall 314







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04

Probability Seminar
Jacopo Borga, MIT

TBA
3:00 PM
Fine Hall 224







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04

Joint PU/IAS Groups and Dynamics Seminar
Special Lecture
Shamgar Gurevich, University of Wisconsin - Madison

A look at representations of SL(2,q) through the lens of size: rank, eta correspondence, applications
3:15 PM
IAS- Simonyi Classroom S 114







Nov
04

Joint PU/IAS Groups and Dynamics Seminar
Special Lecture
Roger Howe , Yale University

A further look at the oscillator semigroup and the eta correspondence for dual pairs over finite fields
4:15 PM
IAS - Simonyi Hall 101







Nov
04

Joint PU/IAS Groups and Dynamics Seminar
Special Lecture
Sophie Kriz, Princeton

Howe duality over finite fields
5:00 PM
IAS - Simonyi Hall 101







Nov
05

Differential Geometry & Geometric Analysis Seminar
Hao Fang, University of Iowa

TBA
3:00 PM
Fine Hall 314







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06

International Polyhedral Products Seminar
Li Yu, Nanjing University

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10:30 AM






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06

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Dmitrii Zakharov, MIT

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3:00 PM
Fine Hall 224







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06

Joint PU/IAS Number Theory
Yingkun Li, Wisconsin

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3:30 PM
IAS - Simonyi Hall 101







Nov
10

Analysis Seminar
Javier Gomez-Serrano, Brown University

TBA
3:00 PM
Fine Hall 314







Nov
10

Joint PU/IAS Arithmetic Geometry Seminar
Ben Heuer, Frankfurt

TBA
3:30 PM
Fine Hall 224







Nov
10

Minerva mini-course
Robert Lipshitz, Minerva Distinguished Visitor & University of Oregon

…on Khovanov homology
4:30 PM
Fine Hall 314







Nov
10

PACM Colloquium
Stas Shvartsman, Princeton

TBA
4:30 PM
Fine Hall 214







Nov
11

Joint PU/IAS Symplectic Geometry Seminar
Shaoyun Bai, MIT

TBA
1:00 PM
Fine Hall 401







Nov
11

Algebraic Geometry Seminar
Jeff Baudin, EPFL

TBA
3:00 PM
Fine Hall 314







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11

Joint PU/IAS Groups and Dynamics Seminar
Aaron Brown, Northwestern University

TBA
4:30 PM
Fine Hall 314







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13

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Nick Kuhn, University of Virginia

TBA
1:00 PM






Nov
13

Discrete Mathematics Seminar
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3:00 PM
Fine Hall 224







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13

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3:00 PM
Fine Hall 314







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13

Joint PU/IAS Number Theory
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3:30 PM
Fine Hall 110







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13

Topology Seminar
Mark Brittenham, University of Nebraska at Lincoln

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4:30 PM
Fine Hall 314







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17

Analysis Seminar
Zhongkai Tao, IHES

TBA
3:00 PM
Fine Hall 314







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17

Joint PU/IAS Arithmetic Geometry Seminar
Søren Galatius, Columbia

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3:30 PM
IAS - Simonyi Hall 101







Nov
17

PACM Colloquium
Andrew Blumberg, Columbia

TBA
4:30 PM
Fine Hall 214







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18

Algebraic Geometry Seminar
Stefano Filipazzi, Duke

TBA
3:00 PM
Fine Hall 314







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18

Probability Seminar
Lorenzo Zambotti, Paris 6

TBA
3:00 PM
Fine Hall 224







Nov
18

Joint PU/IAS Groups and Dynamics Seminar
Andreas Weiser, IAS

TBA
4:30 PM
IAS - Simonyi Hall 101







Nov
20

Analysis of Fluids and Related Topics
In-jee Jeong, Seoul National University

TBA
3:00 PM
Fine Hall 314







Nov
20

Discrete Mathematics Seminar
John Byrne, U Delaware

TBA
3:00 PM
Fine Hall 224







Nov
20

Joint PU/IAS Number Theory
Kate Stange, UC Boulder

TBA
3:30 PM
IAS - Simonyi Hall 101







Nov
24

Joint PU/IAS Arithmetic Geometry Seminar
Alexander Petrov, MIT

TBA
3:30 PM
Fine Hall 224







Nov
24

PACM Colloquium
Hongkai Zhao, Duke

TBA
4:30 PM
Fine Hall 214







Nov
24

Minerva mini-course
Robert Lipshitz, Minerva Distinguished Visitor & University of Oregon

Refinements of the s-invariant
4:30 PM
Fine Hall 314







Nov
25

Algebraic Geometry Seminar
Junyao Peng, Princeton

TBA
3:00 PM
Fine Hall 314







Dec
01

Joint PU/IAS Arithmetic Geometry Seminar
Andrew Senger, University of Maryland

TBA
3:30 PM
IAS - Simonyi Hall 101







Dec
02

Algebraic Geometry Seminar
Ben Bakker, UIC & IAS

TBA
3:00 PM
Fine Hall 314







Dec
02

Probability Seminar
Yizhe Zhu, USC

TBA
3:00 PM
Fine Hall 224







Dec
02

Joint PU/IAS Groups and Dynamics Seminar
Dubi Kelmer, Boston College

TBA
4:30 PM
IAS - Simonyi Hall 101







Dec
03

Department Colloquium
Jinyoung Park, Courant Institute of Mathematical Sciences New York University

Threshold phenomena for random discrete structures
4:30 PM
Fine Hall 314







Dec
04

Joint PU/IAS Number Theory
Miao (Pam) Gu, UMich

TBA
3:30 PM
IAS - Simonyi Hall 101







Dec
04

Horizons Seminar
Jinyoung Park, Courant Institute of Mathematical Sciences New York University

A Fireside Chat - Paths to Math: a Conversation
7:00 PM
McDonnell Hall A01







Dec
08

Joint PU/IAS Arithmetic Geometry Seminar
Vincent Pilloni, Orsay

TBA
3:30 PM
IAS - Simonyi Hall 101







Dec
11

Joint PU/IAS Number Theory
Alexandra Florea, UC Irvine

TBA
3:30 PM
IAS - Simonyi Hall 101







Dec
15

Joint PU/IAS Arithmetic Geometry Seminar
Robert Cass, Claremont McKenna College

TBA
3:30 PM
IAS - Simonyi Hall 101







Dec
18

Joint PU/IAS Number Theory
Shilin Lai, Michigan

TBA
3:30 PM
IAS - Simonyi Hall 101






















作者: 酒哥    时间: 5 小时前
上面这些顶流的华人数学家还是缺乏重大原创,没有0--1的工作,多数是10--20的工作,极个别2--10的工作。这已经是华人数学天花板了。主要还是copying、跟风、在别人已有的框架内做点改进锦上添花,维持一下界面和秩序。当然这些工作总要有人做, 但好比音乐演出团体中的角色,不能大家都是鼓手吹号伴唱,也弄作曲家、几个指挥、第一第二小提琴主唱等。





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