Maryam Mirzakhani(born May 1977) is an Iranian mathematician, Professor of Mathematics (since September 1, 2008) at Stanford University.

Maryam Mirzakhani 是今年非常有力的竞争者, 和任何候选人站在一起都是那样出众引人注目. 她还是 IMO 满分.

1995 年, 今年中国领队姚一隽去加拿大参加 IMO 的时候, 这一年也是张筑生第一次做领队, 一共有 14 个满分, 其中有两个女生: 咱们中国的朱晨畅, 现在在德国 Gottingen University; 来自伊朗的 Maryam Mirzakhani, 8 月 16 日上午作 ICM 一小时报告.

## Conjecture

There exist elliptic curve groups $$E(\Bbb Q)$$ of arbitrarily large rank.

Martin-McMillen 2000 年有一个 $$r\geq24$$ 的例子:

\begin{equation*}\begin{split}y^2+xy+y&=x^3-120039822036992245303534619191166796374x\\&+ 504224992484910670010801799168082726759443756222911415116\end{split}\end{equation*}

Hasse-Weil $$L$$-function $$L(s, E)$$ 在 $$s=1$$ 处的零点的阶数 $$r_a$$ 称为 $$E$$ 的 analytic rank(解析秩).

Manjul Bhargava, Christopher Skinner, Wei Zhang(张伟) 7 月 7 日在 arXiv 上传的论文 “A majority of elliptic curves over $$Q$$ satisfy the Birch and Swinnerton-Dyer conjecture“, 宣布了取得的进展:

1. $$\Bbb Q$$ 上的椭圆曲线, when ordered by height(同构类以高排序), 至少有 $$66.48\%$$ 满足 BSD conjecture;
2. $$\Bbb Q$$ 上的椭圆曲线, when ordered by height, 至少有 $$66.48\%$$ 有有限 Tate–Shafarevich group;
3. $$\Bbb Q$$ 上的椭圆曲线, when ordered by height, 至少有 $$16.50\%$$ 满足 $$r=r_a=0$$, 至少有 $$20.68\%$$ 满足 $$r=r_a=1$$.

Art Levinson Steps Down as Chair of Breakthrough Prize in Life Sciences Foundation, Succeeded by Cori Bargmann
Online Nominations For 2015 Breakthrough Prizes in Fundamental Physics and Life Sciences are Open Through June 30, 2014

June 23, 2014 (San Francisco) – The Breakthrough Prize Foundation announces five winners of the inaugural Breakthrough Prize in Mathematics:

Simon Donaldson, Stony Brook University and Imperial College London, for the new revolutionary invariants of 4-dimensional manifolds and for the study of the relation between stability in algebraic geometry and in global differential geometry, both for bundles and for Fano varieties.

Maxim Kontsevich, Institut des Hautes Études Scientifiques, for work making a deep impact in a vast variety of mathematical disciplines, including algebraic geometry, deformation theory, symplectic topology, homological algebra and dynamical systems.

Jacob Lurie, Harvard University, for his work on the foundations of higher category theory and derived algebraic geometry; for the classification of fully extended topological quantum field theories; and for providing a moduli-theoretic interpretation of elliptic cohomology.

Terence Tao, University of California, Los Angeles, for numerous breakthrough contributions to harmonic analysis, combinatorics, partial differential equations and analytic number theory.

Richard Taylor, Institute for Advanced Study, for numerous breakthrough results in the theory of automorphic forms, including the Taniyama-Weil conjecture, the local Langlands conjecture for general linear groups, and the Sato-Tate conjecture.

The Breakthrough Prize in Mathematics was launched by Mark Zuckerberg and Yuri Milner at the Breakthrough Prize ceremony last December. It aims to recognize major advances in the field, honor the world’s best mathematicians, support their future endeavors and communicate the excitement of mathematics to general public.

The laureates will be presented with their trophies and \$3 million each at the Breakthrough Prize ceremony in November.

All five recipients of the Prize have agreed to serve on the Selection Committee, responsible for choosing subsequent winners of the prize from the pool of contenders nominated by the mathematics community. From 2015 onwards, one Breakthrough Prize in Mathematics will be awarded every year.

Mark Zuckerberg said: “Mathematics is essential for driving human progress and innovation in this century. This year’s Breakthrough Prize winners have made huge contributions to the field and we’re excited to celebrate their efforts.”

Yuri Milner commented: “Mathematics is the most fundamental of the sciences – the language they are all written in. The best mathematical minds benefit us all by expanding the sphere of human knowledge.”

Yuri Milner曾指出, 在1950年代, “时代”杂志封面人物除政治家外, 还会有像爱因斯坦这样等对人类贡献巨大的科学家, 而当今世界充斥新闻的只是为大众提供娱乐服务的球星和歌手. 大奖评委方面表示, 颁发世界上“金额最大科学奖”的目的就是要吸引更多优秀人才投身到科学研究领域, 让科学家变成高知名度的明星.

2014年度邵逸夫数学科学奖颁予 George Lusztig

George Lusztig, 1946 年于罗马尼亚蒂米甚瓦拉出生, 现为美国麻省理工学院Abdun-Nur 数学讲座教授. 1968年于罗马尼亚布加勒斯特大学毕业, 1971年于美国普林斯顿大学取得硕士和博士学位. 1971年至1977年于英国华威大学任教, 1974年成为教授. 自1978年起, 他一直在麻省理工学院兼职教授. 2005年获罗马尼亚科学院数学研究所授予荣誉院士. 他是英国皇家学会, 美国人文与科学学院及美国国家科学院院士.

The Shaw Prize in Mathematical Sciences is awarded to George Lusztig

for his fundamental contributions to algebra, algebraic geometry, and representation theory, and for weaving these subjects together to solve old problems and reveal beautiful new connections.

Lusztig received the 1985 AMS Cole Prize in Algebra “for his fundamental work on the representation theory of finite groups of Lie type”, particularly for his contributions to the classification of the irreducible representations in characteristic zero of the groups of rational points of reductive groups over finite fields. He was also awarded the 2008 AMS Steele Prize for Lifetime Achievement. The citation for the Steele Prize noted that Lusztig’s work “has entirely reshaped representation theory and in the process changed much of mathematics.”

Yakov G. Sinai, Princeton University and the Landau Institute for Theoretical Physics, Russian Academy of Sciences, is being awarded the 2014 Abel Prize “for his fundamental contributions to dynamical systems, ergodic theory, and mathematical physics.” Sinai received the AMS Steele Prize for Lifetime Achievement in 2013 and is a Fellow of the AMS.

The Abel Prize Committee cites Sinai’s discovery of surprising connections between order and chaos and his development of the use of probability and measure theory in the study of dynamical systems. The citation continues: “His achievements include seminal works in ergodic theory, which studies the tendency of a system to explore all of its available states according to certain time statistics; and statistical mechanics, which explores the behavior of systems composed of a very large number of particles, such as molecules in a gas… Sinai has trained and influenced a generation of leading specialists in his research fields.” Among his other awards are the Wolf Prize in Mathematics (1997), the Nemmers Prize in Mathematics (2002), the Henri Poincaré Prize from the International Association of Mathematical Physics (2009), and the Dobrushin International Prize from the Institute of Information Transmission of the Russian Academy of Sciences (2009).

On behalf of the American Mathematical Society, it is a great pleasure to congratulate Yakov Sinai of Princeton University and the Landau Institute, recipient of the 2014 Abel Prize. Sinai’s work has changed our understanding of change; his influence can be seen from number theory to physics. Congratulations!
David Vogan, AMS President

The Abel Prize is awarded by the Norwegian Academy of Science and Letters and recognizes contributions of extraordinary depth and influence to the mathematical sciences. Awarded annually since 2003, the prize carries a cash award of NOK 6,000,000 (approximately one million US). Sinai will receive the prize at an award ceremony in Oslo on May 20. Read more about Yakov Sinai, his achievements, and the Abel Prize.

Yitang Zhang wins the 2014 Rolf Schock Prize in Mathematics, for his spectacular breakthrough concerning the possibility of an infinite number of twin primes. The Royal Swedish Academy of Sciences decided the laureate.

Open Problems in Mathematics

Open Problems in Mathematics 是一个新创办的期刊(journal), 官网是 Open Problems in Mathematics

## 杂志的定位(Focus and Scope)

Open Problems in Mathematics is a depository for significant open problems in mathematics. The articles are limited to four pages, must be focused on an open problem or multiple open problems, and should focus on problems that have been open for at least 3 years. A sponsor (an expert in the field) must certify that the problem is likely to inspire valuable research, in his or her opinion.