Sanjeev Arora is an Indian American theoretical computer scientist, best known for his work on probabilistically checkable proofs and, in particular, the PCP theorem. He is the Charles C. Fitzmorris Professor of Computer Science at Princeton University, his research interests include computational complexity theory, uses of randomness in computation, probabilistically checkable proofs, computing approximate solutions to NP-hard problems, geometric embeddings of metric spaces, he received a B. S. in Mathematics with Computer Science from MIT in 1990 and received a Ph. D. in Computer Science from the University of California, Berkeley in 1994 under Umesh Vazirani. Earlier, in 1986, Sanjeev Arora had topped the prestigious IIT JEE but transferred to MIT after 2 years at IIT Kanpur, he was a visiting scholar at the Institute for Advanced Study in 2002-03. He was awarded the Gödel Prize for his work on the PCP theorem in 2001 and again in 2010 for the discovery of a polynomial time approximation scheme for the Euclidean travelling salesman problem.
In 2008 he was inducted as a Fellow of the Association for Computing Machinery. In 2011 he was awarded the ACM Infosys Foundation Award, given to mid-career researchers in Computer Science. Arora has been awarded the Fulkerson Prize for 2012 for his work on improving the approximation ratio for graph separators and related problems. In 2012 he became a Simons Investigator. Arora was elected to the National Academy of Sciences on May 2, 2018, he is a coauthor of the book Computational Complexity: A Modern Approach and is a founder, on the Executive Board, of Princeton's Center for Computational Intractability. He and his coauthors have argued that certain financial products are associated with computational asymmetry which under certain conditions may lead to market instability. Sanjeev Arora's Homepage Sanjeev Arora at the Mathematics Genealogy Project
James Harris Simons
James Harris Simons known as Jim Simons is an American mathematician, billionaire hedge fund manager, philanthropist. He is known as a quantitative investor and in 1982 founded Renaissance Technologies, a private hedge fund based in Setauket-East Setauket, New York. Although Simons retired from the fund in 2009, he remains its non-executive adviser, he is known for his studies on pattern recognition. He developed the Chern–Simons form, contributed to the development of string theory by providing a theoretical framework to combine geometry and topology with quantum field theory. From 1968 to 1978, Simons was a mathematics professor and subsequent chair of the mathematics department at Stony Brook University; as reported by Forbes, his net worth as of February 2019 is estimated to be $21.5 billion. In 2016, asteroid 6618 Jimsimons, discovered by Clyde Tombaugh in 1936, was named after Simons by the International Astronomical Union in honor of his contributions to mathematics and philanthropy. James Harris Simons was born on April 25, 1938 to an American Jewish family, the only child of Marcia and Matthew Simons, raised in Brookline, Massachusetts.
His father owned a shoe factory. When James Simons was a teenager, he worked a job in the basement stockroom of a garden supply store, his inefficiency at the job resulted in his demotion as a floor sweeper. He received a bachelor's degree in mathematics from the Massachusetts Institute of Technology in 1958 and a PhD in mathematics, from the University of California, under supervision of Bertram Kostant in 1961, at the age of 23. Simons' mathematical work has focused on the geometry and topology of manifolds, his 1962 Berkeley PhD thesis, written under the direction of Bertram Kostant, gave a new and more conceptual proof of Berger's classification of the holonomy groups of Riemannian manifolds, now a cornerstone of modern geometry. He subsequently began to work with Shing-Shen Chern on the theory of characteristic classes discovering the Chern–Simons secondary characteristic classes of 3-manifolds, which are related to the Yang-Mills functional on 4-manifolds, have had a profound effect on modern physics.
These and other contributions to geometry and topology led to Simons becoming the 1976 recipient of the AMS Oswald Veblen Prize in Geometry. In 2014, he was elected to the National Academy of Sciences of the USA. In 1964, Simons worked with the National Security Agency to break codes. Between 1964 and 1968, he was on the research staff of the Communications Research Division of the Institute for Defense Analyses and taught mathematics at the Massachusetts Institute of Technology and Harvard University joining the faculty at Stony Brook University. In 1968, he was appointed chairman of the math department at Stony Brook University. Simons was asked by IBM in 1973 to attack the block cipher Lucifer, an early but direct precursor to the Data Encryption Standard. Simons founded Math for America, a nonprofit organization, in January 2004 with a mission to improve mathematics education in United States public schools by recruiting more qualified teachers, he funds a variety of research projects. For more than two decades, Simons' Renaissance Technologies' hedge funds, which trade in markets around the world, have employed mathematical models to analyze and execute trades, many automated.
Renaissance uses computer-based models to predict price changes in financial instruments. These models are based on analyzing as much data as can be gathered looking for non-random movements to make predictions. Renaissance employs specialists with non-financial backgrounds, including mathematicians, signal processing experts and statisticians; the firm's latest fund is the Renaissance Institutional Equities Fund. RIEF has trailed the firm's better-known Medallion fund, a separate fund that contains only the personal money of the firm's executives. "It's startling to see such a successful mathematician achieve success in another field," says Edward Witten, professor of physics at the Institute for Advanced Study in Princeton, NJ, considered by many of his peers to be the most accomplished theoretical physicist alive... In 2006, Simons was named Financial Engineer of the Year by the International Association of Financial Engineers. In 2007, he was estimated to have earned $2.8 billion, $1.7 billion in 2006, $1.5 billion in 2005, $670 million in 2004.
Simons shuns the limelight and gives interviews, citing Benjamin the Donkey in Animal Farm for explanation: "God gave me a tail to keep off the flies. But I'd rather have had no tail and no flies." On October 10, 2009, Simons announced he would retire on January 1, 2010 but remain at Renaissance as nonexecutive chairman. In 1996, his son Paul, aged 34, was riding a bicycle. In 2003, his son Nicholas, aged 24, drowned on a trip to Indonesia, his son Nat Simons is an philanthropist. Simons is a major contributor to Democratic Party political action committees. According to the Center for Responsive Politics, Simons is ranked the #5 donor to federal candidates in the 2016 election cycle, coming behind co-CEO Robert Mercer, ranked #1 and donates to Republicans. Simons has donated $7 million to Hillary Clinton's Priorities USA Action, $2.6 million to the House and Senate Majority PACs, $500,000 to EMILY's List. He donated $25,000 to Republican Senator Lindsey Graham's super PAC. Since 2006 Simons has contributed about $30.6 million to federal campaigns.
Since 1990, Renaissance Technologies has contributed $59,081,152 to
Maryam Mirzakhani was an Iranian mathematician and a professor of mathematics at Stanford University. Her research topics included Teichmüller theory, hyperbolic geometry, ergodic theory, symplectic geometry. In 2005, as a result of her research, she was honored in Popular Science's fourth annual "Brilliant 10" in which she was acknowledged as one of the top 10 young minds who have pushed their fields in innovative directions. On 13 August 2014, Mirzakhani was honored with the Fields Medal, the most prestigious award in mathematics. Thus, she became both the first, to date, the only woman and the first Iranian to be honored with the award; the award committee cited her work in "the dynamics and geometry of Riemann surfaces and their moduli spaces". On 14 July 2017, Mirzakhani died of breast cancer at the age of 40. Mirzakhani was born on 12 May 1977 in Iran; as a child, she attended Tehran Farzanegan School, part of the National Organization for Development of Exceptional Talents. In her junior and senior year of high school, she won the gold medal for mathematics in the Iranian National Olympiad, thus allowing her to bypass the national college entrance exams.
In 1994, Mirzakhani achieved the gold medal level in the International Mathematical Olympiad in Hong Kong, scoring 41 out of 42 points. She was the first female Iranian student; the following year, in 1995, she became the first Iranian student to achieve a perfect score and to win two gold medals in the International Mathematical Olympiad held in Canada. In her life, she collaborated with friend and Olympiad silver medalist, Roya Beheshti Zavareh, on their book Elementary Number Theory, Challenging Problems, published in 1999. Mirzakhani and Zavareh together were the first women to compete in the Iranian National Mathematical Olympiad and won gold and silver medals in 1995. On March 17, 1998, after attending a conference consisting of gifted individuals and former Olympiad competitors and Zavareh, along with other attendees boarded a bus in Ahvaz en route to Tehran; the bus was involved in an accident wherein it fell off a cliff, killing seven of the passengers—all Sharif University students.
This incident is considered to be a national tragedy in Iran. Mirzakhani and Zavareh were two of the few survivors. In 1999, she obtained a Bachelor of Science in mathematics from the Sharif University of Technology. During her time there, she received recognition from the American Mathematical Society for her work in developing a proof for Shor's Algorithm, she went to the United States for graduate work, earning a Ph. D. in 2004 from Harvard University, where she worked under the supervision of the Fields Medalist Curtis T. McMullen. At Harvard she is said to have been "distinguished by... determination and relentless questioning", despite not being a native English-speaker. She used to take her class notes in Persian. Mirzakhani was a 2004 research fellow of the Clay Mathematics Institute and a professor at Princeton University. In 2009, she became a professor at Stanford University. Mirzakhani made several contributions to the theory of moduli spaces of Riemann surfaces. Mirzakhani's early work solved the problem of counting simple closed geodesics on hyperbolic Riemann surfaces by finding a relationship to volume calculations on moduli space.
Geodesics are the natural generalization of the idea of a "straight line" to "curved spaces". More formally, a curve is a geodesic if no slight deformation can make it shorter. Closed geodesics are geodesics which are closed curves—that is, they are curves that close up into loops. A closed geodesic is simple. A previous result, known as the "prime number theorem for geodesics", established that the number of closed geodesics of length less than L grows exponentially with L — it is asymptotic to e L / L. However, the analogous counting problem for simple closed geodesics remained open, despite being "the key object to unlocking the structure and geometry of the whole surface," according to University of Chicago topologist Benson Farb. Mirzakhani's 2004 PhD thesis solved this problem, showing that the number of simple closed geodesics of length less than L is polynomial in L. Explicitly, it is asymptotic to c L 6 g − 6, where g is the genus and c is a constant depending on the hyperbolic structure.
This result can be seen as a generalization of the theorem of the three geodesics for spherical surfaces. Mirzakhani solved this counting problem by relating it to the problem of computing volumes in moduli space—a space whose points correspond to different complex structures on a surface genus g. In her thesis, Mirzakhani found a volume formula for the moduli space of bordered Riemann surfaces of genus g with n geodesic boundary components. From this formula followed the counting for simple closed geodesics mentioned above, as well as a number of other results; this led her to obtain a new proof for the formula discovered by Edward Witten and Maxim Kontsevich on the intersection numbers of tautological classes on moduli space. Her subsequent work focused on Teichmüller dynamics of moduli space. In particular, she was able to prove the long-standing c
Jon Michael Kleinberg is an American computer scientist and the Tisch University Professor of Computer Science at Cornell University known for his work in algorithms and networks. He is a recipient of the Nevanlinna Prize by the International Mathematical Union. Jon Kleinberg was born in 1971 in Massachusetts, he received a Bachelor of Science degree in computer science from Cornell University in 1993 and a Ph. D. from Massachusetts Institute of Technology in 1996. He is the older brother of fellow Cornell computer scientist Robert Kleinberg. Since 1996 Kleinberg has been a professor in the Department of Computer Science at Cornell, as well as a visiting scientist at IBM's Almaden Research Center, his work has been supported by an NSF Career Award, an ONR Young Investigator Award, a MacArthur Foundation Fellowship, a Packard Foundation Fellowship, a Sloan Foundation Fellowship, grants from Google, Yahoo!, the NSF. He is a member of the American Academy of Arts and Sciences. In 2011, he was elected to the United States National Academy of Sciences.
In 2013 he became a fellow of the Association for Computing Machinery. Kleinberg is best known for his work on networks and for his HITS algorithm, developed while he was at IBM. HITS is an algorithm for web search that builds on the eigenvector-based methods used in algorithms and served as the full-scale model for PageRank by recognizing that web pages or sites should be considered important not only if they are linked to by many others, but if they link to many others. Search engines themselves are examples of sites that are important because they link to many others. Kleinberg realized that this generalization implies two different classes of important web pages, which he called "hubs" and "authorities"; the HITS algorithm is an algorithm for automatically identifying the leading hubs and authorities in a network of hyperlinked pages. Kleinberg is known for his work on algorithmic aspects of the small world experiment, he was one of the first to realize that Stanley Milgram's famous "six degrees" letter-passing experiment implied not only that there are short paths between individuals in social networks but that people seem to be good at finding those paths, an simple observation that turns out to have profound implications for the structure of the networks in question.
Kleinberg has written numerous papers and articles as well as a textbook on computer algorithms, Algorithm Design, co-authored the first edition with Éva Tardos and sole authored the second edition. Among other honors, he received a MacArthur Foundation Fellowship known as the "genius grant" in 2005 and the Nevanlinna Prize in 2006, an award, given out once every four years along with the Fields Medal as the premier distinction in Computational Mathematics, his new book is entitled "Networks and Markets: Reasoning About a Highly Connected World", published by Cambridge University Press in 2010. Cornell's Association of Computer Science Undergraduates awarded him the "Faculty of the Year" award in 2002. Still the Rebel King -Video Interview with Jon Kleinberg, ACM Infosys Foundation Award recipient by Stephen Ibaraki Yury Lifshits, Four Results of Jon Kleinberg: a talk for St. Petersburg Mathematical Society
Daniel Ioan Tătaru is a Romanian mathematician at University of California, Berkeley. He earned his doctorate from the University of Virginia in 1992, under supervision of Irena Lasiecka, he won the 2002 Bôcher Memorial Prize for his research on partial differential equations. In 2012 he became a fellow of the American Mathematical Society. In 2013 he was selected as a Simons Investigator in mathematics. Website at UC Berkeley Daniel Tătaru publications indexed by Google Scholar "Daniel Tătaru's results". International Mathematical Olympiad
Dan Boneh is a professor in applied cryptography and computer security at Stanford University. Born in Israel in 1969, Boneh obtained his Ph. D. in Computer Science from Princeton University in 1996 under the supervision of Richard J. Lipton. Boneh is one of the principal contributors to the development of pairing-based cryptography from the Weil Pairing, along with Matt Franklin of the University of California, Davis, he joined the faculty of Stanford University in 1997, became professor of computer science and electrical engineering. He teaches massive open online courses on the online learning platform Coursera. In 1999 he was awarded a fellowship from the Lucile Packard Foundation. In 2002, he co-founded; the company was acquired by Hewlett Packard in 2015. In 2018, Boneh became co-director of the newly founded Center for Blockchain Research at Stanford, predicting at the time that "Blockchains will become critical to doing business globally." 2016 Elected to the US National Academy of Engineering 2016 Fellow of the Association for Computing Machinery 2014 ACM-Infosys Foundation award 2014 ACM Prize in Computing 2013 Gödel Prize, with Matthew K. Franklin and Antoine Joux, for his work on the Boneh–Franklin scheme 2005 RSA Award 1999 Sloan Research Fellowship 1999 Packard Award Some of Boneh's results in cryptography include: 2018: Verifiable Delay Functions 2015: Privacy-preserving proofs of solvency for Bitcoin exchanges 2010: Efficient Identity-Based Encryption from Learning with Errors Assumption 2010: He was involved in designing tcpcrypt, TCP extensions for transport-level security 2005: A homomorphic cryptosystem 2005: The first broadcast encryption system with full collision resistance 2003: A timing attack on OpenSSL 2001: An efficient identity-based encryption system based on the Weil pairing.
1999: Cryptanalysis of RSA when the private key is less than N0.292 1997: Fault-based cryptanalysis of public-key systems 1995: Collision resistant fingerprinting codes for digital data 1995: Cryptanalysis using a DNA computer Some of his contributions in computer security include: 2007: "Show that the time web sites take to respond to HTTP requests can leak private information." 2005: PwdHash a browser extension that transparently produces a different password for each site Dan Boneh's Home Page Dan Boneh's Stanford Research Group
Andrei Yuryevich Okounkov is a Russian mathematician who works on representation theory and its applications to algebraic geometry, mathematical physics, probability theory and special functions. He is a professor at Columbia University and the academic supervisor of HSE International Laboratory of Representation Theory and Mathematical Physics. In 2006, he received the Fields Medal "for his contributions to bridging probability, representation theory and algebraic geometry." He received his doctorate at Moscow State University in 1995 under Alexandre Kirillov and Grigori Olshanski. He has been a professor at Columbia University since 2010, he was a professor at Princeton University from 2002 to 2010, an assistant and associate professor at the University of California, an instructor at the University of Chicago. He has worked on the representation theory of infinite symmetric groups, the statistics of plane partitions, the quantum cohomology of the Hilbert scheme of points in the complex plane.
Much of his work on Hilbert schemes was joint with Rahul Pandharipande. Okounkov, along with Pandharipande, Nikita Nekrasov, Davesh Maulik, has formulated well-known conjectures relating the Gromov–Witten invariants and Donaldson–Thomas invariants of threefolds. In 2006, at the 25th International Congress of Mathematicians in Madrid, Spain, he received the Fields Medal "for his contributions to bridging probability, representation theory and algebraic geometry." In 2016 he became a fellow of the American Academy of Sciences. Newton–Okounkov body Andrei Okounkov home page at Columbia Andrei Okounkov home page at Princeton O'Connor, John J.. "Andrei Okounkov", MacTutor History of Mathematics archive, University of St Andrews. Andrei Okounkov at the Mathematics Genealogy Project EMS Prize 2004 citation Fields Medal citation Andrei Okounkov's articles on the Arxiv Daily Princetonian story BBC story