DOCSLIB.ORG

The Abel Prize Laureate 2014

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Abel Prize Laureate 2014 The Abel Prize Laureate 2014 Yakov G. Sinai Princeton University, USA, and Landau Institute for Theoretical Physics, Russian Academy of Sciences www.abelprize.no Yakov G. Sinai receives the Abel Prize for 2014 “for his fundamental contributions to dynamical systems, ergodic theory, and mathematical physics” for studying the complexity of a system dynamical systems as well as in the attempts Citation through a measure-theoretical description to tackle real-life complex chaotic behavior of its trajectories. It has led to very important such as turbulence. advances in the classification of dynamical Sinai’s other pioneering works in systems. mathematical physics include: random Sinai has been at the forefront of walks in a random environment (Sinai’s ergodic theory. He proved the first ergodicity walks), phase transitions (Pirogov–Sinai theorems for scattering billiards in the style theory), one-dimensional turbulence (the of Boltzmann, work he continued with statistical shock structure of the stochastic Bunimovich and Chernov. He constructed Burgers equation, by E–Khanin–Mazel– Markov partitions for systems defined by Sinai), the renormalization group theory iterations of Anosov diffeomorphisms, which (Bleher–Sinai), and the spectrum of discrete led to a series of outstanding works showing Schrödinger operators. the power of symbolic dynamics to describe Sinai has trained and influenced a various classes of mixing systems. generation of leading specialists in his The Norwegian Academy of Science and Some of these phenomena can be foreseen With Ruelle and Bowen, Sinai discovered research fields. Much of his research has Letters has decided to award the Abel Prize with great accuracy, while others seem to the notion of SRB measures: a rather general become a standard toolbox for mathematical for 2014 to evolve in a chaotic, unpredictable way. Now and distinguished invariant measure for physicists. His works had and continue it has become clear that order and chaos are dissipative systems with chaotic behavior. to have a broad and profound impact on Yakov G. Sinai intimately connected: we may find chaotic This versatile notion has been very useful mathematics and physics, as well as on the Princeton University, USA, and Landau behavior in deterministic systems, and in the qualitative study of some archetypal ever-fruitful interaction of these two fields. Institute for Theoretical Physics, Russian conversely, the statistical analysis of chaotic Academy of Sciences systems may lead to definite predictions. Yakov Sinai made fundamental “for his fundamental contributions to contributions in this broad domain, dynamical systems, ergodic theory, and discovering surprising connections between mathematical physics” order and chaos and developing the use of probability and measure theory in the study Ever since the time of Newton, of dynamical systems. His achievements differential equations have been used by include seminal works in ergodic theory, mathematicians, scientists and engineers to which studies the tendency of a system to explain natural phenomena and to predict explore all of its available states according how they evolve. Many equations incorporate to certain time statistics; and statistical stochastic terms to model unknown, mechanics, which explores the behavior of seemingly random, factors acting upon that systems composed of a very large number evolution. The range of modern applications of particles, such as molecules in a gas. of deterministic and stochastic evolution Sinai’s first remarkable contribution, equations encompasses such diverse inspired by Kolmogorov, was to develop an issues as planetary motion, ocean currents, invariant of dynamical systems. This invariant physiological cycles, population dynamics, has become known as the Kolmogorov–Sinai Photo: Princeton University, Department of Mathematics and electrical networks, to name just a few. entropy, and it has become a central notion 4 5 The deep contributions made by Sinai London Mathematical Society (1992), the Biography early in his career led to his being invited Hungarian Academy of Sciences (1993), the to lecture at the International Congress of United States National Academy of Sciences Mathematicians in Stockholm in 1962. Sinai (1999), the Brazilian Academy of Sciences has since been an invited speaker at several (2000), the Academia Europaea (2008), the important international conferences and has Polish Academy of Sciences (2009) and the given many prestigious lectures worldwide. Royal Society of London (2009). He has spoken four times at the International He has received honorary degrees Congress of Mathematicians. He was a from Warsaw University (1993), Budapest Yakov G. Sinai was born on 21 September During 1997-1998 Yakov Sinai was plenary speaker at the 1st Latin American University of Science and Technology (2002), 1935 in Moscow, Russia. Both of his parents, Thomas Jones Professor at Princeton Congress in Mathematics in 2000. In 2001 he the Hebrew University in Jerusalem (2005), Gregory Sinai and Nadezda Kagan, were University and in 2005 he was Moore was appointed Chairman of the Fields Medal and Warwick University (2010). microbiologists with research careers. His Distinguished Scholar at the California Institute Committee of International Mathematical Professor Sinai is also respected as a grandfather, the mathematician Benjamin of Technology in Pasadena, California. Union, which decided on the awards of the teacher at Princeton. In the words of a former Fedorovich Kagan, was head of the Yakov Sinai is one of the most influential Fields Medals at the Congress in Beijing in student, “It’s quite inspirational to be in his Department of Differential Geometry at mathematicians of the twentieth century. the following year. class … People feel an immediate urge to Moscow State University. Kagan had great He has achieved numerous groundbreaking participate – there is a radiance which comes influence on his grandson. He retired from results in the theory of dynamical systems, Awards and honours from him and inspires us.”2 He is also known his chair at Moscow State University in in mathematical physics and in probability Yakov Sinai has received many distinguished for his persistence in the face of obstacles, be 1952, the year in which his grandson Yakov theory. Many mathematical results are named international awards. In 2013 he was awarded they bureaucratic or theoretical, a trait which Grigorevich entered the Faculty of after him, including Kolmogorov–Sinai the Leroy P. Steele Prize for Lifetime Achieve- has served him well throughout the years. Mechanics and Mathematics. entropy, Sinai’s billiards, Sinai’s random walk, ment from the American Mathematical — Yakov Sinai received his B.S. (1957), his Sinai-Ruelle-Bowen measures, and Pirogov- Society. Other awards include the Wolf Prize Ph.D. (1960), and his doctorate (1963) from Sinai theory. Sinai is highly respected in in Mathematics (1997), the Nemmers Prize For his 70th birthday in 2005 a special issue Moscow State University. His advisor was both physics and mathematics communities in Mathematics (2002), the Henri Poincaré of the Moscow Mathematical Journal was the prominent Andrey Kolmogorov. Sinai was as the major architect of the most bridges Prize from the International Association dedicated to Sinai: “Yakov Sinai is one of a Scientific Researcher at the Laboratory connecting the world of deterministic of Mathematical Physics (2009) and the the greatest mathematicians of our time. of Probabilistic and Statistical Methods at (dynamical) systems with the world of Dobrushin International Prize from the Institute The list of international prizes awarded to Moscow State University from 1960 to 1971. probabilistic (stochastic) systems. Perhaps it of Information Transmission of the Russian him as a sign of recognition of his scientific In 1971 he became a Professor at Moscow is only to be expected that he is the author Academy of Sciences (2009). Among his contributions is extremely long, and the list State University and a Senior Researcher at of an article titled “Mathematicians and many recognitions are the Boltzmann Gold of his fundamental results is even longer. 1 the Landau Institute of Theoretical Physics, Physicists = Cats and Dogs?” Medal from the Commission on Statistical His permanent interest in mathematics and Russian Academy of Sciences. Since 1993 During the past half-century Yakov Sinai Physics of the International Union of Pure and his exceptional scientific enthusiasm inspire he has been a Professor of Mathematics has written more than 250 research papers Applied Physics (1986) and the Dirac Medal several generations of scientists all over the at Princeton University, USA, but has and a number of books. Sinai and his wife from the Abdus Salam International Centre for world. His mere presence at a seminar or at concurrently kept his position at the Landau Elena B. Vul, a mathematician and physicist, Theoretical Physics in Trieste (1992). a conference makes scientific life brighter Institute of Theoretical Physics. The Landau have also written a number of joint papers. Many mathematical societies and and more exciting.” Institute was founded in 1964 and is located Yakov Sinai has supervised more than 50 academies have elected Sinai to membership in Chernogolovka, some 40 kilometers Ph.D. students. or honorary membership: the American northeast of Moscow; it is at the heart of 2 Dennis Kosygin, as quoted in The Daily Princetonian, 1 Bulletin (New Series) of the American Mathematical
Load more

Recommended publications
  • Gromov Receives 2009 Abel Prize
    Gromov Receives 2009 Abel Prize . The Norwegian Academy of Science Medal (1997), and the Wolf Prize (1993). He is a and Letters has decided to award the foreign member of the U.S. National Academy of Abel Prize for 2009 to the Russian- Sciences and of the American Academy of Arts French mathematician Mikhail L. and Sciences, and a member of the Académie des Gromov for “his revolutionary con- Sciences of France. tributions to geometry”. The Abel Prize recognizes contributions of Citation http://www.abelprisen.no/en/ extraordinary depth and influence Geometry is one of the oldest fields of mathemat- to the mathematical sciences and ics; it has engaged the attention of great mathema- has been awarded annually since ticians through the centuries but has undergone Photo from from Photo 2003. It carries a cash award of revolutionary change during the last fifty years. Mikhail L. Gromov 6,000,000 Norwegian kroner (ap- Mikhail Gromov has led some of the most impor- proximately US$950,000). Gromov tant developments, producing profoundly original will receive the Abel Prize from His Majesty King general ideas, which have resulted in new perspec- Harald at an award ceremony in Oslo, Norway, on tives on geometry and other areas of mathematics. May 19, 2009. Riemannian geometry developed from the study Biographical Sketch of curved surfaces and their higher-dimensional analogues and has found applications, for in- Mikhail Leonidovich Gromov was born on Decem- stance, in the theory of general relativity. Gromov ber 23, 1943, in Boksitogorsk, USSR. He obtained played a decisive role in the creation of modern his master’s degree (1965) and his doctorate (1969) global Riemannian geometry.
    [Show full text]
  • Prvních Deset Abelových Cen Za Matematiku
    Prvních deset Abelových cen za matematiku The first ten Abel Prizes for mathematics [English summary] In: Michal Křížek (author); Lawrence Somer (author); Martin Markl (author); Oldřich Kowalski (author); Pavel Pudlák (author); Ivo Vrkoč (author); Hana Bílková (other): Prvních deset Abelových cen za matematiku. (English). Praha: Jednota českých matematiků a fyziků, 2013. pp. 87–88. Persistent URL: http://dml.cz/dmlcz/402234 Terms of use: © M. Křížek © L. Somer © M. Markl © O. Kowalski © P. Pudlák © I. Vrkoč Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz Summary The First Ten Abel Prizes for Mathematics Michal Křížek, Lawrence Somer, Martin Markl, Oldřich Kowalski, Pavel Pudlák, Ivo Vrkoč The Abel Prize for mathematics is an international prize presented by the King of Norway for outstanding results in mathematics. It is named after the Norwegian mathematician Niels Henrik Abel (1802–1829) who found that there is no explicit formula for the roots of a general polynomial of degree five. The financial support of the Abel Prize is comparable with the Nobel Prize, i.e., about one million American dollars. Niels Henrik Abel (1802–1829) M. Křížek a kol.: Prvních deset Abelových cen za matematiku, JČMF, Praha, 2013 87 Already in 1899, another famous Norwegian mathematician Sophus Lie proposed to establish an Abel Prize, when he learned that Alfred Nobel would not include a prize in mathematics among his five proposed Nobel Prizes.
    [Show full text]
  • Programme 2009 the Abel Prize Ceremony 19 May 2009 Procession Accompanied by the “Abel Fanfare” Music: Klaus Sandvik
    Programme 2009 The Abel Prize Ceremony 19 May 2009 Procession accompanied by the “Abel Fanfare” Music: Klaus Sandvik. Performed by three musicians from the Staff Band of the Norwegian Defence Forces Their Majesties King Harald and Queen Sonja enter the hall Soroban Arve Henriksen (trumpet) (Music: Arve Henriksen) Opening by Øyvind Østerud President of the Norwegian Academy of Science and Letters Eg veit i himmerik ei borg Trio Mediæval, Arve Henriksen (Norwegian folk tune from Hallingdal, arr. Linn A. Fuglseth) The Abel Prize Award Ceremony Professor Kristian Seip Chairman of the Abel Committee The Committee’s citation His Majesty King Harald presents the Abel Prize to Mikhail Leonidovich Gromov Acceptance speech by Mikhail Leonidovich Gromov Closing remarks by Professor Øyvind Østerud President of the Norwegian Academy of Science and Letters Till, till Tove Trio Mediæval, Arve Henriksen, Birger Mistereggen (percussion) (Norwegian folk tune from Vestfold, arr. Tone Krohn) Their Majesties King Harald and Queen Sonja leave the hall Procession leaves the hall Other guests leave the hall when the procession has left to a skilled mathematics teacher in the upper secondary school is called after Abel’s own Professor Øyvind Østerud teacher, Bernt Michael Holmboe. There is every reason to remember Holmboe, who was President of the Norwegian Academy of Science and Letters Abel’s mathematics teacher at Christiania Cathedral School from when Abel was 16. Holmboe discovered Abel’s talent, inspired him, encouraged him, and took the young pupil considerably further than the curriculum demanded. He pointed him to the professional literature, helped Your Majesties, Excellencies, dear friends, him with overseas contacts and stipends and became a lifelong colleague and friend.
    [Show full text]
  • Issue 73 ISSN 1027-488X
    NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Feature History Interview ERCOM Hedgehogs Richard von Mises Mikhail Gromov IHP p. 11 p. 31 p. 19 p. 35 September 2009 Issue 73 ISSN 1027-488X S E European M M Mathematical E S Society Geometric Mechanics and Symmetry Oxford University Press is pleased to From Finite to Infinite Dimensions announce that all EMS members can benefit from a 20% discount on a large range of our Darryl D. Holm, Tanya Schmah, and Cristina Stoica Mathematics books. A graduate level text based partly on For more information please visit: lectures in geometry, mechanics, and symmetry given at Imperial College www.oup.co.uk/sale/science/ems London, this book links traditional classical mechanics texts and advanced modern mathematical treatments of the FORTHCOMING subject. Differential Equations with Linear 2009 | 460 pp Algebra Paperback | 978-0-19-921291-0 | £29.50 Matthew R. Boelkins, Jack L Goldberg, Hardback | 978-0-19-921290-3 | £65.00 and Merle C. Potter Explores the interplaybetween linear FORTHCOMING algebra and differential equations by Thermoelasticity with Finite Wave examining fundamental problems in elementary differential equations. This Speeds text is accessible to students who have Józef Ignaczak and Martin completed multivariable calculus and is appropriate for Ostoja-Starzewski courses in mathematics and engineering that study Extensively covers the mathematics of systems of differential equations. two leading theories of hyperbolic October 2009 | 464 pp thermoelasticity: the Lord-Shulman Hardback | 978-0-19-538586-1 | £52.00 theory, and the Green-Lindsay theory. Oxford Mathematical Monographs Introduction to Metric and October 2009 | 432 pp Topological Spaces Hardback | 978-0-19-954164-5 | £70.00 Second Edition Wilson A.
    [Show full text]
  • “To Be a Good Mathematician, You Need Inner Voice” ”Огонёкъ” Met with Yakov Sinai, One of the World’S Most Renowned Mathematicians
    “To be a good mathematician, you need inner voice” ”ОгонёкЪ” met with Yakov Sinai, one of the world’s most renowned mathematicians. As the new year begins, Russia intensifies the preparations for the International Congress of Mathematicians (ICM 2022), the main mathematical event of the near future. 1966 was the last time we welcomed the crème de la crème of mathematics in Moscow. “Огонёк” met with Yakov Sinai, one of the world’s top mathematicians who spoke at ICM more than once, and found out what he thinks about order and chaos in the modern world.1 Committed to science. Yakov Sinai's close-up. One of the most eminent mathematicians of our time, Yakov Sinai has spent most of his life studying order and chaos, a research endeavor at the junction of probability theory, dynamical systems theory, and mathematical physics. Born into a family of Moscow scientists on September 21, 1935, Yakov Sinai graduated from the department of Mechanics and Mathematics (‘Mekhmat’) of Moscow State University in 1957. Andrey Kolmogorov’s most famous student, Sinai contributed to a wealth of mathematical discoveries that bear his and his teacher’s names, such as Kolmogorov-Sinai entropy, Sinai’s billiards, Sinai’s random walk, and more. From 1998 to 2002, he chaired the Fields Committee which awards one of the world’s most prestigious medals every four years. Yakov Sinai is a winner of nearly all coveted mathematical distinctions: the Abel Prize (an equivalent of the Nobel Prize for mathematicians), the Kolmogorov Medal, the Moscow Mathematical Society Award, the Boltzmann Medal, the Dirac Medal, the Dannie Heineman Prize, the Wolf Prize, the Jürgen Moser Prize, the Henri Poincaré Prize, and more.
    [Show full text]
  • Oslo 2004: the Abel Prize Celebrations
    NEWS OsloOslo 2004:2004: TheThe AbelAbel PrizePrize celebrationscelebrations Nils Voje Johansen and Yngvar Reichelt (Oslo, Norway) On 25 March, the Norwegian Academy of Science and Letters announced that the Abel Prize for 2004 was to be awarded to Sir Michael F. Atiyah of the University of Edinburgh and Isadore M. Singer of MIT. This is the second Abel Prize awarded following the Norwegian Government’s decision in 2001 to allocate NOK 200 million to the creation of the Abel Foundation, with the intention of award- ing an international prize for outstanding research in mathematics. The prize, amounting to NOK 6 million, was insti- tuted to make up for the fact that there is no Nobel Prize for mathematics. In addi- tion to awarding the international prize, the Foundation shall contribute part of its earnings to measures for increasing inter- est in, and stimulating recruitment to, Nils Voje Johansen Yngvar Reichelt mathematical and scientific fields. The first Abel Prize was awarded in machine – the brain and the computer, break those rules creatively, just like an 2003 to the French mathematician Jean- with the subtitle “Will a computer ever be artist or a musical composer. Pierre Serre for playing a key role in shap- awarded the Abel Prize?” Quentin After a brief interval, Quentin Cooper ing the modern form of many parts of Cooper, one of the BBC’s most popular invited questions from the audience and a mathematics. In 2004, the Abel radio presenters, chaired the meeting, in number of points were brought up that Committee decided that Michael F. which Sir Michael spoke for an hour to an Atiyah addressed thoroughly and profes- Atiyah and Isadore M.
    [Show full text]
  • Excerpts from Kolmogorov's Diary
    Asia Pacific Mathematics Newsletter Excerpts from Kolmogorov’s Diary Translated by Fedor Duzhin Introduction At the age of 40, Andrey Nikolaevich Kolmogorov (1903–1987) began a diary. He wrote on the title page: “Dedicated to myself when I turn 80 with the wish of retaining enough sense by then, at least to be able to understand the notes of this 40-year-old self and to judge them sympathetically but strictly”. The notes from 1943–1945 were published in Russian in 2003 on the 100th anniversary of the birth of Kolmogorov as part of the opus Kolmogorov — a three-volume collection of articles about him. The following are translations of a few selected records from the Kolmogorov’s diary (Volume 3, pages 27, 28, 36, 95). Sunday, 1 August 1943. New Moon 6:30 am. It is a little misty and yet a sunny morning. Pusya1 and Oleg2 have gone swimming while I stay home being not very well (though my condition is improving). Anya3 has to work today, so she will not come. I’m feeling annoyed and ill at ease because of that (for the second time our Sunday “readings” will be conducted without Anya). Why begin this notebook now? There are two reasonable explanations: 1) I have long been attracted to the idea of a diary as a disciplining force. To write down what has been done and what changes are needed in one’s life and to control their implementation is by no means a new idea, but it’s equally relevant whether one is 16 or 40 years old.
    [Show full text]
  • The Abel Prize 2003-2007 the First Five Years
    springer.com Mathematics : History of Mathematics Holden, Helge, Piene, Ragni (Eds.) The Abel Prize 2003-2007 The First Five Years Presenting the winners of the Abel Prize, which is one of the premier international prizes in mathematics The book presents the winners of the first five Abel Prizes in mathematics: 2003 Jean-Pierre Serre; 2004 Sir Michael Atiyah and Isadore Singer; 2005 Peter D. Lax; 2006 Lennart Carleson; and 2007 S.R. Srinivasa Varadhan. Each laureate provides an autobiography or an interview, a curriculum vitae, and a complete bibliography. This is complemented by a scholarly description of their work written by leading experts in the field and by a brief history of the Abel Prize. Interviews with the laureates can be found at http://extras.springer.com . Order online at springer.com/booksellers Springer Nature Customer Service Center GmbH Springer Customer Service Tiergartenstrasse 15-17 2010, XI, 329 p. With DVD. 1st 69121 Heidelberg edition Germany T: +49 (0)6221 345-4301 [email protected] Printed book Hardcover Book with DVD Hardcover ISBN 978-3-642-01372-0 £ 76,50 | CHF 103,00 | 86,99 € | 95,69 € (A) | 93,08 € (D) Out of stock Discount group Science (SC) Product category Commemorative publication Series The Abel Prize Prices and other details are subject to change without notice. All errors and omissions excepted. Americas: Tax will be added where applicable. Canadian residents please add PST, QST or GST. Please add $5.00 for shipping one book and $ 1.00 for each additional book. Outside the US and Canada add $ 10.00 for first book, $5.00 for each additional book.
    [Show full text]
  • Randomness and Computation
    Randomness and Computation Rod Downey School of Mathematics and Statistics, Victoria University, PO Box 600, Wellington, New Zealand [email protected] Abstract This article examines work seeking to understand randomness using com- putational tools. The focus here will be how these studies interact with classical mathematics, and progress in the recent decade. A few representa- tive and easier proofs are given, but mainly we will refer to the literature. The article could be seen as a companion to, as well as focusing on develop- ments since, the paper “Calibrating Randomness” from 2006 which focused more on how randomness calibrations correlated to computational ones. 1 Introduction The great Russian mathematician Andrey Kolmogorov appears several times in this paper, First, around 1930, Kolmogorov and others founded the theory of probability, basing it on measure theory. Kolmogorov’s foundation does not seek to give any meaning to the notion of an individual object, such as a single real number or binary string, being random, but rather studies the expected values of random variables. As we learn at school, all strings of length n have the same probability of 2−n for a fair coin. A set consisting of a single real has probability zero. Thus there is no meaning we can ascribe to randomness of a single object. Yet we have a persistent intuition that certain strings of coin tosses are less random than others. The goal of the theory of algorithmic randomness is to give meaning to randomness content for individual objects. Quite aside from the intrinsic mathematical interest, the utility of this theory is that using such objects instead distributions might be significantly simpler and perhaps giving alternative insight into what randomness might mean in mathematics, and perhaps in nature.
    [Show full text]
  • CURRICULUM VITAE November 2007 Hugo J
    CURRICULUM VITAE November 2007 Hugo J. Woerdeman Professor and Department Head Office address: Home address: Department of Mathematics 362 Merion Road Drexel University Merion, PA 19066 Philadelphia, PA 19104 Phone: (610) 664-2344 Phone: (215) 895-2668 Fax: (215) 895-1582 E-mail: [email protected] Academic employment: 2005– Department of Mathematics, Drexel University Professor and Department Head (January 2005 – Present) 1989–2004 Department of Mathematics, College of William and Mary, Williamsburg, VA. Margaret L. Hamilton Professor of Mathematics (August 2003 – December 2004) Professor (July 2001 – December 2004) Associate Professor (September 1995 – July 2001) Assistant Professor (August 1989 – August 1995; on leave: ’89/90) 2002-03 Department of Mathematics, K. U. Leuven, Belgium, Visiting Professor Post-doctorate: 1989– 1990 University of California San Diego, Advisor: J. W. Helton. Education: Ph. D. degree in mathematics from Vrije Universiteit, Amsterdam, 1989. Thesis: ”Matrix and Operator Extensions”. Advisor: M. A. Kaashoek. Co-advisor: I. Gohberg. Doctoraal (equivalent of M. Sc.), Vrije Universiteit, Amsterdam, The Netherlands, 1985. Thesis: ”Resultant Operators and the Bezout Equation for Analytic Matrix Functions”. Advisor: L. Lerer Current Research Interests: Modern Analysis: Operator Theory, Matrix Analysis, Optimization, Signal and Image Processing, Control Theory, Quantum Information. Editorship: Associate Editor of SIAM Journal of Matrix Analysis and Applications. Guest Editor for a Special Issue of Linear Algebra and
    [Show full text]
  • Your Project Title
    Curriculum vitae Alfonso Sorrentino Curriculum Vitae • Personal Information Full Name: Alfonso Sorrentino. Citizenship: Italian. Researcher unique identifier (ORCID): 0000-0002-5680-2999. Contact Information: Address: Dipartimento di Matematica, Universit`adegli Studi di Roma \Tor Vergata" Via della Ricerca Scientifica 1, 00133 Rome (Italy). Phone: (+39) 06 72594663 Email: [email protected] Website: http://www.mat.uniroma2.it/∼sorrenti • Research Interests Hamiltonian and Lagrangian systems: Aubry-Mather-Ma~n´etheory, KAM theory, weak KAM theory, Integrable systems, geodesic flows, Stability and Instability. Twist maps and symplectic maps: low-dimensional (topological) dynamics, Aubry-Mather theory. Billiards: dynamics, integrability, spectral properties, rigidity phenomena. Dissipative systems: conformally symplectic Aubry-Mather theory. Hamilton-Jacobi equation: Homogenization, Symplectic Homogenization, Hamilton-Jacobi on net- works and ramified spaces. Symplectic and contact geometry/topology: general theory, Hofer and Viterbo geometries, applica- tions to dynamics. • Education 2004 - 2008: Ph.D. in Mathematics, Princeton University (USA). Thesis Title: On the structure of action-minimizing sets for Lagrangian systems. Advisor: Prof. John N. Mather. Degree Committee: John N. Mather (President), Elon Lindenstrauss,Yakov Sinai and Bo0az Klartag. 2003 - 2004: M.A. in Mathematics, Princeton University (USA). Exam Committee: John Mather (President), Alice Chang and J´anosKoll´ar. 1998 - 2003: Laurea degree in Mathematics, Universit`adegli Studi \Roma Tre". Thesis Title: On smooth quasi-periodic solutions of Hamiltonian Systems. Supervisor: Prof. Luigi Chierchia. Evaluation: 110/110 cum laude. • Academic Positions 2014 - present: Associate Professor in Mathematical Analysis (01/A3, MAT/05) (tenured position) at Dipartimento di Matematica, Universit`adegli Studi di Roma \Tor Vergata", Rome (Italy). 2012 - 2014: Researcher in Mathematical Analysis MAT/05 (tenured position) at Dipartimento di Matematica e Fisica, Universit`adegli Studi \Roma Tre", Rome (Italy).
    [Show full text]
  • Ergodic Theory Plays a Key Role in Multiple Fields Steven Ashley Science Writer
    CORE CONCEPTS Core Concept: Ergodic theory plays a key role in multiple fields Steven Ashley Science Writer Statistical mechanics is a powerful set of professor Tom Ward, reached a key milestone mathematical tools that uses probability the- in the early 1930s when American mathema- ory to bridge the enormous gap between the tician George D. Birkhoff and Austrian-Hun- unknowable behaviors of individual atoms garian (and later, American) mathematician and molecules and those of large aggregate sys- and physicist John von Neumann separately tems of them—a volume of gas, for example. reconsidered and reformulated Boltzmann’ser- Fundamental to statistical mechanics is godic hypothesis, leading to the pointwise and ergodic theory, which offers a mathematical mean ergodic theories, respectively (see ref. 1). means to study the long-term average behavior These results consider a dynamical sys- of complex systems, such as the behavior of tem—whetheranidealgasorothercomplex molecules in a gas or the interactions of vi- systems—in which some transformation func- brating atoms in a crystal. The landmark con- tion maps the phase state of the system into cepts and methods of ergodic theory continue its state one unit of time later. “Given a mea- to play an important role in statistical mechan- sure-preserving system, a probability space ics, physics, mathematics, and other fields. that is acted on by the transformation in Ergodicity was first introduced by the a way that models physical conservation laws, Austrian physicist Ludwig Boltzmann laid Austrian physicist Ludwig Boltzmann in the what properties might it have?” asks Ward, 1870s, following on the originator of statisti- who is managing editor of the journal Ergodic the foundation for modern-day ergodic the- cal mechanics, physicist James Clark Max- Theory and Dynamical Systems.Themeasure ory.
    [Show full text]