Caltech News tagged with "mathematics"
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enPractical Mathematics: An Interview with Andrew Stuart
http://www.caltech.edu/news/practical-mathematics-interview-andrew-stuart-52808
<div class="field field-name-news-writer field-type-ds field-label-inline clearfix"><div class="field-label">News Writer: </div><div class="field-items"><div class="field-item even">Robert Perkins</div></div></div><div class="field field-name-field-images field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><div class="ds-1col file file-image file-image-jpeg view-mode-full_grid_9 clearfix ">
<img src="http://s3-us-west-1.amazonaws.com/www-prod-storage.cloud.caltech.edu/styles/article_photo/s3/AStuart-Caltech-9427-NEWS-WEB.jpg?itok=qcTpckFi" alt="Andrew Stuart" /><div class="field field-name-field-caption field-type-text field-label-hidden"><div class="field-items"><div class="field-item even">Andrew Stuart</div></div></div><div class="field field-name-credit-sane-label field-type-ds field-label-hidden"><div class="field-items"><div class="field-item even">Credit: Credit: Caltech</div></div></div></div></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>New Caltech faculty member <a href="http://www.cms.caltech.edu/people/5854/profile">Andrew Stuart</a> is interested in how the current era of data acquisition interacts with centuries of human intellectual development of mathematical models that describe the world around us. As an applied mathematician in the Division of Engineering and Applied Science (EAS), he generates the mathematical and algorithmic frameworks that allow researchers to interface data with mathematical models. His work is informed by—and has applications for—diverse arenas such as weather prediction, carbon sequestration, personalized medicine, and crowd forecasting. Originally from London, Stuart earned his bachelor's degree at Bristol University and then a combined master's/PhD at Oxford University. He worked as a postdoc at MIT in the late '80s, as a lecturer at the University of Bath in England from 1989 to 1992, and then as professor at Stanford University and the University of Warwick in England. He relocated to Southern California this summer. Recently, Stuart answered a few questions about his research and his new life at Caltech.</em></p><h3>What brought you to Caltech?</h3><p>The high quality research in engineering and applied science as well as the high quality of undergraduate and graduate students. I'm excited by the opportunity to develop my mathematical research in new directions, both in terms of applications and in terms of underpinning mathematical methodologies. There's an undeniable beauty to pure mathematics, but what has always driven my interests in mathematics is the potential for diverse applications, and the role of mathematics in unifying these different fields. Caltech provides enormous potential for collaboration in areas of interest to me, in the EAS and Geology and Planetary Sciences divisions for example, and also at JPL.</p><h3>For example?</h3><p>Weather forecasting. Netwon's laws, describing conservation of mass, momentum and energy, in principle have enormous predictive power. But lack of precise knowledge of the initial state of the atmosphere, together with physical effects on scales too small to resolve efficiently on the computer, mean that the "butterfly effect" (in which small changes in complex systems ultimately yield major effects) can lead to poor forecasts. Data provides a potential resolution to this problem, or at least an amelioration of it. Right now we have satellites, aircraft, and weather balloons all collecting vast amounts of data; figuring out how best to use these data can substantially improve the accuracy of our forecasting. A lot of good applied mathematics is about formulating the right problems, as well as finding algorithms for solving them.</p><h3>How did you get into your field?</h3><p>I grew up in an academic household; I saw that it was a challenging, stimulating, and intellectually rewarding career. My dad, who worked at Imperial College in fluid mechanics, loved his job and I was very aware of this. I then developed an excitement for mathematics that grew once I started majoring in the field as an undergraduate student.</p><h3>What are you looking forward to about being in Southern California?</h3><p>The great combination of urban culture and outdoors life. I enjoy cinema, art, reading novels, and hiking. Recently I have been to Kings Canyon and Sequoia, and I have also visited MOCA (Museum of Contemporary Art) Grand Avenue. </p></div></div></div>Thu, 27 Oct 2016 19:53:52 +0000rperkins52808 at http://www.caltech.eduCaltech Offers Open Online Course on Quantum Cryptography
http://www.caltech.edu/news/caltech-offers-open-online-course-quantum-cryptography-52456
<div class="field field-name-news-writer field-type-ds field-label-inline clearfix"><div class="field-label">News Writer: </div><div class="field-items"><div class="field-item even">Robert Perkins</div></div></div><div class="field field-name-field-images field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><div class="ds-1col file file-image file-image-jpeg view-mode-full_grid_9 clearfix ">
<img src="http://s3-us-west-1.amazonaws.com/www-prod-storage.cloud.caltech.edu/styles/article_photo/s3/Vidick-Thomas_6349-NEWS-WEB.jpg?itok=w3ajQ3Gn" alt="photo of Thomas Vidick" /><div class="field field-name-field-caption field-type-text field-label-hidden"><div class="field-items"><div class="field-item even">Thomas Vidick, Assistant Professor of Computing and Mathematical Sciences</div></div></div><div class="field field-name-credit-sane-label field-type-ds field-label-hidden"><div class="field-items"><div class="field-item even">Credit: Lance Hayashida/Caltech Office of Strategic Communications</div></div></div></div></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>This summer, Caltech's <a href="http://eas.caltech.edu/people/5373/profile">Thomas Vidick</a> spent a month delivering a series of lectures about quantum cryptography… to an empty room. On October 9, students around the world will be able to enjoy them.</p><p>Vidick, assistant professor of computing and mathematical sciences in the Division of Engineering and Applied Science, is participating in a massive open online course (MOOC) that will be available, along with two other courses from Caltech, to thousands of students through the <a href="https://www.edx.org/school/caltechx">edX online education platform</a>.</p><p>The class—<a href="https://youtu.be/DERsAtboQ5k">CS/Ph 120, Quantum Cryptography</a>—is cotaught by Vidick and his longtime colleague Stephanie Wehner from QuTech at the Delft University of Technology. Both Vidick and Wehner also will have classroom components to their courses, at their respective institutions.</p><p>Vidick says that he was inspired to teach the course through conversations with his PhD advisor at Berkeley, Umesh Vazirani, who taught a MOOC titled "Quantum Mechanics and Quantum Computation."</p><p>Vidick's course focuses on the ways in which quantum mechanics can be used to create secure lines of communication. Though the concept was first proposed in the 1970s, it has only recently gone mainstream, with the first quantum bank transaction taking place in 2004.</p><p>"It's a hot topic, but there are very few resources for people wanting to go beyond just the basics. Very few schools will even have a quantum cryptography course," Vidick says.</p><p>So far, CS/Ph 120 has 5,500 registered students—small, by the standards of MOOCs, which average 43,000 students, according to a 2014 study by a researcher at the Open University in the United Kingdom. Even so, Vidick expects that just about 200 will stick out the program to the end, given that the average completion rate for MOOCs sits around 6.5 percent.</p><p>For the dozen or so Caltech students and 40 Delft students who will attend in-person, the class will use the "flipped classroom" model, in which the lectures are done online, with time in the classroom spent cementing what the students have learned and diving deeper into the concepts.</p><p>While no prior knowledge of quantum mechanics is necessary, students will need to have a strong grasp of linear algebra, a branch of mathematics central to engineering, in order to follow along, Vidick says. "Making the course accessible does not mean dumbing it down, and the less mathematically inclined might find it challenging," he cautioned in a recent post to his <a href="https://mycqstate.wordpress.com/2016/09/09/coming-to-a-theater-near-you/">personal blog</a>, announcing the course.</p><p>The edX course launches on October 9, although in-class students already have begun meeting, to go over the basics of linear algebra, quantum information, computer science, and cryptography—concepts that will be used throughout.</p><p>Online, students will have access to video lectures, lecture notes, quizzes, and links to additional resources.</p><p>This will be Vidick's first MOOC and his first time teaching quantum cryptography—but he says he is looking forward to the challenge.</p><p>"Every time I finish teaching a class I want to teach it again right away, because it's like <em>'Now</em> I know how to do it,'" Vidick says.</p><p>Students can enroll online at <a href="https://www.edx.org/course/quantum-cryptography-caltechx-delftx-qucryptox">https://www.edx.org/course/quantum-cryptography-caltechx-delftx-qucryptox</a>.</p></div></div></div><div class="field field-name-field-pr-links field-type-link-field field-label-above"><div class="field-label">Related Links: </div><div class="field-items"><div class="field-item even"><a href="https://youtu.be/DERsAtboQ5k" class="pr-link">Quantum Cryptography | CaltechX and DelftX on edX | Course About Video</a></div></div></div>Wed, 28 Sep 2016 19:33:22 +0000rperkins52456 at http://www.caltech.eduLifetime of Numbers: Q&A with Barry Simon
http://www.caltech.edu/news/lifetime-numbers-qa-barry-simon-51679
<div class="field field-name-news-writer field-type-ds field-label-inline clearfix"><div class="field-label">News Writer: </div><div class="field-items"><div class="field-item even">Whitney Clavin</div></div></div><div class="field field-name-field-images field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><div class="ds-1col file file-image file-image-jpeg view-mode-full_grid_9 clearfix ">
<img src="http://s3-us-west-1.amazonaws.com/www-prod-storage.cloud.caltech.edu/styles/article_photo/s3/8281502675_b7efd457f1_k.jpg?itok=jdJbM4v2" alt="" /><div class="field field-name-field-caption field-type-text field-label-hidden"><div class="field-items"><div class="field-item even">Barry Simon</div></div></div><div class="field field-name-credit-sane-label field-type-ds field-label-hidden"><div class="field-items"><div class="field-item even">Credit: Caltech </div></div></div></div></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><a href="https://www.pma.caltech.edu/content/barry-m-simon">Barry M. Simon</a>, professor of mathematics, emeritus, will be featured on the cover of the<a href="http://www.ams.org/journals/notices/201607/"> <em>Notices of the American Mathematical Society</em></a> on the occasion of <a href="http://www.fields.utoronto.ca/activities/16-17/modern-physics">a special math conference</a> being held this month for his 70th birthday. Simon, who is known as the one of the founding fathers of modern mathematical physics, was recently awarded <a href="/news/simon-receives-lifetime-achievement-award-48745">the 2016 Leroy Steele Prize for Lifetime Achievement of the American Mathematical Society (AMS)</a>.</p><p>Simon has made impactful contributions to the mathematical areas of quantum field theory, statistical mechanics, Schroedinger operators, and the theory of orthogonal polynomials. He has published nearly 400 scientific papers and authored 21 books, including the four-volume textbook series, "Methods of Modern Mathematical Physics," written with Michael Reed in the 1970s. He has also coauthored two popular manuals on how to use Windows computers.</p><p>We recently spoke with Simon about his career, mentoring students, and future goals.</p><h3>You are known as a founding father of mathematical physics. Can you tell us more about the field and how you helped establish it?</h3><p>Modern mathematical physics attempts to establish areas of theoretical physics under the ground rules of rigorous mathematics. There are times that this provides new insights to theoretical physics but, in any event, as my mentor the late Arthur Wightman [Princeton] taught me, intellectual honesty requires the community to understand basic physics at this level of precision.</p><p>I regard the founders of mathematical physics to be a generation before me, notably Wightman, Tosio Kato [UC Berkeley], and David Ruelle [Institut des Hautes Études Scientifiques]. I advanced the field in several ways. My books with Mike Reed served as an introduction to the field and lured a generation of talented people to the area. And I was fortunate enough to be one of the first researchers in a number of areas that allowed me to write seminal papers still widely cited today.</p><h3>When you look back at your decades-spanning career, what do you feel most proud of?</h3><p>The <em>Notices</em> article lists a number of accomplishments and I hesitate to single out only a few, but I'd mention my work on eigenvalue perturbation theory; the work with Francesco Guerra [University of Rome] and Lon Rosen [University of British Columbia] using statistical mechanical methods in Euclidean Quantum Field Theory; my work with Elliott Lieb [Princeton] on Thomas Fermi theory; the work with Jürg Frölich [ETH Zurich], Tom Spencer [Institute for Advanced Study], Freeman Dyson [Institute for Advanced Study], and Lieb on continuous symmetry breaking in statistical mechanics; and my foundational work in ergodic Schoedinger operators and on singular continuous spectrum. Finally, in the past 15 years, I've introduced important new ideas into the spectral theory of orthogonal polynomials.</p><p>I'm also proud of my books and the impact they've had. Perhaps most of all, I am proud of my impact on students, postdocs, and collaborators. There is a special thrill to giving a boost to the careers of young people.</p><h3>The<em> New York Times</em> wrote an article about you winning a math contest when you were 16. Can you tell us about the contest? And did you know then that you wanted to be a lifelong mathematician?</h3><p>This was the exam sponsored by the Mathematical Association of America. Before my year, there were only three perfect scores. I had only one problem wrong but when I was told which one it was, I was dumfounded because I was sure I had it right. The issue was that I interpreted it in a different way from how the exam writers intended it. I appealed and made the case successfully that the wording was ambiguous and thus achieved the second perfect score that year. It was the drama of the appeal that caught the eye of the <em>Times</em>. The actual problem I appealed was part of the article and my brother, Rick, included the text of the article in his contribution to the page of "Barry Stories" put together from my <a href="http://www.math.caltech.edu/SimonFest/stories.html">60th birthday conference</a>.</p><p>At that time, I hardly wanted to be a mathematician. The teacher who had the biggest influence on me in high school was <a href="https://www.youtube.com/watch?v=O_TaUeCLaUU">Sam Marantz</a>, a physics teacher. So while I knew I liked mathematics, I wanted to be a physicist and both my BA, from Harvard, and PhD, from Princeton, are in physics. I knew I wanted to combine my two interests and went to Princeton to study, where I learned that Wightman had done exactly that. For various reasons, all the courses I taught at Caltech were in math, but at Princeton I taught in both departments including the basic undergraduate quantum mechanics. My research in the recent past has focused more on pure math topics so I am perhaps more mathematician than physicist now, but I've always had a joint appointment and been proud of it.</p><h3>Can you help explain to non-mathematicians the importance of math, and specifically of your areas of research?</h3><p>Galileo once said that "the book of nature is written in the language of mathematics." So one importance of mathematics is its central role in all areas of modern science. The remarkable fact is that most mathematicians are not motivated by the applications but by the internal beauty and fascination of the subject. But despite their motivation, what they discover has significant applications in the outside world. For example, something as esoteric as the study of prime numbers is the basis of the encryption you use whenever you connect to your bank's website!</p><h3>In the American Mathematical Society feature story about your career, several colleagues mention how fast you are at writing papers. Can you share your trick?</h3><p>No trick to convey. I've been blessed with a mind that thinks logically and manages to see deep connections so that I am able to write clearly on my first draft. Unlike many scientists I know, I enjoy writing, which makes the process quicker. And I've always worked hard.</p><h3>One of the pictures in the <a href="http://www.ams.org/publications/journals/notices/201607/rnoti-p740.pdf">Notices feature story</a> shows you wearing boxing gloves with Greek letters on them. Is there a story behind this?</h3><p>In about 1995, Caltech decided to redesign its required curriculum. I was the mathematician on the committee chaired by Dave Stevenson, a professor of planetary science. One of things we changed was to decrease the basic calculus classes to one quarter, and I was persuaded to teach the new Math 1a, which I did for six years.</p><p>This course was as much to introduce students to rigorous proof, which many of them hadn't seen in high school, and the centerpiece of that was the use of what are called ε-δ proofs. I was fond of saying "ε and δ are a calculus student's finest weapons." One year, I had an especially lively group of students and, on the last day, when I walked into the auditorium where the class was given there was a pair of boxing gloves on my desk, one with an ε and one with a δ. I've received lots of positive comments from other mathematicians about that picture.</p><p>I have a story about Math 1a that I especially like. I was aware that many students taking that class who taken several years of calculus were offended that we felt they didn't really understand the subject without rigorous proof and they found the course difficult because the approach we thought was essential for them was so foreign to their experience. One day, I was stopped by a student who introduced himself and said: "I'm a senior now and I took Math 1a from you as a freshman. At the time I thought it was the worst course I'd ever taken. I now think it is the best course."</p><h3>How did you get involved in writing Windows manuals?</h3><p>In the mid-1980s as PCs were first coming in, IBM gave a grant to Caltech that let math faculty get IBM XTs. My colleague Rick Wilson, professor of mathematics, emeritus, and I became fascinated with the guts of the machines and developed some expertise in the architecture underlying DOS [disk operating system]. Rick became a first-class assembly-language programmer. This was before there was an active Internet but there was a bulletin board called CompuServe where I met lots of nerds.</p><p>We suddenly found ourselves as shareware authors. We got involved in a CompuServe group trying to set up an API [application programming interface] for resident programs to avoid getting in each other's way. One of the other people involved had done some writing for <em>PC Magazine</em>, at the time the leading computing magazine, and he suggested that I go see them to talk about this API. I did, and by coincidence, one of the editors I met with asked if I knew any mathematics! He was looking for a reviewer for a new program called Mathcad. Soon after, I was the standard reviewer of mathematical software for <em>PC Magazine</em> and many other programs like Visual BASIC.</p><p>Another person, Woody Leonard, I met through CompuServe who knew of my expertise from this writing suggested we write a book about the soon to be released Windows 95. I wouldn't call it a manual—it wasn't so much a detailed how-to as a book to give the reader background for understanding what they are doing. In an era when <em>DOS for Dummies</em> was a bestseller, one wag dubbed our book "Windows for Dummies Not."</p><p>In reference to the phrase popularized during the first gulf war, "mother of all battles," we called our book, <em>The Mother of All Windows Books</em>. We had a version with one of the first CD ROMs of software sold with the book and dubbed that version CD Mom. The books had a fair amount of corny humor and were a lot of fun to write. In all, we published four books together and I had a solo book on Outlook.</p><p>I was struck by the following: A typical math book sells 500–1500 copies. Reed and I were proud of the fact that by 1995, 20 years after it was published, we'd sold almost 15,000 copies of volume one. Well, <em>The Mother of All Windows Books</em> sold 15,000 copies on its first day (and about 50,000 total).</p><h3>You have mentored more than <a href="http://www.genealogy.ams.org/id.php?id=11905">30 graduate students</a>. What is your favorite part of mentoring?</h3><p>When a student starts working for me, one of the first things I give them is a warm-up problem. I get to share in the excitement they feel the first time they realize they can make their own original contributions. And for those that go on in academia, it is always a joy when they get tenure.</p><h3>What is coming up next for you and your research?</h3><p>I officially retired this past June 30. One nice thing I can do without official responsibilities is spend more time in Israel where the majority of my kids and grandkids live. But I expect to continue working. The English mathematician G. H. Hardy once remarked that "young men should prove theorems, old men should write books." While I violated that by publishing the first volume of Reed-Simon at age 26, it does make sense. My five volume, 3,200-page <em>Comprehensive Course in Analysis</em> was published last December, and I've got three book projects in planning stages.</p><p>I also have various research projects under way. Two that excite me are a joint project with two Israeli colleagues that explores some connections between spectral theory and probability theory, and a joint project with two former postdocs that will follow through on our breakthrough last year settling a 40-year-old conjecture in the theory of Chebyshev polynomials. I've also been polishing my website and started an <a href="http://www.math.caltech.edu/simon/selecta.html">online "Selecta</a>," which will include biographical notes and notes on some sets of my papers.</p></div></div></div>Wed, 10 Aug 2016 18:21:47 +0000wclavin51679 at http://www.caltech.eduPhysics and Mathematics Professors Named Simons Investigators
http://www.caltech.edu/news/physics-and-mathematics-professors-named-simons-investigators-51251
<div class="field field-name-news-writer field-type-ds field-label-inline clearfix"><div class="field-label">News Writer: </div><div class="field-items"><div class="field-item even">Lori Dajose</div></div></div><div class="field field-name-field-images field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><div class="ds-1col file file-image file-image-jpeg view-mode-full_grid_9 clearfix ">
<img src="http://s3-us-west-1.amazonaws.com/www-prod-storage.cloud.caltech.edu/styles/article_photo/s3/SimonsInvestigators-2016.jpg?itok=h99I9I_0" alt="" /><div class="field field-name-field-caption field-type-text field-label-hidden"><div class="field-items"><div class="field-item even">Anton Kapustin and Vladimir Markovic.</div></div></div><div class="field field-name-credit-sane-label field-type-ds field-label-hidden"><div class="field-items"><div class="field-item even">Credit: Caltech</div></div></div></div></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><a href="http://pma.caltech.edu/content/anton-n-kapustin">Anton Kapustin</a> (PhD '97), the Earle C. Anthony Professor of Theoretical Physics and Mathematics, and <a href="http://pma.caltech.edu/content/vladimir-markovic">Vladimir Markovic</a>, the John D. MacArthur Professor of Mathematics, have been named Simons Investigators. These appointments are given annually to "support outstanding scientists in their most productive years, when they are establishing creative new research directions," according to the Simons Foundation, which grants the awards. Investigators receive $100,000 annually for five years.</p><p>Kapustin studies mathematical physics, particularly dualities—relations between two superficially very different models of quantum fields, which help scientists study the behavior of strongly interacting elementary particles.</p><p>"Recently, my research has focused on the classification of exotic states of quantum matter," Kapustin says. "Such states have been proposed to be useful for building a quantum computer. Surprisingly, it turns out that the classification problem can be attacked using methods of topology, a branch of geometry which studies properties of geometric shapes which are not affected by continuous deformations."</p><p>Markovic focuses on various aspects of low-dimensional geometry, which is the study of shapes and forms that certain topological spaces can take.</p><p>"The main themes of my research are manifolds—a particular kind of topological space—and more generally groups, and their geometric, topological and dynamical properties," says Markovic. "Beside this, I have been very interested in certain partial differential equations and geometric flows including harmonic mappings and heat flows."</p><p>"I am excited to be named Simons Investigator," he adds. "This award will enable me to have more time to focus on my research, learn new fields, and test and develop my mathematical ideas."</p></div></div></div><div class="field field-name-field-pr-links field-type-link-field field-label-above"><div class="field-label">Related Links: </div><div class="field-items"><div class="field-item even"><a href="http://www.caltech.edu/news/two-caltech-professors-named-simons-investigators-47457" class="pr-link">Two Caltech Professors Named Simons Investigators</a></div></div></div>Thu, 07 Jul 2016 04:18:44 +0000ldajose51251 at http://www.caltech.eduShou Receives Fellowship for Graduate Studies in Germany
http://www.caltech.edu/news/shou-receives-fellowship-graduate-studies-germany-50934
<div class="field field-name-news-writer field-type-ds field-label-inline clearfix"><div class="field-label">News Writer: </div><div class="field-items"><div class="field-item even">Lori Dajose</div></div></div><div class="field field-name-field-images field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><div class="ds-1col file file-image file-image-jpeg view-mode-full_grid_9 clearfix ">
<img src="http://s3-us-west-1.amazonaws.com/www-prod-storage.cloud.caltech.edu/styles/article_photo/s3/LShou-DAAD-NEWS-WEB.jpg?itok=idCH5amT" alt="" /><div class="field field-name-field-caption field-type-text field-label-hidden"><div class="field-items"><div class="field-item even">Laura Shou</div></div></div><div class="field field-name-credit-sane-label field-type-ds field-label-hidden"><div class="field-items"><div class="field-item even">Credit: Courtesy of L. Shou</div></div></div></div></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Laura Shou, a senior in mathematics, has received a Graduate Study Scholarship from the German Academic Exchange Service (DAAD) to pursue a master's degree in Germany. She will spend one year at the Ludwig-Maximilians-Universität München and the Technische Universität München, studying in the theoretical and mathematical physics (TMP) program.</p><p>The DAAD is the German national agency for the support of international academic cooperation. The organization aims to promote international academic relations and cooperation by offering mobility programs for students, faculty, and administrators and others in the higher education realm. The Graduate Study Scholarship supports highly qualified American and Canadian students with an opportunity to conduct independent research or complete a full master's degree in Germany. Master's scholarships are granted for 12 months and are eligible for up to a one-year extension in the case of two-year master's programs. Recipients receive a living stipend, health insurance, educational costs, and travel.</p><p>"As a math major, I was especially interested in the TMP course because of its focus on the interplay between theoretical physics and mathematics," Shou says. "I would like to use mathematical rigor and analysis to work on problems motivated by physics. The TMP course at the LMU/TUM is one of the few programs focused specifically on mathematical physics. There are many people doing research in mathematical physics there, and the program also regularly offers mathematically rigorous physics classes."</p><p>At Caltech, Shou has participated in the Summer Undergraduate Research Fellowship (SURF) program three times, conducting research with Professor of Mathematics Yi Ni on knot theory and topology, with former postdoctoral fellow Chris Marx (PhD '12) on mathematical physics, and with Professor of Mathematics Nets Katz on analysis. She was the president of the Dance Dance Revolution Club and a member of the Caltech NERF Club and the Caltech Math Club.</p><p>Following her year in Germany, Shou will begin the mathematics PhD program at Princeton.</p></div></div></div>Tue, 07 Jun 2016 18:04:59 +0000ldajose50934 at http://www.caltech.eduOoguri Receives Chunichi Award
http://www.caltech.edu/news/ooguri-receives-chunichi-award-50716
<div class="field field-name-news-writer field-type-ds field-label-inline clearfix"><div class="field-label">News Writer: </div><div class="field-items"><div class="field-item even">Robert Perkins</div></div></div><div class="field field-name-field-images field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><div class="ds-1col file file-image file-image-jpeg view-mode-full_grid_9 clearfix ">
<img src="http://s3-us-west-1.amazonaws.com/www-prod-storage.cloud.caltech.edu/styles/article_photo/s3/Ooguri_Hirosi.jpeg?itok=lNXz9oTK" alt="" /><div class="field field-name-field-caption field-type-text field-label-hidden"><div class="field-items"><div class="field-item even">Hirosi Ooguri</div></div></div><div class="field field-name-credit-sane-label field-type-ds field-label-hidden"><div class="field-items"><div class="field-item even">Credit: Bill Youngblood for Caltech</div></div></div></div></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><a href="https://www.pma.caltech.edu/content/hiroshi-hirosi-ooguri-oguri">Hirosi Ooguri</a>, the Fred Kavli Professor of Theoretical Physics and Mathematics and founding director of the Walter Burke Institute for Theoretical Physics, will be the 2016 recipient of the Chunichi Cultural Award. Founded in 1947 by Japanese newspaper Chunichi Shimbun to commemorate the enacting of the Japanese constitution, the award celebrates individuals or organizations who have made significant contributions to the arts, humanities, and natural or social sciences. Other awardees this year include physicist and 2015 Nobel Laureate Takaaki Kajita, poet Toru Kitagawa, and biologist Ikue Mori, each of whom will receive the 2 million yen ($20,000) prize. Previous recipients include six other Nobel laureates and one Fields medalist.</p><p>The prize honors Ooguri for the "development of innovative methods of modern mathematics in high energy theory," according to the prize citation. His research focuses on creating new theoretical tools in quantum field theory and superstring theory, which may ultimately lead to a unified theory of the forces and matter in nature. He is particularly renowned for his work on topological string theory, which has had broad applications ranging from black hole physics to algebraic geometry and knot theory in mathematics.</p><p>This April, Ooguri was elected as a fellow of the <a href="/news/american-academy-arts-and-sciences-elects-two-caltech-50547">American Academy of Arts and Sciences</a>. He is also the recipient of the <a href="http://www.caltech.edu/content/physicist-hirosi-ooguri-awarded-novel-research-black-holes">Leonard Eisenbud Prize for Mathematics and Physics</a> from the American Mathematical Society, the Nishina Memorial Prize, the Humboldt Research Award, the <a href="/news/two-caltech-professors-named-simons-investigators-47457">Simons Investigator Award</a>, and is a <a href="http://www.caltech.edu/content/caltech-faculty-named-ams-fellows">fellow of the American Mathematical Society</a>. He also received Japan's <a href="/news/superstring-theorist-honored-science-writing-prize-43479">Kodansha Prize for Science Books</a> for his popular Introduction to Superstring Theory in 2014.</p><p>Ooguri will receive the Chunichi Award at a ceremony to be held in Japan on June 3.</p></div></div></div>Wed, 11 May 2016 19:14:51 +0000abenter50716 at http://www.caltech.eduTom M. Apostol, 1923–2016
http://www.caltech.edu/news/tom-m-apostol-1923-2016-50698
<div class="field field-name-news-writer field-type-ds field-label-inline clearfix"><div class="field-label">News Writer: </div><div class="field-items"><div class="field-item even">Lori Dajose</div></div></div><div class="field field-name-field-images field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><div class="ds-1col file file-image file-image-jpeg view-mode-full_grid_9 clearfix ">
<img src="http://s3-us-west-1.amazonaws.com/www-prod-storage.cloud.caltech.edu/styles/article_photo/s3/Apostol_Tom_2013.jpg?itok=nPx20o1A" alt="" /></div></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Tom M. Apostol, professor of mathematics, emeritus, passed away on May 8, 2016. He was 92.</p><p>Apostol was born in Helper, Utah, on August 20, 1923. He received his bachelor of science in chemical engineering in 1944 and a master's degree in mathematics in 1946, both from the University of Washington, Seattle. In 1948, he received his PhD in mathematics from the University of California, Berkeley. In 1950, he arrived at Caltech as an assistant professor; he was named associate professor in 1956, professor in 1962, and professor emeritus in 1992.</p><p>Apostol was the author of several influential textbooks. For more than five decades, undergraduate introductory mathematics courses at Caltech have used Apostol's two-volume text, "<em>Calculus</em>," which is often referred to by Caltech students as "Tommy 1" and "Tommy 2." These volumes, as well as many of his other textbooks in mathematical analysis and analytic number theory, have been translated into Greek, Italian, Spanish, Farsi, and Portuguese. Apostol also worked with a Caltech team that produced <em>The Mechanical Universe . . . and Beyond</em>, a 52-episode video lecture series based on <em>The Mechanical Universe: Introduction to Heat and Mechanics</em> and <em>Beyond the Mechanical Universe: From Electricity to Modern Physics</em>, the introductory physics textbooks that Apostol coauthored.</p><p>Apostol later was the creator, director, and producer of <em>Project MATHEMATICS!</em>, a series of award-winning computer animated videos that explore basic topics in high school mathematics such as the Pythagorean Theorem, scaling, sines and cosines, and the history of mathematics. The nine videos, which are still available for order through the Caltech bookstore, are estimated to have been viewed by 10 million people worldwide.</p><p>"Tom was a great scholar and a beloved teacher and mentor. Generations of Caltech students benefited from his passion and dedication," says Fiona Harrison, the Benjamin M. Rosen Professor of Physics and the Kent and Joyce Kresa Leadership Chair of the Division of Physics, Mathematics and Astronomy.</p><p>"Tom Apostol was a great human being and mathematician, and an inspiration to many. He was very famous the world over for his immense talent for mathematical exposition," says Dinakar Ramakrishnan, Caltech's Taussky-Todd-Lonergan Professor of Mathematics and executive officer for mathematics. "His books set a high standard but remained accessible to many, as decades of Caltech undergraduates would testify, while his videos have stimulated high school students to pursue the beauty of mathematics."</p><p>In 1982, Apostol received an award for teaching excellence from the Associated Students of the California Institute of Technology (ASCIT). In 1998 the Mathematical Association of America (MAA) awarded him the annual Trevor Evans Award, presented to authors of an exceptional article that is accessible to undergraduates, for his piece entitled "What Is the Most Surprising Result in Mathematics?" (Answer: the prime number theorem). In 2005, 2008, and 2010, he was awarded MAA's Lester R. Ford Award, given to recognize authors of articles of expository excellence. He additionally served as a visiting lecturer for the MAA and as a member of hits Board of Governors.</p><p>He was <a href="http://www.caltech.edu/news/caltech-faculty-named-ams-fellows-37310">named</a> as one of the inaugural class of Fellows of the American Mathematical Society in 2012.</p><p>Apostol, who was an American of Greek descent, spent four months in Greece as a visiting professor of mathematics at the University of Patras in 1978. Additionally, he spent eight years as a member of an Electoral Committee selecting faculty for the University of Crete. In 2001, he was elected as a corresponding member of the Academy of Athens.</p><p>Apostol is survived by his wife, Jane Apostol; his stepson, Stephen Goddard; his sisters, Kay Navrides and Betsie Strouzas; and his brother, John Apostol.</p><p>A <a href="/content/memorial-service-reception-tom-apostol">memorial service</a> is being planned for later this year.</p></div></div></div><div class="field field-name-field-pr-links field-type-link-field field-label-above"><div class="field-label">Related Links: </div><div class="field-items"><div class="field-item even"><a href="http://www.caltech.edu/content/memorial-service-reception-tom-apostol" class="pr-link">Memorial Service on 10/25/16</a></div></div></div>Mon, 09 May 2016 22:04:33 +0000abenter50698 at http://www.caltech.eduSimon Receives Lifetime Achievement Award
http://www.caltech.edu/news/simon-receives-lifetime-achievement-award-48745
<div class="field field-name-news-writer field-type-ds field-label-inline clearfix"><div class="field-label">News Writer: </div><div class="field-items"><div class="field-item even">Kathy Svitil</div></div></div><div class="field field-name-field-images field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><div class="ds-1col file file-image file-image-jpeg view-mode-full_grid_9 clearfix ">
<img src="http://s3-us-west-1.amazonaws.com/www-prod-storage.cloud.caltech.edu/styles/article_photo/s3/BSimon_059-AS-NEWS-WEB%5B1%5D.jpg?itok=zUgFFThf" alt="" /><div class="field field-name-field-caption field-type-text field-label-hidden"><div class="field-items"><div class="field-item even">Barry Simon</div></div></div><div class="field field-name-credit-sane-label field-type-ds field-label-hidden"><div class="field-items"><div class="field-item even">Credit: Bob Paz</div></div></div></div></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Barry M. Simon, the International Business Machines (IBM) Professor of Mathematics and Theoretical Physics at Caltech, has been awarded the 2016 Leroy Steele Prize for Lifetime Achievement of the American Mathematical Society (AMS) for his "tremendous impact on the education and research of a whole generation of mathematical scientists through his significant research achievements, highly influential books, and mentoring of graduate students and postdocs," according to the prize citation.</p><p>In conferring the award, the AMS noted Simon's "career of exceptional achievement," which includes the publication of 333 papers and 16 books. Simon was specifically recognized for proving a number of fundamental results in statistical mechanics and for contributing to the construction of quantum fields in two space‐time dimensions—topics that, the AMS notes, have "grown into major industries"—as well as for his "definitive results" on the general theory of Schrödinger operators, work that is crucial to an understanding of quantum mechanics and that has led to diverse applications, from probability theory to theoretical physics. He has also made fundamental contributions to the theory of orthogonal polynomials and their asymptotics.</p><p>"Barry Simon is a powerhouse in mathematical physics and has had an outstanding career which this award attests to," says Vladimir Markovic, the John D. MacArthur Professor of Mathematics. "Caltech is lucky to have him."</p><p>"Barry is a driving force in mathematics at Caltech and has had enormous influence as a scholar, a teacher, and a mentor," says Fiona Harrison, the Benjamin M. Rosen Professor of Physics and holder of the Kent and Joyce Kresa Leadership Chair for the Division of Physics, Mathematics and Astronomy.</p><p>Simon spoke at the International Congress of Mathematics in 1974 and has since given almost every prestigious lecture available in mathematics and physics. He was named a fellow of the American Academy of Arts and Sciences in 2005, and was among the inaugural class of AMS fellows in 2012. In 2015, Simon was awarded the <a href="http://www.caltech.edu/news/simon-wins-international-mathematics-prize-46655">International János Bolyai Prize of Mathematics</a> by the Hungarian Academy of Sciences, given every five years to honor internationally outstanding works in mathematics, and in 2012, he was given <a href="http://www.caltech.edu/news/caltech-professor-barry-simon-wins-henri-poincare-prize-23607">the Henri Poincaré Prize</a> by the International Association of Mathematical Physics. The prize is awarded every three years in recognition of outstanding contributions in mathematical physics and accomplishments leading to novel developments in the field.</p><p>Simon received his AB from Harvard College in 1966 and his doctorate in physics from Princeton University in 1970. He held a joint appointment in the mathematics and physics departments at Princeton for the next decade. He first arrived at Caltech as a Sherman Fairchild Distinguished Visiting Scholar in 1980 and joined the faculty permanently in 1981. He became the IBM Professor in 1984.</p></div></div></div>Thu, 12 Nov 2015 20:25:39 +0000schabner48745 at http://www.caltech.eduKatz Receives Prestigious Award for Mathematics
http://www.caltech.edu/news/katz-receives-prestigious-award-mathematics-47197
<div class="field field-name-news-writer field-type-ds field-label-inline clearfix"><div class="field-label">News Writer: </div><div class="field-items"><div class="field-item even">Lori Dajose</div></div></div><div class="field field-name-field-images field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><div class="ds-1col file file-image file-image-jpeg view-mode-full_grid_9 clearfix ">
<img src="http://s3-us-west-1.amazonaws.com/www-prod-storage.cloud.caltech.edu/styles/article_photo/s3/NKatz_7578-NEWS-WEB%5B1%5D.jpg?itok=KRBzC2lo" alt="" /></div></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Caltech professor of mathematics <a href="http://pma.caltech.edu/content/nets-h-katz">Nets Katz</a> has received the 2015 Clay Research Award from the Clay Mathematics Institute. The award was given jointly to Katz and his collaborator, MIT professor of mathematics Larry Guth, for their solution of the Erdős distance problem and for "other joint and separate contributions to combinatorial incidence geometry."</p><p>Combinatorial incidence geometry is the study of possible configurations, or arrangements, between geometric objects such as points or lines. One basic open problem in this field is the Erdős distance problem, for which Katz received the Clay award. The Erdős distance problem examines a set "large" number of points distributed in various arrangements in a two-dimensional plane. In some configurations, like a lattice or grid, the points are evenly spaced. In others, as in a random distribution of points, the spacing between points is varied. The problem asks how many times the same distance can occur between these points, and what is the minimum number of distinct distances possible between these points.</p><p>In 2010, Guth and Katz proved that the minimum number of unique distances between <em>n</em> points, regardless of their spatial configuration, is the number of points <em>n</em> divided by the logarithm of <em>n</em>: <em>n/log(n).</em></p><p>Katz's work on the Erdős problem is an example of his larger research interest in coincidences. By demonstrating that there is a minimum number of unique distances between points, even when in a uniform arrangement like a lattice, Katz showed that coincidences—such as many sets of points having the same distance between them—can occur only a limited number of times.</p><p>Katz received his PhD from the University of Pennsylvania and was a professor of mathematics at Indiana University Bloomington before joining Caltech's faculty in 2013. He was named a Guggenheim Fellow in 2012. Previously, his research was in harmonic analysis, a field concerned with representing functions as superpositions of basic oscillating mathematical "waves."</p><p>The Clay Mathematics Institute is a private foundation "dedicated to increasing and disseminating mathematical knowledge." Given annually, the Clay Research Award recognizes contemporary mathematical breakthroughs.</p></div></div></div>Thu, 02 Jul 2015 14:03:10 +0000schabner47197 at http://www.caltech.eduPrime Numbers, Quantum Fields, and Donuts: An Interview with Xinwen Zhu
http://www.caltech.edu/news/prime-numbers-quantum-fields-and-donuts-interview-xinwen-zhu-45000
<div class="field field-name-news-writer field-type-ds field-label-inline clearfix"><div class="field-label">News Writer: </div><div class="field-items"><div class="field-item even">Jessica Stoller-Conrad</div></div></div><div class="field field-name-field-images field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><div class="ds-1col file file-image file-image-jpeg view-mode-full_grid_9 clearfix ">
<img src="http://s3-us-west-1.amazonaws.com/www-prod-storage.cloud.caltech.edu/styles/article_photo/s3/Xinwen_Zhu_6301-CC-NEWS-WEB.jpg?itok=z0gPGPZQ" alt="" /><div class="field field-name-field-caption field-type-text field-label-hidden"><div class="field-items"><div class="field-item even">Xinwen Zhu, associate professor of mathematics</div></div></div><div class="field field-name-credit-sane-label field-type-ds field-label-hidden"><div class="field-items"><div class="field-item even">Credit: Lance Hayashida/Caltech Office of Strategic Communications</div></div></div></div></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>In 1994, British mathematician Andrew Wiles successfully developed a proof for Fermat's last theorem—a proof that was once partially scribbled in a book margin by 17th-century mathematician Pierre de Fermat but subsequently eluded even the best minds for more than 300 years. Wiles's hard-won success came after digging into a vast web of mathematical conjectures called the Langlands program. The Langlands program, proposed by Canadian mathematician Robert Phelan Langlands in the 1960s, acts as a bridge between seemingly unrelated disciplines in mathematics, such as number theory—the study of prime numbers and other integers—and more visual disciplines such as geometry. </em></p><p><em>However, to get the ideas he needed for his history-making proof, Wiles only scratched the surface of the Langlands program. Now Xinwen Zhu, an associate professor of mathematics at Caltech, is digging deeper, looking for further applications of this so-called unifying theory of mathematics—and how it can be used to relate number theory to disciplines ranging from quantum physics to the study of donut-shaped geometric surfaces. </em></p><p><em>Zhu came to Caltech from Northwestern University in September. Originally from Sichuan, China, he received his bachelor's degree from Peking University in 2004 and his doctorate from UC Berkeley in 2009. </em></p><p><em>He recently spoke with us about his work, the average day of a mathematician, and his new life in California.</em></p><p> </p><p><strong>Can you give us a general description of your research?</strong></p><p>My work is in mathematics, related to what's called Langlands program. It's one of the most intrinsic parts of modern mathematics. It relates number theory—specifically the study of prime numbers like 2, 3, 5, 7, and so on—to topics as diverse as geometry and quantum physics.</p><p> </p><p><strong>Why do you want to connect number theory to geometry and quantum physics?</strong></p><p>Compared to number theory, geometry is more intuitive. You can see a shape and understand the mathematics that are involved in making that shape. Number theory is just numbers—in this case, just prime numbers. But if we combine the two, then instead of thinking about the primes as numbers, we can visualize them as points on a Riemann surface—a geometric surface kind of represented by the shape of a donut—and the points can move continuously. Think of an ant on a donut—the ant can move freely on the surface. This means that a point on the donut has some intrinsic connections with the points nearby. In number theory it is very difficult to say that any relationship exists between two primes, say 5 and 7, because there are no other primes between them, but there <em>are</em> points between any two points. It is still very difficult to envision, but it gives us a more intuitive way to think about the numbers.</p><p>We want to understand certain things about prime numbers—for example, the distribution of primes among all natural numbers. But that's difficult when you're working with just the numbers; there are very few rules, and everything is unpredictable. The geometric theory here adds a sort of geometric intuition, and the application to quantum field theory adds a physical intuition. Thinking about the numbers and equations in these contexts can give us new insights. I really don't understand exactly how physicists think, but physicists are very smart because they have this intuition. It's just sort of their nature. They can always make the right guess or conjecture. So our hope is to use this sort of intuition to come back to understand what happens in number theory.</p><p> </p><p><strong>Mathematicians don't really have lab spaces or equipment for experiments, so what does a day at the office look like for you? </strong></p><p>Usually I just think. And unfortunately, it's usually without any result, but that's fine. Then, after months and months, one day there is an idea. And that's how we do math. We read papers sometimes to keep our eyes on what the newest development is, but it's probably not as important as it is for other disciplines. Of course, one can also get new ideas and stimulation from reading, so we keep our eyes on what's going on this week.</p><p> </p><p><strong>A two-part question: How did you get first get interested in math in general, and how did you get interested in this particular field that you're in now?</strong></p><p>My interest in math began when I was a child. People can usually count numbers at a pretty early age, but I was interested in math and could do calculations a little bit quicker and a bit younger than others. It came naturally to me. Also, my grandfather was a chemist and physicist, and he always emphasized the importance of math.<br /><br />But to be honest, I didn't really know anything about this aspect of the Langlands program until I was in graduate school at Berkeley. My adviser, Edward Frenkel, brought me into this area.</p><p> </p><p><strong>What are you most excited about in terms of your move to Caltech?</strong></p><p>I think this is, of course, a fantastic place. The undergraduates here are very strong, and the graduate school is also very good, so I'm also very excited to work with all of those young people. Also, the physics department here is very good, and as I said, quantum field theory has recently provided promising new ways to think about these old problems from number theory. Caltech professors Anton Kapustin and Sergei Gukov have played central roles in revealing these connections between physics and the Langlands problem.</p><p> </p><p><strong>Is there anything else that you're looking forward to about living in Pasadena?</strong></p><p>I'm from Sichuan [province in China], and one thing that I miss is the food. It's hot and spicy, and now it's also kind of popular in the U.S. And there are very good Szechwan restaurants in the San Gabriel Valley. Actually, maybe the best Szechwan food in the U.S. is right here.</p><p> </p><p><strong>Aside from your research and professional interests, do you have any other hobbies?</strong></p><p>Yes, I've been playing the game Go for more than 20 years. It's a board game that is kind of like chess. It's interesting, and it's very complicated. Many years ago, you'd play with a game set and one opponent, but now you can also play it online. And that's good for me because after moving from place to place, it's hard to consistently find someone to play with.</p></div></div></div>Fri, 05 Dec 2014 22:43:48 +0000jsconrad45000 at http://www.caltech.edu