News from The Division of Physics, Mathematics and Astronomyhttps://pma.divisions.caltech.edu/news/rssen-usWed, 02 Dec 2020 11:39:21 +0000The Warrior-Scholar Project Brings Caltech STEM Education to Soldiers and Veteranshttps://divisions.caltech.edu/sitenewspage-index/warrior-scholar-project-caltech-stem-soldiers-veterans<p>Soldiers are no strangers to boot camp, but those who participate in the <a href="https://www.warrior-scholar.org/">Warrior-Scholar Project</a> (WSP) trade drill sergeants and physical training for world-class researchers and an intensive introduction to education in science and technology. This summer, 17 active-duty service members and veterans completed a weeklong academic boot camp featuring scientists from Caltech and the Jet Propulsion Laboratory, which the Institute manages for NASA.</p><p>"Having the chance to go to Caltech made me experience the same sort of energized feeling so many others have used to catapult themselves into higher education," says William Doran, a U.S. Air Force veteran who completed the summer 2020 WSP session at Caltech.</p><p>The Warrior-Scholar Project began in 2012 as a way to support enlisted military members and veterans who sought to make the leap from the U.S. Armed Forces to top-tier colleges and universities. Typically, participants stay on campus for their one- or two-week academic sessions. This summer, Caltech's first year as a participant, the program had to adapt to the COVID-19 pandemic, and, just like Caltech's traditional students, the WSP students made the adjustment to remote learning. The Caltech/JPL program gave the military veterans access to instructors such as Lee Rosenthal, a graduate student in astrophysics; Renee Ludlam, a postdoctoral scholar in physics; and Jamie Rollins, a scientist with the Laser Interferometer Gravitational-wave Observatory (<a href="https://www.ligo.caltech.edu/">LIGO</a>).</p><p>Rollins's physics talk laid out principles of two-dimensional motion and fundamental equations such as those that govern force and velocity, then added in acceleration and gravity to allow the students to calculate how far a ball thrown with a certain angle and force will travel before it lands. Rollins says the most important component was the introduction to principles of mathematics and algebra and the critical-thinking skills needed to solve problems in college-level physics courses. "The people who participate in the program come from backgrounds where they haven't had a lot of formal exposure to this material," Rollins says, "so I really tried to encourage people to ask questions, and I got some good ones throughout the lectures and also afterwards. It was a good group of people who are very motivated."</p><p>Ludlam helped to teach the group the basics of coding in the Python language. She then led a research project on idealized rocket motion that tasked students with applying material from their physics lectures to a simulated launch, an especially fitting topic since the Warrior-Scholar Project occurred during the week of the Mars Perseverance rover launch. "It was such an incredible experience to watch the students learn, problem solve, and grow during such a short period of time," she says. "I showed them videos of rocket launches on the first day, and, by the end of the week, they had set up their own rocket launch to send a rover to Mars."</p><p>For <a href="https://science.jpl.nasa.gov/people/Moustakas/">Leonidas Moustakas</a>, astrophysicist and section manager at JPL, the importance of the Warrior-Scholar Project lies not only in the material but also in the introduction it offers to the rigor and culture of STEM, which he believes is invaluable for veterans who want to move from the military into higher education. He gave a cosmology presentation that walked WSP students through what he calls the "juicy parts of the science": the formation of the universe, the quest to understand dark matter and energy, and how math provides a framework to simplify physics and create models to understand the cosmos. Moustakas also personalized his lecture by sharing the path through multiple countries and universities that him to become a scientist at JPL.</p><p>Moustakas initially worried about his ability to connect over Zoom with students, especially those not accustomed to remote learning. Those fears proved to be unfounded as the WSP students peppered him with questions about cosmology and JPL. "It was clear there were three or four people that were just geeking out to the max and others who had never seen this before but were asking great questions from a pure curiosity point of view," Moustakas says.</p><p>Rollins and Moustakas both became involved in the first year of WSP at Caltech through recommendations from colleagues at other universities that had participated in the program, and both said they were gratified to be able to collaborate with members of the military community. Similarly, Air Force veteran Doran, who says he struggled in school previously, found the chance to connect with Caltech and JPL researchers was invaluable.</p><p>"The eagerness of WSP instructors to listen to us and explain how they navigated their transition has made my own difficult switch to college seem far less daunting," he says. "Similarly, the willingness of Caltech researchers to instruct us over Zoom reinforced to me that my education is important, so much so that they and JPL scientists are taking time out of their day to be available to teach us."</p>https://divisions.caltech.edu/sitenewspage-index/warrior-scholar-project-caltech-stem-soldiers-veteransUrmila Mahadev Awarded Maryam Mirzakhani New Frontiers Prizehttps://divisions.caltech.edu/sitenewspage-index/urmila-mahadev-awarded-maryam-mirzakhani-new-frontiers-prize<p><a href="https://eas.caltech.edu/people/umahadev">Urmila Mahadev</a>, assistant professor of computing and mathematical sciences at Caltech, is one of three recipients of the 2021 Maryam Mirzakhani New Frontiers Prize, sponsored by the Breakthrough Prize Foundation. The Maryam Mirzakhani New Frontiers Prize, which was established in 2019 and named for the famed Iranian mathematician who passed away in 2017, was increased from one to three recipients this year "due to the intense interest generated by the Prize and the extremely high quality of nominations," according to the <a href="https://breakthroughprize.org/">Breakthrough Prize website</a>. The award recognizes early-career women in mathematics.</p><p></p><img alt="Urmila Mahadev" class="richtext-image Right Large" data-alt="Urmila Mahadev" data-embedtype="image" data-format="RightAlignLarge" data-id="7594" height="150" src="https://web-prod-storage.s3.amazonaws.com/main.oscweb.caltech.edu/images/Mahadev-original.max-1000x1000.jpg" width="110"><p>Mahadev's award citation says that she is receiving the Maryam Mirzakhani prize "for work that addresses the fundamental question of verifying the output of a quantum computation." During her graduate work at UC Berkeley, Mahadev came up with a solution to a pressing problem of quantum computing: How do you verify that the machine's answers are indeed correct? The goal of quantum computing is to solve problems that are insurmountable to classical computers, such as computing the properties of complex molecules. But if classical computers cannot solve the problems, how can the quantum solutions be verified?</p><p>Mahadev solved the puzzle by coming up with a protocol that allows for interactions between classical and quantum computers in such a way that a classical computer can verify a quantum solution. According to an <a href="https://www.quantamagazine.org/graduate-student-solves-quantum-verification-problem-20181008/">article in <i>Quanta</i> magazine</a>, the protocol enables "users with no quantum powers of their own … to put a harness on a quantum computer and drive it wherever they want, with the certainty that the quantum computer is following their orders."</p><p>Writing in a <a href="https://quantumfrontiers.com/2018/08/05/the-quantum-wave-in-computing/">blog</a> on the website for Caltech's Institute of Quantum Information and Matter (IQIM), Thomas Vidick, professor of computing and mathematical sciences, calls Mahadev's research "one of the most outstanding ideas to have emerged at the interface of quantum computing and theoretical computer science in recent years … it is such a wonderful idea! It stuns me every time Urmila explains it."</p><p>In addition to Mahadev, Caltech alumnus Eric Adelberger (BS' 60, PhD '67), along with his colleagues at the University of Washington, Jens H. Gundlach and Blayne Heckel, have received the 2021 Breakthrough Prize in Fundamental Physics "for precision fundamental measurements that test our understanding of gravity, probe the nature of dark energy, and establish limits on couplings to dark matter," according to the award citation.</p><p>Adelberger works on experiments that make precision measurements of gravity as a means to better understand dark matter and dark energy, and to search for a unified quantum theory of gravity. His experiments look for evidence of new physics, including extra dimensions, through tests of the equivalence principle, the observation that objects fall with the same acceleration.</p><p>According to a <a href="https://www.washington.edu/news/2020/09/10/four-uw-professors-win-2021-breakthrough-prize-so-called-oscars-of-science/">news release from the University of Washington</a>, Adelberger and his colleagues "took the two-century-old torsion balance concept and developed it into a supremely sensitive 21st-century instrument to look for new fundamental physics. They tested the equivalence principle, the inverse square law, and measured the gravitational constant with unprecedented precision and sensitivity. For example, their latest inverse-square law test probed gravity at ultra-short distances, establishing that any extra dimension must be curled up with a radius less than one-third the diameter of a human hair."</p><p>In addition to this research, Adelberger and his collaborators have developed technology for the Caltech- and MIT-managed Laser Interferometer Gravitational-wave Observatory, or LIGO.</p><p>More information about the Breakthrough Prize is at their <a href="https://breakthroughprize.org">website.</a></p>https://divisions.caltech.edu/sitenewspage-index/urmila-mahadev-awarded-maryam-mirzakhani-new-frontiers-prizeJuggling in Dublinhttps://divisions.caltech.edu/sitenewspage-index/juggling-dublin<p><a href="https://pma.caltech.edu/people/david-conlon">David Conlon</a>, a professor of mathematics who joined the Caltech faculty in 2019, grew up in rural Ireland, where his grandparents were farmers and his father was a policeman. As a kid, he says, he always enjoyed math but he did not realize he wanted to pursue a career in the discipline until he attended a major mathematics competition in Taiwan, the International Mathematical Olympiad, when he was about 15 years old.</p><p>"That was really the start," he says. "I never looked back from there."</p><p>Conlon, who specializes in combinatorics and number theory, earned his bachelor's degree in math from Trinity College Dublin in 2003 and his PhD from the University of Cambridge in 2009. He transferred to Caltech after serving as a professor at the University of Oxford from 2011 to 2019.</p><p>Conlon is perhaps most well known for his work in Ramsey theory, which is named after an early 20th-century British mathematician named Frank Plumpton Ramsey. A special case of Ramsey theory, sometimes called the "friends and strangers theorem," can be understood if you think about a room full of people. Some of the people might know each other and others will be strangers. What Ramsey proved is that, for a group of six people, there will always be at least three people who know each other, or at least three people who do not know each other (watch this <a href="https://www.youtube.com/watch?v=xdiL-ADRTxQ">explanatory video</a> to better grasp the concept). In mathematical terms, this means that the Ramsey number of 3 is 6.</p><p>As the numbers grow higher, it becomes harder to pin down the Ramsey number. For example, the Ramsey number of 5 is only known to fall somewhere between 43 and 48. Early in his PhD work, Conlon made the first significant improvement on a general estimate for Ramsey numbers since 1935.</p><p>We recently connected with Conlon via Zoom to discuss Ramsey numbers and other mathematical problems that he is working on, and also to learn how he is passing time in quarantine (one distraction: juggling). Conlon is currently working remotely in Dublin, where he happened to be when the coronavirus pandemic struck.</p><h3>What is it that appeals to you about Ramsey theory?</h3><p>A lot of what we do in school and even college is calculations. You are basically taught a bunch of algorithms and you are trying to solve those algorithms. But as you evolve in the field of mathematics, you start to prove things. One of the things I came across very early in my training for the Mathematical Olympiad was Ramsey theory, which involves proofs. Ramsey theory is really about trying to show that any system contains very ordered subsystems. If you take any system whatsoever, then you can show that some small piece within it is very regular, very well behaved.</p><p>The example about the people in the room is a very commonly studied situation. There are loads of papers on this. We know that the Ramsey number of 3 is 6. That means that if you have six people in a room, you are guaranteed that at least three of them all know each other, or that at least three of the people are strangers. If you want to guarantee that at least four people all know each other or are strangers, you would need to have 18 people in the room. Or, in other words, the Ramsey number of 4 is 18. When you go up to the number 5, we no longer have an exact answer; the Ramsey number of 5 is between 43 and 48. The uncertainty just gets bigger and bigger from there. If you want to guarantee that you have a gathering containing 20 people who are friends or strangers, you would need to assemble more people than there are in the world.</p><h3>Can you tell us more about the math problems you are working on now?</h3><p>I'm still working on Ramsey numbers and trying to further reduce the uncertainty in the estimates. I made some progress in this field already, and shrunk the uncertainty. Essentially, the problem had stayed static since 1935 and I moved it for the first time. I'm also working on something we call books, which are a type of graph where you have connecting points and edges. About a year ago, I made a substantial step toward understanding these books, and this work might eventually improve the original question of Ramsey numbers even more.</p><p>A lot of what I work on stems from questions that originated with the polymath Paul Erdős. He would take the problems that other mathematicians would tell him about and then travel around the world and bring them to other people. He kept asking lots of questions, and I think he has more mathematical papers than anybody ever. One of the highest goals in my area is trying to solve these Erdős problems. I've solved several, but there are many more that I would still like to solve.</p><h3>Are there any practical applications for your work?</h3><p>The closest thing to potential applications for my work lies in theoretical computer science. A lot of the graph theory I work on is related to the vertices and connections of computer networks. Sometimes, I go to conferences with computer scientists. One program was about pseudo-randomness, which has to do with random-like objects that are produced by non-random means. They look random, but they're not actually random. Myself and a few other mathematicians were invited along with a fleet of computer scientists to try and align our different understandings of pseudo-randomness. At first blush, our notions of pseudo-randomness seem very, very different, but the computer scientists have made some major progress in Ramsey theory, on explicitly constructing Ramsey graphs. I'm hopeful that if we mathematicians could understand their work better, it could lead to exciting breakthroughs.</p><h3>What do you see as the purpose of mathematics?</h3><p>Numbers let us uncover the nature of the world. I have proved some things before and been surprised by the fact that they were true. Somehow the world had conspired to make this thing true. At the same time, a lot of what we do is cobbled together and the math is not always perfectly elegant. When I started my PhD, I was waiting for some miracle to pop out of the math and reveal a deep truth. But now it feels like we are building a house brick by brick. It takes time and effort.</p><h3>How are you spending your time in quarantine in Dublin?</h3><p>I'm working hard on finishing up several ongoing projects, but I'm punctuating the work with long walks through Dublin, especially down by the water in the evenings. I've also been practicing my juggling, which I've been doing since I was about 18. When you do 20 minutes a day, your skills start to accelerate. I'm up to five balls. Every time you add a ball, the whole arrangement becomes higher and faster, so you have to be much more precise in your throws. Sometimes it feels a lot like math, where you're often keeping many balls in the air at once.</p>https://divisions.caltech.edu/sitenewspage-index/juggling-dublinReimagining a Community-Building and Mentorship Program for Incoming Studentshttps://divisions.caltech.edu/sitenewspage-index/fsri-virtual-freshmen-summer-research-institute<p>For more than a decade, the <a href="https://diversity.caltech.edu/fsri">Freshman Summer Research Institute</a> (FSRI) has been a crucial equity-based program at Caltech, meant to ease the transition between high school and the Caltech experience for students from underrepresented or underserved communities. Each year, incoming freshmen have come to the Institute's Pasadena campus during the summer to gain experience with hands-on research and the kind of proof-based mathematics that lies at the core of a Caltech education. Because of the COVID-19 pandemic, the Caltech Center for Inclusion & Diversity (CCID), which hosts the program, could not bring this year's cohort to campus. "People were excited to come to Caltech, and all of a sudden they couldn't physically come," says Hanna Song, senior director for inclusion & diversity. "How can we create a community within our incoming first-year students, especially those who are underrepresented? That was our challenge."</p><p>The virtual version of FSRI that Song and her team, in conjunction with faculty from across campus, designed more than met that challenge, allowing for a larger pool of students to join than ever before (up from 22 in 2019 to 32 in this summer's program) and opening up a variety of new opportunities. "FSRI has been a grind, but it's been fantastic and completely worth it," says incoming first-year Leo Williams. "Despite being so far apart and never meeting in person, through all the classes and virtual hangouts, I feel like I've found a family with FSRI."</p><p>In its in-person incarnation, FSRI consists of a four-week intensive on-campus math course and a five-week summer research assignment in which each incoming student is matched with a Caltech graduate-student or faculty mentor. To create an online version of the FSRI research component, CCID worked with Justin Bois (PhD '07), Caltech teaching professor of biology and biological engineering, who runs a three-week computer programming boot camp in the Python language for his graduate students and postdocs. Bois tweaked the programming boot camp for the FSRI students, giving them not only a jump-start on their computer science education but also a way to contribute to data-heavy research projects across the Institute and JPL (which Caltech manages for NASA) by assisting with data analysis. Matching students with JPL mentors was something that would not have been possible with the on-campus version of FSRI, Song notes, because of the logistical challenge of transporting people to the Lab's secure location.</p><p>One of this summer's students worked with physics graduate student Rhondale Tso, who is affiliated with the Laser Interferometer Gravitational-wave Observatory (<a href="https://www.ligo.caltech.edu/">LIGO</a>) project that was the first to observe gravitational waves; the student contributed to Tso's research investigating astrophysics and relativity through gravitational-wave observations. Another mentor, postdoctoral scholar in planetary science Juliette Becker, challenged her mentee to use Python to search data sets for exoplanets and then run computer simulations to understand their orbits. Virtual FSRI featured faculty mentors as well. One student worked with Allen and Lenabelle Davis Professor of Economics Federico Echenique who seeks to improve algorithms that match organ donors to recipients to make the process more efficient and save more lives.</p><p>Not all the projects were entirely virtual. Mike Vicic (PhD '99), lab course instructor for chemistry and chemical engineering, used his experience <a href="/about/news/mike-vicic-che-130-diy-microscope-centrifuge">adapting his courses for remote learning</a> to help FSRI organizers and mentors adapt their research into projects that could be done safely from FSRI students' homes under the unusual circumstances of the COVID-19 pandemic. With Vicic's encouragement, visitor in geobiology Gabriella Weiss taught her mentee how to collect water samples while hiking and send them to campus for in-lab analysis. Graduate student Suzy Beeler, who studies competition among <i>E. coli</i> bacteria, taught her student how to recover DNA by using simple strawberries. "You need rubbing alcohol, dishwashing detergent, and fruit, and then something to collect the DNA with, like a toothpick or a shish kebab skewer," Vicic says. "And that's pretty much it."</p><p>FSRI's math component introduces Caltech's approach to the discipline, which is driven by proofs and a group approach to problem-solving, and can be daunting for new students.</p><p>To make the mathematics section work remotely, says Taso Dimitriadis, FSRI Director, the organizers built upon resources that Caltech had already established. For example, all incoming first-years can take the online Math 0 course in the summer before coming to campus as an introduction to Caltech mathematics. This summer, FSRI math lecturer Robert Pelayo (PhD '07) created a program that gave the FSRI students a two-week head start on Math 0. The students participated in a two-hour math boot camp four days a week that featured prerecorded math lectures on video, which allowed students to learn at their own pace. The math class ended with a TA-led small-group workshop, with 10 or 11 students per group or "pods."</p><p>The students also participated in the iPad loaner program, which the provost's office had made available to Caltech undergraduates when remote learning became the norm during the spring term. This gave FSRI students from disparate locations and time zones the opportunity to collaborate, an essential part of the Caltech learning experience.</p><p>This emphasis on collaboration also helped the pods of students form connections. In previous years, FSRI's impact on new first-year students was not only academic but also social. Students went through their math training together, traveled around the Los Angeles area on trips, and formed a community long before the first day of the fall term. This year, Dimitriadis says, "it has been challenging to form a cohort remotely because the common experiences are so separate." So, the Center for Inclusion & Diversity had to be creative in designing remote ways for people to connect. "We're doing a talent show, we've done group mixes and matches, like friend dates. We've done scavenger hunts and a bunch of games that you can do online to facilitate community building."</p><p>Says incoming first-year Angelina Torres: "Having to connect over the internet didn't mean that the FSRI community couldn't bond, it just meant that we had to work hard to find new ways to bond. In the end, I feel like I've been able to make lasting connections with my mentors and peers just as I would have if FSRI were held in-person."</p>https://divisions.caltech.edu/sitenewspage-index/fsri-virtual-freshmen-summer-research-instituteMath Professor and Students Take 'Random Walk' Togetherhttps://divisions.caltech.edu/sitenewspage-index/math-professor-and-students-take-random-walk-together<p>Some people like to take random walks through the woods, while others might stroll through their own neighborhood. In the world of math, a random walk is in fact more random than this; it would be the equivalent of flipping a coin to decide which direction you would take with each step.</p><p>Recently, Caltech's <a href="https://pma.caltech.edu/people/omer-tamuz">Omer Tamuz</a>, professor of economics and mathematics, along with two of his graduate students, Joshua Frisch and Pooya Vahidi Ferdowsi, and their colleague Yair Hartman from Ben-Gurion University in Israel, solved a long-standing math problem related to random walks. The solution was published last summer in the journal <i>Annals of Mathematics</i>.</p><p>"I remember talking to the students about a realization we had regarding this problem, and then the next morning I found out they had stayed up late into the night and figured it out," says Tamuz.</p><p>"We were very lucky in that this project actually got us the solution we wanted. That's very rare in a math project," says Frisch. "Something like 90 percent of the projects you work on, you are not going to be able to solve. With about 10 percent, you start making progress and work much harder. And even then, you don't always solve those. Part of being a mathematician is getting used to failure. Sometimes you work on something for months and have to give up and go on to the next project."</p><p>Mathematicians imagine random walks in spaces with different dimensions and geometries. In the new study, the Caltech team imagined random walks on "groups," which are objects that can have very diverse geometries. For some groups, the random walks will eventually, after much time has elapsed, converge to a specific direction. In those cases, the walks are said to be path dependent, which means that something that happened in the beginning affects the outcome. Or, in other words, something that happens early on the walk influences where it winds up. But for other groups, the direction of the walks does not converge, and their history does not affect their future.</p><p>"For a random process, is it true that in the long run, everything washes out and whatever happens will happen regardless of what took place earlier? Or is there a memory of what took place before?" asks Tamuz. "Say you have two societies, and one of them makes some technological advancement while the other suffers a natural disaster. Are these differences going to persist forever, or will they eventually disappear and we'll forget that once there was an advantage? In random walks, it has been long known that there are groups that have these memories while in other groups the memories are erased. But it was not really clear which groups have this property and which don't—that is, what makes a group have memory? This is what we figured out."</p><p>The solution, says Tamuz, had to do with finding a "geometric way of describing an algebraic property of the groups." To understand the gist of this, think of a circle. You can describe the circle geometrically (as the set of all points at a given distance from one point), or you can describe it with an algebraic equation. In the case of the random-walk problem, the mathematicians found a new way of thinking about the connections between the geometric and algebraic properties of the groups they were studying.</p><p>"We were actually shocked by how easy it was to solve the problem once we figured out this connection," says Ferdowsi, who explains that though the solution "just flowed out," the team faced a "considerable" delay while he was in his home country of Iran and unable to obtain a visa to come back to Caltech. "In the end, we were delighted to have solved a longstanding open problem in math."</p><p>Frisch says that the big realization they had for this math problem actually grew from a previous problem that was much harder. "I had been bashing my head for a few months on it and couldn't make any progress," he says, "But then we had this eureka idea that applied not only to what we were working on then but also to this more recent problem. It feels really good when you realize, 'Oh my god, this is actually going to work.'"</p><p>The <i>Annals of Mathematics</i> study, titled, "<a href="https://resolver.caltech.edu/CaltechAUTHORS:20190725-090144871">Choquet-Deny groups and the infinite conjugacy class property</a>," was supported by the National Science Foundation and the Simons Foundation.</p>https://divisions.caltech.edu/sitenewspage-index/math-professor-and-students-take-random-walk-togetherNikolai Makarov Honored with 2020 Schock Prizehttps://divisions.caltech.edu/sitenewspage-index/nikolai-makarov-honored-2020-schock-prize<p>Nikolai G. Makarov, the Richard Merkin Distinguished Professor of Mathematics at Caltech, has been awarded the 2020 Rolf Schock Prize in mathematics. The Schock Prizes, which also include awards for logic and philosophy, art, and music, were established and endowed by Rolf Schock, a philosopher and artist who passed away in 1986. They are awarded every three years and decided upon by three committees of the Swedish Royal Academies.</p><p>Makarov is being honored for his "significant contributions to complex analysis and its applications to mathematical physics," according to the award citation. A professor at Caltech since 1991, Makarov, who was born in Russia, received his undergraduate degree from Leningrad University in 1982 and his doctorate from Steklov Mathematical Institute in Leningrad in 1986.</p><p>He has worked in the areas of complex analysis, which investigates functions of complex variables. This field is vital to many branches of mathematics and has numerous applications in the natural sciences and engineering.</p><p>His most famous results concern harmonic measure in two dimensions, stating that the hitting probability distribution on the boundary for Brownian motion in two-dimensional simply connected domains (domains without holes) is one-dimensional. Brownian motion is the random movement of small particles floating in a fluid or gas, which was studied by Albert Einstein in the early 20th century.</p><p>Makarov has also made important contributions in the field of Coulomb gas and growth phenomena in a two-dimensional space. In recent years, he has also produced innovative results in conformal field theory in quantum mechanics, particularly its relationship to complex analysis and probability theory.</p><p>This year's prize ceremony is scheduled to take place on October 19, 2020, at the Royal Academy of Fine Arts in Stockholm.</p><p>Read more about 2020 Schock Prizes at <a href="https://www.kva.se/en/pressrum/pressmeddelanden/schockprisen-belonar-skapandet-av-teorier-konst-och-musik">https://www.kva.se/en/pressrum/pressmeddelanden/schockprisen-belonar-skapandet-av-teorier-konst-och-musik</a>.</p><p></p><p></p>https://divisions.caltech.edu/sitenewspage-index/nikolai-makarov-honored-2020-schock-prizeThe Evolution of Shapehttps://divisions.caltech.edu/sitenewspage-index/evolution-shape<p>New Professor of Mathematics Lu Wang says she first became interested in math in elementary school. Her sixth grade teacher, she says, was passionate about math and taught her that math could be a creative endeavor.</p><p>Today, Wang is just as enamored with math as her teacher. Her speciality is an area known as geometric flow, which involves analyzing the evolution of shapes. The field has known applications in computer graphics and image processing, but Wang says her drive is to "pursue the beauty."</p><p>Wang grew up in Beijing, China. She earned her bachelor's degree in mathematics from Peking University in 2006 and her PhD in mathematics from MIT in 2011. She became a J. J. Sylvester Assistant Professor at Johns Hopkins University in 2011, a Chapman postdoctoral fellow at Imperial College London in 2014, and a tenure-track assistant professor at University of Wisconsin-Madison in 2015. She joined Caltech's faculty in the fall of 2019.</p><h4>What does the field of geometric flow entail?</h4><p>Geometric flow is the study of the shapes of objects and how they can evolve or change. This evolution process is described by partial differential equations. Imagine the shape of a dumbbell with two lobes connected by a long neck. This shape can evolve in ways such that the neck gets smaller and then pinches down to a point, leaving two spheres. The spheres can also shrink down to points. Those points are basically called singularities, and that's when the topology of the shape has changed.</p><p>The topology of an object can be understood by thinking of a donut and a coffee cup. They both have one hole, so they have the same topology. But if one of these objects were pinched to a point, its topology would have changed. I'm interested in understanding how this topological change happens.</p><h4>Are there practical applications for this kind of work?</h4><p>Yes, people use the equations I study for computer graphics and image processing, for example to essentially sharpen the image. Personally, I am motivated by the beauty of math. I think of math as art in some senses. I don't think about how useful my research results are, but focus on the pursuit of beauty and coming up with simple and clean solutions to problems.</p><h4>What are some of the reasons you chose to come to Caltech for math?</h4><p>In the math department here, we have a lot of chances to teach and to interact with young people. Not many departments have these same teaching opportunities. Sometimes, I'll run out of ideas for a problem and get stuck, but I have found that working with young people helps freshen me up and makes me think about things differently. Teaching helps me become unstuck.</p><h4>Can you tell us more about your math teachers growing up?</h4><p>When I was in elementary school, I was very interested in Chinese literature, but then I was lucky to have a very passionate sixth grade math teacher who introduced me to math. My teachers at Peking University were also very good—they have one of the top math programs in the country. My sixth grade math teacher was a woman, while most of my teachers after that were males. One thing I like to do is to inspire more women to go into math. I have participated in various related activities—for example, I co-organized the Women and Non-binary People in Mathematics at Wisconsin (WIMAW) lectures, and I taught in the Institute for Advanced Study Women and Mathematics Program.</p><h4>What does a typical day look like for you?</h4><p>I usually start with checking newly posted articles on the website <a href="http://www.arxiv.org/">www.arxiv.org</a>. I like to listen to classical music, like Chopin, while I am drawing on paper and doing computations. I am constantly communicating ideas with collaborators over email or Skype, or meeting with my students to discuss research projects. Sometimes, when I feel stuck or tired, I like to take a walk around campus or go to the gym.</p>https://divisions.caltech.edu/sitenewspage-index/evolution-shapeDonald S. Cohen (1934–2020)https://divisions.caltech.edu/sitenewspage-index/donald-s-cohen-19342020<p>Donald S. Cohen, Charles Lee Powell Professor of Applied Mathematics, Emeritus, passed away on January 9. He was 85 years old.</p><p>Cohen was one of the first faculty members recruited for Caltech's newly formed applied mathematics program in 1965, starting as an assistant professor of mathematics. He was named associate professor of applied mathematics in 1967 and earned tenure in 1971. Colleagues and former students remember Cohen's outgoing personality, quick wit, and engaging lectures.</p><p>"Don was an inspiring teacher and mentor to several generations of students and colleagues. His energetic presentation of the material he taught, together with his humor and infectious enthusiasm, made his classes memorable," says Guruswami Ravichandran, chair of the Division of Engineering and Applied Science.</p><p>Hans Hornung, C. L. "Kelly" Johnson Professor of Aeronautics, Emeritus, moved into the office next to Cohen upon his arrival at Caltech in 1987, and remembers his colleague and friend as a brilliant teacher who was always ready with a quip or friendly banter. "He was always very funny, with a quick and witty sense of humor," Hornung recalls.</p><p>Cohen's research covered a variety of topics, including early work in the theory of reaction-diffusion equations (which are used to model systems with multiple interacting components, such as chemical reactions). His later research on nonlinear differential equations, pattern formation, stability, and bifurcations had a significant impact on mathematical biology and chemical engineering.</p><p>He formulated models that led to the development of quantitative studies of population dynamics in biological systems, using techniques that he was able to adapt to analyzing the stability of chemical reaction systems. Later, he focused on mathematical models in the materials science of polymer films, studying how the properties of polymers could be tailored to control time release of pharmaceuticals.</p><p>"Don was a truly broad thinker and used his outstanding mathematical modeling skills to provide deep insights into phenomena of interest in materials problems ranging from physical to biological sciences," Ravichandran says.</p><p>Cohen was born in Providence, Rhode Island, in 1934. He earned a bachelor's degree in physics from Brown University in 1956 and a master's degree in mathematics from Cornell University in 1959 for his studies on probability and statistics. He earned a doctorate in applied mathematics from the Courant Institute at New York University in 1962.</p><p>At Caltech, he was a popular teacher who received awards for undergraduate teaching excellence in 1979, 1987, and 1998; in 2000, he was awarded the Richard P. Feynman Prize for Excellence in Teaching. "He had a special ability to make the analysis of even complicated problems seem easy. His playful style in solving problems always entertained, engaged, and challenged students," wrote Thomas Hou, Charles Lee Powell Professor of Applied and Computational Mathematics, of Cohen in <a href="http://eas.caltech.edu/engenious/five/emeritus">an article marking his retirement in 2003</a>.</p><p>"Having Don Cohen as a PhD advisor was a wonderful experience, " says William Kath (PhD '81), now a professor at Northwestern University. Kath recalls the way Cohen was a seemingly bottomless font of humorous stories that would somehow always manage to convey an important life lesson to his students. While advising his own graduate students, Kath often passes these same lessons on to the next generation.</p><p>At Caltech, Cohen was responsible for the creation of Introductory Methods of Applied Mathematics, an in-depth applied mathematics course designed to give undergraduates necessary tools to solve problems in their field, typically those that involve differential equations and special functions. "Don started and built the course from scratch. Ever since, it has been the heart of applied mathematics education at Caltech," Hornung says.</p><p>"It rapidly became one of the largest classes at Caltech, de facto core, even when it was not required by the student's major," says Dave Stevenson, Marvin L. Goldberger Professor of Planetary Science, who has taught the course several times. "Students noted later in their careers that it was a very valuable experience. It could only work at Caltech because of the special nature of our students, and it did not have an exactly comparable counterpart at other institutions."</p><p>Former student Donald Schwendeman (PhD '86), now a professor and department head at the Rensselaer Polytechnic Institute in New York state, credits a meeting with Cohen with helping him decide to attend Caltech as a graduate student: "Cohen's outgoing personality made a big impression on me, but the main point that came through from our first meeting, as I recall, was that Caltech was a place that looked after its grad students." Schwendeman later served as a teaching assistant for Cohen's introductory applied mathematics class.</p><p>"He was a great, no-nonsense teacher," recalls fellow former TA Gregor Kovacic (PhD '90), also now a professor at Rensselaer. "He once told us green TAs how he taught the proof of [a mathematical formula known as] Cauchy's formula: He drew on the blackboard two circles and a pair of close connecting lines between them, with arrows in the opposite directions, and said 'this is the proof.' We were stunned, but yes, it is," Kovacic says.</p><p>Cohen served as the executive officer of applied mathematics from 1988 to 1993 and chair of the Division of Engineering and Applied Science in 1990. He also served as chair of the faculty from 1983 to 1985, and from 1986 to 1987 he chaired the faculty advisory committee of the Caltech Board of Trustees to select Caltech's fifth president. In 1998, he was named Charles Lee Powell Professor of Applied Mathematics. He retired in 2003.</p><p>Beyond Caltech, Cohen served in numerous national organizations, including the Society for Industrial and Applied Mathematics, the American Mathematical Society, and the American Association for the Advancement of Science. From 1993 to 1995, he served as the director of the Center for Nonlinear Studies at Los Alamos National Laboratory.</p>https://divisions.caltech.edu/sitenewspage-index/donald-s-cohen-19342020Caltech Faculty Honored with Breakthrough and New Horizons Prizeshttps://divisions.caltech.edu/sitenewspage-index/caltech-faculty-honored-breakthrough-and-new-horizons-prizes<p>Caltech's Katherine L. (Katie) Bouman has been named a recipient of the 2020 Breakthrough Prize for Fundamental Physics as part of the Event Horizon Telescope (EHT) team that generated the first-ever image of a black hole, while Xie Chen and Xinwen Zhu have each received 2020 New Horizons prizes from the same foundation for their work in physics and mathematics, respectively.</p><p>The Breakthrough Prize, now in its eighth year, is considered the world's most generous science prize. Each Breakthrough Prize is $3 million and the 347 authors of the six EHT papers will divide the award.</p><p>"I was stunned and absolutely thrilled to hear the news," says <a href="http://eas.caltech.edu/people/klbouman">Bouman</a>, assistant professor of computing and mathematical sciences and Rosenberg Scholar in Caltech's Division of Engineering and Applied Science. "I'm so lucky to work with an amazingly talented group of individuals that continues to push the boundaries of science every day. It is such a privilege and an honor to share this award with each one of them."</p><p>Their arresting image of the black hole at the center of the galaxy Messier 87, or M87, captured headlines in April. Given the black hole's distance and the wavelength of light needed to create the image, <a href="/about/news/how-take-picture-black-hole">the EHT team had to build a virtual telescope</a> the size of the earth using radio telescopes around the globe that were synchronized through a network of atomic clocks.</p><p>They then employed multiple classes of imaging algorithms to translate the data they gathered into an image showing the black hole silhouetted against hot gas swirling around it. The EHT's award citation notes that their image "matched expectations from Einstein's theory of gravity: a bright ring marking the point where light orbits the black hole, surrounding a dark region where light cannot escape the black hole's gravitational pull."</p><p>A graduate of the University of Michigan, Ann Arbor, and MIT, Bouman <a href="/about/news/seeing-farther-and-deeper-interview-katie-bouman">joined Caltech's faculty in June</a>, following a postdoctoral fellowship at the Harvard-Smithsonian Center for Astrophysics. "This first black hole image is really just the beginning," she says. "Now that we have access to a laboratory of extreme gravity, we are already thinking of all the ways that we can improve our instrument and algorithms to learn even more. Hopefully soon, we will not just be able to show the world a static black hole image, but a dynamic black hole video of gas spiraling towards an event horizon."</p><p>Caltech's Xie Chen and Xinwen Zhu will receive 2020 New Horizons prizes, which honor promising junior researchers with $100,000 awards for early-career achievements in physics and mathematics.</p><p><a href="http://pma.divisions.caltech.edu/people/xie-chen">Chen</a>, associate professor of theoretical physics at Caltech, is being honored for her "incisive contributions to the understanding of topological states of matter and the relationships between them." She specializes in both the fields of condensed matter physics and quantum information, with a focus on many-body quantum mechanical systems with unconventional emergent phenomena.Her work has potential applications in quantum computing and other related technologies. Chen received her bachelor's degree from Tsinghua University in 2006 and her PhD from MIT in 2012.</p><p>Chen's award is shared with former Caltech postdoctoral researcher Lukasz Fidkowski, now at the University of Washington, along with two others.</p><p><a href="http://pma.divisions.caltech.edu/people/xinwen-zhu">Zhu</a>, a professor of mathematics at Caltech, is being honored for his "work in arithmetic algebraic geometry including applications to the theory of Shimura varieties and the Riemann-Hilbert problem for p-adic varieties." He focuses on the Langlands program—an attempt to unify separate disciplines of math—with applications to both number theory and quantum physics. Zhu found new bridges between the geometric and arithmetic aspects of the Langlands programs and solved outstanding problems in both sides. He received his bachelor's degree from Peking University in 2004 and his PhD from UC Berkeley in 2009.</p><p>Former Caltech postdoctoral researcher Samaya Nissanke, now at the University of Amsterdam, is also a recipient of a 2020 New Horizons Physics prize, along with two others, for "the development of novel techniques to extract fundamental physics from astronomical data."</p><p><a href="https://breakthroughprize.org/">The Breakthrough Prize</a> was founded by Sergey Brin of Google, and Anne Wojcicki of 23andMe; Jack Ma of Alibaba, and Cathy Zhang; Yuri Milner, a venture capitalist and physicist, and Julia Milner; and Mark Zuckerberg of Facebook, and Priscilla Chan. The award will be presented at the eighth annual Breakthrough Prize gala awards ceremony on Sunday, November 3, at NASA Ames Research Center in Mountain View, California, and broadcast live on National Geographic.</p><p>Previous Caltech winners of the Breakthrough Prize include <a href="https://magazine.caltech.edu/esblog/glitz-qubits-main">Alexei Kitaev</a>, the Ronald and Maxine Linde Professor of Theoretical Physics and Mathematics, and <a href="/about/news/john-h-schwarz-wins-fundamental-physics-prize-41536">John H. Schwarz</a>, the Harold Brown Professor of Theoretical Physics, Emeritus, who won the Fundamental Physics prize in 2012 and 2014 respectively. Alexander Varshavsky, the Howard and Gwen Laurie Smits Professor of Cell Biology, <a href="/about/news/caltech-cell-biologist-wins-3-million-breakthrough-prize-life-sciences-41525">received the Breakthrough Prize in Life Sciences</a> in 2014. In 2016, a special Breakthrough Prize in Fundamental Physics was announced <a href="/about/news/ligo-team-awarded-special-breakthrough-prize-fundamental-physics-50657">to honor the LIGO team</a>.</p><p>Previous Caltech winners of the New Horizons Prize include Rana Adhikari, professor of physics, and Maksym Radziwill, professor of mathematics at Caltech, <a href="/about/news/rana-adhikari-and-maksym-radziwill-honored-2019-new-horizons-prizes-84118">who both won in 2019</a>.</p>https://divisions.caltech.edu/sitenewspage-index/caltech-faculty-honored-breakthrough-and-new-horizons-prizesPhilip Isett Wins Clay Awardhttps://divisions.caltech.edu/sitenewspage-index/philip-isett-wins-clay-award<p>Philip Isett, assistant professor of mathematics at Caltech, has been awarded a 2019 <a href="https://www.claymath.org/research">Clay Research Award</a>, presented by the Clay Mathematics Institute for "outstanding achievements of the world's most gifted mathematicians." Isett is receiving the award, together with Tristan Buckmaster of Princeton University and Vlad Vicol of New York University, for the "profound contributions that each of them has made to the analysis of partial differential equations, particularly the Navier-Stokes and Euler equations," according to the award citation.</p><p>The Navier-Stokes equations, proposed in 1822 by Claude-Louis Navier and George Gabriel Stokes, are used to describe fluid dynamics. They are very useful for solving practical problems such as those related to the weather, or the airflow around automobiles or the wings of planes. The Euler equations, named after Leonhard Euler (pronounced "Oiler"), an 18th-century Swiss scientist, are a special case of Navier-Stokes where there is zero internal friction, or viscosity, and are especially interesting for studying turbulence. In 2016, Isett solved a problem related to the Euler equations known as Onsager's conjecture, named after its proposer Lars Onsager, who won the Nobel Prize in Chemistry in 1968.</p><p>"Onsager's conjecture is a problem about the way energy is dissipated in turbulent fluid flow, which is described theoretically by a mechanism called an 'energy cascade,'" says Isett. "Having a confirmation of Onsager's conjecture means roughly that the idea of energy dissipation due to energy cascades is logically consistent with other predictions in turbulence theory about how velocity fluctuates within a turbulent fluid flow."</p><p>Isett received bachelor's degrees in math and economics, with a minor in physics, from the University of Maryland, College Park, in 2008. He earned his PhD in mathematics from Princeton University in 2013. After working at the Massachusetts Institute of Technology as a C.L.E. Moore Instructor and a National Science Foundation postdoctoral scholar, Isett became an assistant professor at the University of Texas at Austin in 2016. He joined Caltech in 2018, and recently <a href="/about/news/caltech-mathematics-professor-wins-2019-sloan-fellowship-85369">won a Sloan Research Fellowship</a>.</p>https://divisions.caltech.edu/sitenewspage-index/philip-isett-wins-clay-award