News from The Division of Physics, Mathematics and Astronomyhttps://pma.divisions.caltech.edu/news/rssen-usSat, 17 Apr 2021 10:22:41 +0000Women Advocating for Womenhttps://divisions.caltech.edu/sitenewspage-index/women-advocating-for-women<p>Across Caltech, around a dozen of what have become known as "women-in" groups—led by graduate students and composed of women-identified graduate and undergraduate students, postdocs, staff, and faculty—grapple with some of the most difficult issues faced by women seeking successful and rewarding careers in STEM fields traditionally dominated by men.</p><p>On their own, the groups carry out gender-related advocacy work and host an array of events including journal clubs, invited speakers, professional development and skill-building workshops, and community events. When they come together under the aegis of the Institute's Women's Engagement Board (WEB), a 55-member organization facilitated by the Caltech Center for Inclusion & Diversity (CCID), they find an even stronger sense of community and interconnectedness. WEB, whose membership is made up of the leaders of the women-in groups, was launched in 2016 with the shared goal of building a more inclusive Caltech campus.</p><p>"Every month, the WEB meeting is the highlight of my day," says Clare Singer, a third-year graduate student in the Division of Geological and Planetary Sciences and vice president of Women in GPS (WinG). "We're all doing the same things in parallel. In a recent meeting, one of the women in the group brought up an issue that she was facing in her department, and we all brainstormed with her."</p><p>The WEB meetings provide a forum, says Monique Thomas, program coordinator with CCID, for members to connect and talk about programming within their own groups as well as projects they can work on collaboratively to support all women on campus. "Themes and threads" start to emerge around common challenges for women across divisions, she says, and CCID's role is to understand the issues that are coming up and to "be there to support the women as individuals and as scientists in their divisions."</p><p>Yazmin Gonzalez, CCID's new assistant director, who will be taking on oversight of WEB this spring, says affinity spaces such as WEB and the women-in groups help individuals realize they are not alone in whatever they might be going through. "It's about validation and also recognition that there are certain systems that need to be shifted. The fact that folks can see their experiences reflected in the experiences of somebody else in another division is very powerful."</p><p>"It's been really eye opening and helpful," says Women in Biology and Biological Engineering (WiBBE) co-chair and third-year graduate student Acacia Hori, "as a catalyst for creating cross-disciplinary, cross-department relationships that empower us to advocate for graduate student support, changes to admissions policies, or things like that. But also, it's just great to be able to meet people through this shared aspect of our lives."</p><p>A recent screening of <i>Picture a Scientist</i>, a 2020 documentary on gender equity in science that featured women scientists telling their stories, provided an opportunity to discuss discrimination, microaggressions, the intersection of race and gender, sexual harassment, and other issues faced by women in STEM. "There's a lot to unpack," says CCID program coordinator Alison Tominaga, "so WEB organizers partnered with the CCID and the Equity and Title IX Office to offer a separate space for people who had raw emotions of anger, sadness, and frustration to process and to discuss the film."</p><p>WEB also hosts panel discussions, including one that featured Dotty and Dick Hayman Professor of Mechanical Engineering Melany Hunt talking about her experiences and her work on Giving Voice, a project she developed that creates recorded vignettes that illustrate the challenges that disproportionately affect women in science and engineering labs and classrooms.</p><p>While the individual women-in groups' activities vary, working to effect positive change for Caltech women is a priority for all. "It's about advocating, voicing our needs, and voicing our positions," says Rochelle Diamond, director of Caltech's Flow Cytometry/Cell Sorting Facility, manager of a BBE research group, and a member of WiBBE. Diamond, who has long been involved in advocacy work and is chair emeritus of the National Organization of Gay and Lesbian Scientists and Technical Professionals, was part of a recent successful effort to garner more support for postdocs and graduate students with children to help them meet the costs of childcare. And Dawna Bagherian, who is on track to graduate with a PhD in neuroscience this spring, successfully campaigned in her role as co-chair of Chen Institute Women in Neuroscience (CWiN) to get free menstrual products provided in all of the restrooms on campus. "It feels like such a little thing," she says, "but it was a long journey to get there, and I'm glad that we got that done."</p><p>Many of the activities organized by the women-in groups center around building community through game nights, happy hours, and other social events. As WiBBE's Hori says, "It's not always the seminar-style talks that make the strongest connections. The social events are a great way to make those connections that you can then expand on later."</p><p>The groups have also hosted coffee chats or lunch hour conversations with women speakers who talk about their career paths and navigating systemic challenges that women in academia, and particularly in STEM, face. For Women's History Month, many of the groups developed special programs: WiBBE, for instance, organized a presentation on Nobel Prize-winning cytogeneticist Barbara McClintock, who spent time at Caltech from the 1930s to the '50s as a research fellow and visiting professor.</p><p>Through journal clubs, women in the campus groups share articles in the social science literature about women in STEM and then meet for group discussions. "We talk about stuff like imposter syndrome," says WinG's Singer, "or issues of getting spoken over during lab meetings. We also talk about topics related to job searching, balancing work and family, and the ‘two-body problem,' trying to find a career in the same place as your spouse." Other issues include navigating the barriers often encountered by women on the pathway to their degree.</p><p>Mentoring has been another priority for some of the women-in groups, including Women in BBE, which before the pandemic had a successful program that matched women with scientists at the next step of their professional development in their division. Plans are in place to pick this up again once conditions allow. The groups also work on professional development for women, putting together programs such as a graduate school application workshop that was recently coordinated by Women in PMA.</p><p>Many of the groups are also active in their support for underrepresented minorities. "Increasing diversity is a huge subject," says Diamond. "Our underrepresented minorities can feel isolated, and that can be really rough, particularly if you're intersectional."</p><p>"I think there are particular challenges for women of color in STEM," adds CCID's Tominaga, who is the adviser for Caltech's Asian American Pacific Islander (AAPI) group and advocacy chair for Asian Pacific Americans at Caltech (APACT), an employee resource group. Tominaga is in the process of putting together affinity spaces for AAPI women. Another affinity space, Women of Color in STEM (WOC), also hosted by CCID, invites those who identify as women of color to come together for community.</p><p>In addition to her role in CWiN, Bagherian is also part of the organizing committee for Caltech for Black Lives, an ally organization of Caltech students and staff dedicated to supporting the work of the Black Scientists & Engineers of Caltech (BSEC). "It's been nice to have my hands in both spaces because it's enabled me to say, for example, ‘Caltech for Black Lives is doing this. Let's try and get our organization involved.'"</p><p>The women-in groups have become proactive in talking to potential students, too. "I've noticed increasingly," says Singer, "that prospective students will ask me, ‘What is it like to be a woman in this department?' It wasn't at the front of my mind when I was applying to grad schools, but I think this is becoming even more of a priority for them."</p><p>For Hori, being part of a women-in group has been a revelation, if a somewhat unexpected one. "I didn't realize how helpful this would be until I was actually in the group and really enjoying the companionship and camaraderie with other women scientists. It makes me feel so empowered and so welcome on this campus, even if things are not always perfect; just knowing that these are solvable problems and that there are things that we can do as we work together really helps."</p>https://divisions.caltech.edu/sitenewspage-index/women-advocating-for-womenMath Professor Makes Breakthrough in Ramsey Numbershttps://divisions.caltech.edu/sitenewspage-index/math-professor-makes-breakthrough-in-ramsey-numbers<p>How many people would you need at a party to guarantee that at least three individuals know each other, or that at least three do not know each other? Working this out with pen and paper may take a while, but many mathematicians will readily tell you the answer is six. This party scenario, also called the "friends and strangers" theorem, is based on a concept known as Ramsey numbers, named after early 20th-century British Mathematician Frank Ramsey.</p><p>Now, imagine that more people are invited to this hypothetical party. How many would be required to ensure that at least five people know each other, or, conversely, that at least five are strangers? The answer is not clear. Indeed, mathematicians only know that the number of required people would be at least 43 and no more than 48. The actual answer falls somewhere in this range but is unknown. Add even more people to the party, and the uncertainty in the problem quickly becomes enormous.</p><p>Now, for the first time in decades, Caltech professor of mathematics David Conlon and his colleague Asaf Ferber of UC Irvine have shrunk that uncertainty by exponential amounts, for a special category of Ramsey numbers known as multicolor Ramsey numbers. The researchers describe their work in a study appearing in the journal <i>Advances in Mathematics.</i></p><p>"One of the most stubborn numbers in math has finally budged," wrote Kevin Harnett in an <a href="https://www.quantamagazine.org/new-math-proof-raises-lower-bounds-of-graph-randomness-20201104/">article about the research in Quanta magazine.</a></p><p>"The solution came along very, very quickly," says Conlon. "We were surprised that it worked so well, actually."</p><p>Mathematicians think about Ramsey number problems in the form of points connected by lines, which they call graphs. The people at the party from the example above are essentially the points in these graphs. If individuals know each other, a line of one color, say blue, would be drawn between their respective points. If they do not know each other, they would be connected by a red line.</p><p>In the case described above, with six people attending the party, at least three people know each other, or at least three people do not know each other. Thus on the graph representing this situation, there would be at least one blue triangle, or one red triangle.</p><p>"We are interested in what patterns emerge in these scenarios," says Conlon. "Ramsey numbers tell us that even when things look chaotic, there are still patterns to be found."</p><p>In the new study, Conlon and Ferber looked at Ramsey numbers where three or more colors are used to connect the points in the graphs (thus the term "multicolor"). For example, if you used the colors blue, green, and red to connect points, 17 points would be required to guarantee at least one blue, or one red, or one green triangle. From our two-color example above, we know it takes only six points to guarantee one red or one blue triangle. Essentially, more points are needed in the scenarios with multiple colors.</p><p>Additionally, when the mathematicians want to identify not triangles but shapes containing four, five, or more points, the uncertainty in the total number of required points rises even faster for multicolor problems.</p><p>For their work, Conlon and Ferber used a new type of proof to shrink the multicolor Ramsey uncertainties by exponential amounts. They say they used a hybrid approach that blended older strategies, in which randomness comes into play, with newer strategies that are more deterministic.</p><p>"We found there is a better way to solve the problem than to color the connections between points at random," says Conlon. "We blended this approach with one where we know exactly what we are coloring a certain color."</p><p>Conlon says he is now returning to the problem of two-color Ramsey numbers. For his PhD work in 2009, he made the first significant improvements since 1935 in the reduction of the uncertainty of the solutions. To really make dramatic improvements for this type of problem, he says, something entirely new is needed.<br/></p><p>"The two-color case is likely to require such a substantial new idea that I think the math would prove useful in other unsolved math problems," says Conlon. "In math, you start out because you are interested in the thing for its own sake, but further down the line, it becomes important or interesting for other reasons."</p><p>The study, titled, "<a href="https://authors.library.caltech.edu/107121/">Lower bounds for multicolor Ramsey numbers</a>," was funded by the National Science Foundation.</p>https://divisions.caltech.edu/sitenewspage-index/math-professor-makes-breakthrough-in-ramsey-numbers2020: A Year In Reviewhttps://divisions.caltech.edu/sitenewspage-index/2020-year-review<p><i>At Caltech, as throughout the rest of the world, 2020 was a year like no other. This unprecedented year was filled with personal and professional challenges as well as fast-breaking and paradigm-shifting events, all of which were framed by (and helped to shape) incredible advances and discoveries in science, engineering, and technology, realized thanks to the ingenuity, insight, and perseverance of Caltech's community of researchers and scholars, students and staff.</i></p><p>In <b>January</b>, the Zwicky Transient Factory telescope <a href="/about/news/first-asteroid-found-inside-orbit-venus">discovered</a> the first asteroid to orbit around the sun, entirely within the orbit of the planet Venus. In other space news, NASA <a href="/about/news/nasa-retires-spitzer-space-telescope-infrared-explorer">retired</a> the Spitzer Space Telescope after 16 years of astronomical discoveries. Researchers developed <a href="/about/news/bionic-jellyfish-swim-faster-and-more-efficiently">a tiny prosthetic device</a> that enables jellyfish to swim more efficiently, which could one day enable the use of jellyfish to record information about the ocean.</p><p>Though it was still unknown that the year would become dominated by the novel coronavirus that was just beginning to make the news, Caltech issued <a href="https://together.caltech.edu/updates/general/1242020">precautionary information</a> about COVID-19.</p><p>In <b>February</b>, researchers developed a <a href="/about/news/sweat-sensor-detects-stress-levels-may-find-use-space-exploration/">sweat sensor</a> to quantitatively measure a person's stress levels. Additionally, researchers discovered that a biomarker for <a href="/about/news/biomarker-parkinsons-disease-may-originate-gut">Parkinson's disease</a> may originate in the gut and also discovered that ultrasound can be used to selectively <a href="/about/news/ultrasound-can-selectively-kill-cancer-cells">kill cancer cells</a>.</p><p>In <b>March</b>, the United States experienced drastic changes as the COVID-19 pandemic took hold. In early March, Caltech <a href="https://together.caltech.edu/updates/general/362020">canceled</a> all large public events and issued new travel restrictions. By the middle of the month, the Institute announced that all courses for the <a href="https://together.caltech.edu/updates/general/3132020">spring quarter</a> would be moved online. Several laboratories <a href="/about/news/caltech-scientists-turn-research-toward-fighting-coronavirus-pandemic/">shifted</a> their research to focus on the novel coronavirus. A Q&A with Caltech alumnus and virologist <a href="/about/news/tip-iceberg-virologist-david-ho-bs-74-speaks-about-covid-19">David Ho</a> (BS '74) garnered more than a million views on the Caltech website.</p><p>In <b>April</b>, the Institute made the decision to shift to a <a href="https://together.caltech.edu/updates/general/4162020">virtual commencement</a> ceremony. As it became clear that COVID primarily attacked the respiratory system, NASA developed a COVID-19 <a href="/about/news/nasa-develops-covid-19-prototype-ventilator-37-days">prototype ventilator</a> in 37 days, and it was quickly <a href="/about/news/nasa-developed-ventilator-authorized-fda-emergency-use">authorized</a> by the FDA for emergency use.</p><p>By <b>May</b>, many scientists had adjusted to the new constraints on research made necessary by the pandemic. Researchers developed an ultrafast <a href="/about/news/new-ultrafast-camera-takes-70-trillion-pictures-second">camera</a> that can capture 70 trillion frames per second. The Caltech Alumni Association announced that its 83rd <a href="/about/news/caltechs-83rd-annual-seminar-day-goes-virtual-for-first-time">annual Seminar Day</a> would be virtual for the first time ever. Caltech alumnus and astronaut Bob Behnken (MS '93, PhD '97) made a <a href="https://www.washingtonpost.com/technology/2020/05/25/who-spacex-launch-astronauts/?arc404=true">historic flight</a> to the International Space Station.</p><p>Additionally, the <a href="https://scienceexchange.caltech.edu/topics/covid-19-coronavirus-sars-cov-2">Caltech Science Exchange</a> launched, with its inaugural topic being the COVID-19 pandemic and the novel coronavirus that caused it.</p><p>In <b>June</b>, Caltech held its first-ever <a href="https://commencement.caltech.edu/">virtual commencement</a>. Research continued, with discoveries about <a href="/about/news/where-are-my-keys-and-other-memory-based-choices-probed-brain">neurons</a> responsible for memory-based decision-making and studies of how fracking triggers <a href="/about/news/natural-fluid-injections-triggered-cahuilla-earthquake-swarm">earthquake swarms</a>. Astronomy news continued to make headlines, with LIGO's discovery of a <a href="/about/news/ligo-virgo-finds-mystery-object-mass-gap">mysterious object</a> and images of a <a href="/about/news/black-hole-collision-may-have-exploded-light">black hole collision</a> flaring with light.</p><p>In <b>July</b>, as COVID-19 cases began to rise, Caltech launched its <a href="https://together.caltech.edu/updates/general/7282020">pilot testing program</a>. Many researchers who had pivoted their focus toward COVID-19 were beginning to publish results, such as the first-ever <a href="/about/news/images-antibodies-they-neutralize-covid-19-virus">images of human antibodies </a>latching onto SARS-CoV-2 proteins. Fall term was initially announced as being partially in person, but that decision had to be rolled back as state and county regulations made <a href="https://together.caltech.edu/updates/general/7142020">in-person instruction</a> impossible. On July 14, <a href="https://caltech.us5.list-manage.com/track/click?u=55135e6f2a2e08560e9e602c7&id=27d96e8268&e=dd2ad64163">the federal government rescinded the new visa policy</a> that required international students to take at least one in-person class during the coronavirus pandemic or face deportation to their home countries.</p><p>Led by the Black Scientists and Engineers of Caltech (BSEC) and the campus community, Caltech <a href="/campus-life-events/campus-announcements/more-inclusive-caltech">responded</a> to the national protests against police brutality by developing a detailed plan for making progress on diversity, equity, and inclusion efforts, including the development of a <a href="/campus-life-events/campus-announcements/committee-naming-and-recognition">task force</a> to address naming and recognition policies on campus.</p><p>As research operations continued at Caltech, scientists announced the discovery of bacteria that <a href="/about/news/bacteria-metal-diet-discovered-dirty-glassware">feed on metal</a>.</p><p>In <b>August</b>, the Institute confirmed that the fall term would be done entirely via <a href="https://together.caltech.edu/updates/general/81320">remote learning</a>. Though no laboratories had focused on coronaviruses before the COVID-19 pandemic, Caltech's Merkin Institute helped <a href="/about/news/merkin-institute-catalyzes-covid-19-research-at-caltech">catalyze</a> the transition by offering grants for projects. The summer issue of <i>Caltech</i> magazine was printed, leading with a story on campus efforts into <a href="https://magazine.caltech.edu/post/caltech-researchers-focus-on-the-novel-coronavirus-that-causes-covid-19">COVID-19 research</a>.<br/></p><p>By <b>September</b>, many professors had devised <a href="/about/news?ordering=date&search=%22continuing+series+about+innovative+ways+the+Caltech+community+has+approached+remote+teaching+and+learning+during+the+COVID-19+pandemic%22&category=&tag=&year=&submit=Search">innovative new plans</a> for teaching virtually. Social scientists published results of a study examining <a href="/about/news/pandemic-progressed-peoples-perceived-risks-went">risk perception</a> and behavior during the pandemic.</p><p>Research continued, with LIGO and VIRGO detecting their most <a href="/about/news/a-bang-in-ligovirgo-detectors-signals-most-massive-gravitational-wave-source-yet">massive black hole collision</a> yet and physicists showing the usefulness of <a href="/about/news/molecular-approach-quantum-computing">molecules in quantum computing</a>. Earthquake research continued to be a Caltech staple, with studies illustrating how <a href="/about/news/undersea-earthquakes-shake-climate-science">undersea earthquakes</a> can help climate scientists monitor the temperature of the oceans and how laboratory <a href="/about/news/lab-grown-earthquakes-reveal-frictional-forces-acting-beneath-our-feet">simulations of earthquakes</a> can reveal the physics of real earthquakes.</p><p>In <b>October</b>, the community celebrated virtually as two <a href="https://www.alumni.caltech.edu/daa/">Distinguished Alumni</a>, <a href="/about/news/alumna-andrea-ghez-awarded-2020-nobel-prize-physics">Andrea Ghez</a> (MS '89, PhD '93) and <a href="/about/news/alumnus-charles-m-rice-wins-2020-nobel-prize-physiology-or-medicine">Charles Rice</a> (PhD '81), were named Nobelists. Several Caltech faculty members received funding from the federal government to lead and participate in <a href="/about/news/caltech-faculty-advance-future-quantum-science-efforts">quantum information science centers</a> around the country.</p><p>The Institute launched its monthly <a href="/campus-life-events/master-calendar/filter?date_start=&date_end=&type=all&search=&past=0&mc=1&series=367">Watson Lecture series</a>, adapted for virtual audiences, as well as a virtual version of Public Programming's <a href="https://events.caltech.edu/">CaltechLive!</a> community events program. The Caltech Science Exchange published pieces answering common questions about <a href="https://scienceexchange.caltech.edu/topics/voting-elections">voting and elections</a>. <i>Caltech</i> magazine published its fall issue, leading with <a href="https://magazine.caltech.edu/post/scientists-and-engineers-share-their-experiences-and-perspectives-on-how-to-create-a-more-inclusive-caltech">community stories</a> of how to create a more inclusive Caltech.</p><p>COVID-19 research continued to produce results, such as a molecular analysis of <a href="/about/news/how-sars-cov-2-disables-human-cellular-alarm-system">how the virus disables cells</a> and how <a href="/about/news/characterizing-covid-19-antibodies-potential-treatments">antibodies could lead to potential treatments</a>. Researchers also developed a prototype of a <a href="/about/news/caltech-researcher-unveils-sensor-rapidly-and-simultaneously-detects-covid-19-infection-status-severity-and-immunity">rapid test</a> to determine infection and severity.</p><p>Caltech continued its commitment to its diversity, equity, and inclusion plan by expanding the <a href="/about/news/expanding-wave-pipeline">WAVE program</a> and holding an expanded, virtual <a href="/about/news/fsri-virtual-freshmen-summer-research-institute">Freshman Summer Research Institute</a> program. The Institute also <a href="/about/news/caltech-joins-lawsuit-block-new-visa-rules">joined a lawsuit</a> opposing new restrictions by the Department of Homeland Security and the U.S. Department of Labor on H-1B visas.</p><p>In <b>November</b>, the Institute announced that construction on the Tianqiao and Chrissy Chen Institute for Neuroscience Building was <a href="https://neuroscience.caltech.edu/about/building-update">completed.</a></p><p>Historians announced the discovery of previously unknown copies of Isaac Newton's historic <a href="/about/news/hundreds-copies-newtons-emprincipiaem-found-new-census"><i>Principia</i></a> textbook. Astronomers solved a 16-year-old <a href="/about/news/merging-stars-produce-glowing-blue-ring-nebula">mystery of an ultraviolet ring</a> in space, nicknamed the Blue Ring Nebula, and detected the most powerful <a href="/about/news/magnificent-burst-within-our-galaxy">fast radio burst</a> ever seen within our galaxy.</p><p><a href="/about/news/robotics-engineers-take-covid-19">Robotics engineers</a> turned their tools toward modeling the pandemic's spread, and researchers found that a new <a href="/about/news/caltechs-ai-driven-covid-19-model-routinely-outperforms-competitors">model using artificial intelligence</a> outperforms other models. The Institute rolled out its <a href="https://together.caltech.edu/updates/general/11182020">surveillance testing program</a>.</p><p>In <b>December</b>, NASA announced that the Caltech-led <a href="/about/news/caltech-led-lunar-trailblazer-mission-approved-begin-final-design-and-build">Lunar Trailblazer Mission</a> to the moon could proceed with its final design and build. Researchers took an important step toward establishing a <a href="/about/news/quantum-internet-tested-caltech-and-fermilab">quantum internet</a>. The president updated the community on concrete actions taken toward the Institute's <a href="/campus-life-events/campus-announcements/update-diversity-equity-and-inclusion">diversity, equity, and inclusion</a> goals.</p>https://divisions.caltech.edu/sitenewspage-index/2020-year-reviewJuggling 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-shapeCaltech 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