Mathematics

ŷ��ڱ��Ƶ students follow their noses, disprove math conjecture

Anonymous — Thu, 30 Nov 2023 18:03:21 +0000

ŷ��ڱ��Ƶ students follow their noses, disprove math conjecture Anonymous (not verified) Thu, 11/30/2023 - 11:03

Daniel Long

Summer Haag and Clyde Kertzer made major news in the math world while working on a summer research project

Prior to the end of the 2022-2023 academic year, graduate student Summer Haag and junior Clyde Kertzer were looking for summer research opportunities in mathematics, their subject of study.

It was an REU (Research Experience for Undergrads) with Katherine (Kate) Stange, ŷ��ڱ��Ƶ Boulder associate professor in the Department of Mathematics, and James Rickards, a postdoctoral researcher in the same department, that caught their eye, as it dealt with a topic in which they both had an abiding interest: number theory.

“I knew in undergrad that number theory is what I wanted to do,” says Haag. “When I saw Kate and James were doing a number theory REU, I said, ‘That one! I want that one!’”

ŷ��ڱ��Ƶ Boulder students Clyde Kertzer and Summer Haag disproved a longstanding conjecture in mathematical number theory during their summer research experience.

“I’ve taken a bunch of number theory courses here at ŷ��ڱ��Ƶ that I’ve really enjoyed,” says Kertzer, who withdrew his applications to other REUs when he was accepted into the one with Stange and Rickards. “I was super excited.”

The REU would explore a branch of number theory called Apollonian circle packings, which are fractals, or never-ending patterns, made up of infinite circles just touching each other but never overlapping.

Neither Haag nor Kertzer had much experience with circle packings.

“I’d seen quadratic forms before, and I’d seen Mobius inversions, but I’d never seen them pertaining to circle packings,” says Haag. “I was excited to learn that stuff.”

“I went to the library and got a book, the only book I could find on circle packings, and started reading,” says Kertzer.

Room to explore

For the first few weeks of the REU, Stange and Rickards gave Haag and Kertzer the background information they’d need for the project and taught them how to use code that Rickards had developed to gather data on circle packings. After that, they gave Haag and Kertzer room to explore.

“We set out with a fun project idea that would give students a chance to experience research by collecting data, looking for patterns and proving them,” says Stange. “We didn't have a very definitive goal.”

“We had a long list of possible problems to explore,” Rickards adds. “There was no real end goal in sight.”

ŷ��ڱ��Ƶ Boulder scholars Katherine Stange (left) and James Rickards research number theory, an aspect of which includes Apollonian circle packings.

That changed, however, when Haag and Kertzer’s explorations produced data that called a well-known math conjecture into question.

The local-global conjecture, widely accepted for the better part of two decades, predicts the curvatures of the circles inside a circle packing. According to this conjecture, if a researcher knows the curvatures of a few circles in a packing (the “local” circles), that researcher can then predict the curvatures of the circles in the rest of the packing (the “global” circles).

Time and again, evidence seemed to support the local-global conjecture, to the point that pretty much everyone familiar with it assumed it was true.

“Even though it hadn’t been proven, it was almost guaranteed to be true,” says Haag.

Two numbers instead of one

But then, while entering numbers into Rickards’ code, Haag and Kertzer decided to do something that hadn’t yet been done. Instead of entering one number into the code, they entered two and looked at the resultant packings.

That’s when things got interesting. Numbers that, according to the local-global conjecture, should have appeared together in the same packings didn’t.

Stange likens the situation to a jail. It was as though the numbers that were supposed to be locked up had dug a tunnel when no one was looking and escaped.

Katherine Stange partnered with engineering PhD graduate Daniel Martin to create a pattern for an Apollonian circle packing puzzle laser cut from wood; the pattern can be found here.

Haag, Kertzer, Stange and Rickards all knew what this data meant for the local-global conjecture, which is why Rickards’ immediate reaction was to double-check his code for errors. But there were none. The code was correct. The local-global conjecture, on the other hand, was not.

Over the next few days, Stange and Rickards put together a proof of their findings, working so fast, so feverishly and so precisely that Haag and Kertzer couldn’t help but be inspired.

“It was really impressive,” says Kertzer. “That’s the point where we want to be as mathematicians.”

The four published a paper in the preprint server arXiv with a title as unambiguous as its content is eye-opening: “The Local-Global Conjecture for Apollonian Circle Packings Is False.”

Not bad for a summer research project.

The playful side of math

But what Haag and Kertzer found even more gratifying than disproving a major outstanding conjecture was experiencing first-hand the creative side of mathematics research. It wasn’t all formulas and rules. It was intuition, exploration, play.

“Some advice Kate gave me will stick with me for a while,” Kertzer recalls. “‘If you’re not sure, just follow your nose.’”

Math research, Stange explains, “often feels like exploring a jungle. You aren't sure what you'll find, but the creativity comes in deciding what leaf to turn over, which path to take, what questions you are trying to answer, and how you will go about answering them. Some of the deepest insights in mathematics come from creative leaps connecting apparently unconnected ideas.”

Luckily for Haag and Kertzer, there is plenty more jungle to explore.

“Some of my students are so thoroughly confused that I want to do research in math,” Haag says. “They’re like, ‘Isn’t math done? How many questions could possibly be unsolved in math?’”

Haag smiles when she answers: “So many.”

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Summer Haag and Clyde Kertzer made major news in the math world while working on a summer research project.

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ŷ��ڱ��Ƶ mathematician wins high recognition from peers

Anonymous — Mon, 20 Nov 2023 15:42:28 +0000

ŷ��ڱ��Ƶ mathematician wins high recognition from peers Anonymous (not verified) Mon, 11/20/2023 - 08:42

Agnès Beaudry is named a fellow of the American Mathematical Society, the sixth ŷ��ڱ��Ƶ Boulder faculty member to garner this distinction

Agnès Beaudry, an associate professor of mathematics at the University of ŷ��ڱ��Ƶ Boulder, is one of 40 mathematical scientists from around the world who have been named fellows of the American Mathematical Society (AMS) for 2024, the society announced this month.

Agnès Beaudry, a ŷ��ڱ��Ƶ Boulder associate professor of mathematics, is a 2024 American Mathematical Society fellow.

AMS members designated as fellows have made outstanding contributions to the “creation, exposition, advancement, communication and utilization of mathematics.” The society said it is pleased to honor the 2024 Class of Fellows, who are being recognized by their peers for their contributions to the field.

“It is my pleasure to congratulate and welcome the new class of AMS Fellows, honored for their outstanding contributions to the mathematical sciences and to our profession,” said AMS President Bryna Kra. “This year's class was selected from a large and excellent pool of candidates, highlighting the many ways in which our profession is advanced, and I look forward to working with them in service to our community.”

Beudry said she was grateful: “I’m incredibly honored to have been selected for the new class of AMS Fellows. I am extremely thankful to those who nominated me, and also to all of the mentors, collaborators and other amazing individuals I have the chance to work with as a mathematician.”

Beaudry is an algebraic topologist and a stable homotopy theorist. “Algebraic topology studies geometric objects by associating to them algebraic data called invariants. These help us understand and detect features of the geometric objects,” she explained.

Beaudry studies chromatic homotopy theory and its interactions with equivariant homotopy theory. She also works with condensed-matter physicists to apply tools from algebraic topology to the study of phases of matter.

Beaudry joined the ŷ��ڱ��Ƶ Boulder faculty in 2016 and became an associate professor in 2022. She holds a PhD in mathematics from Northwestern University and a BA, with honors, in mathematics from McGill University.

Sebastian Casalaina-Martin, professor and chair of the ŷ��ڱ��Ƶ Boulder Department of Mathematics, said the university is lucky to have her. "Being named an AMS fellow is a terrific honor, marking Dr. Beaudry's profound impact on the field, and I am delighted to have this opportunity to celebrate Dr. Beaudry being recognized in this way."

The American Mathematical Society is dedicated to advancing research and connecting the diverse global mathematical community through publications, meetings and conferences, MathSciNet, professional services, advocacy and awareness programs.

Beaudry is the sixth faculty member at ŷ��ڱ��Ƶ Boulder to be named an AMS fellow.

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Agnès Beaudry is named a fellow of the American Mathematical Society, the sixth ŷ��ڱ��Ƶ Boulder faculty member to garner this distinction.

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A ŷ��ڱ��Ƶ statistician’s global mission help students tackle real-world problems

Anonymous — Thu, 06 Apr 2023 22:51:21 +0000

A ŷ��ڱ��Ƶ statistician’s global mission help students tackle real-world problems Anonymous (not verified) Thu, 04/06/2023 - 16:51

Jaxon Parker

Fulbright project to launch a new statistics course in Indonesia to provide interdisciplinary training and help students make data-driven decisions in everyday life

Data is an increasingly important facet of today’s interconnected world, but not every country can employ data for the benefit of its communities. A mathematician’s Fulbright Scholar project will create a new course in Indonesia designed to train students to solve local issues with data.

Eric Vance, an associate professor in applied mathematics at the University of ŷ��ڱ��Ƶ Boulder, is the director of the Laboratory for Interdisciplinary Statistical Analysis (LISA), which trains students in data science through collaborations with researchers, policymakers and business owners.

For the past 13 years, Eric Vance has been the director of the Laboratory for Interdisciplinary Statistical Analysis (LISA), first at Virginia Tech, and now, at the University of ŷ��ڱ��Ƶ Boulder. In his work with LISA, Eric trains statisticians and data scientists to move between theory and practice.

“Being able to understand and reason with statistics, such as to debunk misinformation, is necessary to be a responsible citizen,” Vance says. “Because so many researchers, policymakers and businesses use data, they need to collaborate with statisticians so they can make good decisions and get the most out of their data.”

Vance has worked on and supervised numerous interdisciplinary projects using data at ŷ��ڱ��Ƶ Boulder, such as a data humanities class, a study linking cardiovascular disease and hearing loss and a digital map of precolonial Africa.

But Vance also has worked on a global vision of data analysis and interdisciplinary training through LISA 2020, a network of 35 “stat labs,” or statistics and data science collaboration laboratories that span across Africa, South America and South Asia.

“I saw this model where my students were getting great experience working on real projects, and the researchers and policymakers they were working with benefited tremendously. We were seeing positive impacts for society,” Vance says. “I realized that this was a fantastic model that was not just relevant in the United States, but it was relevant worldwide and especially in developing countries.”

Now, Vance has set his sights on a new stat lab being developed by IPB University in Indonesia, where he plans on living with his family for a year while on sabbatical. His work there is supported by the Fulbright Scholars Program, the U.S. government’s flagship program of international educational and cultural exchange.

“IPB is the premier statistics and data science program in Indonesia,” Vance says. “They were really keen on implementing this vision of a stat lab to both educate their students in real applications of data science and enable research and responsible data-driven decisions in their community.”

Each of the stat labs in the LISA 2020 network are individually run, but they share a core framework that emphasizes interdisciplinary collaboration. With a Fulbright award, Vance intends to study the growth of IPB’s stat lab and share its projects’ outcomes with the world.

“I’m excited to be able to witness and document the birth of a new stat lab,” Vance says. “I’m very curious as to what are the universal aspects of this teaching method and what are the aspects that are dependent on cultural and national contexts.”

Although Vance will not directly lead or teach IPB’s stat lab, he will regularly meet with and advise both faculty and students over the lab’s first year to see how his ideas of teaching collaborative data science will be put into practice.

Students are going to be exposed to a variety of problems and see how statistics and data science are applied in lots of different projects beyond the ones that they are personally involved with. They may work with a biology student one month and then the next be working with a local government official who is trying to best allocate their budget.”

“Students are going to be exposed to a variety of problems and see how statistics and data science are applied in lots of different projects beyond the ones that they are personally involved with,” Vance says. “They may work with a biology student one month and then the next be working with a local government official who is trying to best allocate their budget.”

Through his observation, Vance also hopes to learn new ideas from IPB’s emergent collaborative laboratory.

“By translating what I know from the U.S. into Indonesian culture, I’m going to learn more about what will work in the U.S.,” Vance says.

Vance’s research on IPB’s stat lab will be conducted from September to May 2024, which will likely be submitted to Statistics Education Research Journal.

Along with working to understand the stat lab’s development and the challenges it may face, Vance also looks forward to experiencing life in a new country with his family.

“It will be a challenge to move my whole family to Indonesia for a year,” Vance says. He has a 3-year-old son and a 1-year-old daughter with his wife, Marina, an assistant professor in mechanical engineering at ŷ��ڱ��Ƶ Boulder, who also was awarded by Fulbright for a project in Indonesia.

“We’ll have to figure out how to navigate living in a new culture, in a new country. And not just be there as travelers, but to set down some roots so that we really feel like we’re part of the community,” Vance says. “Personally, I’m most excited about trying new foods and completely changing my diet.”

Fulbright project to launch a new statistics course in Indonesia to provide interdisciplinary training and help students make data-driven decisions in everyday life.

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Movie on ŷ��ڱ��Ƶ prof, Manhattan Project mathematician to screen in Boulder

Anonymous — Thu, 10 Nov 2022 20:20:42 +0000

Movie on ŷ��ڱ��Ƶ prof, Manhattan Project mathematician to screen in Boulder Anonymous (not verified) Thu, 11/10/2022 - 13:20

Danny Long

‘Adventures of a Mathematician’ tells the story of Stanisław Ulam, a critical figure in the development of the hydrogen bomb

A young mathematician leaves his home country of Poland in the early days of the Third Reich, sails to the United States, and, within a decade, joins perhaps the most famous and consequential team of thinkers of the 20th century.

It’s the stuff movies are made of, one movie in particular, Adventures of a Mathematician (2020), which is screening at the Boulder Jewish Film Festival at 6:30 p.m. on Nov. 13 in the Dairy Arts Center’s Gordon Gamm Theater.

Directed by Thor Klein (Lost Place, 2013), Adventures of a Mathematician tells the story of Stanisław (Stan) Ulam, the mathematician responsible for solving the problem of how to initiate fusion in the hydrogen bomb.

At the top of the page: Ulam’s friendship with John “Johnny” von Neumann facilitated his move to Los Alamos (photo courtesy of Kathryn Bernheimer). Above: Stanisław Ulam in 1945 (Wikimedia Commons).

Born in 1909 in Lwów, Poland (then Lemberg, Austria-Hungary), Ulam showed early signs of what he would later call a “mathematical impulse.” At the age of 12, for example, while learning Albert Einstein’s special theory of relativity so that he could better understand physics and astronomy, he realized that, as he says in an interview published in 1985, he “needed to learn some mathematics.”

But he didn’t just learn some mathematics. He learned a lot of mathematics—much of it on his own. “I was 16 when I really learned calculus all by myself from a book.”

Ulam went on to study math at the Lwów Polytechnic Institute, eventually earning his PhD in 1933, the same year Hitler became chancellor of Germany.

Hitler’s rise to power boded ill for a young Jewish academic like Ulam. According to Norman Bentwich in his 2012 book The Rescue and Achievement of Refugee Scholars, Hitler’s government purged more than 1,200 Jewish scholars and scientists from German universities alone.

“In 1934, the international situation was becoming ominous,” Ulam says in his autobiography, also titled Adventures of a Mathematician.

“There were increasing displays of inflamed nationalism, extreme rightist outbreaks and anti-Semitic demonstrations. I did not consciously recognize these portents of things to come but felt vaguely that if I was going to earn a living by myself and not continue indefinitely to be supported by my father, I must go abroad.”

For the remainder of the 1930s, Ulam spent summers in Poland and his academic years in the United States, during which time he made many valuable friends, including Hungarian-American mathematician John von Neumann, or as Ulam called him, “Johnny.” Then, in 1939, he secured his first semi-permanent position, a one-year lectureship at Harvard. He set sail for the East Coast, bringing with him his 17-year-old brother, Adam, as Europe was growing increasingly dangerous.

“Our father and uncle Szymon accompanied us to Gdynia, a Polish port on the Baltic Sea, to see us off on the Polish liner Batory,” Ulam writes. “This was the last time we were to see either of them.”

Eleven days later, at a hotel on Columbus Circle in New York City, Ulam received news that Germany had bombed Poland. The war had begun.

“I suddenly felt as if a curtain had fallen on my past life, cutting it off from my future.”

The war weighed heavily on Ulam. He lost family to the Holocaust. In 1943, after teaching at the University of Wisconsin-Madison for three years, he was becoming restless.

“I was not happy with teaching,” he says. “It seemed a waste of my time; I felt I could do more for the war effort.”

So he contacted his old friend Johnny, who had recently joined a secret project in an undisclosed location in the Southwest. Though unsure what the work would entail, Ulam expressed an interest in it, and two weeks later, he received a letter signed by theoretical physicist and future Nobel laureate Hans Bethe inviting him to become part of “an unidentified project that was doing important work, the physics having something to do with the interior of stars.”

The undisclosed location turned out to be Los Alamos, New Mexico, and the “important work” was the Manhattan Project.

Ulam accepted the job. He was 34 years old. He and his wife, Françoise Aron Ulam, two months pregnant at the time, gathered their things and made for New Mexico.

The movie poster for Adventures of a Mathematician.

Klein’s film centers on Ulam’s time at Los Alamos and explores the moral dilemmas that arose there.

Kathryn Bernheimer, director of the Boulder Jewish Film Festival and author of The Fifty Greatest Jewish Movies and The Fifty Funniest Films of All Time, first saw Adventures of a Mathematician last year as a juror for the Moscow Jewish Film Festival.

“I found it interesting,” she says. It deals with the personal stories of these men, often Jewish, who, despite being “very, very committed to defeating the Nazis, had some conflicts morally and ethically over what they were doing.”

One reason for the film’s draw, Bernheimer notes, is that it is neither a documentary nor a mere listing of Ulam’s many accomplishments.

“It is a human drama about a man at the center of an international crisis, the story of an immigrant uniquely able to make a contribution to his adopted homeland by fighting the forces that drove him from Europe and decimated his people. It is the personal life story of the most significant and brilliant mathematician of his time,” she says.

Adventures of a Mathematician is precisely the kind of film Bernheimer enjoys sharing at the Boulder Jewish Film Festival, in part because it doesn’t offer easy answers.

“I always try to find films that are good conversation films,” she says. She looks for films that “you can’t stop talking about,” films that “you argue about in the car all the way home.” Adventures of a Mathematician, she says, is one of those films.

After the war, Ulam worked briefly at the University of Southern California in Los Angeles before returning to Los Alamos in 1946 to research thermonuclear weapons with von Neumann, Edward Teller, Nicholas Metropolis and Stan Frankel.

During the two decades following, while continuing his work at Los Alamos, Ulam held several visiting professorships, including at the University of ŷ��ڱ��Ƶ Boulder, where in 1967 he became professor and chair of the Department of Mathematics.

National Center for Atmospheric Research data scientist and jazz musician David Fulker (Math’66, ‘71) took two classes with Ulam and remembers him well—not as a stuffy lecturer scribbling busily on the blackboard, face turned away, but as an open, personable raconteur who would lean against his desk, and sometimes sit cross-legged on top of it, looking his pupils in the eye.

“Often storytelling was his way of introducing a complex topic,” says Fulker. “He might tell us about something like the Dirac delta function, and that might be mixed with stories about his knowing Paul Dirac.”

It was a teaching method Fulker relished. “Ulam was one of my favorite professors,” he says.

Ulam retired in 1975. Until his death in 1984, he spent his summers in ŷ��ڱ��Ƶ and Los Alamos and his winters in Florida. But his fascination with math and his appreciation for its far-reaching implications never waned, as he says in his autobiography:

“It is still an unending source of surprise for me … how a few scribbles on a blackboard or on a sheet of paper could change the course of human affairs.”

'Adventures of a Mathematician' is screening in the Dairy Arts Center’s Gordon Gamm Theater at the Boulder Jewish Film Festival on Nov. 13 at 3:30 p.m.

‘Adventures of a Mathematician’ tells the story of Stanislaw Ulam, a critical figure in the development of the hydrogen bomb.

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College announces inaugural class of social justice scholars

Anonymous — Fri, 01 Jul 2022 15:34:43 +0000

College announces inaugural class of social justice scholars Anonymous (not verified) Fri, 07/01/2022 - 09:34

This new program, headed up by the social sciences division, recognizes students that are taking a stand

The College of Arts and Sciences at the University of ŷ��ڱ��Ƶ Boulder is excited to announce the 2022 inaugural class of social justice scholars.

The social justice scholars program is a brand-new program that aims to elevate social justice as an orienting theme in the social sciences divisional work, demonstrating how different disciplines can effectively converge to tackle some of society’s biggest problems.

Up to ten undergraduate students (rising seniors) will be chosen on an annual basis to serve as social justice scholars their senior year. Each scholar will be awarded $5,000 that will become of a part of their financial aid package. Each year’s cohort will take part in social events and seminars throughout the year designed to build connections between each other, faculty in the division and members of the community engaged in related activity.

“Whether it was work for community organizations (both nationally and internationally), or service to fellow students at ŷ��ڱ��Ƶ, this year’s social justice scholars have clearly defined a high level of excellence and achievement. What is more, their stories give hope that there is a very strong current of empathy, intelligence and energy directed at what we in the social sciences hold as a foundational goal: social justice,” said David Brown, the college’s divisional dean for the social sciences.

This year’s recipients are:

Aliya Trapp, international affairs and ethnic studies
Molly Fox, leadership and community engagement and sociology (minor in business analytics)
Rachel Hill, political science and mathematics (minor in philosophy)
Meenakshi Manoj, international affairs and economics
Shae Stokes, sociology and philosophy
Sibonelly Espitia Sanchez, sociology and psychology
Gabriela Mejia, cinema studies and ethnic studies (minor in leadership studies)
Peri Cooper, International affairs and theatre
Natasha Panepinto, political science (minor in Spanish)
Blen Abamecha, ethnic studies
Isla DePuy-Bravo, international affairs (minors in Spanish and political science)
Makayla Sileo, speech, language and hearing sciences (minors in sociology and leadership studies)
Maymuna Jeylani, ethnic studies and secondary education (minor in leadership studies)

For these students, the resounding response at being chosen has been one of excitement.

“I can't think of a better opportunity to finish out my time here than serving as a Social Justice Scholar. I am excited to see not only what this experience has to offer me, but to learn how I can leave an impact on both the program and the university and Boulder community that has given me so much,” said Panepinto.

Espitia Sanchez agrees, adding: “My studies have confirmed the frequent occurrence of everyday social problems, exposing just how cruel the world can be and how many victims of social injustices exist in all corners of the world. I’ve become incredibly inspired and determined to not only address social justice issues, but learn to contribute to their solutions during my time at ŷ��ڱ��Ƶ.”

For those interested in applying for 2023, applications need to be submitted through AcademicWorks by May 14, 2023.

The application consists of a two-page, single-spaced letter explaining how your course of study, work in the community or interest and participation in addressing social justice issues forms an important part of your experience at ŷ��ڱ��Ƶ Boulder. In addition to the written statement, provide an unofficial copy of your transcript. All applicants must have an overall GPA of at least 3.0.

The selection committee will be looking for students who have crafted a course of study that addresses social justice issues or have participated in related clubs, programs or organizations.

The selection will be announced by June 1, 2023.

Aliya Trapp

The Social Justice Scholars program seemed like an amazing and unique opportunity to get involved in activism within the Boulder community with my fellow classmates. Social activism has always been an important cornerstone in my life, and I knew this program would give me the ability to increase my knowledge on being more effective and having a greater impact. I am incredibly honored to apart of the inaugural year.

Molly Fox

As a transfer student to ŷ��ڱ��Ƶ Boulder, I saw the potential for a social science degree to grow my formal training in social justice and elevate my understanding of my place in the issues that I want to pursue. As I continue engaging in social justice research, public action projects and volunteering through my senior year, I hope to only grow my motivation and fascination with how social systems function to produce such ill effects in society, and how those same systems hold the answers for sustainable solutions for the future. Excited for the ways I will grow and the people I will meet through this program!

Rachel Hill

Rachel Hill is a senior studying political science and math. Originally from Littleton, ŷ��ڱ��Ƶ, she attended Columbine High School and started gun violence prevention work when she was sixteen. Since then, she has worked to lobby and testify for common sense gun legislation at local, state and federal levels. Following the Boulder King Soopers shooting, she has turned her passion toward helping her local community heal from the effects of gun violence. She is also currently serving as Student Body President here at ŷ��ڱ��Ƶ.

Meenakshi Manoj

My name is Meenakshi Manoj, and I'm an international affairs and economics double major at ŷ��ڱ��Ƶ Boulder. I'm excited to be part of the Social Justice Scholars program! I have previously worked with the Office of State Planning and Budget at the Governor's office in pursuing better equity goals in legislation. I'm currently hoping to establish a student organization on campus devoted to dealing with and combatting sexual assault on campus at large. I'm looking forward to the opportunities and connections this program will bring!

Shae Stokes

Hello! My name is Shae and I am a rising senior pursuing a double major in sociology and philosophy at ŷ��ڱ��Ƶ Boulder, as well as a certificate in animals and society. Animal welfare is one of my greatest passions, both for its own sake and because animal agriculture is closely connected to numerous other social justice issues affecting people and our planet. I am honored to be able to further develop my skills as a social justice activist through this program!

Sibonelly Espitia Sanchez

As a sociology and psychology double major, I have developed passions to understand the world we live in and the individuals which inhabit it. My studies have confirmed the frequent occurrence of everyday social problems, exposing just how cruel the world can be and how many victims of social injustices exist in all corners of the world. I’ve become incredibly inspired and determined to not only address social justice issues, but learn to contribute to their solutions during my time at ŷ��ڱ��Ƶ.

Gabriela Mejia

Gabriela Mejia is a film student based in Boulder, ŷ��ڱ��Ƶ who is pursuing a BFA in Cinema Studies and Ethnic Studies with a minor in Multicultural Leadership.She works towards diversity and inclusivity both in front and behind the camera and casts women of color as leads in her films and is committed to working with a female-helmed crew.

Peri Cooper

My whole life, I’ve loved stories, from books to art to theatre. I loved the way that they can solve problems and create a world that doesn’t really exist in real life. I want to help make that a reality. We live in a world filled with prosperity and amazing things, but not everyone gets to experience those in the same way. For the world to become more equitable, that must start with us.

Natasha Panepinto

Social justice is something I have cared deeply about long before I arrived at ŷ��ڱ��Ƶ Boulder. I was lucky enough to have parents who shared my passion and took me to marches and protests whenever they had the chance. Throughout my last three years at ŷ��ڱ��Ƶ, I have continued to pursue this passion, taking every opportunity offered, despite the complications of the COVID-19 pandemic. Although it was constantly changing and interrupting things, I was able to take numerous courses that gave me a better understanding of social justice and why we need it. These courses combined with my participation in ŷ��ڱ��Ƶ in DC, establishment of the student organization Leading Women of Tomorrow, and service on the Appellate Court have given me an extremely memorable and meaningful experience at ŷ��ڱ��Ƶ. That said, I can't think of a better opportunity to finish out my time here than serving as a social justice scholar. I am excited to see not only what this experience has to offer me, but to learn how I can leave an impact on both the program and the university and Boulder community that has given me so much.

Blen Abamecha

I am interested in the Social Justice Scholars Program because I want to be in a space alongside other scholars who not only want to make a change but are taking steps to end racial injustice by actively doing social justice work. As a Black woman in Boulder, I feel like this is a community where I would feel a sense of belonging and collaboration on campus which is really important to me. I love that we will also be working with alumni and leaders because I'd love to build connections with them and hopefully be inspired by the work they have contributed to their communities. I am excited to meet and form/strengthen relationships with other students in this program who have similar values as me.

Isla DePuy-Bravo

I was born and raised in North Denver to two very unique parents whose engagement with political/social issues inspired my interest in social justice issues from a young age. My studies at ŷ��ڱ��Ƶ Boulder have aligned with and prompted further interests regarding socioeconomic injustices and inequities facing those less privileged than I. As the daughter of an immigrant from Central America, issues pertaining to immigration and the harsh realities faced by immigrants have led to my eager desire to develop the skills to advocate for those in vulnerable and unsafe circumstances. I am eager to continue my academic and life journey to make tangible improvements in the lives of others and feel that with the guidance and knowledge from the Social Justice Scholarship program I will be even better equipped to do so.

Makayla Sileo

My name is Makayla and I hope to spend my life seeing, listening, learning and advocating for those on the fringes of society. I love art, reading, writing, hiking, camping, being active and, most importantly, spending quality time with quality humans. My parents raised my sister and I to “leave the campsite better than we found it” and I believe this is how we make the world a more compassionate place. I cannot wait to take this idea and bring it to the Social Justice Scholars community.

Maymuna Jeylani

I was very interested in the Social Justice Scholar program because my experience at ŷ��ڱ��Ƶ has been one rife with racial and social hardships and I think of my being at ŷ��ڱ��Ƶ as an act of resistance in which there are many ways I engage in social justice. I'm interested in seeing how this program can engage me and help me address social justice problems, especially those with personal diasporic meanings as I am Black and Somali.

This new program, headed up by the social sciences division, recognizes students that are taking a stand

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Seventeen students are named 2022 Van Ek Scholars

Anonymous — Thu, 28 Apr 2022 19:56:20 +0000

Seventeen students are named 2022 Van Ek Scholars Anonymous (not verified) Thu, 04/28/2022 - 13:56

The award, considered one of the College of Arts and Sciences' highest honors, is given to students for academic achievement and service

The College of Arts and Sciences has awarded the Jacob Van Ek scholarship, one of the college's highest honors, to 17 exceptional undergraduates.

These students were nominated by faculty at the University of ŷ��ڱ��Ƶ Boulder for their superior academic achievement and service to the university, the Denver and Boulder communities, or larger national and international communities. The five-person Van Ek Scholars Award committee selected the winners, who receive a $230 award and a certificate of recognition.

They have done so much for the ŷ��ڱ��Ƶ Boulder community, as well as in their respective communities."

"We had amazing nominations submitted from faculty this year," says Brenda Navarrete, scholarship coordinator in the College of Arts and Sciences. "They have done so much for the ŷ��ڱ��Ƶ Boulder community as well as in their respective communities."

"They are very deserving, and I am excited to see the amazing things they will achieve after graduating!”

The award is named for Jacob Van Ek, who arrived at ŷ��ڱ��Ƶ as a young assistant professor shortly after earning his doctorate at what is now known as Iowa State University in 1925. Within three years he was a full professor and, by 1929, he was dean of the College of Liberal Arts, serving until 1959.

The following students are this year’s Jacob Van Ek Scholar Award recipients:

Areyana Janae Andrea Proctor, journalism
Elicia Azua, psychology
Evi Judge, linguistics and speech, langauge and hearing sciences
Jack Barker, environmental studies
Julia Hoa Leone, international affairs and Jewish studies
Kelila Rose Fitch-Cook, women and gender studies
Kathryn Hoesly, Chinese
Leen Salah Eldin Abbas, integrative physiology
Mackayla Coley, political science
Morgan Knuesel, physics and mathematics
Megan Lenard, psychology and sociology
Michelle Tracy Leung, environmental studies and ecology and evolutionary biology
Nicole Bouzan, molecular, cellular and developmental biology
Noopur Naik, molecular, cellular and developmental biology
Ruth Woldemichael, ethnic studies and international affairs
Sophia Choubai, integrative physiology
Ty Donovan McCaffrey, ecology and evolutionary biology

The award, considered one of the College of Arts and Sciences' highest honors, is given to students for academic achievement and service

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Mathematicians win prestigious NSF CAREER Awards

Anonymous — Tue, 15 Mar 2022 22:30:35 +0000

Mathematicians win prestigious NSF CAREER Awards Anonymous (not verified) Tue, 03/15/2022 - 16:30

ŷ��ڱ��Ƶ Boulder’s Agnès Beaudry and Sean O’Rourke will use the support to advance homotopy theory and random matrix theory

Two young mathematicians at the University of ŷ��ڱ��Ƶ Boulder have won Early Career Development Program (CAREER) awards from the National Science Foundation (NSF) to advance homotopy theory and, separately, probe the applications of random matrix theory.

Agnès Beaudry, assistant professor of mathematics, has won $475,000 in support for a five-year research project, and Associate Professor Sean O'Rourke has won $430,000 in support of a five-year research project.

The CAREER Program, one of the NSF’s most prestigious awards, supports early career faculty who have the potential to serve as academic role models in research and education and to lead advances in the mission of their department or organization.

Beaudry’s project has two main themes, both of which include the study of stable invariants.

An invariant is an algebraic quantity assigned to a geometric object. The invariant is considered topological, or geometrically unaltered, if a continuous deformation of the object does not change the algebraic quantity assigned to it. It is stable if it is insensitive to certain dimensional shifts.

Above: Agnès Beaudry is a algebraic topologist and homotopy theorist at ŷ��ڱ��Ƶ Boulder.

The first line of investigation is in equivariant chromatic homotopy theory, a field of mathematics that studies structural properties of stable invariants for topological spaces with symmetries. A classical example of such invariants is K-theory, which this award studies.

The second line of investigation is part of a multi-disciplinary collaboration with mathematicians and physicists; it uses stable invariants to study the phase of matter., which is a family of quantum systems, or a collection of interacting particles, that share common properties.

For certain types of quantum systems, the phase type can be detected by stable invariants. This project aims to construct new stable invariants of phases and to study stable invariants of quantum systems equipped with certain symmetries.

The project has an educational component, one goal of which is to make the two areas of research accessible to graduate students and advanced undergraduates through graduate workshops.

The educational plan also includes undergraduate and graduate research. In particular, the project will conduct research in collaboration with existing initiatives at ŷ��ڱ��Ƶ Boulder that work to promote diversity, equity and inclusion in science, technology, engineering and math (STEM).

Beaudry said she was very thankful for the award. “Equivariant stable homotopy theory (the technical name for the study of stable invariants and their symmetries), has seen a lot of exciting developments recently, and this award explores questions that have been opened by these new advances,” she said, adding:

“And then the fact that this abstract machinery can be used in physics to understand phases of matter is surprising and fascinating. I’ve been extremely lucky that my path through mathematics has put me in a position where I can have the opportunity to work in these two areas with amazing mathematicians and physicists. The award will allow me to share this privilege with students, helping them join these areas of research. … I look forward to giving students from all kinds of backgrounds the opportunity to learn about these exciting topics.”

O'Rourke’s project, which has funding under the American Rescue Plan Act of 2021, will focus on random matrix theory and its applications. Random matrices arise naturally in many fields, including statistics, data science, computer science and physics, his abstract notes.

For example, random matrices were originally introduced in physics to study the nuclei of heavy atoms.

O’Rourke’s project aims to understand the properties of certain random matrix models that arise in diverse domains, including control theory, statistical genetics and the study of neural networks.

Beyond supporting my own research and the research of my graduate students, this award also recognizes the importance of mathematics education and research at the undergraduate and high school levels.”

“This research opens the door to a deeper understanding of applications in these domains and has the potential to create avenues of future fundamental research in random matrix theory and related fields,” he states.

The overarching research goal of this project is to understand the behavior of the eigenvectors (a nonzero vector) and eigenvalues (when eigenvectors are scaled) of random matrices with dependent entries. The research program will be divided into three themes, he states.

The first theme concerns the eigenvalues and eigenvectors of matrices arising in the study of random networks and graphs, including matrices that appear in synchronization problems and network control theory.

Motivated by open questions in statistical genetics, the second theme concerns the spectral properties of sample covariance matrices constructed from dependent random samples.

The third theme is inspired by the theoretical study of neural networks and involves random matrix products.

O’Rourke’s project also features educational components that integrate research and teaching. These components include a summer academy for high school students interested in advanced mathematics and undergraduate and graduate student mentoring, training, and research.

“It is a great honor to receive this award, and I am grateful for the opportunities it provides. Beyond supporting my own research and the research of my graduate students, this award also recognizes the importance of mathematics education and research at the undergraduate and high school levels,” O’Rourke said.

Including Beaudry and O’Rourke, 174 ŷ��ڱ��Ƶ Boulder faculty members have won NSF CAREER Awards since 1996.

ŷ��ڱ��Ƶ Boulder’s Agnès Beaudry and Sean O’Rourke will use the support to advance homotopy theory and random matrix theory.

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Alumnae skirt convention

Anonymous — Mon, 07 Mar 2022 23:46:56 +0000

Alumnae skirt convention Anonymous (not verified) Mon, 03/07/2022 - 16:46

Clay Bonnyman Evans

Two graduates recall when they were the only female math undergrads at ŷ��ڱ��Ƶ Boulder

For Ann Lowdermilk and Marlene Pratto, talent in mathematics always felt like the most normal thing in the world. But many of their male classmates and math professors at the University of ŷ��ڱ��Ƶ Boulder in the late 1950s and early ‘60s weren’t quite sure what to make of the aliens in their midst.

“Marlene and I were the only two ‘skirts’ in Hellems Hall,” recalls Lowdermilk (Math’60), of Denver. “We usually sat together, and they didn’t know what to do with two women; they didn’t even know what to do with one woman!”

But there were professors who not only welcomed the two young women, but encouraged them, including the late Arne Magnus, who created an independent study program for them, and Robert McKelvey. Magness eventually became chair of mathematics at ŷ��ڱ��Ƶ State University and McKelvey finished his career at the University of Montana.

“We had all men in our classes,” says Pratto (Math’60), who has lived in Greensboro, North Carolina since 1969. “A lot of them were older than we were, returning veterans. I think they mostly ignored us. We didn’t study with them.”

At the top of the page: Hellems Hall was home to the Department of Mathematics in the late 1950s and early 1960s. Above: Marlene Pratto (left) was one of only two female math undergrads at ŷ��ڱ��Ƶ Boulder during her time as a student.

Lowdermilk does recall at least one time when she stirred the attention of a male classmate: when she returned for her senior year wearing an engagement ring.

“The young man sitting behind me said something and I said, ‘Yes, I’m engaged,’” she recalls. After a brief pause, he sighed and said, ‘To think I had just about screwed up enough courage to ask you to coffee…’”

But both Pratto and Lowdermilk were used to being fish out of water at a time when far fewer women went to college and those who did typically went into nursing, education or home economics.

Even in high school, they were the odd women out. But if anything, being in the minority gave them more, not less, confidence.

Attending Smiley Junior High School and Denver East High School, Lowdermilk was smart enough to earn full-ride scholarships to both ŷ��ڱ��Ƶ College (CC) and ŷ��ڱ��Ƶ Boulder. The CC offer came in first, and she accepted. But she believed ŷ��ڱ��Ƶ Boulder’s Department of Math was better, and she was never in doubt when its offer came in.

“I ditched the CC scholarship and took the one at ŷ��ڱ��Ƶ. My advisor said I should not do that, and I said, ‘Just watch me,’” she says. “When you were a woman in an all-male area, you had to learn to simply stand up for yourself. You couldn’t just fade back in the corner.”

Pratto credits a seventh-grade teacher in Pueblo, Miss Seacat, for sparking her interest in math and science.

“She was a little person, but she made science so dynamic and so interesting. I just loved it,” she says.

She was soon besting the boys in math competitions. She was thrilled when her high-school math teacher John Armstrong (a ŷ��ڱ��Ƶ Boulder alumnus) convinced the powers that be to provide “math analysis”—analogous to calculus—in time for her to take the course her senior year.

When the time came to go to college, she had no option to go out of state or attend a private school, so she faced a choice between ŷ��ڱ��Ƶ Boulder, ŷ��ڱ��Ƶ State University and the ŷ��ڱ��Ƶ School of Mines.

“When (a Mines representative) came to Pueblo Central (High School), he said you’ll double our enrollment of women if you come. That didn’t sound too good,” Pratto recalls. “I’d been to ŷ��ڱ��Ƶ for Engineering Days and as part of the all-state orchestra, and I liked it.”

Like Lowdermilk, she received a scholarship to attend ŷ��ڱ��Ƶ Boulder in mathematics.

The two women met the summer before their freshman year while taking placement exams and remained friends throughout their ŷ��ڱ��Ƶ Boulder careers and beyond.

Lowdermilk worked full adult shifts in payload control during the summer for United Airlines, where her father worked. After graduating from ŷ��ڱ��Ƶ Boulder, she went to work in the operations department of Martin Marietta in Denver.

“My last day was May 6, 1961, the day Alan Shepard went up into space and came down 15 minutes later,” she says. “I would have stayed longer, but as women did at that time, I married and followed my husband, who was a highway contractor. If my husband had not traveled all over the western states, I would have gone on to get advanced degrees.”

After that, she moved to ŷ��ڱ��Ƶ’s Western Slope, and later rural Utah, to raise a family while her husband helped build I-70.

Math is one of the best degrees you can get. It sets you up to do a whole bunch of things. You learn to think at least somewhat logically and can solve problems.”

“I was a real city girl living with a two-year-old and a baby in a town with 300 registered Mormon souls in Emory, Utah, and the surrounding area,” she says. “I learned how to can, bake bread, quilt, all things I’d never have any association with before. But that’s what women did down there.”

Pratto worked as a summer trainee in mathematics at the National Bureau of Standards (now the National Institute for Science and Technology) from her sophomore year on and accepted a full-time position upon graduation. As in school and college, she had few women colleagues.

“One day I was handed a book and told, ‘Tomorrow we’ll program the computer.’ I said, ‘What’s a computer? What’s a program?’” she says. “The next day I sat down with the guy I was working with and wrote a program, and that’s how we learned.”

In 1969, her husband took a faculty position at the University of North Carolina at Greensboro, and she decided to retire from programming.

“That lasted until about December, when I thought, ‘This is Dullsville, U.S.A.’ … I called the local technical college”—and historically Black university—“North Carolina A&T, which had the largest Black engineering school in the country.”

Asked if she could teach Fortran to engineering faculty, she said yes and began teaching part-time. Eventually, the mother of young children began working from home on programming projects from her dining room table, creating the school’s computer registration system, among other things.

Both long retired, the two friends remain bullish on women and girls studying and entering STEM fields.

“Math is one of the best degrees you can get. It sets you up to do a whole bunch of things. You learn to think at least somewhat logically and can solve problems,” Pratto says. “I can’t think of a better major, then or now.”

Two graduates recall when they were the only female math undergrads at ŷ��ڱ��Ƶ Boulder.

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Mathematician’s dissertation wins top prize in logic

Anonymous — Mon, 24 Jan 2022 22:36:54 +0000

Mathematician’s dissertation wins top prize in logic Anonymous (not verified) Mon, 01/24/2022 - 15:36

Marcos Mazari-Armida, a postdoctoral researcher at ŷ��ڱ��Ƶ Boulder, wins 2021 Sacks Prize from the Association of Symbolic Logic

A University of ŷ��ڱ��Ƶ Boulder mathematician has won the Sacks Prize, which recognizes the year’s best dissertation on mathematical logic, the Association of Symbolic Logic has announced.

Marcos Mazari-Armida, a Burnett Meyer Postdoctoral Fellow at ŷ��ڱ��Ƶ Boulder who earned his PhD from Carnegie Mellon University, is the 2021 winner. He is in the first year of a three-year appointment at ŷ��ڱ��Ƶ Boulder.

Mazari-Armida specializes in model theory, a subfield of mathematical logic that studies the relationship between mathematical objects and the languages used to communicate about those objects.

Mazari-Armida showed in his dissertation that abstract elementary classes, which are a semantic framework to study model theory, can affect traditional mathematics in interesting ways. Using the framework of abstract elementary classes, Mazari-Armida linked the 50-year-old model-theoretic notion of “superstability” to the classical 100-year-old algebraic notion of a “Noetherian ring.”

At the top of the page: A section of Marcos Mazari-Armida's dissertation. Above: Marcos Mazari-Armida, winner of the Sacks Prize.

He is also interested in whether, given an infinite cardinal and a class of structures, there is a single model in the class of the desired cardinality that contains all the models in the class of that cardinality. Through his research, Mazari-Armida showed that there are universal models in the class of torsion abelian groups for purity.

“I am incredibly honored to have won the Sacks Prize,” Mazari-Armida said. “I am very grateful to my advisor Rami Grossberg for all of his support.”

He also acknowledged that many of the results in his thesis rely on significant developments achieved by other researchers throughout the years. “I thank them for the beautiful mathematics they developed.”

The Sacks Prize was established to honor the late Professor Gerald Sacks of the Massachusetts Institute of Technology and Harvard University for his unique contribution to mathematical logic, particularly as an adviser to many standout PhD students.

The prize became an Association of Symbolic Logic prize in 1999. The Sacks Prize includes a cash award and five years’ free membership in the group. This is an international prize, with no restriction on the nationality of the candidate or the university where the doctorate is granted.

The Association for Symbolic Logic is an international organization that supports research and critical studies in logic. Its primary function is to provide an effective forum for the presentation, publication and critical discussion of scholarly work in this area of inquiry.

Logic is an ancient discipline that has undergone striking modern developments through the introduction of rigorous formal methods, stimulated largely by foundational problems in mathematics, the group states. “Symbolic logic” is a term intended to encompass the entire field of logical inquiry, undertaken in this modern spirit.

The association was founded in 1936, when great advances in logic were beginning to be made. Its first members were mainly mathematicians and philosophers who perceived a common ground and sought to strengthen it.

Recent research in other areas such as computer science, linguistics and cognitive science has also been inspired by logic, and the current membership and activities of the association reflects such expanding interests, the group says.

Mazari-Armida is the second mathematician affiliated with ŷ��ڱ��Ƶ Boulder to win the prize. The first was Rene Schipperus, who earned his PhD from ŷ��ڱ��Ƶ Boulder in 1999 under the guidance of the late Richard Laver, professor of mathematics.

He is also the second Latin American to have won the prize. The first one was Antonio Montalbán in 2005.

Marcos Mazari-Armida, a postdoctoral researcher at ŷ��ڱ��Ƶ Boulder, wins 2021 Sacks Prize from the Association of Symbolic Logic

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Mathematician, physicist win junior faculty development award

Anonymous — Fri, 16 Jul 2021 16:06:19 +0000

Mathematician, physicist win junior faculty development award Anonymous (not verified) Fri, 07/16/2021 - 10:06

ŷ��ڱ��Ƶ Boulder’s Kyle Luh and Shuo Sun recognized as emerging leaders in their fields

At the top of the page: Nanophotonics using photons. Above: Kyle Luh

Two young faculty members at the University of ŷ��ڱ��Ƶ Boulder have been awarded the Ralph E. Powe Junior Faculty Enhancement Award, the Oak Ridge Associated Universities (ORAU), an association working to advance national priorities in science, education, security and health, announced last month.

Shuo Sun

Kyle Luh, assistant professor of mathematics, and Shuo Sun, assistant professor of physics, and their fellow recipients will receive $5,000 in seed money for the 2021-22 academic year to enhance their research as they launch their academic careers. Each recipient’s institution matches the award, and winners may use the $10,000 grants to purchase equipment, continue research or travel to professional meetings.

“As a research institution, ORAU is proud to recognize and support the research and professional development of the 35 emerging leaders who are receiving Powe Awards this year,” said Ken Tobin, ORAU vice president for research and university partnerships.

Luh’s research interests include random matrix theory, random graphs and probabilistic combinatorics. He is also interested in the applications of these fields to statistics, theoretical computer science, physics, data science and machine learning.

Luh earned a master’s in physics in 2012, a master’s in mathematics in 2015, and his PhD in mathematics in 2017, all at Yale.

Sun, who is also an associate fellow at JILA (a joint institute of ŷ��ڱ��Ƶ Boulder and the National Institute of Standards and Technology), focuses his research in the areas of quantum optics, nanophotonics (the study of the behavior of light) and experimental quantum information science.

Sun joined the ŷ��ڱ��Ƶ Boulder faculty in 2020 after earning his PhD in electrical engineering at the University of Maryland, College Park. During his PhD work, he developed the first spin-photon quantum switch and the first single-photon transistor using a solid-state spin. His group studies strong light-matter interactions at the quantum limit by coupling solid-state artificial atoms with nanophotonic structures.

Michael Ritzwoller, professor and chair of physics, said the department is pleased by Sun’s recognition as an emerging leader in his fields. “Professor Sun’s exciting research program will be aided through this acknowledgement,” Ritzwoller said.

Powe Awards recognize faculty members for their work in any of five science and technology disciplines: engineering or applied science; life sciences; mathematics and computer science; physical sciences; and policy, management or education.

Since the program’s inception, Oak Ridge Associated Universities has awarded 804 grants totaling about $4 million.

The awards are named for Ralph E. Powe, who served as the ORAU councilor from Mississippi State University for 16 years. Powe participated in numerous committees and special projects during his tenure and was elected chair of ORAU’s Council of Sponsoring Institutions. He died in 1996.

Including Luh and Sun, seven ŷ��ڱ��Ƶ Boulder faculty members have won the Powe Award.

ŷ��ڱ��Ƶ Boulder’s Kyle Luh and Shuo Sun recognized as emerging leaders in their fields.

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