Mathematics

51�Թ�� mathematician honored by peers

Rachel Sauer — Thu, 06 Nov 2025 18:48:23 +0000

51�Թ�� mathematician honored by peers Rachel Sauer Thu, 11/06/2025 - 11:48

Katherine Stange is named a fellow by the American Mathematical Society, becoming the second person in the math department to garner AMS recognition

Katherine Stange, a professor of mathematics at the 51�Թ��, is one of 40 mathematicians from around the world to be named a 2026 fellow of the American Mathematical Society.

Katherine Stange, a 51�Թ�� professor of mathematics, has been named a 2026 fellow of the American Mathematical Society.

AMS members designated as fellows have made “outstanding contributions to the creation, exposition, advancement, communication and utilization of mathematics,” according to the society.

“I am honored to congratulate the 2026 class of AMS fellows,” said AMS President Ravi Vakil. “Their research and service endeavors help ensure the health of the mathematical sciences on a daily basis. AMS fellows are selected from a substantial pool of accomplished candidates. Their collective achievements highlight the many ways individuals devote themselves to our beautiful and essential subject.”

“I'm grateful to my nominators and to all my colleagues, collaborators, students and mentors, who make mathematics such a beautiful and fun endeavor,” said Stange.

Stange’s area of research includes arithmetic geometry, elliptic curves, algebraic and integer sequences, cryptography, arithmetic dynamics, Apollonian circle packings and game theory.

Stange becomes the second 51�Թ�� Department of Mathematics professor to be named an AMS fellow; Agnes Beaudry was named a fellow in 2024.

Goals of the AMS fellows program include creating a class of mathematicians recognized by their peers for their professional contributions, lifting the profession through the provision of an honor, and supporting the advancement of mathematicians to leadership positions in both their institutions and the broader society.

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Katherine Stange is named a fellow by the American Mathematical Society, becoming the second person in the math department to garner AMS recognition.

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CU grad Erin Macdonald makes it so

Rachel Sauer — Tue, 15 Apr 2025 22:18:50 +0000

CU grad Erin Macdonald makes it so Rachel Sauer Tue, 04/15/2025 - 16:18

Bradley Worrell

The 2009 math and astrophysics double major has successfully transformed herself from a scientist to an educator to a storyteller sailing with the enterprise known as Star Trek

As she worked toward completing her bachelor’s degrees in astrophysics and mathematics at the 51�Թ�� in the late 2000s, Erin Macdonald often enjoyed watching Star Trek: The Next Generation with her college friends. Today, she is a science advisor for the entire Star Trek franchise.

“I don’t think I could have ever conceived it, that being able to work in television and movies was a real thing that people could actually do,” Macdonald says in retrospect. “And if you told me that I would see my name in TV credits—not to mention in the Star Trek font with the Star Trek theme playing—it’s almost unbelievable.”

It’s been a remarkable journey from academia to Hollywood, Macdonald acknowledges. Still, she is quick to add that in a multiverse of possibilities, the outcome was never assured, and it did not happen at warp speed.

51�Թ�� alumnus Erin Macdonald, who double majored in mathematics and astrophysics, is a science advisor for the Star Trek franchise and author of Star Trek: My First Book of Space. (Photo: Bradley Worrell)

Raised in Fort Collins, Colorado, Macdonald did not grow up watching Star Trek. However, she was deeply motivated to study science after being inspired by the protagonist astronomer Ellie Arroway in the movie Contact, as well as by fictional FBI agent and medical doctor Dana Scully in the popular TV show The X-Files.

“I watched The X-Files growing up, and Dana Scully for me was just the coolest woman who ever existed. That really sparked an excitement to be a scientist,” she says. “And then when Contact came out, watching Dr. Ellie Arroway use a telescope to find aliens, and seeing her legitimately work as an astronomer was the first time I ever saw that as a career.”

Still, there were some obstacles to overcome, Macdonald says, including the fact that math did not come naturally to her.

“In high school, I had friends who were taking classes that seemed to get it. And for me, I felt like I was trudging through mud trying to understand things—but knowing that I had to get through the math,” she says. Finally, when taking a Calculus 3 course at 51�Թ��, she says she experienced a breakthrough when she came to understand how math worked with physics, and then “everything just clicked.” It prompted her to immediately declare a double major in mathematics and astrophysics.

Gaining another role model

It also was in college that Macdonald was first exposed to Star Trek through a tightknit group of fellow students who were big fans of the TV shows.

“In the Venn diagram of physics majors and Star Trek fans, there is a big intersection,” she says with a laugh. “I was in my early 20s and (fictional) Voyager Captain Catherine Janeway became my new Scully. She was someone who had gone from being a science officer to a captain. At that point, I knew I wanted to get my PhD, but I didn’t necessarily want to be a researcher as a career. So, Janeway was a role model, how she was a leader and a problem-solver and a mentor. It was something I aspired to.”

After graduating from 51�Թ�� in May 2009, Macdonald enrolled at the University of Glasgow in Scotland, where she earned her PhD in astrophysics in 2012. Normally, a master’s degree would be the next educational step after obtaining an undergraduate degree, but Macdonald credits the quality of the education she received at 51�Թ��—and particularly the research opportunity and mentorship of astrophysics and planetary sciences Professor Jeremy Darling—with allowing her to immediately advance to working toward a doctorate.

After obtaining her PhD, Macdonald spent two years doing post-doctoral research at Cardiff University in Wales, United Kingdom. She later moved back to Colorado, where she worked as an adjunct professor in the community college system and as an educator at the Denver Museum of Nature & Science for about a year, then transitioned to work as an aerospace engineer for a contractor based in the Denver area.

“In the Venn diagram of physics majors and Star Trek fans, there is a big intersection,” says 51�Թ�� alumnus Erin Macdonald. (Photo: Bradley Worrell)

It was during her time working for the contractor, and while attending pop culture conventions for fun, that Macdonald hit upon the idea that she could combine her deep knowledge of astrophysics with her love of science fiction to give talks on the science of science fiction TV shows, movies and videogames at fan conventions.

“After a while in the private sector, I found I really missed teaching. I was already going to conventions, so I proposed giving talks,” she says, adding that event organizers were receptive to the idea. “For topics, a popular one is physics and Star Trek. I’d say, ‘I did my PhD in gravitational physics, so let me explain how (theoretically) warp drives work, because I actually know the science of how warp drives work.’”

To boldly go …

In 2017, Macdonald moved to the Los Angeles area, where she continued to work in the aerospace industry while also giving science/science fiction talks at fan conventions, or as she describes herself in that time: “rocket scientist by day, warp engineering expert by evening.” It was during that period that she began meeting actors and writers at fan events, which ultimately led to industry connections with executives at CBS, the producer of all things Star Trek.

Macdonald was initially hired to give talks at CBS-sponsored events, including Star Trek Cruises. That led to an introduction with the co-executive producer of Star Trek Discovery, who asked Macdonald to serve as a science advisor for the show as season 3 began production.

“I believe I did a good job on that season, so I think the executives saw value in hiring a science advisor to be available to all of their shows to maintain consistency across the franchise, to understand all of the made-up technologies that we have in Star Trek and to be able to communicate that to the writers as well,” she says. “That’s been going on since 2019, so almost five years now.”

Meanwhile, Macdonald has written four screenplays, and she has done voice acting for Star Trek Prodigy, an animated Star Trek show, during which she had the opportunity to work with Kate Mulgrew, the actress who played Captain Janeway on Star Trek Voyager.

“When I started working on Star Trek Prodigy, they were bringing Captain Janeway back as a teacher for young kids. I was going to help write some of her lines, and that was when I had this huge epiphany of—I’m not meant to become Captain Janeway; I’m meant to write Captain Janeway and create characters that inspire kids to become scientists.”

“When I started working on Star Trek Prodigy, they were bringing Captain Janeway back as a teacher for young kids. I was going to help write some of her lines, and that was when I had this huge epiphany of—I’m not meant to become Captain Janeway; I’m meant to write Captain Janeway and create characters that inspire kids to become scientists,” she says. “And so now, I find that storytelling lets me sort of inspire and motivate the next generation of STEM professionals, and that’s what I want to do as a career.”

Macdonald has found her voice as a storyteller in several different ways. In 2022, she published Star Trek: My First Book of Space, an illustrate children’s board book that uses Star Trek to talk about science, technology, engineering, arts and math (STEAM), and she wrote and narrated the Audible Original “The Science of Sci-Fi” in collaboration with The Great Courses.

Additionally, in 2021, McDonald created Spacetime Productions, a film development and production company devoted to giving representation to traditionally marginalized voices, including those in the LGBTQIA+ community. The company has produced two short films including Identiteaze, released on the streaming service Nebula earlier this summer.

Reflecting on her journey from scientist to educator to storyteller, Macdonald says her success is the result of recognizing good opportunities, trusting her instincts, perseverance and, most importantly, putting in the time and work to achieve her goals.

“You know, I didn’t quit my PhD and move to LA with no plan. I took those important steps in between,” she says. “And it took me until well into my 30s for me to realize what I wanted, to be a storyteller and create those Dana Scullys and Captain Janeways, as opposed to becoming one of those characters. And that’s OK. All of those steps along the way helped inform the work I do now.”

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The 2009 math and astrophysics double major has successfully transformed herself from a scientist to an educator to a storyteller sailing with the enterprise known as 'Star Trek.'

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Katherine Stange named 2025-26 Birman Fellow

Rachel Sauer — Tue, 10 Dec 2024 15:41:57 +0000

Katherine Stange named 2025-26 Birman Fellow Rachel Sauer Tue, 12/10/2024 - 08:41

The American Mathematical Society recognition supports mid-career female researchers whose achievements demonstrate potential for further contributions to mathematics

Katherine Stange, a professor in the 51�Թ�� Department of Mathematics, has been named the 2025-26 American Mathematical Society (AMS) Joan and Joseph Birman Fellow.

The Joan and Joseph Birman Fellowship for Women Scholars is a mid-career research fellowship that aims “to address the paucity of women at the highest levels of research in mathematics by giving exceptionally talented women extra research support during their mid-career years,” according to the AMS. Fellows are those “whose achievements demonstrate significant potential for further contributions to mathematics.”

Katherine Stange, a 51�Թ�� professor of mathematics, has been named the 2025-26 American Mathematical Society (AMS) Joan and Joseph Birman Fellow.

“I am both honored and humbled by this award,” Stange says. “As my career has unfolded, I've learned the incredible value of community in mathematics, and I feel a great debt of gratitude to my amazing collaborators and the support of my mathematical community.

“Joan and Joseph Birman's vision, to support the careers of women reconciling the many aspects of work and life, goes beyond these individual awards; and so, I hope to support those around me, just as I have been privileged by the support of so many.”

Fellows can use the $50,000 award in any way that most effectively enables their research, including child care, release time, participation in special research programs and travel support.

Stange, a number theorist, earned her bachelor of mathematics degree at the University of Waterloo and her PhD at Brown University under the mentorship of Joseph H. Silverman. She held postdoctoral positions at Harvard University, Stanford University and the Pacific Institute for Mathematical Sciences at Simon Fraser University and is a fellow of the Association for Women in Mathematics.

Describing her research, Stange says, “I enjoy simple-seeming questions that lead to a richness of structure; and arithmetic questions with geometric and especially visual access points.”

Her areas of interest include elliptic curves, Apollonian circle packings, Kleinian groups, algebraic divisibility sequences, Diophantine approximation, continued fractions, quaternion algebras and quadratic and Hermitian forms. Stange is especially interested in cryptography, including elliptic-curve and isogeny-based cryptography, as well as quantum algorithms, “in part for the surprising way mathematical structures can have an outsize influence on human affairs,” she notes. “I enjoy problems that involve experimental, algorithmic and especially visual mathematics, using a computer and other tools.

“There’s a great deal of hidden beauty in number theoretical problems waiting to be illustrated.”

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The American Mathematical Society recognition supports mid-career female researchers whose achievements demonstrate potential for further contributions to mathematics.

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CU students follow their noses, disprove math conjecture

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

CU 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, 51�Թ�� 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!’”

51�Թ�� 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 CU 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.”

51�Թ�� 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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CU mathematician wins high recognition from peers

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

CU 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 51�Թ�� faculty member to garner this distinction

Agnès Beaudry, an associate professor of mathematics at the 51�Թ��, 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 51�Թ�� 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 51�Թ�� 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 51�Թ�� 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 51�Թ�� to be named an AMS fellow.

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Agnès Beaudry is named a fellow of the American Mathematical Society, the sixth 51�Թ�� faculty member to garner this distinction.

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A CU statistician’s global mission help students tackle real-world problems

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

A CU 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 51�Թ��, 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 Colorado 51�Թ��. 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 51�Թ��, 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 51�Թ��, 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 CU prof, Manhattan Project mathematician to screen in 51�Թ��

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

Movie on CU prof, Manhattan Project mathematician to screen in 51�Թ�� 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 51�Թ�� 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 51�Թ�� 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 51�Թ�� 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 51�Թ��, 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 Colorado 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 51�Թ�� 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 51�Թ�� 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 CU, 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 51�Թ�� 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 CU.”

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 51�Թ��. 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 51�Թ�� 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 51�Թ��, 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, Colorado, 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 51�Թ�� 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 CU.

Meenakshi Manoj

My name is Meenakshi Manoj, and I'm an international affairs and economics double major at 51�Թ��. 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 51�Թ��, 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 CU.

Gabriela Mejia

Gabriela Mejia is a film student based in 51�Թ��, Colorado 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 51�Թ��. 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 CU, 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 CU 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 CU. 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 51�Թ�� 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 51�Թ��, 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 51�Թ�� 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 CU has been one rife with racial and social hardships and I think of my being at CU 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 51�Թ�� for their superior academic achievement and service to the university, the Denver and 51�Թ�� 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 51�Թ�� 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 51�Թ�� 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 CU 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

51�Թ��’s Agnès Beaudry and Sean O’Rourke will use the support to advance homotopy theory and random matrix theory

Two young mathematicians at the 51�Թ�� 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 51�Թ��.

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 51�Թ�� 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 51�Թ�� faculty members have won NSF CAREER Awards since 1996.

51�Թ��’s Agnès Beaudry and Sean O’Rourke will use the support to advance homotopy theory and random matrix theory.

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Mathematics

51�Թ�� mathematician honored by peers

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