Yaiza Canzani AWM – Sadosky Prize

The 2022 AWM Sadosky Research Prize in Analysis is awarded to Yaiza Canzani in recognition of outstanding contributions in spectral geometry and microlocal analysis.

Canzani has established herself as a leading expert in spectral geometry, producing breakthrough results on nodal sets, random waves, Weyl Laws, Lp-norms, and other problems on eigenfunctions and eigenvalues on Riemannian manifolds. Over the past three years, in collaboration with Galkowski, Canzani developed a framework to extract information on the structure of Laplace eigenfunctions from their concentration and propagation behavior in phase space. The outcome of this endeavor is a series of works that are the first to provide quantitative improvements over the standard bounds, under purely dynamical assumptions, for pointwise bounds, Lp-norms, integral averages, and the error term in the pointwise Weyl Law. Canzani’s work is ground-breaking and further development of her framework will continue to greatly advance the field.

Canzani, in collaboration with Hanin, carried out a detailed study of scaling limits of the spectral function of the Laplacian, successfully answering Zelditch’s scaling asymptotics conjecture and applying it to prove local universality properties of nodal sets. Her work has opened up the possibility to study random waves on general manifolds; previous techniques had restricted their study to specific classes such as the sphere or the torus. In a beautiful paper with Sarnak, Canzani studied the topology and nesting configurations of the zero sets of monochromatic random waves. Such results seemed quite out of reach even to the leading experts in the area, but Canzani’s technical brilliancy and new ideas made it possible to obtain them.

Canzani’s publication record is stellar, with already 24 articles of impressive breadth in top journals. Similarly impressive is the number of worldwide invited talks she presented at distinguished events.

After receiving her Ph.D. from McGill University in 2013, she held postdoctoral positions at Harvard University and the Institute for Advanced Studies. In 2016 she joined UNC Chapel Hill as a tenure-track Assistant Professor of Mathematics and was later awarded the prestigious Sloan Research Fellowship and an NSF Career Award.

Canzani is a remarkable young mathematician whose ground-breaking and original work has greatly impacted the mathematical community and she continues working on a host of exciting and ambitious new projects that she is well equipped to attack. Canzani undoubtedly deserves the recognition that the AWM-Sadosky Prize provides.

Response from Yaiza Canzani
I am honored and delighted to receive the AWM-Sadosky Research Prize in Analysis. It is a particular privilege to receive an award commemorating Cora Sadosky. And I am truly gratified to be awarded a prize by the AWM whose effort to promote equal opportunity plays a key role in the future of our profession.

I am deeply grateful to all of my mentors throughout the years for their support, advice, and guidance. Federico Rodriguez-Hertz, my undergraduate mentor, was instrumental in advancing my career by helping me both find a Ph.D. position and prepare to succeed in it. Dmitry Jakobson and John Toth, my teachers and mentors during my Ph.D., have become good friends and collaborators. Working with them is a joy. In addition, during my postdoc, I had the good fortune to work with Peter Sarnak who continues to provide invaluable guidance and share his talent and passion for mathematics.

Receiving the Award
Yaiza was not able to receive the award in-person as the event was cancelled due to COVID-19, however she is featured in this video which replaced the in-person award ceremony.

Hydrodynamic Spin Lattices

Oblique view of a hydrodynamic spin lattice of walking droplets.

A hundred years after the birth of quantum mechanics, Professor Pedro Sáenz, with the UNC Mathematics department, has utilized a new hydrodynamic system to visualize behaviors reminiscent of electronic spin systems, providing new insight into how particles may operate on the quantum level. His findings were published in the journal Nature recently.

In the Physical Mathematics Laboratory in UNC-Chapel Hill’s College of Arts & Sciences, Professor Sáenz and his students combine theory, simulations and experiments to better understand fundamental problems in physics and engineering. They work to demonstrate that some odd behaviors displayed by electrons and other atomic-sized particles can be recreated with larger particles visible to the human eye.

One such experiment includes the close observation of tiny vibrating liquid droplets.

Modeling the motion of microscopic particles has big implications for quantum computations and spintronics. A better understanding of these behaviors could also have widespread applications across multiple scientific fields, including physics, engineering and computer science.

“The system consists of millimeter-scale droplets spontaneously ‘walking’ on the surface of a vibration bath through a resonant interaction with their own wave field,” said Sáenz, who is the lead author on the paper.

This walking-droplet system, discovered 16 years ago by a group in Paris, demonstrates behaviors previously thought to be exclusive to quantum particles. In their paper published in Nature, Saenz and his colleagues take it a step further.

“We have been able to demonstrate how orbiting droplets coupled through waves spontaneously arrange themselves into collective states that resemble magnetic spin ordering,” Sáenz said.

For example, consider the spin property of electrons, which can be thought of as an internal rotation about a spin axis. When the microscopic particles are arranged in a “spin lattice,” the way in which these spins are collectively oriented determines the magnetic properties of the material.

John Bush, a professor of applied mathematics at MIT and senior author on the paper, said this system has the potential to solve long-standing problems in modeling microscopic particles. “Back in the early days of quantum mechanics, researchers developed a mathematical framework, but didn’t have the means to generate the associated physical picture,” Bush said. “A number of us now believe that a plausible physical picture is emerging from this system.”

“We don’t want to accept that something exists for no reason — which you sometimes have to do in quantum mechanics,” Sáenz added. In our case, we can explain all the details. We don’t have to accept what we cannot see.”

Bush added that this work is what scientists should be doing in trying to understand the physical world.

“We don’t just want an equation that gives us the answer. We want to have a mechanistic understanding at the deepest level,” he said.

By permission from the College of Arts & Sciences; written by By Mary Lide Parker

Pedro Saenz

July 21, 2021

Pedro Sáenz is an assistant professor and director of the Physical Mathematics Laboratory in the Department of Mathematics within the UNC College of Arts & Sciences. He works to demonstrate that some odd behaviors displayed by electrons and other atomic-sized particles can be recreated with larger particles visible to the human eye.

This interview with Dr. Saenz was featured in the July 2021 issue of UNC’s research magazine, Endeavors

Q: When you were a child, what was your response to this question: “What do you want to be when you grow up?”

A: I grew up in a very rural part of Spain, in a village of just 400 people, so my interests at the time ranged from things like construction — building cabins with my friends — to exploration of the nearby mountains. In college, I ended up studying mechanical engineering, and now I teach mathematics and do research in physics. I guess I have always liked interdisciplinary work.

Q: Share the pivotal moment in your life that helped you choose your field of study.

A: My father was a farmer and my mother a factory worker, so for me to go to college was already a big step for my family. Then I moved to Edinburgh for a gap-year with the intention of eventually coming back to Spain. After a series of unplanned events, I started my PhD there. That’s when I really discovered my passion for fundamental research.

Q: Tell us about a time you encountered a tricky problem. How did you handle it and what did you learn from it?

A: Once, I had been working on a project for months and, toward the end, thought that measuring and averaging the amplitude of very small waves might yield an interesting observation. This was an unexpected — and frustrating — last-minute thought for an otherwise complete work that I wanted to submit for publication as soon as possible. The measurements I wanted to make were challenging and could have delayed me for weeks, even months. By distancing myself from the problem, I realized that all I needed could be done with data we already possessed. In the end, it took me 10 minutes to make the calculation, and the prediction was correct.

When I find myself in front of a problem that I’m struggling with, I try to recognize it and do something different. I’ve lost count of the number of times when I’ve felt stuck and frustrated. Oftentimes, I stop working, go for a run, and come up with an idea that allows me find a way around a problem.

Q: Describe your research in 5 words.

A: Large-scale recreations of atomic processes.

Q: What are your passions outside of research?

A: Coming from Spain, cooking and socializing over food is a big part of my culture. During the summer, we often get together to cook paella and spend the afternoon eating and chatting about anything.

I’m also a regular runner and love doing exercise outdoors, things like kayaking in summer and skiing in winter. I enjoy going on hikes and road trips. Visiting any national park is a great excuse that allows me to combine both.

The image above shows Dr. Saenz hiking Yosemite in 2019.

With Permission from Endeavors Magazine

SIAM NExT Fellow Manuchehr Aminian

Congratulations to a Ph.D. graduate from our department. Dr. Manuchehr “Nuch” Aminian, has been selected as the recipient of the 2021 SIAM Project NExT Fellowship!

SIAM recognizes the importance of supporting the professional development of junior faculty, especially in the areas of teaching and applied mathematics education. While the Activity Group on Applied Mathematics Education, SIAG/ED, certainly addresses this need, SIAM began annually sponsoring two Project NExT, New Experiences in Teaching, Fellows for the first time last year.

Project NExT, which is run by the Mathematical Association of America, MAA, supports the professional development of new or recent Ph.D.s in the mathematical sciences. As per the MAA, the program “addresses all aspects of an academic career, improving the teaching and learning of mathematics, engaging in research and scholarship, finding exciting and interesting service opportunities, and participating in professional activities.”

In 2020, Carl Giuffre, Adelphi University, and Lidia Mrad, Mount Holyoke College, became the first two SIAM Project NExT Fellows. The 2021 SIAM Project NExT Fellowship was recently awarded to Manuchehr Aminian and Alvaro Ortiz.

Aminian is an Assistant Professor at California State Polytechnic University, Pomona. His research interests include the analysis of passive tracers in advection-diffusion systems, anomaly detection and feature selection in large biological data sets, and mathematical data science in general.

Aminain strongly believes that genuine application problems and numerical mathematics can positively impact both mathematics students and other majors. Math educators must take a leading role in familiarizing students – the future leaders – with modeling, data, and algorithms, all of which already play a central role in everyday life. He has incorporated these ideas into a variety of classes during his early teaching career, ranging from first-semester calculus for biologists to undergraduate numerical analysis.

Aminian has found his SIAM membership to be extremely useful for keeping up with the cutting edge of applied mathematics via conferences, activity groups, and the print version of SIAM News. Project NExT complements his objectives by promoting evidence-based teaching practices&mdashsuch as inquiry-based learning and projects&mdashand providing a peer network of early-career faculty with whom to compare notes and effect broader change in the applied mathematics community and beyond.

Christianson Excellence Award

Congratulations to Hans Christianson, one of two faculty members at UNC to receive the 2021 Johnston Teaching Excellence Award! Carolina honored twenty-five faculty members and teaching assistants for their accomplishments with 2021 University Teaching Awards. Given annually, these awards acknowledge the University’s commitment to outstanding teaching and mentoring for graduate and undergraduate students.

“Throughout a challenging year in the midst of a global pandemic, the winners quickly adapted to new ways of teaching. They persevered to maintain their focus on helping students become critical thinkers and problem solvers, while inspiring them to take on the most important challenges facing society,” said Executive Vice Chancellor and Provost Robert A. Blouin. “Our award winners are shining examples of the University’s commitment to effective, innovative teaching.”

Excerpt from award citation – “Dr. Christianson’s classroom is also a collaborative space, where students work with him to consider, reconsider and parse through strategies to approach and solve a problem. Dr. Christianson’s students also see that he is committed to meeting them where they are to ensure they get as much out of his class as possible”.

Who was the best teacher you had and why?
As an undergraduate at the University of Minnesota, I had two great professors who influenced me a lot. Dennis Hejhal and Victor Reiner both taught me that education does not end outside the classroom, and an “A student” goes to office hours at least four times a semester. I tell this to all my students. They both also taught me that original research in mathematics is attainable as an undergraduate and can be one of the most influential parts of education.

What does it take to be a good professor in 2021?
Teaching in 2021 is so intertwined with the pandemic that it is difficult to separate what parts of the job constitute teaching and what parts constitute student support. It is always important to respect and listen to the students and even more so with remote instruction. Taking time to listen to the concerns and struggles of students helps make sure they know there is a human being on the other end of the line whose top priorities are the health and safety of the students, as well as their academic success, and informs the instructor about the pace and content of lectures. With so many unknowns with remote teaching, being flexible and patient with students, and colleagues!, is essential.

Tell us a story about something creative you’ve done to engage your students.
Teaching evolves constantly, and remote instruction presented us all with new obstacles. I like to interact with my students a lot during lectures. One thing I tried, whihc failed, last semester was to get a laugh track going that I could play whenever I tell a joke. One thing I tried, which suceeded, was to frequently change my Zoom background with photos I have taken in the last few years. I started my lectures with “Broadcasting today from in front of [insert photo quip]…” My favorite was a giant apple pie at Thanksgiving. At the end of the semester, a student posted on our Piazza forum: “Full Collection: ‘Today we are broadcasting from…’”, with a list of my quotes – they had been keeping track all semester! Knowing I was reaching my students, if only for a laugh, during the most difficult semester any of us have had was one of the high points in my career.

Women in Science: Yaiza Canzani

When you were a child, what was your response to this question: “What do you want to be when you grow up?”
When I was younger, it was much easier for me to think about what I didn’t want to be. I knew, for example, that I would never end up doing anything related to sports — I’m too much of a couch person!

Share the pivotal moment in your life that helped you choose research as a career path.
I come from Uruguay, and over there you choose your career when you are 18 years old. Then, you spend the four years of your undergrad taking courses directly related to your election. I think I was too young to make such a decision. What I knew at the time was that I was good at math, and that I really liked chemistry.

There is only one public university in Uruguay, and the buildings for the different careers are spread across the capital, Montevideo. I chose to do math because the math department was a 10-minute walk from home, while the chemistry building was an hour away by bus (ha!). I was 18 — what can I say! After starting the career in math, though, I realized that I loved it, and it became clear to me that doing research in math would lead me to a happy life. So I kept going.

What’s an interesting/funny story from your time doing research?
Doing research in pure math means that you spend endless hours in front of a blank page of paper. One time, when I was stuck on one of my research projects, I learned to decorate cakes — something that, it turns out, helps my brain find peace. So I guess this hobby could be considered a byproduct of my research experience. But I should disclose that I don’t actually like eating cake!

What advice would you give to up-and-coming female researchers in your field?
Have fun challenging yourself. Math research can sometimes be very hard since most of the time you will not have a clue of how to attack a problem. But that’s the fun part: You get to push your own boundaries — and you may end up proving something new that wasn’t known until you put your mind to it. So push through the hard times. Don’t quit. Remind yourself that you are in it for the fun.

Also, never isolate yourself. Get out of your office, talk to colleagues, go to conferences, share your work, and try to constantly learn as much as possible from others. And, most importantly, while doing these zillion things make sure you also have a happy life outside academia. That will help you get through those hard moments where you are dead stuck — it definitely helped me.

Jason Metcalfe Recognized

Congratulations to Jason Metcalfe who has been appointed Bowman and Gordon Gray Distinguished Term Professor in the College of Arts & Sciences!

The Bowman and Gordon Gray Professorships support excellence in undergraduate teaching at the University of North Carolina at Chapel Hill. They were established in 1980 – though funding was available to appoint the first Bowman and Gordon Gray Professors in 1979 – by Gordon Gray and the estate of his brother, Bowman Gray Jr.

Bernard Gray, UNC Class of 1972 and Gordon’s son, significantly enhanced the professorships with a gift in 1999 that doubled the annual salary supplement, extended the award period from three to five years, provided an annual fund for research support and included a highly valued sabbatical. They remain today among the University’s most esteemed awards for outstanding undergraduate teaching.

These professorships bestow special recognition on College of Arts and Sciences faculty members for their distinguished undergraduate teaching. Any tenured associate or full professor in the College is eligible for the five-year, non-renewable professorship. To date, more than 70 faculty members have been honored as Bowman and Gordon Gray Professors.

Inaugural MPE Prize

The Society for Industrial and Applied Mathematics, SIAM, and the SIAM Activity Group on Mathematics of Planet Earth, SIAG/MPE, have announced the establishment of a new prize, the SIAG/MPE Prize, to be known as the “MPE Prize.” The Prize will be awarded every two years, beginning in 2020, to one individual for significant scientific work in topic areas that are relevant to MPE or for sustained or seminal contributions to the scientific agenda of the SIAG/MPE.

The inaugural MPE Prize has been awarded to Professor Christopher K.R.T. Jones, the Bill Guthridge Distinguished Professor of Mathematics at the University of North Carolina at Chapel Hill and Director of the Mathematics and Climate Research Network, MCRN. The award recognizes Professor Jones for his leadership in engaging mathematicians in climate research, and for fundamental research contributions to Lagrangian data assimilation.

McCombs Awarded Tanner Award

Tanner Awards for Excellence in Undergraduate Teaching – this award was created in 1952 with a bequest by Kenneth Spencer Tanner, class of 1911, and his sister, Sara Tanner Crawford, and by them also on behalf of their deceased brothers, Simpson Bobo Tanner, Jr. and Jesse Spencer Tanner, establishing an endowment fund in memory of their parents, Lola Spencer and Simpson Bobo Tanner. The award was established to recognize excellence in inspirational teaching of undergraduate students, particularly first- and second-year students. Each of the five winners receives a one-time stipend of $7,500 and a framed citation.

Marc McCombs has been a Teaching Professor of Mathematics at UNC since 1989

Hometown Kind of hard to say. I was born in Huntsville, Alabama. By the time I graduated from high school, my family had lived in Tennessee, Florida, Virginia, Germany and North Carolina. I entered Carolina as a freshman in 1978 and promptly decided that I had finally found my hometown.

Excerpt from award citation “When I look back on my time at Chapel Hill, I am reminded of the impact that Professor McCombs’ class had on me. One of the most fundamental lessons I learned was how great things come from small intentional actions adding up.”

Who was the best teacher you ever had and why?
Carolina math professors Sue Goodman and Karl Petersen continually inspire me through their unflagging commitment to helping students recognize that mathematics is not a secret club, accessible only to an exclusive few. Nor is a mathematics teacher some inscrutable fountainhead of complicated equations and esoteric jargon. The specific content details are, of course, important in a math class. Far more important, however, is creating an environment in which students can discover their ability to approach a complicated task both creatively and analytically.

What is something you’ve learned from your students?
Eight years ago, a student in my first year seminar on math and art asked if the course syllabus included origami techniques. When I told him that I had always felt too intimidated to try to make origami, he volunteered to teach some of his favorite folding techniques to the rest of us. Thanks to his enthusiasm and generosity, I discovered an artistic voice I never believed I had.

What is something people would be surprised to learn about you?
My origami sculpture and fractal artwork were recently exhibited in the Swedish Museum of Science and Technology in Stockholm.

What does it take to be a good professor in 2020?
A good professor in 2020 must effectively meet the challenge of inviting and fostering engagement and participation in courses whose class roll exceeds 150 students. The UNC Center for Faculty Excellence and the BeAM makerspaces have been invaluable resources in my efforts to help students stay connected to the human relevance of academic explorations. Mary Oliver’s poem, “Instructions for Living a Life,” articulates with sublime eloquence the importance of this connection.

Pay attention.
Be astonished.
Tell about it.

What’s the most creative thing you’ve done to engage your students?
I’ve enlisted my 8-year-old chocolate lab to be the official mascot for my classes. Uma frequently stars in class examples and test questions and currently has 241 followers on Instagram, uma_mccombs. I bring her to campus every couple of weeks to hang out with students and share her math insight and encouragement.

Story by The Well, February 26th, 2020

Malawsky Named Churchill Scholar

Daniel Malawsky, a UNC senior majoring in biostatistics and mathematics, is one of 15 American scholars who were selected for the Churchill Scholarship by the Winston Churchill Foundation of the United States.

It was one of Winston Churchill’s wishes that bright American students be able to study at Churchill College, the school of mathematics, science and engineering named in his honor within the University of Cambridge in Cambridge, England.

Next year, a UNC student will be among them.

Daniel Malawsky, a senior biostatistics and mathematics major, is one of fifteen American students to receive the Churchill Scholarship to study at Churchill College. Malawsky will be using the scholarship, in addition to the Gates Cambridge Scholarship, to work on his Master’s degree and Ph.D., respectively.

“I worked in the lab at Oxford last summer and really loved England, and I thought, ‘I have to be in the U.K. for graduate school,’” Malawsky said. “I love the science culture there, and I love the institutions there so I looked for scholarships that would allow me to study in England and I found those two.”

The Churchill Scholarship is a science, engineering and math scholarship that allows scholars to conduct independent research while completing their graduate studies.

Malawsky works in data analysis in the Gershon Lab, helping with neuroscience research that looks into why certain kinds of brain tumors are resistant to some treatments.

For his graduate work, Malawsky hopes to study population genetics for groups that are typically underrepresented in medical research.

David spends almost twenty hours a week in the lab and is skilled at finding data differences that most people would overlook, Seth Weir, a research technician in the Gershon Lab, said.

“Aside from his scientific prowess, Danny is an ideal friend and lab member to have because of his easygoing personality and ability to connect and talk with anyone,” Weir said.

A mission of the Gershon Lab is to include undergraduates in research, said Dr. Timothy Gershon, an associate professor of neurology and principal investigator for the Gershon Lab. Gershon said he prioritized hiring Malawsky because of his skill set in computational work that complemented the lab.

“The lesson that I would hope people would take from reading about Danny’s story is to feel empowered, to feel like you can be successful as an undergraduate,” said Gershon. “You don’t need to feel intimidated by issues of hierarchy or status.”