math-news

COVID Connections

January 4, 2021

Creating a Virtual Symposium

Tanya Vickers

Rising to the Challenge

Science is about preparing the next generation of innovators, explorers, and connoisseurs of curiosity. For the last 29 years the College of Science ACCESS program has been the “first step” on this journey of discovery. The ACCESS program runs from June to August and is open only to first-year students freshmen and transfers).

A cornerstone of the ACCESS experience is the opportunity for the student cohort to share their work with faculty and peers during a research poster symposium. The symposium is a powerful learning experience that mirrors professional science conferences and a career in the field, and plays a key role in the program.

When COVID-19 hit the U.S., the longstanding tradition of the Spring Research Symposium was in jeopardy. As the director of ACCESS , I was driven to find a way to continue the capstone symposium, and provide talented first-year student scientists the opportunity to showcase their research, in spite of social distancing.

With just six weeks until the event we decided to design, build, and launch a novel virtual research symposium platform. The sudden shift and short time-frame presented a real challenge, but it was also an opportunity to pursue and explore innovative approaches to current standards that, if not for CO VID-19, would have been stagnant.

It’s been six months since the Virtual Symposium, and we are still surprised by its success. The merits and results of the virtual platform challenged the notion that in-person is best. The in-person symposium normally saw about 200 guests. In contrast, the virtual symposium reeled in nearly 6,000-page views in three days and 260 guests attended the live zoom presentations.

Thinking Differently

COVID-19 upended and reshaped our everyday lives and challenged everyone to find new approaches to routine activities and novel fixes for nascent problems, much like scientists do on a regular basis.

When the on-campus student research experience was cut short in March, it didn’t mark the end of learning for the 2019-2020 ACCESS cohort. Research faculty agreed to continue mentoring remotely, which included helping the students report their research in a scientific poster they would present virtually. Unfortunately, the technology for a virtual research poster presentation did not exist.

That’s when I began the process of envisioning and creating the Virtual Symposium platform, as it’s now known. I started with identifying the critical elements of an in-person research symposium and considering how to transpose them to a virtual model. My experience teaching and using Canvas (used to deliver course content) shaped the content, and with the collaboration and support of Micah Murdock, Associate Director of Teaching and Learning Technologists (TLT ), a novel virtual research symposium was fully realized.

Embracing Technology

The platform was a lofty goal that required three defining features: a webpage for students to introduce their project, a message board for peers, guests, and mentors to pose questions, and a live Zoom presentation with question and answer.

Each student had a personal webpage that included their research poster, a 3-minute video summary of their research project, and a short personal bio. These elements provided guests with an introduction and interactions analogous to an in-person symposium.

In-person symposia can feel rushed, but the virtual platform offered the advantage of providing guests more time to preview projects on their own, before using one, or both, forum tools—the student scientist’s discussion board, or the 30-minute Zoom live session scheduled on the last day—to ask questions or comment.

Building For the Future

Throughout this process, we wanted to build a tool with the future, as well as other disciplines and applications, in mind. We are proud to announce that the platform has already seen use for the School of Biological Sciences Virtual Retreat, ACCESS Alumni Career Panel, and a number of campus-wide projects. Most recently, the Virtual Symposium was chosen to serve as the cornerstone of the new College of Science high school outreach platform SCIENCE NO W—engaging students, presenters, and elite scientists from across the U.S. and around the world.

As a species and as scientists, we always look forward to new ideas and what can be done. In our darkest hours, we find a space for new forms of unity and growth, and can challenge ourselves to create and expand. CO VID has been undeniably difficult, but the development of new platforms and technologies, like the Virtual Research Symposium, show that sometimes, when we are forced to make changes to long held traditions, the outcome goes beyond finding an equivalent, making what we thought was “best” even better.

Special thanks to Dean Peter Trapa, ACCESS Program Manager, Samantha Shaw, and to the ACCESS students and mentors for believing in the vision of a Virtual Research Symposium.

For more information on the Virtual Symposium platform contact: tanya.vickers@utah.edu.

 

by Tanya Vickers

 

Karl Schwede

December 10, 2020

Fellow of the American Mathematical Society

Professor Karl Schwede in the U’s Department of Mathematics has been named a member of the 2021 Class of Fellows of the American Mathematical Society (AMS). The Society recognizes members who have made outstanding contributions to the creation, exposition, advancement, communication and utilization of mathematics. Schwede joins 14 other professors in the department who were previously named fellows by the AMS.

“It’s an honor to be named as a fellow of the American Mathematical Society, and I’m grateful for the recognition of my peers in the profession,” said Schwede.

Schwede received his undergraduate degree in mathematics from Whitman College and a Ph.D. in mathematics from the University of Washington. Math was originally third on his list of interests in college, but as he took more advanced math courses, his focus changed to mathematics.

Schwede does basic research in mathematics, studying algebra, geometry and particularly singularities. Much of his work is in the setting of modular arithmetic (also known as clock arithmetic), the same setting as much of our modern communication systems. For example, 5 hours after 10 is 3 or 5+10 = 3. “In this area, I have primarily studied singularities of geometric shapes by algebraic means,” said Schwede. Recently, he has begun working in mixed characteristic, which connects the positive characteristic of clock arithmetic with classical (5+10 = 15) geometric worlds.

He joined the U’s Math Department in 2014 as an associate professor and became a professor in 2018. Last spring, Schwede received a Simons Fellows Award in Mathematics from the Simons Foundation.

 

by Michelle Swaner, originally published in @theU

Women in Mathematics

November 10, 2020

Women in Mathematics

Last spring, the Math Department’s student chapter of the Association for Women in Mathematics (AWM) planned a conference, with speakers, mini courses, breakout sessions, and professional development panels. About 60 participants were expected. Unfortunately, when the pandemic hit in March, everything changed, and the conference was canceled.

Despite the setback, the chapter still moved forward and will host a series of online activities and communications for attendees. In recognition of these remarkable efforts, the chapter was recently selected as the winner of the 2020 AWM Student Chapter Award for Scientific Excellence. Christel Hohenegger, associate professor of mathematics, serves as faculty advisor for the chapter.

"We are very thankful and excited to have won this award and receive national recognition,” said Claire Plunkett, vice president of the chapter for 2020-2021. “This is a national award from the AWM, and we are one of more than a hundred student chapters, so it’s a great honor to be chosen. We feel the award reflects how our chapter's activities have continued to grow and gain momentum over the past several years, and we’re excited to continue to sponsor events and expand our activities.”

For the academic year, the chapter has invited four speakers and all talks will be held on Zoom. Confirmed speakers include Nilima Nigam, professor of mathematics at Simon Fraser University; Kristin Lauter, principal researcher and partner research manager for the Cryptography and Privacy Research group at Microsoft Research; and Christine Berkesch, associate professor of mathematics at the University of Minnesota. The annual conference has been rescheduled for June 2021.

In addition, the chapter will continue to host joint monthly lunch discussions with the SIAM (Society for Industrial and Applied Mathematics) student chapter; a professor panel in which faculty research is shared with students; joint LaTeX (a software system for document preparation) workshops held with the SIAM student chapter; a screening of a documentary called Picture aScientist, a discussion co-hosted with other women in STEM groups; and bi-weekly informal social meetings. For more information about the U’s AWM chapter, visit http://www.math.utah.edu/awmchapter/.

 - first published by the Department of Mathematics

2020 Research Scholar

June 21, 2020

Delaney Mosier

Delaney Mosier receives top College of Science award.

Delaney Mosier, a graduating senior in mathematics, has been awarded the 2020 College of Science Research Scholar Award for her cutting-edge work in the area of sea ice concentration, using partial differential equation models.

“I am humbled to receive this award,” said Delaney. “The College of Science is teeming with groundbreaking research, so it’s an overwhelming honor to be considered one of the top researchers in the College. I’m proud to be a representative of the amazing research going on in the field of mathematics.”

Delaney is also proud to receive the award as a woman. “I strive to be a positive role model for girls and women in STEM. I hope that by earning this award, I can inspire other women to consider working on mathematics research.”

In his letter of support for Delaney’s nomination, Distinguished Professor Ken Golden, who has served as her supervisor and mentor, discussed her research abilities, natural leadership skills, and mathematical prowess, indicating that Delaney is one of the most talented and advanced students he has seen in his 30+ years of mentoring.

Super Student

The College of Science Research Scholar Award, established in 2004, honors the College’s most outstanding senior undergraduate researcher. The Research Scholar must be a graduating undergraduate major of the College of Science, achieve excellence in science research, have definite plans to attend graduate school in a science/math field, and be dedicated to a career in science/math research.

Studying the Behavior of Sea Ice

Delaney studies patterns in the behavior of sea ice in polar regions. She’s interested in how physical processes affect these patterns on a short-term basis and how climate change can affect them in the long-term.

The primary goal of her research with Dr. Golden is to understand better how and why sea ice is changing over time. Considered relatively low order, their model allows them to study intimately the details of the sea ice pack, which can provide insights that might not yet be apparent to the climate science community. Her work tries to answer one of the most important research questions of the modern age: Why is polar sea ice melting so rapidly and will it ever recover?

She has always been passionate about the environment and finds the project exciting because it incorporates mathematics along with studying climate. “My project is very dynamic,” she noted. “Each time I meet with Dr. Golden, we discuss something new to incorporate into our model or seek a new way to understand it. It’s thrilling to be a part of such unique and innovative work.”

Utah Strong

She became seriously interested in math because of her 7th grade algebra teacher. “Mrs. Hein fostered an exploratory environment—I collaborated with my peers and was often challenged to explore the world of mathematics for myself,” she said. “I couldn’t get enough of it. To this day, math remains the one activity that I can completely lose myself in. Math challenges my mind in exhilarating and motivating ways.”

Mentors at the U

Delaney credits Dr. Golden with helping her pursue a variety of opportunities that have furthered her career as a mathematician. She also has praise for Dr. Courtenay Strong, associate professor of atmospheric sciences, and Dr. Jingyi Zhu, associate professor of mathematics, who have served as mentors and helped guide her research.

“My friend and roommate, Katelyn Queen, has been a wonderful mentor and inspiration to me throughout my journey,” said Delaney. “She is always willing to give me advice and support me in my endeavors. I have watched her excel in her first year of graduate school, and that has inspired me in moving forward.” She also thanks fellow students and her parents for their love and support. “My parents are simply the best,” said Delaney.

Her favorite teacher at the U is Dr. Karl Schwede, professor of mathematics. “I had Dr. Schwede for several classes and learned so much,” she said. “He has high standards for his students, which motivated me and helped me to retain the material. He is also supportive and helpful.”

When she isn’t studying or doing research, she loves to dance and listen to music. She was a competitive Irish dancer from ages 11 – 17. She is also an avid reader, especially during the summer.

The Future

Goodbye Salt Lake City

Delaney will begin her Ph.D. studies in applied mathematics this fall. She hasn’t yet decided if she will work in industry, continue with climate research, or become a professor. “Whatever I decide to do, my goal is to use mathematics to have an impact on the world,” she said.

 

by Michele Swaner

 

 

McKay Hyde

June 1, 2020

McKay Hyde (Honors B.A. Mathematics, B.A. Physics ’97) always enjoyed math and science, but it was taking a series of physics classes at the U, between his junior and senior year in high school, that changed his life. “I always enjoyed mathematics,” he said. “But physics showed me how mathematics could be used to solve real-world problems. That was tremendously exciting to me and still is.”

The Hyde Family

Today Hyde is managing director in Equities Engineering for the New York office of Goldman Sachs and is responsible for building systems to manage securities inventory and collateral, working closely with teams across Engineering, as well as the Finance, Operations and Securities divisions. “I like being part of a cross-functional team, building relationships and working together to find solutions that impact the organization and the clients we serve,” he said. “The combination of using mathematics and computer science applied to practical problems is very rewarding.”

He joined Goldman Sachs in 2006 and was named managing director in 2010. At Goldman Sachs, Hyde has had a range of responsibilities. He was head of the global Market Risk Technology team within Finance and Risk Engineering. Before that, Hyde led the Trading Strats team for Interest Rate Products in New York as well as the Core Quant Strats team, which developed models, algorithmic trading methods, and pricing infrastructure used by a number of trading desks. (“Strat” is a term that originated with Goldman Sachs to describe individuals that use tools from mathematics and computer science to build financial models In his Core Quant Strat role, Hyde led the build out of the Strat teams in Bengaluru (formerly Bangalore), India, known as “The Silicon Valley of India.”

McKay Hyde, BS'97

Roots in Utah and at the U

Hyde grew up in Salt Lake City and North Salt Lake, graduating from Woods Cross High School. He met his wife, Marie, in an “outstanding” honors class taught by Professor Emeritus Jack Newell (“Education and Identity”), who served as dean and principal architect of the U’s Liberal Education Program. In his first two years at the U Hyde was also active in the U’s music program, playing the trumpet in several university bands—Concert, Marching, Pep, and Jazz.

Hyde gives credit to the education he received at the U with helping prepare him for a career in the financial sector. “I received a tremendous education in physics and mathematics, including research experience working in the Cosmic Ray group and in probability theory. The U provides great value as an institution—a quality education at a reasonable cost,” he said.

He also has great memories of three professors who made a difference for him during his undergraduate years: Davar Khoshnevisan (professor and current chair of the Math Department), Hyde’s undergraduate research advisor in mathematics; Martha Bradley, former dean of the Honors College, and the late Professor Gale Dick, whose “physics lectures were a work of art,” said Hyde.

Using Agile Principles in Undergraduate Research

Hyde believes students should be encouraged to participate in research opportunities early in their undergraduate years, and he applauds the decision of the College of Science to focus on a new program called the Undergraduate Research Initiative. “Research is very different from coursework—it’s really a separate skill,” said Hyde. “Engaging and encouraging undergrads to work together in research opportunities provides a far richer educational experience that really pays off in preparing students for demanding careers.”

To that end, Hyde thinks the same concepts and principles that teams use in Agile software development can effectively be applied to something like the Undergraduate Research Initiative program. “Creating an Agile environment—whether in software development or research—is essentially the same,” said Hyde.

“It involves developing and supporting a culture that encourages a team of people to work toward a common goal. To that end, a large project or research problem can be broken down into smaller tasks. A scrum master or team leader evaluates the special skills and talents of each individual on the team, assigns them to specific tasks, and the team comes together frequently—typically during a daily stand up —over focused sprints—typically 2-3 weeks long—to complete those tasks yielding demonstrable progress at the end of each sprint. By repeating this process, the team improves while building confidence and trust through repeated accomplishment of its goals.”

Previous Academic Career

After earning degrees at the U in 1997 Hyde completed a Ph.D. in Applied and Computational Mathematics from the California Institute of Technology in 2003. Hyde worked as a postdoc in the School of Mathematics at the University of Minnesota and later joined Rice University as an assistant professor of computational and applied mathematics.

When Hyde first left academia to work at Goldman Sachs, he wondered if he would need to dress and act like a “stereotypical banker.” But he discovered it was a much easier transition. “I found smart people from technical fields applying their skills in the area of finance,” he said. “It made me realize the importance of being open to new opportunities—taking the skills and talents you have and using them in different fields or industries to build relationships with others and do meaningful work. That’s really what it’s all about.”

Hyde and his wife, Marie, enjoy living in New Jersey and are the parents of four children: a son studying music at Berklee College of Music; a daughter at Brigham Young University (currently serving a church mission in Peru); and a son and daughter in high school.

 - First Published in Discover Magazine, Fall 2019

Goldwater Winner

April 13, 2020

Isaac Martin

Isaac Martin awarded prestigious Goldwater Scholarship.

The College of Science is pleased to announce that Isaac Martin, a junior studying mathematics and physics, has been awarded Utah's second Goldwater Scholarship for 2020-21.

During middle school and most of high school, Isaac lived in Dubai with his family, where he attended an online high school, allowing him to focus on science and math classes. When his family moved to Utah the summer before his senior year, he decided to attend Salt Lake Community College (SLCC) instead of finishing high school, taking as many math and physics classes as he could.

“It was incredible because I had never had teachers like that before,” said Isaac. “My professors at SLCC were more than happy to talk with me after class and during office hours. They were the main reason I was able to complete SLCC's catalog of math and physics courses in a year. They were instrumental in my decision to switch out of my pre-declared computer engineering major into a math and physics double major at the U.”

Transition to Math

During Isaac’s first four semesters at the U, he intended to pursue a physics Ph.D. and focused primarily on physics classes; however, after brief stints in two different labs, he realized mathematics is a better fit for his talents and interests.

Last summer, Isaac participated in a Research Experience for Undergraduates (REU) program at the University of California, Santa Barbara, and his work has since resulted in a publication. Isaac has been planning to attend the University of Chicago’s REU math program this summer, but if that doesn’t happen due to COVID-19 concerns, he will continue working on positive characteristic commutative algebra with his U supervisors, Thomas Polstra, a National Science Foundation postdoc, and Professor Karl Schwede.

He is indebted to professors in the Math Department, including Dr. Adam Boocher, previously a postdoc at the U and now assistant professor of mathematics at the University of San Diego; Professor Srikanth Iyengar; Dr. Schwede, Dr. Polstra; and Professor Henryk Hecht. “The thing I appreciate most about my mentors is their willingness to take time out their day to talk to me and offer advice,” said Isaac. “My conversations with them are mathematically insightful, but they also reassure me that I'm worth something as a person and am good enough to pursue a career in math.”

Career Goals

When he’s not doing math, Isaac is most likely either playing piano, rock climbing, running in the foothills, or beating his roommates in Smash Bros Ultimate. “I used to have a huge passion for video game programming and would compete in game jams, which are game development competitions held over 36- or 48-hour time intervals,” said Isaac. “I haven’t been able to do that much in the last few years, but would like to pick it up again as a hobby.”

Isaac hopes to have a career in academia as a pure mathematics researcher. “I'd especially like to study problems in commutative algebra and representation theory with relevance to mathematical physics,” he said. Isaac also remains interested in the world of condensed matter. “There is so much novel mathematics dictating theoretical condensed matter, and I expect many exciting breakthroughs will happen there in the near future.”

 

The Goldwater Scholarship

 

 

As the result of a partnership with the Department of Defense National Defense Education Programs (NDEP), Mrs. Peggy Goldwater Clay, Chair of the Board of Trustees of the Barry Goldwater Scholarship and Excellence in Education Foundation, announced that the Trustees of the Goldwater Board have increased the number of Goldwater scholarships it has awarded for the 2020-2021 academic year to 396 college students from across the United States. “As it is vitally important that the Nation ensures that it has the scientific talent it needs to maintain its global competitiveness and security, we saw partnering with the Goldwater Foundation as a way to help ensure the U.S. is developing this talent,” said Dr. Jagadeesh Pamulapati, Director of the NDEP program, as he explained the partnership. With the 2020 awards, this brings the number of scholarships awarded since 1989 by the Goldwater Foundation to 9047 and a scholarship total to over $71M.

From an estimated pool of over 5,000 college sophomores and juniors, 1343 natural science, engineering and mathematics students were nominated by 461 academic institutions to compete for the 2020 Goldwater scholarships. Of students who reported, 191 of the Scholars are men, 203 are women, and virtually all intend to obtain a Ph.D. as their highest degree objective. Fifty Scholars are mathematics and computer science majors, 287 are majoring in the natural sciences, and 59 are majoring in engineering. Many of the Scholars have published their research in leading journals and have presented their work at professional society conferences.

Goldwater Scholars have impressive academic and research credentials that have garnered the attention of prestigious post-graduate fellowship programs. Goldwater Scholars have been awarded 93 Rhodes Scholarships, 146 Marshall Scholarships, 170 Churchill Scholarships, 109 Hertz Fellowships, and numerous other distinguished awards like the National Science Foundation Graduate Research Fellowships.

 

by Michele Swaner

 

 

50th Anniversary

April 8, 2020

GOLDEN Anniversary
1970-2020

July 1, 2020, marks the 50-year anniversary of the College of Science, comprised of the School of Biological Sciences, and Departments of Chemistry, Mathematics, and Physics & Astronomy.

A Brief History

Henry Eyring

When the University of Deseret was founded in 1850 in the Territory of Utah, it was primarily a training school for teachers. The newly formed university taught only a handful of topics, including algebra, astronomy, botany, chemistry, geometry, and zoology. Indeed, mathematics and physical sciences were well represented from the earliest days of the university.

By the 1920s, only six organized schools existed at the U: Arts and Sciences, Business, Education, Engineering and Mines, Law, and a two-year Medical School.

James M. Sugihara, PhD 1947

Between 1948 and 1958, through two reorganizations, the School of Arts and Sciences expanded to become the College of Letters and Science. However, the composition was enormous, including departments of air science, anthropology, botany, chemistry, English, experimental biology, genetics and cytology, history, journalism, languages, mathematics, military science and tactics, naval science and tactics, philosophy, physics, political science, psychology, sociology, speech and theater arts, and zoology.

By the late 1960s, Pete D. Gardner, a prominent organic chemist at the U, had convinced the central administration that mathematics and physical sciences would be most effective if separated from the large, amorphous College of Letters and Science.

Therefore, on July 1, 1970, the College of Letters and Science was replaced by three new colleges: Humanities, Social and Behavioral Science, and the College of Science.

The disciplines of biology, chemistry, mathematics, and physics and astronomy were ideally consolidated in one cohesive academic unit. Gardner was appointed as the first dean of the College and served from 1970 to 1973.

The College of Science utilized seven buildings in 1970, including Chemistry (the north wing was finished in 1968), South Biology (completed in 1969), North Biology (the James Talmage Building), Life Sciences (built in 1920 and former home the of School of Medicine), the John Widtsoe Building (housed both the chemistry and the physics departments), the James Fletcher Building and South Physics. The total faculty consisted of about 80 tenured or tenure-track professors across all four departments.

Modern Day Powerhouse

Today the College of Science is one of the largest colleges within the University of Utah, offering undergraduate and graduate degrees in biology, chemistry, mathematics, and physics and astronomy, plus specialized degrees such as a doctorate in chemical physics.

The College supports nearly 2,000 undergraduate science majors and 475 graduate students and employs 143 full-time tenured or tenure-track faculty. The College also employs hundreds of adjunct and auxiliary faculty, postdoctoral fellows, research assistants, lab technicians, and support staff.

Last year, the College received about $36 million in external research funding, which is nearly seven percent of the University’s total external research revenue.

“The exceptional caliber of the College’s faculty has been a driving force behind the University’s ascension as a world-class research university,” says Peter Trapa.

The College has constructed new educational and research facilities in recent years, including the Thatcher Building for Biological and Biophysical Chemistry and the Crocker Science Center on Presidents Circle. The two buildings combined serve thousands of students each year with professional academic advising, expanded classrooms, and cutting-edge labs and instrumentation.

This year, a new project–the Stewart Building for Applied Sciences – was approved by the Utah legislature to renovate the historic William Stewart building and construct a 100,000 square-foot addition to house the Department of Physics & Astronomy and the Department of Atmospheric Sciences.

The proposed Applied Sciences Center will be 140,729 square-feet in size, consisting of 40,729 square feet of renovated space and 100,000 square feet of new construction. Undergraduate teaching labs, research labs, and classrooms will comprise 90% of the footprint and faculty offices will use 10% of the space. The new facility will support more than 40 faculty members, 200 undergraduate majors, 115 graduate students, and nearly 5,000 students taking STEM courses each year at the U.

Building the Future

As the 21st century unfolds amidst a global pandemic, the importance of science and mathematics will only continue to increase.  Our quality of life and economic future depends on the next generation of scientists. The College of Science is refreshing its strategic plan to further strengthen and enhance its academic and educational programs and its scientific leadership in the nation. Emerging priorities include:

  • Fully implement the Science Research Initiative (SRI) in the Crocker Science Center to serve 500 undergraduates per year with specialized research opportunities.
  • Establish new endowed faculty chair positions in each department, and increase the number of endowed professorships and graduate fellowships.
  • Continue to increase the amount of external research funding received in the College per year.
  • Invest in new and existing research directions to strengthen the College’s faculty.
  • Continue to advance our commitment to diversity, and foster inclusive communities of faculty, staff, and students.
  • Increase the six-year graduation rate of declared Science majors, and increase the total number of STEM graduates at the University.

Pearl Sandick, Associate Dean for Faculty Affairs, has led an effort that has distilled the input of faculty, staff, and students into a coherent plan for the future.

“The College will be prepared to meet the demands of the next 50 years in science education and research,” says Sandick. “We will see our way through the current crisis,  with an enhanced focus and commitment to student success, providing the facilities and rigorous training needed to boost the number of STEM graduates in Utah.”

The College is sincerely grateful for its numerous friends and supporters over the last 50 years. Each gift, large and small, propels the College forward. Please join us to write the next chapter, and the following 50 chapters, in the College of Science.   

Commutative Algebra

January 3, 2020

Can commutative algebra solve real-world problems?

Srikanth Iyengar

“When we first study advanced math, we learn to solve linear and quadratic equations, generally a single equation and in one variable,” said Srikanth Iyengar, Professor of Mathematics at the U. “But most real-world problems aren’t quite so easy—they often involve multiple equations in multiple variables.”

Finding explicit solutions to such equations is generally not feasible nor useful—it’s much more helpful to look for overall structure in the collection of all possible solutions. These solution sets are called algebraic varieties. The word algebraic indicates their origin is from polynomial equations, as opposed to equations involving things like trigonometric and exponential functions. Over the centuries, mathematicians have developed various tools to study these objects. One of them is to study functions on the space of solutions, and algebra is a good way to begin. These functions form a mathematical structure called a commutative ring. Commutative algebra is the study of commutative rings and modules, or algebraic structures over such rings.

Iyengar’s research focuses on understanding these structures, which have links to different areas of mathematics, particularly topology and representation theory.

Iyengar joined the Mathematics Department in 2014. He grew up in Hyderabad, India, and received a master’s degree and Ph.D. from Purdue University. Before joining the U, he taught at the University of Nebraska-Lincoln.

The foundation of commutative algebra lies in the work of 20th century German mathematician David Hilbert, whose work on invariant theory was motivated by questions in physics.

Srikanth Iyengar, Professor of Mathematics at the University of Utah

As a subject on its own, commutative algebra began under the name “ideal theory” with the work of mathematician Richard Dedekind, a giant of the late 19th and early 20th centuries. In turn, Dedekind’s work relied on the earlier work of Ernst Kummer and Leopold Kronecker. The mathematician responsible for the modern study of commutative algebra was Wolfgang Krull, who introduced concepts that are now central to the study of the subject, as well as Oscar Zariski, who made commutative algebra a foundation for the study of algebraic varieties.

“One of the things I enjoy about my research is how commutative algebra has so many connections to other things,” said Iyengar. “It makes for rich and lively research. Commutative algebra is continually reinvigorated by problems and perspectives from other fields.” Funding for Iyengar’s research is from the National Science Foundation. The Humboldt Foundation and the Simons Foundation have also provided support.

Commutative rings arise in diverse contexts in mathematics, physics, and computer science, among other fields. Within mathematics, besides functions on algebraic varieties, examples of commutative rings include rings of algebraic integers—the stuff of number theory. Commutative rings also arise, in myriad ways, in the study of symmetries of objects—algebraic topology, graph theory, and combinatorics, among others. One of the areas of physics where commutative algebra is useful is with string theory.

In recent years, ideas and  techniques from commutative algebra have begun to play an increasingly prominent role in coding theory, in reconstructions, and biology with neural networks.  While not everything Iyengar does day-to-day (or perhaps even in the span of a few years) has a direct impact in the field, mathematicians have a way of impacting other areas far from their original source, often decades later. There are many striking examples of this phenomenon. The “unreasonable effectiveness of mathematics” is well known. The phrase is part of a title of an article published in 1960 by Eugene Wigner, a Hungarian-American mathematician and theoretical physicist.

“I work by thinking about a piece of mathematics—perhaps it’s a research paper or a problem I run into somewhere in a textbook or a talk,” said Iyengar. “This sometimes leads to interesting research projects; at other times, it ends in a dead end. My perspective on research is that it’s more like a garden (or many interconnected gardens) waiting to be explored, rather than peaks to be climbed. Sure, there are landmarks but there’s rarely a point when I can say, Well, this is it—there’s nothing more to be achieved.’’

 

 - by Michele Swaner
  First Published in Discover Magazine, Fall 2019

 

AMS Fellow

November 10, 2019

U Professor and Chair Named Fellow of American Mathematical Society

Davar Khoshnevisan, professor and Chair of the Department of Mathematics, has been named a member of the 2020 Class of Fellows of the American Mathematical Society (AMS). The Society recognizes members who have made outstanding contributions to the creation, exposition, advancement, communication, and utilization of mathematics.

“I believe my selection as a Fellow is the fourteenth induction within the Department of Mathematics at the U, so this is as much a statement about my work as it is about the terrific intellectual environment within the department. It is a big honor to be a part of our program at the U and to help advance our field. The American Mathematical Society plays a crucial role in the development of mathematics worldwide. I am proud that my colleagues and I contribute to this important endeavor.” - Davar Khoshnevisan

 

Khoshnevisan remembers being taught calculus by an uncle when he was very young. As part of the lesson, his uncle would weave in stories about mathematics and mathematicians—famous ones from the history of mathematics, as well as those his uncle had met in his own studies of the subject. “I knew then that mathematics would not be just a job but instead a lifelong pursuit of truth and discovery,” said Khoshnevisan. “I still try to aim for this in my research today.”

Khoshnevisan originally trained to be a researcher in mathematical statistics and probability theory. During the past 10-15 years, his work has largely been in “stochastic analysis,” an area that lies on the intersection of probability theory and function theory. Science and math historians agree that probability theory was born, probably after the 8th century, as a way to study what we now called “cryptography.” Probability theory resurfaced again when mathematicians in the 16th and 17th centuries began analyzing "games of chance."

The mathematical foundations of probability evolved much later in the early decades of the 20th century, which led to an explosion of ideas and to the introduction of new areas of intellectual activity in which “chance” plays a central role. In turn, this has opened up challenging problems in mathematics and created an entirely new paradigm of “stochastic models” that lies at the heart of many science and engineering models today. During the past decade, Khoshnevisan’s work has revolved around developing mathematical ideas and techniques that aid the rigorous analysis of complex systems in science and engineering.

Khoshnevisan received a Ph.D. from University of California, Berkeley, in statistics in 1989. He joined the faculty at the Massachusetts Institute of Technology for a year and the University of Washington for three years before moving to Utah and the U in 1993 as an assistant professor in mathematics. He has been an honorary fellow at the University of Wisconsin-Madison, a visiting member of the Mathematics Research Institute at Berkeley, as well as the Kavli Institute of Theoretical Physics at the University of California, Santa Barbara. He was a Simons Visiting Professor at the Mathematical Research Institute of Oberwolfach in Germany and an invited professor at École Polytechnique Fédérale de Lausanne, the University of Paris, and the University of Lille. He is a 2015 Fellow of the Institute of Mathematical Statistics (IMS) and was an IMS Medallion Lecturer in 2018.

See the original story @ math.utah.edu

Zhao Scholarship

August 22, 2019

Taylor is the first recipient of the Michael Zhao Memorial Scholarship. She’s a senior majoring in mathematics and minoring in computer science and plans to graduate in the spring of 2020.

“The financial assistance provided by the scholarship will be of great help to me in paying for my educational expenses, and it will allow me to concentrate more of my time on studying,” said Walker. “After graduating, I plan on entering the workforce in a math related field. I hope to honor Michael’s legacy in mathematics as I continue to learn about a subject we both enjoy.”

Michael Zhao loved sushi, travel and classical music. His lifelong passion and ardent pursuit, however, was always mathematics. His fascination with math took him from the 100 Club in kindergarten to Cambridge University as a Churchill Scholar. On December 8, 2018, while at Columbia University in New York City chasing his goal of becoming a college professor, Zhao passed away due to a sudden heart attack.

But on April 18, Zhao’s zeal for math continued with the naming of the first recipient of the Michael Zhao Memorial Scholarship. Taylor Walker, a senior studying mathematics and computer science, is the first awardee.

“The scholarship aims to recognize a truly outstanding mathematics student,” said Davar Khoshnevisan, chair of the Department of Mathematics, “which is consistent with celebrating Michael’s memory.”

Zhao grew up in Salt Lake City and attended Skyline High School, where he was first chair in flute and served as captain of the debate team while also attending Canada/USA Mathcamp and taking math courses at the U. As an undergraduate at the U, Zhao received the Eccles Scholarship that supported his studies in the Honors College. Zhao was intrigued by the breadth of study the Honors College offered—a place where he could read Thomas Aquinas and David Hume, while also studying Eastern philosophy and literature from texts like the Bhagavad Gita and the Daodejing.

In 2017 he was the second U student to win the prestigious Churchill Scholarship. “It’s a common perception that skill in mathematics is only due to talent, but hard work counts for much more” Zhao said. “Having mentors is also extremely helpful, and I am indebted to many faculty members, graduate students, and engineers for their guidance and encouragement.”

Many of the faculty in the U’s Math Department have fond memories of working with Zhao. In an interview in 2017, professor of mathematics Gordon Savin, who served as Michael’s honors thesis advisor, said, “Mike is one of the strongest undergraduate students we have had since I have been at the University of Utah, in more than 20 years. For someone his age, he already has an incredible level of maturity and mathematical knowledge."

He also worked with Dragan Miličić. In the same interview, Miličić said, “We often have discussions on various topics related to algebraic geometry, number theory, and representation theory. I was always impressed that talking to Mike feels more like talking with a colleague and not a student.”

Another professor who worked with Zhao was Braxton Osting, who said, “Many people remember Michael as a brilliant student, excelling under an almost impossible course load covering a large range of topics in mathematics and computer science. In spending time with Michael, I also came to know him as a genuinely kind person, generous with his time and helpful to his fellow students.”

After Zhao passed away, math department faculty and fellow Churchill Scholars approached Khoshnevisan with the idea of establishing a scholarship in Zhao’s name. Khoshnevisan got approval from Zhao’s parents. They, along with colleagues, friends and even his high school math teacher, reached out to their community for donations.

The new scholarship, partly funded by the Department of Mathematics and partly by donors, keeps Zhao’s memory alive. If you’d like to contribute to this scholarship, please make checks payable to the Michael Zhao Memorial Scholarship and send donations to the following: Tiffany Jensen Department of Mathematics 155 South 1400 East, JWB 233 Salt Lake City, UT 84112