Department of Mathematics professors selected to present at the International Congress of Mathematicians

Two professors from the University of Utah’s Department of Mathematics have

received invitations to present at the prestigious International Congress of Mathematicians (ICM) in July 2022, in St. Petersburg, Russia. The invitations are an indication of the importance of the work these professors are engaged in and of the caliber of the department.

First held in Zurich, Switzerland, in 1897, the ICM is the largest and most significant conference on pure and applied mathematics, as well as one of the world’s oldest scientific congresses. ICMs are run every four years by the International Mathematical Union in partnership with host country organizers.

Mladen Bestvina

Mladen Bestvina will give a plenary lecture

Mladen Bestvina, Distinguished Professor of Mathematics, has been invited to give a plenary lecture. Plenary lectures are given in the part of the conference that everyone attends. An invitation to give a plenary lecture to the thousands of ICM participants is considered a special distinction in the mathematics field, and criteria for selection are rigorous. This is the second time Bestvina has been invited to speak at the ICM. He was a speaker in the topology section in 2002 in Beijing.

“It is a huge honor for me to be selected to give a plenary talk at the ICM,” said Bestvina. “It’s primarily a recognition of the big advances my field—geometric group theory—has made over the last several decades. When I started my career, the term didn’t even exist, and now geometric group theory has developed into a field involving topology, geometry, and dynamics. In my own work, I always found it more rewarding and satisfying to collaborate with others. Over the years I wrote papers with many collaborators, but I’d like to mention three with whom I wrote quite a few papers and who deserve a lot of credit for my invitation to speak at the ICM: Professor Ken Bromberg, who teaches in our Math Department; Mark Feighn, Professor of mathematics and computer science at Rutgers University; and Koji Fujiwara, a math professor at Kyoto University in Japan.”

Bestvina’s research

Bestvina’s research focuses on symmetries of objects (called “groups” in mathematics) from the point of view of geometry and topology. For example: imagine an infinite chess board—the plane with the usual tiling into squares (ignore the colors of the squares that a chess board would have). What is the group of symmetries? An example of a symmetry is a translation of the entire board by a whole number of squares in the direction of a side of a square. In the language of geometric group theory, this group is “virtually Z+Z.”

“Conversely, suppose someone hands you a group and asks you to understand it,” said Bestvina. “Then you would build an object (a ‘space’) whose group of symmetries is the given group. If the group is virtually Z+Z, you would build the plane and understand the group using Euclidean geometry you learned in high school. There are more complicated groups, and building corresponding spaces and understanding their geometry is a lot of fun,” he said.

Bestvina received the University of Utah’s Distinguished Scholarly and Creative Research Award in 2019. He was born in Croatia and received a Ph.D. in mathematics from the University of Tennessee. He joined the U as a professor in 1993 and became a Distinguished Professor in 2008.

Jon Chaika will give an invited lecture

Jon Chaika, Associate Professor of Mathematics, will give an “invited lecture.” Chaika will present jointly with Barak Weiss, Professor of mathematics at Tel Aviv University.

Invited lectures are organized into sections, and Professors Chaika and Weiss will present within the “Dynamics” section.

“I’m excited for the opportunity to present my math at the ICM,” Chaika said. “The ICM is such an important gathering of the international mathematical community, where we share ideas and discuss and disseminate the latest advances in active research in mathematics.”

Chaika’s research

Chaika’s research is in the field of dynamical systems, which seeks to understand a space and a map by following individual points. This map could represent the passage of time in a physical system. Ergodic theory is a sub-branch of dynamical systems that uses an idea called a measure to do this. A measure is an abstraction of the idea of length or area (or volume). One of the families of systems Chaika studies is billiards in polygons. In these systems, a point travels in a straight line inside a polygon until it hits one of the sides. Once it hits a side, it obeys the law of elastic collision, bouncing off the side the same way a billiard ball would bounce off the side of a pool table. The point then continues to travel in a straight line until it hits the next side, where it again has an elastic collision. Chaika and Giovanni Forni, a mathematician at the University of Maryland, have been able to show there are billiards in polygons in which the flow in different directions is usually uncorrelated.

Chaika received a Simons Fellows Award in Mathematics in 2020. He obtained a Ph.D. in mathematics in 2010 from Rice University and joined the University of Utah in 2013.

“It’s an honor for the U to be so prominently represented at the ICM,” said Davar Khoshnevisan, Professor and Chair of the Department of Mathematics. “We congratulate our colleagues Mladen and Jon and are proud of the international recognition their work is receiving.” Jon Chaika