# Mathematics Colloquium

## Upcoming Colloquium

**Some perspectives by a UCI mathematician**

Dr. Knut Solna, UC Irvine

October 7, 2024

5:30pm-6:30pm in FO3-200A

### Abstract

Many problems are characterized by uncertainty and best modeled using a probabilistic framework. In this talk I will describe aspects of my research relating to mathematical finance where uncertainty plays an important role. I will moreover describe the UCI mathematics program and aspects of applying to a graduate program.

### Biosketch

Knult Solna is a Professor and Vice Chair for Graduate Studies in the Department of Mathematics at UC Irvine. He received his Ph.D. in 1997 from Stanford University, under the supervision of George C. Papanicolaou.

Dr. Solna's research interests span applied mathematics, applied probability, stochastic differential equations, mathematical finance, and waves in random media. He has received numerous accolades, including the Sloan Fellowship, an instructorship award from the University of Utah, a Fulbright Award, and research grants from the Air Force Office of Scientific Research and the National Science Foundation.

In addition to authoring over 100 high-impact research publications, Dr. Solna has written and edited five books on topics such as econometrics, risk management, and mathematical and statistical models for imaging, among others.

The Mathematics Colloquium is a unique opportunity for students to learn about new developments in mathematics and what mathematics and statisticians do after they graduate. Hosted by the Department of Mathematics and Statistics at California State University, Long Beach, the weekly meetings invite guests from universities, research laboratories, and industry to present and discuss current topics in mathematics. All students are encouraged to attend.

## Schedule

The schedule for Fall 2024 will be posted when it becomes available.

Dr. Bogdan Suceavă, CSU Fullerton

### Abstract

In 1827, C.F. Gauss obtained a relation that he described as "remarkable;" the fact that the curvature of a surface depends only on the elements of the first fundamental form. More than a century later, J. F. Nash's Theorem proved that any Riemannian manifold can be embedded into a Euclidean ambient space with dimension sufficiently large. In 1968, S.-S. Chern pointed out that a key technicality in applying Nash's Theorem effectively is finding useful relationships between intrinsic and extrinsic elements which characterize immersions. After 1993, when a groundbreaking work written by B.-Y. Chen on this theme was published, many explorations pursued the investigations of geometric inequalities between intrinsic and extrinsic quantities. With all these developments in mind, we propose a classification of geometric inequalities in the geometry of submanifolds in five classes; some of these relations might be well-known, while others are rather new.

### Biosketch

Bogdan Suceavă studied mathematics at the University of Bucharest (B.Sc. 1994, M.Sc. 1995) and at Michigan State University (Ph.D., 2002). Since 2002, he has worked at Cal State Fullerton, where he wrote most of his over 80 papers in mathematics. He is one of the recipients of a 2020 MAA Polya Award for Expository Writing (for a paper written with A. Glesser, M. Rathbun, and I.M. Serrano). In the fall of 2011, Suceavă established the Fullerton Math Circle, an outreach program of our CSUF Math Department, focused on developing problem-solving skills in mathematics for K-12 students. Suceavă is the recipient of the Cal State Fullerton 2023 L. Donald Shields Excellence in Scholarship and Creativity Award, and an honorary research professor with the Babeş-Bolyai University in Cluj-Napoca, Romania.

Dr. Puttipong Pongtanapaisan, Arizona State University

### Abstract

We learn in calculus that critical points provide key insights into the shape of a graph. In nature, various biological structures, such as systems of worms or water rings, often form naturally tangled configurations. In this talk, I will discuss how rearranging critical points can lead to conclusions about knotted shapes. For instance, if the order of certain local maxima and minima cannot be swapped, it indicates that the polymer cannot fit into a tight tube.

### Biosketch

Puttipong Pongtanapaisan obtained his Ph.D. at the University of Iowa, where he studied knot theory and low-dimensional topology under the supervision of Dr. Maggy Tomova. He was a PIMS Postdoctoral Fellow at the University of Saskatchewan, working with Dr. Chris Soteros to explore knotted objects in lattice tubes by analyzing the arrangement of local maxima and minima of knots and links. Currently, he is a Postdoctoral Associate at Arizona State University.

Dr. Knut Solna, UC Irvine

### Abstract

Many problems are characterized by uncertainty and best modeled using a probabilistic framework. In this talk I will describe aspects of my research relating to mathematical finance where uncertainty plays an important role. I will moreover describe the UCI mathematics program and aspects of applying to a graduate program.

### Biosketch

Knult Solna is a Professor and Vice Chair for Graduate Studies in the Department of Mathematics at UC Irvine. He received his Ph.D. in 1997 from Stanford University, under the supervision of George C. Papanicolaou.

Dr. Solna's research interests span applied mathematics, applied probability, stochastic differential equations, mathematical finance, and waves in random media. He has received numerous accolades, including the Sloan Fellowship, an instructorship award from the University of Utah, a Fulbright Award, and research grants from the Air Force Office of Scientific Research and the National Science Foundation.

In addition to authoring over 100 high-impact research publications, Dr. Solna has written and edited five books on topics such as econometrics, risk management, and mathematical and statistical models for imaging, among others.

Alexandro Ricardo Luna, UC Irvine

### Abstract

We discuss a survey of results concerning the dimensions of the spectra of Sturmian Hamiltonians and give an overview of the dynamical techniques that are used in small coupling regimes. We also present a new result concerning the behavior of the Hausdroff dimension of such a spectrum when the coupling tends to zero and the frequency is of bounded-type.

### Biosketch

Alexandro Ricardo Luna is a 5th year graduate student at University of California, Irvine. Their research interests include spectral theory and dynamical systems. They attended California State University, Fullerton as an undergraduate and have been local to California their whole life.

Jamie Haddock, Harvey Mudd College

### Abstract

The Kaczmarz methods are a family of simple, deterministic or randomized, iterative methods which can be employed for solving consistent systems of linear equations of the form Ax = b, or related problems. These methods have gained popularity in recent times due to their amenability to large-scale data and distributed computing environments. This talk will focus on results in three areas, all related in some way to the Kaczmarz methods: iterative methods for adversarially corrupted systems of linear equations; analyzing the dynamics of simple models of consensus amongst interacting agents; and proving bounds on the concentration and variance of randomized iterative methods.

### Biosketch

Jamie Haddock received her BS in Mathematics from Gonzaga University, and Ph.D. in Applied Mathematics from University of California, Davis. After completing her degrees, Jamie joined UCLA for a three-year postdoctoral fellowship where she was mentored by Prof. Deanna Needell. She arrived at Harvey Mudd College in 2021 and is currently the Iris & Howard Critchell Assistant Professor of Mathematics.

Jamie leverages mathematical tools, such as those from probability, combinatorics, and convex geometry, on problems in data science and optimization, and has been active recently in topics like randomized numerical linear algebra, combinatorial methods for convex optimization, and tensor decomposition for topic modeling. She is especially interested in questions about complex and messy data, like that encountered in medical applications.

Amber Simpson, Binghamton University

Jonathan Bostic, Bowling Green State University

Changho Kim, UC Merced

Robin Wilson, Loyola Marymount University

Konrad Aguilar, Pomona College

Po-Ning Chen, UC Riverside

## Previous Colloquia

The Mathematics Colloquium Archive has the Colloquia from previous semesters.

## Colloquium Committee

For Fall 2024:

- Dr. Pavneet Kaur Bharaj
- Dr. Seungjoon Lee
- Dr. Rolando de Santiago