The University of Arizona

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Friday, March 29, 2024

Program in Applied Mathematics Colloquium

Stochastic Diffusions for Control, Inference, and Learning
Series: Program in Applied Mathematics Colloquium
Location: MATH 501
Presenter: Yongxin Chen, Department of Aerospace Engineering, Georgia Tech

Diffusion processes refer to a class of stochastic processes driven by Brownian motion. They have been widely used in various applications, ranging from engineering to science to finance. In this talk, I will discuss my experiences with diffusion and how this powerful tool has shaped our research programs. I will go over several research projects in the area of control, inference, and machine learning, where we have extensively utilized tools from diffusion processes. In particular, I will present our research on three topics: i) covariance control in which we aim to regulate the uncertainties of a dynamic system; ii) Monte Carlo Markov chain sampling for general inference tasks; iii) and diffusion models for generative modeling in machine learning.

Yongxin Chen is an Associate Professor in the School of Aerospace Engineering at Georgia Institute of Technology. He has served on the faculty at Iowa State University (2017-2018). Prior to that, he spent one year (2016-2017) at the Memorial Sloan Kettering Cancer Center (MSKCC) as a postdoctoral fellow. He received his BSc from Shanghai Jiao Tong University in 2011, and Ph.D. from University of Minnesota in 2016, both in Mechanical Engineering. He is an awardee of the George S. Axelby Best Paper Award of IEEE Transactions on Automatic Control in 2017 and the best paper prize of SIAM Journal on Control and Optimization in 2023. He received the NSF Faculty Early Career Development Program (CAREER) Award in 2020, the Simons-Berkeley Research Fellowship in 2021, the A. V. `Bal’ Balakrishnan Award in 2021, and the Donald P. Eckman Award for outstanding young engineer in the field of automatic control in 2022. His current research interests are in the areas of control theory, machine learning, and robotics. He enjoys developing new algorithms and theoretical frameworks for real world applications.

 

Place: Math Building, Room 501  https://map.arizona.edu/89

Monday, April 1, 2024

Statistics GIDP Colloquium

Multiple Testing of Local Extrema for Detection of Change Points
Series: Statistics GIDP Colloquium
Location: ENR2 S215
Presenter: Dr. Dan Cheng, ASU

Title:  Multiple Testing of Local Extrema for Detection of Change Points

 

Abstract: We propose a new approach to detect the number and location of change points in piecewise linear models under stationary Gaussian noise. Our method transforms the change point detection problem into identifying significant local extrema through kernel smoothing and differentiation of the data sequence. By computing p-values for all local extrema based on the derived peak height distributions of derivatives of smooth Gaussian processes, we utilize the Benjamini-Hochberg procedure to identify significant local extrema as the detected change points. The algorithm provides asymptotic strong control of the False Discovery Rate (FDR) and power consistency, as the length of the sequence and the size of jumps get large. Simulations show that FDR levels are maintained in non-asymptotic conditions and guide the choice of smoothing bandwidth. Compared to traditional change point detection methods based on recursive segmentation, our approach requires only one instance of multiple testing across all candidate local extrema, thereby achieving the smallest computational complexity proportionate to the data sequence length.

Tuesday, April 2, 2024

Analysis, Dynamics, and Applications Seminar

The Weighted Birkhoff Average as an Efficient Test for Chaos
Series: Analysis, Dynamics, and Applications Seminar
Location: MATH 402
Presenter: James Meiss, Department of Applied Mathematics, UC Boulder

Traditional methods to detect chaotic trajectories include visualization and the computation of Lyapunov exponents. Both of these require long time computations of the trajectory and—for Lyapunov—its linearization. Lyapunov exponents converge slowly, if at all, and a number of Lyapunov indicators, including the “Fast” (FLI) and “Mean Exponential Growth” (MEGNO) have been developed to attempt to get around this. An alternative technique, “Frequency Analysis” was developed to indicate trajectories that lie on tori with dynamics conjugate to a rotation, thus giving an indictor for lack of chaos.  A contrasting idea is the “0-1 Test” which maps the trajectory onto a random walk to show chaos.

I will discuss work with Evelyn Sander and Nathan Duignan that uses Weighted Birkhoff Averages as a test for chaos. Birkhoff’s ergodic theorem implies that when an orbit is ergodic on an invariant set, spatial averages of a phase-space function can be computed as time averages. However the convergence of a time average can be very slow. In 2016, Das et al introduced a $C^\infty$ weighting technique that they later showed gives super-polynomial convergence when the dynamics is conjugate to a rigid rotation with frequency that is sufficiently incommensurate (Diophantine). We show that the Weighted Birkhoff Average (WBA) gives a sharp distinction between chaotic and regular dynamics and allows accurate computation of rotation vectors for regular orbits. This allows one to find critical parameter values at which invariant tori are destroyed in Hamiltonian systems and symplectic maps. We apply these methods to circle, torus, area-preserving and three-dimensional angle-action maps.  Comparisons with other techniques show that the WBA is more efficient. It also has the advantage of accurately computing physically relevant quantities like rotation vectors.  We also show that the WBA can detect  “strange non-chaotic attractors”, invariant sets that are geometrically strange but have zero Lyapunov exponents.

 

Place: Math Building, Room 402  https://map.arizona.edu/89

Algebra and Number Theory Seminar

The Buzz about the BHZ: The Life and Times of Brauer’s Height Zero Conjecture
Series: Algebra and Number Theory Seminar
Location: ENR2-S395
Presenter: Mandi A. Schaeffer Fry, University of Denver

In 1955, Richard Brauer, often regarded as the founder of modular representation theory, made one of the first of the so-called “local-global” conjectures in character theory and opened the door to an entire area of research. I’ll discuss the background of this conjecture, known as Brauer’s Height Zero Conjecture (BHZ), and its recent proof, which is joint work with G. Malle, G. Navarro, and P.H. Tiep.

Wednesday, April 3, 2024

Ph.D. Final Oral Dissertation Defense

Multi-Spacecraft Observatory Data Analysis Techniques: Uncertainty Quantification & Comparison
Ph.D. Final Oral Dissertation Defense
Location: MATH 501
Presenter: Theodore (Teddy) Broeren, Program in Applied Mathematics, University of Arizona

Dissertation Title: Multi-Spacecraft Observatory Data Analysis Techniques: Uncertainty Quantification & Comparison

 

Advisor: Kristopher Klein, Lunar & Planetary Sciences

Thursday, April 4, 2024

Mathematics Colloquium

Broadening Interest in Mathematics with Data Science
Series: Mathematics Colloquium
Location: MATH 501
Presenter: Adam Spiegler, University of Colorado. Denver

The rapidly growing demand in data science presents an exciting opportunity for math and statistics departments to redesign courses to benefit both traditional math and statistics majors as well as new students from other disciplines. Creating cohesive undergraduate curriculum entails weaving together content from different courses to steadily develop critical skills necessary to compete in today’s workforce. In this talk I will discuss how the Department of Mathematical and Statistical Sciences at the University of Colorado Denver is integrating data science throughout our undergraduate. I will demonstrate how students experiment with mathematical models in a virtual laboratory using interactive Jupyter notebooks to attract a wider range of students.

(Refreshments will be served in the Math Commons Room at 3:30 PM)

Friday, April 5, 2024

Ph.D. Final Oral Dissertation Defense

Difference Operators and Pentagram Maps Over Rings
Ph.D. Final Oral Dissertation Defense
Location: ENR2 S210
Presenter: Leaha Hand, Department of Mathematics, University of Arizona

Program in Applied Mathematics Colloquium

Mathematical modeling to understand blood clotting and bleeding
Series: Program in Applied Mathematics Colloquium
Location: MATH 501
Presenter: Karin Leiderman, Department of Mathematics, University of North Carolina, Chapel Hill

Hemostasis is the normal, healthy process in which a blood clot forms to stop bleeding in the event of an injury. Blood clot formation is a complex and nonlinear process that occurs under flow and on multiple spatial and temporal scales. Defects and perturbations in the hemostatic system can result in serious bleeding or pathological clot formation, but due to the complexity of the system, the responses to these changes and the underlying mechanisms are challenging to predict. Mechanistic mathematical models of blood clot formation and coagulation can elucidate biochemical and biophysical mechanisms, help interpret experimental data, and guide experimental design. In this talk I will briefly describe such models and show how our integrated mathematical and experimental approach has facilitated the discovery of previously unrecognized interactions within the clotting system.

 

Place: Math Building, Room 501  https://map.arizona.edu/89

Thursday, April 11, 2024

Ph.D. Final Oral Dissertation Defense

Two Spatial Correlation Estimates in Quantum Statistical Mechanics
Ph.D. Final Oral Dissertation Defense
Location: ENR2 S225
Presenter: Eric Roon, Department of Mathematics, University of Arizona

Mathematics Colloquium

Location: MATH 501
Presenter: Xinwen Zhu, Stanford University
(Refreshments will be served in the Math Commons Room at 3:30 PM)

Monday, April 15, 2024

Ph.D. Final Oral Dissertation Defense

Reductions of Some Crystalline Representations in the Unramified Setting
Ph.D. Final Oral Dissertation Defense
Location: ENR2 S395
Presenter: Anthony Guzman, Department of Mathematics, University of Arizona

Tuesday, April 16, 2024

Analysis, Dynamics, and Applications Seminar

Order parameter equations for patterns; their universality, their defects and open challenges
Series: Analysis, Dynamics, and Applications Seminar
Location: MATH 402
Presenter: Alan Newell, Mathematics Department, University of Arizona

Patterns with almost periodic structures can be seen in so many natural contexts; as epidermal ridges on the tips of your fingers, cloud streets, convection rolls, on the growth tips of plants, sunflowers. Their behaviors can, in many situations, be captured by averaging over the local periodic pattern and writing what often turn out to be universal equations for macroscopic variables called order parameters. I will describe how these equations come about, what they express  and how they describe both the evolution of the pattern and their defect structures. There are many open challenges, one of which I will discuss.

Place: Math Building, Room 402  https://map.arizona.edu/89

Wednesday, April 17, 2024

Ph.D. Final Oral Dissertation Defense

L-Functions for a Family of Generalized Kloosterman Sums in Two Variables
Ph.D. Final Oral Dissertation Defense
Location: ENR2 S225
Presenter: Bolun Wei, Department of Mathematics, University of Arizona

Thursday, April 18, 2024

Mathematics Colloquium

Location: MATH 501
Presenter: Benoit Charbonneau, University of Waterloo

Tuesday, April 23, 2024

Analysis, Dynamics, and Applications Seminar

Wave turbulence; its natural asymptotic closure plus many challenges that are still open
Series: Analysis, Dynamics, and Applications Seminar
Location: MATH 402
Presenter: Alan Newell, Mathematics Department, University of Arizona

A successful statistical description of most nonlinear systems is stymied by the lack of closure; the rates of change of lower order moments depend on moments of higher order leading to an infinite hierarchy. Most attempts to enforce an artificial closure fail. However, there is a natural asymptotic closure for fields of weakly nonlinear waves (think of a wind driven ocean surface). I will explain to you what (mild) premises are required to achieve this natural closure and the reasons it occurs. The corresponding kinetic equation for the energy density turns out to have very interesting stationary solutions corresponding to equipartition states and to finite flux solutions of Kolmogorov type, discovered originally by our good colleague Volodja Zakharov. But, despite many successes, the story is far from over as there are still open challenges, some of which I will tell you about.

 

Place: Math Building, Room 402  https://map.arizona.edu/89

Wednesday, April 24, 2024

Ph.D. Final Oral Dissertation Defense

Bayesian Additive Regression Networks
Ph.D. Final Oral Dissertation Defense
Location: Student Union 404
Presenter: Danielle Van Boxel, Program in Applied Mathematics, University of Arizona

Advisors:  Co-Advisor:  Xueying Tang, Dept of Mathematics

 

                 Co-Advisor: Cristian Roman Palacios, School of Information

Thursday, April 25, 2024

Mathematics Colloquium

Location: MATH 501
Presenter: Ian Tobasco, Rutgers University
(Refreshments will be served in the Math Commons Room at 3:30 PM)

Friday, May 10, 2024

Event

College of Science Spring 2024 Convocation
Location: McKale Center-UA Campus
Presenter: TBA

For details, see https://science.arizona.edu/academics/graduation-convocation