
11:00 am

11:00 am
Dr. Mehrdad Kalantar  University of Houston
Operator space complexification revisited
Math 243, Functional Analysis
APM 7218 and Zoom (meeting ID: 94246284235)
AbstractThe complexification of a real space can be described as an induced representation (in the sense of Frobenius). In this language, in particular, the analytical aspects of the concept and its generalizations (e.g. quaternification of real spaces), have very canonical descriptions, which allow vast generalizations of some of the key results, such as Ruan’s uniqueness theorem for “reasonable” operator space complexification.This is joint work with David Blecher.

11:00 am
Zirui Zhang  UC Irvine
Personalized Predictions of Glioblastoma Infiltration: Mathematical Models, PhysicsInformed Neural Networks and Multimodal Scans
Center for Computational Mathematics Seminar
APM 2402 and Zoom ID 990 3560 4352
AbstractPredicting the infiltration of Glioblastoma (GBM) from medical MRI scans is crucial for understanding tumor growth dynamics and designing personalized radiotherapy treatment plans.Mathematical models of GBM growth can complement the data in the prediction of spatial distributions of tumor cells. However, this requires estimating patientspecific parameters of the model from clinical data, which is a challenging inverse problem due to limited temporal data and the limited time between imaging and diagnosis. This work proposes a method that uses PhysicsInformed Neural Networks (PINNs) to estimate patientspecific parameters of a reactiondiffusion PDE model of GBM growth from a single 3D structural MRI snapshot. PINNs embed both the data and the PDE into a loss function, thus integrating theory and data. Key innovations include the identification and estimation of characteristic nondimensional parameters, a pretraining step that utilizes the nondimensional parameters and a finetuning step to determine the patient specific parameters. Additionally, the diffuse domain method is employed to handle the complex brain geometry within the PINN framework. Our method is validated both on synthetic and patient datasets, and shows promise for realtime parametric inference in the clinical setting for personalized GBM treatment.

2:00 pm
Prof. Tom Bohman  Carnegie Mellon University
Notes on 2point concentration in the random graph
Math 269  Combinatorics
APM 7321
AbstractWe say that an integervalued random variable $X$ defined on $G_{n,p}$ is concentrated on 2 values if there is a function $f(n)$ such that the probability that $X$ equals $f(n)$ or $ f(n)+1$ tends to 1 as $n$ goes to infinity. 2point concentration has been a central issue in the study of random graphs from the beginning. In this talk we survey some recent progress in our understanding of this phenomenon, with an emphasis on the independence number and domination number of the random graph.
Joint work with Jakob Hofstad, Lutz Warnke and Emily Zhu.

3:00 pm
Prof. Tingting Tang  San Diego State University
On computing the nonlinearity interval and MAPs of SDPs
APM 7321
AbstractIn this talk, I will talk about the parametric analysis of semidefinite optimization problems w.r.t. the perturbation of the objective function along a fixed direction and on a compact set. For the perturbation along a fixed direction, it is proven that the continuity of the optimal set mapping could fail on a nonlinearity interval and the set of points where this failure occurs is finite. A numerical method is developed to numerically compute the nonlinearity interval and generalize to perturbations on a compact set. For multivariable perturbations, a maximal analytic perturbation set (MAPs) is defined on which the analyticity of the optimal mapping holds. Numerical examples are given to demonstrate the performance.

3:00 pm
Prof. Rayan Saab  UC San Diego
Stochastic algorithms for quantizing neural networks
Math 296  Graduate Student Colloquium
HSS 4025
AbstractNeural networks are highly nonlinear functions often parametrized by a staggering number of weights. Miniaturizing these networks and implementing them in hardware is a direction of research that is fueled by a practical need, and at the same time connects to interesting mathematical problems. For example, by quantizing, or replacing the weights of a neural network with quantized (e.g., binary) counterparts, massive savings in cost, computation time, memory, and power consumption can be attained. Of course, one wishes to attain these savings while preserving the action of the function on domains of interest.
We discuss connections to problems in discrepancy theory, present datadriven and computationally efficient stochastic methods for quantizing the weights of already trained neural networks and we prove that our methods have favorable error guarantees under a variety of assumptions.

10:00 am
Michael Zshornack  UC Santa Barbara
Twist flows and the arithmetic of surface group representations
Math 211B  Group Actions Seminar
APM 7321
AbstractMargulis's work on lattices and a number of questions on the existence of surface subgroups motivate the need for understanding arithmetic properties of spaces of surface group representations. In recent work with Jacques Audibert, we outline one possible approach towards understanding such properties for the Hitchin component, a particularly nice space of representations. We utilize the underlying geometry of this space to reduce questions about its arithmetic to questions about the arithmetic of certain algebraic groups, which in turn, allows us to characterize the rational points on these components. In this talk, I'll give an overview of the geometric methods behind the proof of our result and indicate some natural questions about the nature of the resulting surface group actions that follow.

10:00 am

3:00 pm
Aranya Lahiri  UCSD
Why look at padic groups?
Postdoc seminar
APM 5829
AbstractDo I really do number theory? Sometimes I have no idea how I belong to the number theory group, and not say functional analysis group? Even though the only books I pretend to read are: padic Lie groups, nonarchimidean functional analysis and Lecture notes on formal and rigid geometry? But then I realize I really don't know any functional analysis for that matter. In this talk, in very broad and crude strokes I will try to convince myself that I do number theory. Come burst my bubble.

4:00 pm
Prof. Gunther Uhlmann  University of Washington
Journey to the Center of the Earth
Math 295  Colloquium Seminar
APM 6402
AbstractWe will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It also has several applications in optics and medical imaging among others.
The problem can be recast as a geometric problem: Can one determine the Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will survey some of the known results about this problem.No previous knowledge of differential geometry will be assumed.

1:00 pm
Runqiu Xu  UCSD
How does the discrete Fourier transform on symmetric groups walk you through Hurwitz Cayley graphs?
Food for Thought
APM 6402
AbstractIn this talk, I will give a quick review of representation theory and graph theory. I will explain the symmetric group algebra and its Fourier transform with an explanation of the corresponding characters. I will hint how it could be used to count the number of a specific type of walks on the Cayley graph of permutations.

2:00 pm
Prof. Natalia Komarova  Math, UCSD
Mathematical Methods in Evolution and Medicine
Math 218: Seminar on Mathematics for Complex Biological Systems
APM 6402
AbstractEvolutionary dynamics permeates life and lifelike systems. Mathematical methods can be used to study evolutionary processes, such as selection, mutation, and drift, and to make sense of many phenomena in the life sciences. How likely is a single mutant to take over a population of individuals? What is the speed of evolution, if things have to get worse before they can get better (aka, fitness valley crossing)? Can cooperation, hierarchical relationships between individuals, spatial interactions, or randomness influence the speed or direction of evolution? Applications to biomedicine will be discussed.

4:00 pm
Prof. Padmini Rangamani  UC San Diego
The mathematics of cellular mechanotransduction
2024 Murray and Adylin Rosenblatt Endowed Lectures in Applied Mathematics
Natural Sciences Building Auditorium
Please register here:
https://forms.gle/g1XRxXwsUCkdR8YK8 AbstractCellular function often integrates biochemical and mechanical cues in what is known as mechanotransduction. Mechanotransduction is closely tied to cell shape during development, disease, and wound healing. In this talk, I will showcase how mathematical models have helped shed light on some fundamental problems in this area of research including how cell shape can alter biochemical signaling and how cell mechanics can alter cell shape. Throughout, I will highlight the challenges and opportunities for integrating mathematical models with experimental measurements.

5:10 pm
Prof. Lisa Fauci  Tulane University
Insights from biofluidmechanics: A tale of tails
2024 Murray and Adylin Rosenblatt Endowed Lectures in Applied Mathematics
Natural Sciences Building Auditorium
Please register here:
https://forms.gle/g1XRxXwsUCkdR8YK8 AbstractThe motion of undulating or rotating elastic `tailsâ€™ in a fluid environment is a common element in many biological and engineered systems. At the microscale, we will consider models of the journey of extremely long and flexible insect flagella through narrow and tortuous female reproductive tracts, and the penetration of mucosal tissue by helical flagella of bacteria. At the macroscale, we will probe the neuromechanics and fluid dynamics of the lamprey, the most primitive vertebrate and, hence, a model organism. Using a closedloop model that couples neural signaling, muscle mechanics, fluid dynamics and sensory feedback, we examine the hypothesis that amplified proprioceptive feedback could restore effective locomotion in lampreys with spinal injuries.

11:00 am
Prof. Brian Hall  University of Notre Dame
Heat flow on polynomials with connections to random matrices and random polynomials
Math 243, Functional Analysis
APM 7218 and Zoom (meeting ID: 94246284235)
AbstractIt is an old result of Polya and Benz the backward heat flow preserves the set of polynomials with all real roots. Recent results have shown a surprising connection between the evolution of real roots under the backward heat flow and the notion of “free convolution” in free probability. Free convolution, in turn, is the operation that allows one to compute the eigenvalue distribution for sums of independent Hermitian matrices in terms of the individual eigenvalue distributions.
The story gets even more interesting when one considers polynomials with complex roots. Recent work of mine with Ho indicates that under the heat flow, the complex roots of highdegree polynomials should evolve in straight lines with constant speed. This behavior also connects to random matrix theory and free probability. I will present some conjectures as well as recent rigorous results with Ho, Jalowy, and Kabluchko.

11:00 am

4:00 pm
Paul K. Newton  University of Southern California
Control of evolutionary mean field games and tumor cell population models
UCSD Mathematics Colloquium/MathBio Seminar
AbstractMean field games are played by populations of competing agents who derive their update rules by comparing their own state variable with that of the mean field. After a brief introduction to several areas where they have been used recently, we will focus on models of competing tumor cell populations based on the replicator dynamics mean field evolutionary game with prisoner’s dilemma payoff matrix. We use optimal and adaptive control theory on both deterministic and stochastic versions of these models to design multidrug chemotherapy schedules that suppress the competitive release of resistant cell populations (to avoid chemoresistance) by maximizing the Shannon diversity of the competing subpopulations. The models can be extended to networks where spatial connectivity can influence optimal chemotherapy scheduling.