Dr. George Roman - University of Florida
Tues 10/14 2025
Title: Random Matrix Theory and Hilbert Space
Abstract: Every compact Lie group has a natural well-behaved probability measure known as the Haar measure, which allows for the study of integrals over such groups. Random matrix theory is essentially probability theory performed over certain compact Lie groups of matrices, typically the unitary, orthogonal, and symplectic groups. This theory has applications in probability, number theory, combinatorics, and more, but my research gives evidence for a seemingly-unexplored connection to reproducing kernel Hilbert spaces, which we shall examine in this talk.
Dr. Michael Pilla - Florida Polytechnic University
Tues 9/30 2025
Title: Cesàro-type operators acting on function spaces of several complex variables
Abstract: The celebrated Cesàro operator is a well-known operator with interesting connections to a variety of objects in operator theory. The usual interpretation involves investigating function-theoretic properties of the operator when acting on the Hardy space or, more naturally, its matrix representation acting on complex-valued sequence spaces. Generalizations have been made for Cesàro-type operators acting on weighted Hardy spaces but constructing analogs of theCesàro operator for function spaces of several complex variables such as the Drury-Arveson space has yet to be achieved. In this presentation, several potential definitions along with a few basic properties are introduced and addressed.
Dr. Satyajith Bommana Boyana - Florida Polytechnic University
Tues 09/16 2025
Title: Discontinuous Galerkin Methods for a Convection-Dominated Optimal Control Problem
Abstract: Elliptic optimal control problems with convection-dominated state equations arise naturally in many real-world situations where diffusion effects are relatively small compared to convection (advection/transport). These infinite-dimensional problems are important because they model optimization of physical systems governed by differential equations where material, heat, or momentum transport plays a key role. The numerical solutions to these problems by standard finite element/finite difference methods are polluted by spurious oscillations in convection-dominated regimes. Hence, there is a need for stabilized numerical methods.
By reformulating an infinite-dimensional elliptic optimal control problem, which includes a convection-dominated state equation, as a saddle-point problem, we develop novel discontinuous Galerkin schemes to discretize and solve the saddle-point problem in finite dimensions. We demonstrate the well-posedness of the finite-dimensional discrete problem, prove convergence of the schemes in the energy norm, and establish convergence rates. Several numerical experiments are presented to validate the theoretical findings. This is a collaborative work with Tom Lewis, Sijing Liu, and Yi Zhang.
Dr. Elizabeth Hale - Florida Polytechnic University
Tues 09/16 2025
Title: Fourier Series, Fourier Transform, and Applications
Abstract: This talk will explore applications of the Fourier series and the Fourier transform in various settings. We will first motivate and define the Fourier series and Fourier transform, and then highlight applications to areas such as signal processing and partial differential equations. We will conclude with how the Fourier transform allows us to extend the notion of derivatives, through what are known as fractional differential operators, and discuss some of their properties and estimates.
Dr. Onur Toker - Florida Polytechnic University
Tues 09/02 2025
Title: LIDAR Based Surface Classification and Autonomous Navigation
Abstract: In this talk, we will focus on Point Clouds, i.e. sets of 3-dimensional vectors, output by Lidar sensors. In the first part of the talk, we will focus on simple statistical methods that can be used to determine the surface type (e.g. concrete, lawn, etc.) and possible higher order extensions (aka AI methods). In the second part of the talk, we will focus on quantifying "similarity" between Point Clouds, i.e. sets of 3-dimensional vectors, and possible distance "metrics". At the end, a short demo video will be presented.
Dr. Jonathan Schillinger - Florida State University
Tues 04/01 2025
Title: Fractal Riesz Energy Asymptotics Through Gaussian Means
Abstract: Studying the behavior of the minimal continuous Riesz energy over fractal sets has been a relatively hot topic in the field of Energy Theory. A recent result of Calef in 2010 computed the asymptotics for the minimal Riesz energy as the Riesz parameter s approaches the dimension over self-similar fractal sets. After introducing the problem and going through Calef's second order density arguments, we will discuss how a seemingly unrelated result for the Gaussian energy not only implies Calef's computation, but also extends to non-minimal cases.
Dr. Michael Dabkowski - University of Michigan
Tues 03/18 2025
Title: Compactness of a Linear Product Involving the Blaschke Product
Abstract: For two inner functions that fix the origin on the open unit disk in the complex plane, we consider the question of whether the associated linear product can be compact or finite-rank. We show that the product cannot be rank-one when one has purely atomic Alexandrov-Clark measure and the other
extends continuously to the boundary of When they are finite Blashke products each with two distinct factors, we show the product cannot be compact.
Dr. Chris Kelley - Florida Polytechnic University
Tues 02/18 2025
Title: Mathematical modeling of human motor control and Parkinson’s disease
Abstract: Human motor control includes thousands of neurons processing signals to actuate hundreds of muscles. This complex system is intractable at the neuronal level, but the overall system behaves as a typical engineering control system. Sensory receptors produce measurements that provide feedback to model-based controllers in the brain, which actuate musculoskeletal dynamics. Low-order mathematical modeling of this high-level control system provides insight into human motor control characteristics. Nature drives systems towards optimality—humans aim to accomplish tasks with minimum energy and maximum expected rewards. Thus, optimization principles drive the mathematics of human motor control modeling. These principles capture key characteristics for sensory processing and model-based feedback. Extending these baseline healthy motor control models to capture certain types of neural dysfunction provides insight into disease. In particular, changes to high-level controller parameters can produce both the excitatory (tremor) and inhibitory (bradykinesia) motor symptoms of Parkinson's disease. This talk provides an overview of optimization principles in state estimation and control and how they help to understand human motor control and Parkinson's disease.
Dr. Ian Bentley - Florida Polytechnic University
Tues 02/04 2025
Title: Machine Learning for Nuclear Physics Datasets
Dr. Austin Anderson - Florida Polytechnic University
Tues 11/12 2024
Title: On the Packing Functions of Some Linear Closed Sets of Measure Zero
Abstract: We use a characterization of Minkowski measurability to study the asymptotics of best packing on cut-out subsets of the real line with Minkowski dimension d between 0 and 1. Our main result is a proof that Minkowski measurability is a sufficient condition for the existence of best packing asymptotics on monotone rearrangements of these sets. For each such set, the main result provides an explicit constant of proportionality , depending only on the Minkowski dimension , that relates its packing limit and Minkowski content. We later use the Digamma function to study the limiting value of as d increases toward 1. For sharpness, we use renewal theory to prove that the packing constant of the (1/2,1/3) Cantor set is less than the product of its Minkowski content and proportionality. We also show that the measurability hypothesis of the main theorem is necessary by demonstrating that a monotone rearrangement of the complementary intervals of the 1/3 Cantor set has Minkowski dimension d=log(2)/log(3), is not Minkowski measurable, and does not have convergent first-order packing asymptotics. The aforementioned characterization of Minkowski measurability further motivates the asymptotic study of an infinite multiple subset sum problem.
Dr. Evan Adamek - Florida Polytechnic University
Tues 10/29 2024
Title: The Evanescent Neutron
Dr. Joel Rosenfeld - University of South Florida
Tues 10/15 2024
Title: N/A
Dr. Doug Pfeffer - University of South Florida
Tues 10/01 2024
Title: Understanding Fairness in Hardware Random Number Generators (RNGs)
Abstract: Significant effort has gone into creating human-made devices that hope to produce a random output (hardware Random Number Generators). A classic example is a standard 6-sided die. Given such a device, it is natural to ask whether it is producing outcomes in a ‘fair’ way. The answer to this question begins by looking at the probabilistic side of soliciting outcomes from a (possibly unfair) device a large number of times---maybe even infinitely often---and recording the sequence of observed outcomes. We find that this process produces a recursively defined, fractal-like distribution reminiscent of the ‘Devil’s Staircase’ which we can then analytically compare to the fair distribution in a variety of ways to assess the 'unfairness' of the device itself. This investigation stems from joint work with the Department of Energy at Sandia National Labs.
Dr. Edwar Romero-Ramirez - Florida Polytechnic University
Tues 9/17 2024
Title: N/A
Dr. Joshua Drouin - Florida Polytechnic University
Tues 9/3 2024
Title: Folding Donuts
Abstract: Taking bites out of donuts and squishing them onto the board, we can observe some very interesting (and messy) behaviors. Once we've eaten our fill, like many great minds, we begin to wonder: What happens if I folded these donuts instead of eating them? Join us on a sugar-free journey to discover what lurks in the singularities of donuts.
But wait! There's More! A special showing of recent developments in undergraduate research! Grab your scalpels and super-glue, and prepare to ask the hard-hitting questions: Curves, what are they, where do they come from, and where do they go?
Dr. Ian Bentley - Florida Polytechnic University
Tues 4/16 2024
Title: Determining and Modeling the Shapes of Atomic Nuclei
Abstract: The nucleus of the atom provides an interesting ground to study at intersection of experimental observation and theoretical modeling. Quantum mechanics basics and some resulting rules of thumb will be discussed and applied to nuclei. Experimental evidence for a variety of different nuclear shapes will be presented. One particular nuclear model will be discussed as well as how it is being used to determine the shape of the nucleus. Additionally, other properties resulting from that shape are determined by mapping one space onto another through a neural network that has been developed and tested primarily at Florida Poly.
Dr. Jay Elsinger
Tues 4/2 2024
Title: An elementary approach to Karitonov's Theorem: Polynomials, Perturpations, and a Proof - Oh My!
Abstract: The continuity of the roots of a monic polynomial on its coefficients (over the complex numbers) can be proved using an elementary real analysis approach using essentially just the Bolzano-Weierstrass Theorem. Other approaches require higher-level techniques from either complex analysis or topology, which are not readily accessible to undergraduates. Fortunately, our elementary approach does apply for nonmonic polynomials that occurs in many important areas such as singular perturbation theory, perturbation theory for generalized eigenvalue problems, and, as we will see in this talk, in the stability theory of polynomials – an active area of modern research. Furthermore, the possibility of a change in the degree of the perturbed polynomial from that of the unperturbed polynomial requires a special consideration that does not occur for monic polynomials. Yet, we are still able to provide a short and simple proof on the continuity of the roots of nonmonic polynomials as a function of their coefficients using only elementary results from analysis. Finally, we show how to apply these results to give a new elementary proof of a breakthrough result in the robust stability of polynomials from the late 1970’s, the so-called Kharitonov’s Theorem, that originally used more sophisticated techniques which can be circumvented now using our approach. This is joint work with Aaron Welters and Anthony Stefan at Florida Tech.
Dr. Michael Crescimanno - Youngstown State University
Tues 3/19 2024
Title: Big Bang in a Bottle: Electromagnetically Induced Transparency analogue of Leptogenesis
Abstract: Enantomeric ripening in chemistry, the matter-antimatter asymmetry in the early universe, comparing the effects of driving your car forward or backward over a speedbump and how scallops swim in viscous media are all deeply related manifestations of the same underlying physical principle: the Sakharov Conditions. These conditions lead to universal behavior of systems with a broken discrete symmetry when driven out of equilibrium. After exploring a few illustrative examples of the Sakharov Conditions in action, we test its applicability in a quantum mechanical regime via a recent experiment using Zeeman Electromagnetically Induced Transparency (EIT) in a 87Rb buffer gas vapor cell. This allows us a first glimpse of the effect quantum "coherences" may have on early universe phenomenology.
Dr. Ethan Berkove - Lafayette College
Tues 2/20 2024
Title: Geodesic Taxicab paths in the Sierpinski Carpet and Menger Sponge
Abstract: The Sierpinski carpet and Menger sponge are well-studied connected generalizations of the Cantor set. They are also members of a two-parameter family of connected higher-dimension fractals that can be constructed iteratively from the n-cube. In this talk we focus on determining taxicab paths—piece-wise linear paths that always travel parallel to an axis—between any two points x and y in members of this fractal family. In particular, given points x and y in a fractal, we explicitly construct taxicab geodesics between them. As an application, we compare the taxicab metric to the standard Euclidean metric in the fractals we consider. This is joint work with Elene Karangozishvili and Derek Smith.
Dr. Alexander Joyce - Florida Polytechnic University
Tues 2/6 2024
Title: Asymptotic Cones of Quadratically Defined Sets and Their Applications to QCQPs
Abstract: Optimization on linear programs is well-established with straightforward properties on the existence of solutions. Extending this to quadratically constrained quadratic programs (QCQP), or problems with a quadratic objective function with quadratic constraints, these properties no longer hold. This leads to difficulties with globally solving QCQPs as well as determining the existence of an optimal solution. In this talk, we discuss the application of cones, particularly asymptotic cones of a set defined by a single quadratic constraint, to address these difficulties.
Dr. Evan Cosgrove - Mathworks
Tues 1/23 2024
Title: MATLAB and Simulink Features for Students and Faculty
Dr. Somak Das - Florida Polytechnic University
Tues 10/31 2023
Title: Stochastic Gradient Descent algorithms for control of systems with uncertainty
Abstract: Most problems that are modelled by systems of partial differential equations possess some form of uncertainty. In order to control such a system, we take into account the average cost over different instances for obtaining the optimal control. Stochastic gradient descent algorithms lay out a way to optimize such systems without having to go through large amount of computation making the process cheaper. In this talk we see how different stochastic gradient descent algorithms can be used to obtain the optimal control of systems with uncertainty.
Dr. Omair Zubairi - Florida Polytechnic University
Tues 10/17 2023
Title: Numerical Modeling of Highly Magnetized Neutron Stars
Abstract: Neutron stars are compact stellar objects formed in cataclysmic astrophysical events known as supernovae. They have masses about twice that of the Sun and radii of approximately 10 to 15 kilometers resulting in densities on the nuclear scale. They have high temperatures and large magnetic fields up to 15-20 orders of magnitude greater than our Sun. With such extreme conditions, neutron stars make excellent laboratories for nuclear, particle and astrophysics.
For over the past 80 years, traditional models of non-rotating neutron stars assume them to be perfect spheres; however, this may not be true if high magnetic fields are present. Classes of Neutron stars such as Magnetars exhibit such anisotropies and break from perfect spherical symmetry making them oblate or prolate spheroids.
In this talk, I will present the stellar structure model of highly magnetized neutron stars in the framework of general relativity and the implications this has on the stellar properties such as masses and radii. Additionally, due to the deformation of these compact stars, the gravitational mass quadrupole moment is also affected which in turn suggests that these deformed objects maybe capable of producing gravitational waves.
Dr. Parisa Darbari Kozekanan - Florida Polytechnic University
Tues 10/3 2023
Title: N/A
Dr. Douglas Turner - Florida Polytechnic University
Tues 9/19 2023
Title: Deterring Cartel Formation Using Dynamic Optimization
Abstract: Price fixing harms consumers and violates antitrust laws. Economic theory has identified a variety of factors that impede price fixing cartels. However, empirical results suggest these factors may instead cause cartel formation. Utilizing dynamic optimization techniques, I demonstrate how properly accounting for psychological biases within the firm can explain this puzzle and enhance our understanding of cartel formation.
Dr. Ranses Alfonso Rodriguez - Florida Polytechnic University
Tues 9/5 2023
Title: Exploring Dynamics: From Predator-Prey to the Butterfly Effect
Abstract: In this brief talk, we delve into the fascinating realm of dynamical systems by examining two intriguing examples. First, we investigate the dynamics of a Lotka-Volterra system, a classic model for predator-prey interactions. We uncover the intricate behaviors that emerge from the interplay between species. We explore the concept of equilibrium, identify regions of stability, and highlight the occurrence of limit cycles.
Transitioning to a different realm, we merely touch upon the notion of chaos in the Lorenz system. This iconic system, known for its chaotic behavior, demonstrates the sensitive dependence on initial conditions. We illustrate the captivating trajectory of chaos, emphasizing the butterfly effect and its implications for long-term predictability.
Join us as we navigate through these captivating systems, offering insights into the inherent complexity of dynamical phenomena and showcasing the beauty of chaos.
Dr. Susan LeFrancois - Florida Polytechnic University
Tues 4/11 2023
Title: Public Health and Data Science: Journey Through Current Projects
Dr. Kurt Bryan - Rose-Hulman Institute of Technology
Tues 3/28 2023
Title: Designing a Cruise Control Using ODEs and the Laplace Transform
Abstract: Control Theory plays an essential role in most modern technology, and PID ("Proportional-Integral-Derivative") control is one of the most common classes of control algorithm. This technique is often applied to physical systems that are modeled by differential equations. I'll show a simple application that my students have enjoyed, designing a "cruise control" for an automobile. This application also illustrates a nontrivial application of the Laplace transform (beyond solving ODEs).
Dr. Paniz Abedin - Florida Polytechnic University
Wed 3/15 2023
Title: Efficient Algorithms on Strings with Applications to Computational Biology
Abstract: In this talk we will discuss how to design and analyze efficient text indexing data structures and associated algorithms for processing text data.
Dr. Onur Toker - Florida Polytechnic University
Tues 2/28 2023
Title: Demystifying Artificial Intelligence - A Mathematical Approach
Dr. Aaron Bardall - Florida Polytechnic University
Tues 11/01 2022
Title: The Shape of Water – A Shallow Dive into Variational Calculus
Abstract: Water takes on many shapes. It takes on the shape of a container it occupies. In the absence of a container, large droplets of water will form into puddles while smaller droplets will form a rounder shape. In this talk, we aim to analyze the shape a droplet of fluid, water or otherwise, will take absent a container. Will it form a flat puddle or a round droplet? Will it be somewhere in between? We will use physical modeling and variational calculus to analyze the optimal profile of a two-dimensional droplet. We will also investigate the transition from small droplet to large puddle as the 'volume' of the droplet grows and analyze the effect of other parameters. This is a fun problem which will show how far down the rabbit hole mathematics can go in aiding our understanding of something so simple. This talk is accessible to students with a knowledge of calculus and an interest in physical modeling, optimization, and/or differential equations.
Dr. Ala Alnaser - Florida Polytechnic University
Tues 10/18 2022
Title: Statistical Modeling of Autonomous Vehicles
Abstract: We consider a statistical model of a hybrid vehicle for autonomous vehicles (AV) algorithm development, simulation, and verification. Data was collected using a vehicle equipped with steering, throttle, break, wheel speed and several other sensors and actuators all connected to the vehicle Controller Area Network (CAN). Furthermore, the vehicle is equipped with a lidar, radar and multiple camera sensors, and a vibration resistant GPU desktop. The research vehicle was driven on various types of roads (rural and highway) to generate a rich dataset for various modelling studies. Our preliminary test results show that existing hardware is capable of recording all relevant CAN activity without any data packet loss. We have explored linear differential equation-based models including the air friction and we are planning to explore both nonlinear and AI based more complex models.
Dr. Adam Rumpf - Florida Polytechnic University
Tues 10/04 2022
Title: Modern Problems in Network Optimization
Abstract: This talk is meant to serve as an introduction to network flows models and to some modern problems in network optimization, motivated by an ongoing research project about fortifying sets of interdependent civil infrastructure networks (roads, subways, power lines, telecommunications, etc.) against targeted attacks. While classical network flows problems can be solved very efficiently using the well-known network simplex algorithm, variations of these problems that incorporate additional complexity can be much more computationally difficult to solve. In this talk I will briefly introduce the network simplex algorithm, show how it can be generalized to solve problems that incorporate interdependencies between networks, and finally show how all of this can be used as part of a game theoretic model for planning optimal defenses against an intelligent attacker. This talk is meant to be abundantly accessible, and knowledge of optimization theory and network flows models will not be assumed.
Dr. Aslihan Vuruskan
Tues 09/20 2022
Title: N/A