Spring 2025
■ January 29
Ying Hu, University of Nebraska at Omaha
Title: Seeking Orders in 3-Manifold Groups
Abstract: A left-invariant order on a group is a linear order of group elements such that the order remains invariant under left group multiplication. While abstract groups can be challenging to visualize, introducing a left-invariant order allows us to imagine the relative 'size' between elements.
This talk will explore whether the fundamental group of a 3-dimensional space can be left-ordered. Beginning with basic concepts, we will delve into how this seemingly abstract algebraic question connects deeply to the topological and geometric structure of 3-manifolds. The discussion will provide an accessible overview of this dynamic subject, highlighting recent advances and open questions that continue to inspire new research directions in geometric topology. This talk is designed for a broad audience, and assume no prior knowledge of the topic.
■ March 19
Jinmyung Choi, Drake University
Title: Applications of Biostatistics Ideas and Techniques in Biomedical Data Science: Opportunities and Challenges
Abstract: The completion of the Human Genome Project and advances in omics science and technology have enabled the investigation of molecular and cellular underpinnings of human health and disease. The application of biostatistics ideas and techniques has become essential in analyzing genetics and genomics data, helping to discover better ways to promote human health and prevent and treat human disease. In this talk, I will share my experiences and insights on the application of biostatistics ideas and techniques in biomedical data science. First, I will introduce genome-wide association studies, which aim to identify genetic variants in the human genome associated with health and disease. Second, I will discuss recent advances in omics science and technology that facilitate the discovery of molecular and cellular underpinnings at the systems level, offering exciting opportunities for the application and development of biostatistical data analysis methods. Along the way, I will highlight opportunities and the challenges and in the field of biomedical data science, drawing on my personal research ideas and plans.
Fall 2024
■ October 16, Patterson 222, 4 p.m. - 5 p.m.
Paul Lombardi, University of South Dakota
Title: Feathered Beams Decomposed
Abstract: In music, durations are quantized to subdivisions of time in the form of fractions of the inverse powers of 2 (e.g., 1/2^0, 1/2^1, 1/2^2, etc.). All durations that do not involve tuplets can be represented by sums of these fractions. The gradual transition from one note duration to another through a specified number of intermediate note values requires an accelerando/ritardando beam (i.e., feathered beam). This notation, however, does not indicate exactly how the gradual transition through the intermediate note values is to occur. The various details may be so contradictory that feathered beams may be impossible to realize. Thus, the notation is inherently indeterminate, although it is not often regarded as such. We will explores these concepts and combine rhythmic nomenclature with a graphing system to deconstruct feathered beams using examples from George Crumb’s Night Music I, as well as comments on which composers have used them and whether or not they should.
■ October 23, Patterson 222, 4 p.m. - 5 p.m.
Chad Berner, Iowa State
Title: Operator orbit frames and frame-like Fourier expansions
Abstract: Frames in a Hilbert space that are generated by operator orbits are vastly studied because of the applications in dynamic sampling and signal recovery. In this talk, we discuss that every non-surjective operator generating a frame is similar to a rank one perturbation of a unitary. Additionally, it is known that the Kaczmarz algorithm for stationary sequences in Hilbert spaces generates a frame that arises from a non-surjective operator orbit. In this talk, we discuss that every frame generated by a non-surjective operator in any Hilbert space arises from the Kaczmarz algorithm. Furthermore, we describe some of the unique properties of these frames and their consequences for Fourier expansions for singular measures. Moreover, we discuss the classification of measures that possess Fourier expansions arising from two-sided operator orbit frames as well as describe some measures that possess a relaxation of this property.
■ November 13, Patterson 222, 4 p.m. - 5 p.m.
Etienne Gnimpieba, University of South Dakota
Title: AI/ML-Powered Digital Twins in life science: Mathematical Modeling for Predictive Discovery
Abstract: Digital twins— a virtual representations of physical systems—leverage data-driven insights to simulate and predict life science behavior. This discussion incorporate examples from dynamical systems, operator theory, numerical analysis, and stochastic processes. I will highlight the integration of differential equations (ODEs) and AI/ML methods to develop digital twins capable of predicting context-specific responses, optimizing the systems thinking approach in life science research and innovation. Case studies will be discussed, such as intelligence material design, modeling the cell-microbe-material interactions, which combines dynamical system theory with cutting-edge AI, to provide predictive insights into the understanding of the rule of life between living and the non-living systems ( e.g. the disease mechanisms and drug/therapeutic outcomes).
Spring 2024
■ January 24, 4 p.m. - 5 p.m. , UP 222
Eric Weber, Iowa State University
Title: What is Data Science?
Abstract: Data science" is a buzzphrase making the rounds in academia and industry. But is it more than just a buzzphrase? And if so, what exactly is it? To turn the phrase: "Data science is in the eye of the beholder". And what about machine learning and artificial intelligence? We'll discuss my view of data science as well as several of my current research projects in the area. We'll also talk about some of the mathematics behind data science as it currently stands. Finally, I'll shamelessly promote the graduate program in Iowa State's mathematics department.
■ February 14, 4 p.m. - 5 p.m. , UP 222
Daniel Perry, Augustana University
Title: The universal Lipschitz path space of the Heisenberg group
Abstract: Inspired by the definition of a universal covering of a topological space, we define the universal Lipschitz path space over the Heisenberg group. The universal Lipschitz path space is a length space with a Lipschitz map onto the base space. As is the case with a universal cover of a topological space, the universal Lipschitz path space supports a unique lifting property and is Lipschitz simply connected. However, unlike the universal cover, no Lipschitz simply connected covering space of the Heisenberg group exists as the base space is nowhere Lipschitz semi-locally simply connected. These results follow from the Heisenberg group being a purely 2-unrectifiable metric space when endowed with the Carnot-Carathéordory metric. Further properties of the universal Lipschitz path space as well as applications to calculations of the Lipschitz fundamental group of the Heisenberg group will be discussed.
■ March 27, 4 p.m - 5 p. m., UP 222
Soumodeep Mitra, University of South Dakota
Title: Probing the quantum nature of black holes with ultra-light boson environments
Abstract: We show that the motion of a black hole (BH) through a cloud of an ultra-light scalar field, mimicking dark matter, is one of the best avenues to probe its quantum nature. This is because quantum effects can make the BH horizon reflective, with the largest reflectivity at smaller frequencies/smaller velocities, where the scattering of ultra-light scalar fields is most effective. In particular, we demonstrate that the quantum nature of BHs can lead to less energy flux, but larger frictional force experienced by them, resulting into an increase in the number of cycles in an extreme mass ratio inspiral. This provides a new window to probe the quantum nature of BHs, as well as ultra-light dark matter.
Fall 2023
■ September 27, 4 p.m. - 5 p.m. , UP 117
Michael Puthawala, South Dakota State University
Title: Global Injectivity, Manifold Estimation and Universality of Neural Networks
Abstract: In recent years machine learning, and in particular deep learning has emerged as a powerful and robust tool for solving problems in fields ranging from robotics, to medicine, materials science, cosmology and beyond. As work on applications has advanced, so too has theory advanced to guide, explain, interpret deep learning. In this talk I will provide an overview on some of that theory in three parts. In the first, I will present a connection between injectivity of ReLU layers and vector geometry, which yields a simple criterion for a ReLU network to be end-to-end injective. Second, I will introduce the concept of universality in the context of neural networks and reveal a surprising connection to knot theory, which sheds light on what kinds of manifold-supported functions can be learned by a neural network. Finally, I will discuss a work that exploits the connections between topological covering spaces and locally bilipschitz maps to develop a recipe for constructing neural networks that can learn to approximate `topologically interesting’ maps between manifolds.
■ October 2, 4 p.m. - 5 p.m. , UP 117
Aurel Stan, Ohio State University
Title: Random variables for which the number operator algebra and Weyl algebra intersect nontrivially
Abstract: We introduce first the quantum operators: creation, preservation, and annihilation, and the number operator generated by a random variable X having finite moments of all orders. Every linear operator T, from the space of polynomial random variables in X to itself, can be uniquely written as an infinite sum of terms of the form A_n(X)D^n, where A_n(X) is a polynomial in X, viewed as a multiplication operator and interpreted as a position operator, and D is the classic differentiation operator, interpreted as the momentum operator. We call this sum, the position-momentum decomposition of T. The Weyl algebra is the space of all linear operators T having a finite position-momentum decomposition. We show first that if a continuous random variable has the property that a non-constant polynomial function of its number operator belongs to the Weyl algebra, then its density function satisfies a first order linear equation, which we call the generalized Pearson equation. We apply then this equation to the case when the number operator is quadratic in D, showing that the random variable must be Gaussian or Gamma distributed.
Finally, we discuss the random variables for which the number operator satisfies a quadratic equation in D, proving that these random variables are beta distributed.
■ October 19, 6:30-8 pm, Farber Hall - 71st Annual Harrington Lecture
Yuhlong Lio (University of South Dakota)
Title: Predicting Time to Failure, Even with Incomplete Data: Lifetime Data Analysis via Probability Functions
■ October 25, 4 p.m. - 5 p.m. , UP 117
Dan Van Peursem, University of South Dakota
Title: Building Thinking Classrooms
Abstract: Peter Liljedahl wrote a book “Building Thinking Classrooms in Mathematics” and it has gained a lot of traction in many high schools in South Dakota. This seminar will provide a hands on example of some of the components of this new teaching method, and we will discuss the rationale behind the structure. No need to bring anything, just an inquisitive mind.
■ November 20, 5p.m. - 6 p.m. , UP 202
Seth Gerberding, Texas A&M
Title: Verification: The Euler equations, the Noh Problem, and the mathematics behind reliable simulations in extreme conditions
Abstract: In this talk, I discuss work being done at Los Alamos National Laboratory on computer simulations. In particular, I discuss the concept of verification and its relationship to numerical codes. I also provide some historical context surrounding the lab and why verification is an important question. Finally, I present some results regarding exact solutions to the Noh Problem, an important case where the Euler Equations have a known solution.
Spring 2023
■ March 2 4 p.m. - 5 p.m. UP 202
Catalin Georgescu (USD, Math)
Title: About a Free Group
Abstract: The goal of this talk is to present some connections between dynamical properties of actions of groups on the real line and circle and the algebraic structure of these groups. In particular I will focus on the existence of free subgroups in the group of orientation preserving group of homeomorphisms and discuss a few open problems in this direction.
Fall 2022
■ September 28, 4-5, UP 117
Gabriel Picioroaga (USD, Math)
Title: Convolution in Neural Networks
Abstract: In this talk I will explain the role played by the mathematical operation "convolution" in neural networks. Theoretical properties of convolution and neural networks will be highlighted as well as examples of image classification in Matlab with the help of the already trained nets GoogLeNet and AlexNet.
■ October 25, 4-5, UP 117
Nate Harding (USD, Math)
Title: Universal Approximation Theorems
Abstract: The general notion of a universality condition unveils a unique embedding of some space into another with conditions for isomorphism. In the context of neural networks, the notion manifests as a Universal Approximation Theorem where the closure of the span of an activation function composed with an affine map is considered. In this talk we will discuss historical development of existence theorems and some generalizations of the relevant transforms, emphasizing alternative topologies of the spaces.
Spring 2022
■ April 20 4 p.m. - 5 p.m. UP 202
Robert Stack (Chadron State College)
Title: Data Analytics: Digging into the Data
Abstract: The development of this project began in graduate school in a SPED class (Behavior Modifications). While playing baseball in Vermillion, the concept of the LoC (level of contact) arose. A baseline was established using batting average (BA) and the modification of an alternate batting stance was used to create new baseline data. Fast forward three decades and the concept is still active with a data analytical twist. Once of the most prolific power hitters since he came into the league 8 years ago (averaging 30 HRs and 100 RBIs per year), which included an MVP award in 2020, Rookie of the Year in 2014, and be named an all-star three times, Jose Abreu is a player from whom much can be learned. Comparing his BA to his LoC is the goal. This talk will address the two analytics and statistically compare the two as they are associated with the strike zone locations.
Spring 2020
■ February 12, 4 p.m. - 5 p.m. UP 117
Logan Hale (USD, Human Factors Psychology)
Title: Machine Learning to Understand Emotion
Abstract: Hey, psychologists use Math too! Anytime you interact with a person or a machine, your body, your face, your words, even the tone of your voice give hints as to what you’re feeling at any given moment. In this talk, I will outline how someone’s voice can be broken down to a set of numbers, using algorithms and statistics (and years of research and trial-and-error), that a computer can use to tell what emotions you’re experiencing. Spoiler alert: the machines can tell how we feel better than we can.
Fall 2019
■ September 18, 4 p.m. - 5 p.m. UP 117
Seth Gerberding (USD)
Title: Preserving Identifiability in Linear Compartmental Models by moving Leaks, Outputs, and Inputs
■ October 16, 4 p.m. - 5 p.m. Room TBA
Ramiro LafuenteRodriguez (USD)
Title: Non-Abelian o-groups, their Divisibility and Archimedean Rank
Abstract: I will go over the definition and examples of partially ordered groups, including ordered groups. An explicit description will be given of an example of a non-Abelian o-group of 2x2 matrices over the reals. I will also sketch a generalization of this group to nxn matrices and discuss the Archimedean property of these groups. Finally, the divisibility of these groups will be discussed.
■ November 13, 4 p.m. - 5 p.m. Room TBA
Steven Harding (Iowa State)
Title:The Kaczmarz Algorithm with Nonuniform Relaxation Parameters
Abstract: We modify the proof of Natterer for the relaxed Kaczmarz algorithm with nonuniform relaxation parameters. We show (1) that the Kaczmarz method converges to the solution of minimal norm if the system of equations is consistent and (2) that the Kaczmarz method converges to a parameter-dependent, weighted least squares solution if the system of equations is inconsistent. Our method, in contrast to contemporary work for (1) and (2), readily extends results for alternative Kaczmarz algorithms. In particular, we discuss the results on the distributed Kaczmarz system which was preliminary work for the summer 2019 REU project on large relaxation parameters, which will also be included in the talk. We also address parameter sampling in response to the optimal parameter problem and include some suggestive numerical experiments based on our method
Spring 2019
■ January 23, 4 p.m. - 5 p.m. UP 117
Yuhlong Lio (USD - Department of Mathematical Sciences)
Title: Inference of Probability Distribution Based on Type-I interval Censored Data
Abstract: Type-I interval censor scheme has been applied to collect data in industry lifetime test as well as medical survival study. In this talk, some recent developments of probability modeling will be discussed through two type-I interval censored data from real world.
■ January 28, 4 p.m. - 5 p.m. UP 117
Eric Weber (Iowa State - Department of Mathematics)
Title: A Gentle Introduction to the Kaczmarz Algorithm
Abstract: The Kaczmarz algorithm is an iterative method for solving systems of linear equations that was introduced by Stefan Kaczmarz in 1937. The algorithm is now enjoying a resurgence in interest, as it has been found useful in data science applications. It also has remarkably deep connections to complex and harmonic analysis. We shall introduce the algorithm, demonstrate some of its features, and present some of its applications in an elementary manner--i.e. requiring only some linear algebra. Towards the end of the talk, we shall give a brief overview of an REU project that will be offered in the coming summer.
■ April 18, 4 p.m. - 5 p.m. UP 120
Jasmine Martin (USD - Department of Mathematical Sciences)
Title: The Uncertainty Principle and Applications to Data Recovery
Fall 2018
■ September 19, 4 p.m. - 5 p.m. Patterson Hall 117
Paul Lombardi (USD - Department of Music)
Title: A Tesseract in Boulez’s Structures 1a
Abstract: The French composer Pierre Boulez (1925–2016) was one of the pioneers of the integral serialism technique. Boulez explores this technique in his composition Structures 1a for two pianos (1952). Because of its innovation, this piece is important in the history of western art music. I will show that its serial structure can map onto the surface a tesseract. The tesseract captures symmetries and antisymmetries contained within the piece. Since the audience is assumed to be mathematicians and not musicians, before delving into this analysis, I will first give a historical overview that puts this work into context, then introduce the musical and mathematical nomenclature used in my analysis.
■ October 12, 4 p.m. - 5 p.m. Patterson Hall 117
John Herr (Butler University)
Title:On the Existence of Complex Hadamard Submatrices of the Fourier Matrices
Abstract: We use a theorem of Lam and Leung to prove that a submatrix of a Fourier matrix cannot be Hadamard for particular cases when the dimension of the submatrix does not divide the dimension of the Fourier matrix. We also make some preliminary observations on the connections of such submatrices to the Universal Tiling Conjecture.
This is joint work with my students Bailey Bond, Alex Glickfield, and Troy Wiegand.
■ October 17, 4 p.m. -5 p.m. Patterson Hall 117
Shrey Sanadhya (University of Iowa)
Title: On cocyles of automorphism groups of a standard Borel space
Abstract: Cocycles play an important role in classification of groups of automorphisms of a measure space w.r.t Orbit Equivalence. This theory was developed in papers by Dye, Connes, Feldman, Krieger, Ornstein, Weiss among others. The notion of weak equivalence applied to pairs $(\Gamma, \alpha)$ of automorphism group and its cocycle, refines orbit equivalence. It was studied in works of Bezuglyi, Golodets, Sinelʹshchikov and Hamachi. Our goal is to use the notion of weak equivalence in case of Borel Dynamics to refine the existing classification of Orbit Equivalence. I will report a progress in this direction.
Spring 2018
■ January 25 4 p.m. - 5 p.m. UP 117
Yuhlong Lio (USD Math)
Title: Building R package
Abstract: R software has been used to develop package for teaching mathematics as well as computation subjects.
In this talk, a set of procedures for building R package will be introduced along with examples.
■ March 15 4 p.m. - 5 p.m. UP 117
Weimin Han (Department of Mathematics and Applied Mathematical and Computational Sciences, University of Iowa )
Title: Numerical Analysis of Hemivariational Inequalities
Abstract: Inequality problems in mechanics can be divided into two main categories: that of variational inequalities concerned with convex energy functionals (potentials), and that of hemivariational inequalities concerned with nonsmooth and nonconvex energy functionals (superpotentials). Through the formulation of hemivariational inequalities, problems involving nonmonotone, nonsmooth and multivalued constitutive laws, forces, and boundary conditions can be treated successfully. Hemivariational inequalities have been shown to be very useful across a variety of subjects, ranging from nonsmooth mechanics, physics, engineering, to economics. In this talk, we will start with a gentle description of the basic notions and ideas of the theory of hemivariational inequalities, and will present new results on convergence and optimal order error estimates for numerical solutions of hemivariational inequalities. Numerical examples will be shown on the performance of the numerical methods.
■ March 22 4 p.m. - 5 p.m. UP 117
Nicholas Britten (USD, Math )
Title: Addition property of Algebraic Entropy: some noncommutative cases
■ March 29 4 p.m. - 5 p.m. UP 117
Adam Larios (Department of Mathematics, University of Nebraska-Lincoln )
Title: The Solution's Shadow: Unlocking the Hidden Realm of Partial Differential Equations
Abstract: Are there equations in mathematics that are just too hard to solve? Perhaps-and many of them seem to be nonlinear partial differential equations. But we cannot give up! These equations appear in nearly every scientific discipline, including physics, biology, chemistry, medicine, so we must work towards an understanding of these equations if we are going to make progress in science. Fortunately, there is a certain tool that can unwrap a large amount of the complexity of these equations, which is both elegant and powerful; namely, Fourier spectral analysis. We will see how this tool can be used to understand the behavior of equations governing heat flow, traffic flow, water waves, and flame fronts. This talk should be accessible to students who have taken calculus, but I will aim at also making it interesting to experts.
Spring 2017
■ March 01 4 p.m. - 5 p.m. UP 117
Hon Keung Tony Ng (Southern Methodist University, Dallas, Texas, U.S.A. )
Title: Analysis of System-based Reliability Data
Abstract: In system reliability engineering, systems are made up of different components and these systems can be complex. For various purposes, engineers and researchers are often interested in the lifetime distribution of the system as well as the lifetime distribution of the components which make up the system. In many cases, the lifetimes of an n-component coherent system can be observed, but not the lifetimes of the components. In the recent years, parametric and nonparametric inference for the lifetime distribution of components based on system lifetime lifetimes has been developed. We further investigate the estimation of the parameters in component lifetime distributions based on censored system-level data. Specially, we consider the maximum likelihood estimation and propose alternative computational methods and approximations to the maximum likelihood estimators. Based on the special features of the system lifetime data, we treat the system lifetime data as incomplete data and apply the Expectation-Maximization (EM) algorithm to obtain the MLEs and apply the stochastic EM (SEM) algorithm to approximate the MLEs. Different implementations of the EM and SEM algorithms are proposed and their performances are evaluated. We have shown that the proposed methods are feasible and easy to implement for various families of component lifetime distributions.
■ March 15 4 p.m. - 5 p.m. UP 117
Cindy Yu (Iowa State University)
Title: Generalized Method of Moments Estimator Based On Semiparametric Quantile Regression Imputation
Abstract: In this talk, we consider an imputation method to handle missing response values based on semiparametric quantile regression estimation. In the proposed method, the missing response values are generated using the estimated conditional quantile regression function at given values of covariates. We adopt the generalized method of moments for estimation of parameters defined through a general estimation equation. We demonstrate that the proposed estimator, combining both semiparametric quantile regression imputation and generalized method of moments, is an effective alternative to parameter estimation when missing data is present. The consistency and the asymptotic normality of our estimators are established and variance estimation is provided. Results from limited simulation studies are presented to show the adequacy of the proposed method.
■ March 23 4 p.m. - 5 p.m. UP 117
Elizabeth Arnason (USD)
Title: Matrix Population Models
Abstract: Oftentimes in biology, there are questions regarding the future of populations. Projection matrices can be utilized to solve such problems. These models neatly summarize the structure of the population, which can be found using the population’s life cycle graph. In this talk, we will discuss the different structures of these matrices. The structure chosen is dependent on the attributes of the population in question. Once the model is constructed, mathematical methods can be applied to obtain important information regarding the population. This information can be used to make informed management decisions.
■ April 10 4 p.m. - 5 p.m. UP 117
Jessie Byrnes (USD)
Title: Bayesian Estimate of Stress-Strength Parameter for Burr Type XII Distribution Based on Progressively First Failure-Censored Samples
Abstract: In industry, the lifetimes of components are becoming longer due to rapid advances in manufacturing technology and a sustained quality improvement effort. Therefore, practitioners are encouraged to adopt some type of censoring scheme in lifetime testing in order to save time and money. From the censored data, statistical techniques can be applied to infer a product’s reliability.
For this presentation, the progressive first failure-censoring scheme is used to obtain samples from two Burr Type XII distributions respectively, so that the stress-strength parameter can be inferred. This reliability parameter is evaluated under Bayesian estimation because it lacks a closed form solution under maximum likelihood estimation. Because of computation complexities and no closed forms of estimators, Markov Chain Monte Carlo procedure is proposed for a simulation study. From the simulation results, the Bayesian estimator under a given loss function will be discussed.
Keywords: Lifetime Censoring; Burr Type XII; Stress-strength Parameter; Bayesian Estimate;
Markov Chain Monte Carlo Algorithm
■ April 26 4 p.m. - 5 p.m. UP 117
Jyun-You Chiang (Southwestern University of Finance and Economics, China)
Title: Economic design of two-stage semicircle control chart for dependent variables
Fall 2016
■ October 17 4 p.m. - 5 p.m. Patterson Hall 117
David Pitts (University of Nebraska Lincoln)
Title: Von Neumann Algebras and Extensions of Inverse Semigroups
■ October 21 - joint seminar with USD Math Club
4 p.m. - 5 p.m. Patterson Hall 117
Cristina Oancea (University of North Dakota)
Title: From Functional Analysis to cancer epidemiology: the life path of a mathematician/statistician trying to save lives
■ November 10 4 p.m. - 5 p.m. Patterson Hall 117
Jessie Byrnes (USD)
Title: Bayesian Estimates via Markov Chain Monte Carlo Algorithm
Spring 2016
■ April 13 4 p.m. - 5 p.m. Room AS 103
Ricardo Cervantes (USD)
Title: Temporal Dynamics of various Predator and Prey Models
Abstract: The study of how and why population numbers change in time and space, or equivalently, population dynamics have puzzled humanity from prehistoric times. As ecological systems are characterized by the interaction between species and their surroundings, one of the fundamental goal is to be able to understand how the interaction of individual organism with each other and with the environment can influence population interaction and the composition of communities over a wide range of temporal domains. An important type of interaction which affects population dynamics of all species is predation. One of the reasons why predation is important is that no organism can live, grow, and reproduce without consuming resources. Temporal models describing predator-prey models have been in the focus of ecological science since the early days of this discipline and it continues to draw interest from both applied mathematicians and ecologists as they exhibit a wide range of interesting dynamical behaviors such as steady states, oscillations and chaos.
Fall 2015
■ October 28, 4 p.m. - 5 p.m. AS 107
Jose Flores (USD)
Title: Dynamics of a biological pest control model : How the species interact?
Abstract: In this presentation we analyze a predator-prey model to control a pest by introducing its natural predator.
Spring 2015
■ February 3, 9 a.m. - 10 a.m. AS 105
Eric Weber (Iowa State)
Title: Spectral Theory of Small Hadamard Matrices
Abstract: We prove that if $A$ and $B$ are Hadamard matrices which are both of size $4 \times 4$ or $5 \times 5$ and in dephased form, then $tr(A) = tr(B)$ implies that $A$ and $B$ have the same eigenvalues, including multiplicity. We calculate explicitly the spectrum for these matrices. We also extend these results to larger Hadamard matrices which are permutations of the Fourier matrix and calculate their spectral multiplicities.
■ March 5, 4 p.m. - 5 p.m. AS 106
Mike Janssen (Dordt College)
Title: Symbolic Powers of Ideals: Problems and Progress
Abstract: Symbolic powers of ideals have been the focus of much recent study in commutative algebra and algebraic geometry. Problems in algebraic geometry (e.g., Waring’s problem) and commutative algebra (e.g., the question of containment in ordinary powers of ideals) have motivated much of this work, but symbolic powers also have applications to other fields, such as computer science, combinatorics, and graph theory. We will explore the questions that have motivated the study of symbolic powers of ideals and share recent results in this direction.
■ April 23, 4 p.m. - 5 p.m. AS 106
Edoardo Persichetti (Dakota State)
Title: Post-Quantum Cryptography
Abstract: In this talk I will present the latest development in the post-quantum cryptography area. The talk will include mathematical content related to the major areas of interest, such as multivariate equations, linear codes and lattices, but will be aimed at a general audience. Everybody is welcome!
FALL 2014
■ October 16, 4:15 p.m. - 5:15 p.m., AS 105
Harry Freeman (Counseling & Psychology in Education, USD)
Title: How strong is our love for one person?
Abstract: I am interested in comparing the level of support we expect from our most significant relationship relative to others in our support network. Under what conditions can we make the claim that individuals value a single individual more than all others in their support networks. Can a probability be computed for a non-parametric distribution, or is it better to set an effect size based on the sample using inferential stats?
■ November 5, 4 p.m. - 5 p.m., AS 107
Steven Nathan Harding (Mathematical Sciences, USD)
Title: Generalized Walsh transforms, Cuntz algebras representations and applications in signal processing
Abstract: Many applications such as compression and data representation in the area of signal processing are based on Hilbert spaces and their orthonormal bases. In this talk, we explore old (classic) and new orthonormal bases in the Hilbert space L2[0,1], as well as some of their applications to signal processing. It is well-known that the classic Walsh functions serve as an orthonormal basis for the L2[0,1] space; in a recent paper published by Dutkay, Picioroaga, and Song, the authors developed a generalized form of this basis. In my talk I will discuss convergence and continuity properties of the generalized Walsh series. I will also show how unitary N x N matrices, along with the quadrature mirror filters that implement them, give rise to representations of Cuntz isometries on L2[0,1]. In this setting, a signal can be encoded or encrypted on N-channels according to filters generated by the unitary matrix. Partial results will be presented on the security of an encryption scheme that implements these Cuntz isometries.
■ November 20, 4 p.m. - 5 p.m., AS 105
Benton Duncan (Department of Mathematics, NDSU)
Title: Algebras associated to continuous dynamics
Abstract: I will survey recent results concerning algebras (mostly operator algebras) associated to dynamical systems. Mostly these algebras are of interest to operator algebraists because they give a class of algebras which are "understandable" and "interesting". I will talk about why they are understandable and what makes them interesting.
SPRING 2014
■ January 29, 4 p.m. - 5 p.m., AS 107
Nathan Tintle (Dordt College)
Title: The use of randomization methods in teaching introductory statistics
Abstract: A growing movement in statistics education is to use permutation, bootstrapping and simulation methods (broadly defined as ‘randomization methods’) when teaching introductory statistics to non-math majors (Stat 101). I will provide a history of this movement, with particular attention to a textbook under development by myself and six others (Beth Chance, George Cobb, Allan Rossman, Soma Roy, Todd Swanson and Jill VanderStoep; http://math.hope.edu/isi). I will compare and contrast our approach with the traditional sequence of topics in Stat 101 and a few other randomization-based curriculum projects underway, summarize published assessment data on these approaches and discuss implementation details.
FALL 2013
■ October 2, AS, Room 107, 4 p.m. - 5 p.m.
Yuhlong Lio (USD)
Title: Approximating the Baseline Hazard Function by Taylor Series for Interval-Censored Time-to-Event Data
■ December 4, AS, Room 105, 4 p.m. - 5 p.m.
Marvin Gamble (USD)
Title: Primitive Pythagorean Triples: From here to infinity?
Abstract: Are there an infinite number of primitive Pythagorean triples? Using number theory I will show the answer to this question and how to find these triples. I will prove what numbers can and cannot be used in the triples and prove the method that will be demonstrated.
This should be an interest to all secondary math education majors and next semesters number theory students.
SPRING 2013
■ February 20, AS, Room 104B, 4 p.m. - 5 p.m.
Jiang Nan (USD)
Convergence analysis of the method of lines - A family of second to third order accuracy schemes.
■ April 3, AS, Room 105, 4 p.m. - 5 p.m.
Catalin Georgescu (USD)
About Existence of Solutions of Differential Equations
Abstract: A more than a hundred years old result (the celebrated Picard-Lindelöf theorem) asserts that if an autonomous vector field f(x) is Lipschitz, then the Cauchy problem X(0)=x of the differential equation X'(t)=f(X) has a unique solution. People wondered if the Lipschitz condition can be weakened. This proved to be a very resistant problem, but with serious theoretical and practical implications. There are two milestone steps in this development: the 1989 DiPerna –Lions paper and the 2004 Ambrosio's article, both in Inventiones Mathematicae. I will briefly present the main innovations brought by these two papers, with a focus on the Ambrosio's concept of Lagrangian flow. Then I will show why if the vector field is only bounded measurable, one can find a vector field with no solutions on a set of positive Lebesgue measure. On the other hand, if the vector field is only bounded measurable and with components staying away from zero, it is believed that the existence theorem still holds almost everywhere, but this seems to be a difficult problem in dimension higher than one. This talk wants to be a discussion revolving around the concept of solution of an ODE/PDE.
FALL 2012
■ October 3, AS, Room 107, 4 p.m. - 5 p.m.
Jose Flores (USD)
Bifurcation analysis of a predator-prey model with double Allee effect on prey and ratio-dependent functional response
Abstract: A ratio-dependent predator-prey model with double Allee effect on the prey is proposed. The presentation includes a parametric analysis of the stability properties of the dynamics of the system in which the functional response is a function of the ratio of prey and predator. The model is studied analytically as well as numerically, including stability and bifurcation analysis. We also discuss the biological relevance of the method regarding both coexistence (conservation) and extinction (biological control) issues.
■ October, 24, AS, Room 107, 4 p.m. - 5 p.m.
Ionut Chifan (University of Iowa)
Rigidity in von Neumann algebras
Abstract: In this talk I will survey some very recent and exciting developments in the classification of von Neumann algebras associated with group actions on measure spaces.
■ November, 7, AS, Room 107, 4 p.m. - 5 p.m.
Gabriel Picioroaga (USD)
Processing and encrypting images with Maple
Abstract: Whenever we use a mobile phone or take pictures with a digital camera and process them with a photo editor or shop online we indirectly use built in software based on Linear Algebra, Finite Group Theory, and even College Algebra. In the first part of my talk I will show how with simple Maple programs and insights from basic mathematics courses we can build a photo editor. The prerequisites are a little knowledge of common algebra operations and understanding how an image file is stored as a matrix. I will survey (with lots of picture examples) types of transformations one can apply to an original image to obtain a filtered image, or a smaller image, or a zoom in and out of the image. Also, the known film photography technique of multi-exposure can be adapted digitally and with better results (blending) using a simple algorithm based on number multiplication and roots. For the second part of the talk and if time permits I will explain how Abstract Algebra (Group Theory, Finite Fields) is used in modern encryption algorithms (RSA, AES) and propose a few simple schemes for image encryption which combined could prove stronger. The theoretical framework where these algorithms and their weaknesses are to be investigated is provided by a large group of invertible functions defined on sets of matrices.
■ November 14, AS, Room 107, 4 p.m. - 5 p.m.
Yuhlong Lio (USD)
Implementing Statistical Inference for Burr Type-XII Distribution Based on Sequential Order Statistics , Nan.Jiang, Tzong-Ru Tsai, Y. L. Lio and D.G. Chen
Abstract: Failing a component in a composite system often causes more load on survival components and enhances the hazard rate. Assuming that component lifetimes in a composite system have a Burr type-XII distribution with a power-trend hazard rate function, point estimates of Burr type-XII distribution parameters and interval estimates of the baseline survival function are obtained by using the maximum-likelihood estimation method and Fisher information matrix. A testing procedure is provided to test whether the hazard rate function would change along with the number of failed components. An intensive simulation has been conducted to evaluate the performance of the proposed estimation procedure, and an example is given for illustration.
SPRING 2012
■ March 28, AS, Room 105, 4 p.m. - 5 p.m.
Ginger McKee (Wolfram Research)
Mathematica in Education and Research
Abstract: This talk illustrates capabilities in Mathematica 8 that are directly applicable for use in teaching and research on campus. Topics of this technical talk include:
* Free forum input
* 2D and 3D visualization
* Dynamic interactivity
* On-demand scientific data
* Example-driven course materials* Symbolic interface construction
* Practical and theoretical applications.
Whether or not you're familiar with Mathematica, you'll find this seminar worthwhile--so don't forget to pass the invitation on to your colleagues and students. All attendees will receive an electronic copy of the examples, which can be adapted to individual projects.
FALL 2011
■ September 21, AS, Room 107, 4 p.m. - 5 p.m.
Rodica Curtu (Department of Mathematics, University of Iowa)
Selection of mixed-mode oscillations in a neuronal competition model
Abstract: Mixed-mode oscillations (MMOs) are temporal periodic activity patterns characterized by notable changes in amplitude: during each cycle, there is an alternation between small-amplitude oscillations and large, fast excursions of relaxation type. MMOs arise in a variety of physical systems; in particular, they were observed in in-vitro experiments at both individual neuron and neuronal population levels and, more recently, they were also found in computational neuroscience models. This talk will show the existence of MMOs in a neuronal competition model that involves slow negative feedback and gain function nonlinearities, and depends on a control parameter associated with external constant stimuli. Analytical and numerical investigation of the system uncover an interesting, novel property of the MMOs: they are periodic canards, but their small amplitude oscillations result from a combined effect of the folded node funnel (canard-induced rotations) and the spiraling unstable manifold of a nearby equilibrium (Hopf-induced rotations). One distinctive feature of the model is that the MMOs are periodic solutions that exhibit small amplitude oscillations and canard behavior twice per cycle; this is due to the fact that transition between the dynamics on the slow manifold and that along the fast fibers occurs near a folded node on both lower and upper branches of the slow manifold.
■ October 21, AS, Room 107, 4 p.m. - 5 p.m.
Akim Adekpedjou (Department of Mathematics and Statistics, Missouri University of Science and technology)
Recurrent Events: Modeling and Statistical Inference
Abstract: In various field such as reliability, economics, sociology, biomedical studies, it is often of interest to monitor occurrence of an event. Such event could be the failure of an electronic system, outbreak of a disease, claim filing, etc…. These events recur and so it is of interest to describe their recurrence behavior through a stochastic model. This talk pertains to the modeling and statistical inference with recurrent event data. I will first discuss some results in the single event setting and show how that translate into recurrent events. I will then summarize some important inference and asymptotic results pertaining to the estimation of the distribution function of the gap-time in recurrent event models. These results are based on important aspects of recurrent events that are not accounted for in the current literature. The discussions on the estimation of the distribution function of the gap-time will be followed by the development of chi-squared type test for testing a simple parametric null model. I will next investigate small sample and asymptotic properties of the test as well as power analysis against a sequence of Pitman's alternatives. Application to some real datasets will be demonstrated. Finally some open problems pertaining to recurrent events will be indicated.
Keywords: Recurrent events; Sum-quota constraint; Informative monitoring; Martingales; Gaussian process; Weak convergence; Pitman's alternatives; Goodness of fit.
■ December 14, AS, Room 104B, 1 p.m. - 3 p.m.
Dmitri Kilin (Department of Chemistry, University of South Dakota)
Fall 2010
■ November 10, AS, Room 107, 4 p.m. - 5 p.m.
Dmitri S. Kilin (Department of Chemistry, University of South Dakota)
Computational modeling of physical and chemical properties of nanostructured silicon surfaces for electronics and photovoltaics
Abstract: A new method combining ab initio electronic structure and density matrix approaches has been developed to simulate photo-excited dynamics in silicon-based energy materials. The interaction of electrons with thermalized lattice vibrations provides the dissipative terms in the equation of motion (EOM) for the reduced density matrix of the silicon surface and describes line broadening of optical excitations, dephasing, and population relaxation from the photoexcited state towards thermalized electronic state. The steady state solutions of the EOM in a basis of Kohn-Sham orbitals provide the electronic charge density for excited states responsible for the induction of a photovoltage at the surfaces [1], while time dependent solutions of the EOM provide rates for carrier relaxation induced by lattice vibrations [2]. Our simulations predict that absorption and photovoltage spectra of the silicon surfaces are drastically affected by presence of adsorbates on the surface or by p- or n- doping. The results obtained by our atomistic approach provide insight on trends relevant to the absorption of near IR, visible, and near UV light, which is of interest in measurements of photovoltages and in the utilization of solar energy.
1. D. S. Kilin and D. A. Micha, "Surface Photovoltage at Nanostructures on Si Surfaces: Ab Initio Results" J. Phys. Chem. 113, 3530 (2009).
2. D. S. Kilin and D. A. Micha, "Electronic Relaxation at a Photoexcited Nanostructured Si(111)Surface" J. Phys. Chem. Lett. 1, 1073 (2010).
■ December 1, AS, Room 107, 4 p.m. - 5 p.m.
Catalin Georgescu (USD)
Topological Entropy
Abstract: In a broad sense, a dynamical system is given by the action of a group upon a topological space. How the structure (and topology) of the group influences the dynamics of the action generated a large body of mathematical work. Among the many tools used, topological entropy proved to be one of the most important. Originated from the standard concept of entropy of a physical system, topological entropy is notoriously difficult to compute and most of the open problems related to entropy revolved around this issue and around its dependence on the parameters of the system. I will present the basic properties of entropy and its connections to algebraic and measure entropy, some examples and a brief overview of the relation that exists between entropy and Lyapunov exponents.
Spring 2010
■ February 24, AS, Room 107, 4 p.m. - 5 p.m.
Y.L. Lio (University of South Dakota)
A Novel Estimation Approach for Mixture Transition Distribution Model in High-Order Markov Chains (joint work with D.G. Chen)
Abstract: A transformation is proposed to convert the nonlinear constraints of the parameters in the mixture transition distribution(MTD) model into box-constraints. The proposed transformation removes the difficulties associated with the maximum likelihood estimation (MLE) process in the MTD modeling so that the MLEs of the parameters can be easily obtained via a hybrid algorithm from the evolutionary algorithms and/or quasi-Newton algorithms for global optimization. Simulation studies are conducted to demonstrate MTD modeling by the proposed novel approach through a global search algorithm in R environment. Finally, the proposed approach is used for the MTD modeling of three real data sets.
■ March 3, AS, Room 104B, 4 p.m. - 5 p.m.
Gleb Haynatzki (University of Nebraska Medical Center)
The speaker will give a presentation of the graduate program available at UN Medical Center and discuss career opportunities in Biostatistics and Public Health (data management, pharmaceutical and clinical trials, data analysis, academia and government agencies). The UNMC College of Public Health Biostatistics Department collaborates with scientists, physicians, clinical investigators and other researchers, provides statistical consulting, teaches courses in biostatistics, and conducts methodological research. The Department's expertise includes clinical trials, study design, surviving analysis, general linear models, longitudinal analysis, survey methodology, and analysis of microarray gene-expression data and other high-dimensional data.
■ March 17 AS, Room 107, 4 p.m. - 5 p.m.
Valentin Matache (University of Nebraska at Omaha)
Function theory and composition operators on spaces of analytic functions
Abstract: Composition operators are operators acting on spaces of functions on a set S, by composition to the right with a fixed selfmap of S. They have been systematically studied since the late sixties. However, composition operators were implicitly present in the mathematical literature much earlier than that. The theory of composition operators acting on holomorphic function spaces is by far the most developed. In this talk, we will address some major directions of investigation, emphasizing how the research on those topics mixes operator theory and function theory in a harmonious way, and reporting on the speaker’s own contributions.
■ March 26, AS, Room 107, 4 p.m. - 5 p.m.
Il Woo Cho (St. Ambrose University )
Distorted Histories
Abstract: In this talk, we consider distortions on histories. A Mathematical history is determined by a certain type I von Neumann algebra "M" in a fixed operator algebra B(H), equipped with an automorphism group, which is an one-parameter group satisfying some additional conditions, called an E_0 group. By fixing a finite number of partial isometries in B(H) with a suitable connection with each other, we can show the existence of the distortion of M distorted by the partial isometries. Also, we can characterize the von Neumann algebra distorted by partial isometries.
■ April 14, AS, Room 107, 4 p.m. - 5 p.m.
Nan Jiang (University of South Dakota)
The Convergence of a Class of Methods - semi-discrete case
Abstract: In the talk, we will introduce a class of high resolution schemes, using flux limiters for hyperbolic conservation laws. In the 80's, Sweby [SIAM J. Numer. Anal. 21 (1984)] constructed and predicted the entropy convergence of this family of schemes. However, the convergence issues of these problems have been open. In the last part of this talk, I will present my recent progress in the convergence analysis of this class of schemes, which extends our previous convergence results [Jiang and Yang, Methods and Applications of Analysis, Vol. 12, No. 1 (2005) pp. 089-102]. Remarkably, by showing the the convergence of the schemes with Roe's superbee limiter, our convergence criteria [Yang and Jiang, Methods and Applications of Analysis Vol. 10 (2003), No. 4, 487-512] also guarantee the entropy convergence of any flux limiter method. Thus, the entropy convergence problems of the entire family of Sweby's flux limiter schemes can be put to the rest. The talk is accessible to the senior math major and the graduate students.
Key words and phrases. Conservation law with source terms, schemes with flux limiters, entropy convergence.
Fall 2009
■ October 21, AS, Room 16B, 4 p.m. - 5 p.m.
Clare Wagner (USD)
SMART Board and SMART Notebook Basics
Abstract: This presentation will provide an introduction to how to use a SMART Board in a mathematics classroom. Useful features of SMART Notebook software in preparing lecture outlines prior to teaching in a mathematics classroom will also be shared.
■ November 4, AS, Room 16B, 4 p.m. - 5 p.m.
Jose Flores (USD)
A Leslie-Gower predator-prey model with Allee effect on the prey
Abstract: In this paper we study a predator-prey model described by autonomous bi-dimensional differential equations systems in which we considered the following three properties:
(a) The equation for predator is a logistic function of the Leslie-Gower type, (b) the prey population is affected by the Allee effect, and (c) the functional response is linear function or a function of Holling type I. The interest of our work is in establishing the quantity of limit cycles of the system. The study of this type of mathematical model intends to understand the oscillatory behavior of many real world phenomena in nature.
(*) This work is in collaboration with: Eduardo González-Olivares, Betsabe González-Yañez, Jaime Mena-Lorca and Alejandro Rojas-Palma at the Institute of Mathematics at the Pontificia Universidad Católica de Valparaíso, Valparaíso Chile
■ November 9, AS, Room 104B, 4 p.m. - 5 p.m.
Keith Stroyan (University of Iowa)
Visual Depth Perception from Motion Parallax
Abstract: This talk will explain what "motion parallax" is and describe recent work on how it is combined with smooth eye pursuit to perceive depth. Extensions of the basic geometric theory suggest a number of new experiments that we hope to complete in the next few years. In Vision Res. 49, p.1969, 2009, we proposed a quantitative motion/pursuit law (M/PL) that uses the ratio of retinal image motion over pursuit eye movement to calculate relative depth for objects near central vision. The math was suggested by a number of earlier experiments by my co-author, Mark Nawrot. Our first paper also included two psychophysical experiments that confirmed the theory. In Nature 452, 42-645 (2008) Nadler, Angelaki & DeAngelis showed that macaques can not perceive depth from motion parallax without an extra retinal signal, but did not propose a signal. After seeing our preprint, Nadler, Nawrot, Angelaki & DeAngelis showed that "MT neurons combine visual motion with a smooth eye movement signal to code depth sign from motion parallax," Neuron (in press). They did NOT show that the brain implements the motion/pursuit formula, only that it uses pursuit somehow. We extended the math to two dimensions of the horizontal plane and analyzed how the M/P ratio varies across space and with time as an observer translates laterally. The theory suggests a number of new experiments designed to compare actual depth, the motion/pursuit inputs, and human (or primate) perception outside central vision. We are also working on extensions of the theory to non-lateral motion and I hope to show a "movie" that Alys (undergrad), Colin (grad), and I made to illustrate the geometry of "optic flow."
■ November 18 , AS, Room 16B, 4 p.m. - 5 p.m.
Y. L. Lio (USD)
The Implementation of R program for Acceptance Sampling Plans from truncated Life Tests for Birnbaum-Saunders Distribution
Abstract: Time to failure due to fatigue is one of the common quality characteristics in material engineering applications. The Birnbaum-Saunders distribution has been proved to provide a better fitting for the fatigue data set than the Weibull distribution does. In this talk, the comparison for two sampling plans from truncated life tests for Birnbaum-Saunders distribution will be implemented by R program.
■ December 2 , AS, Room 16B, 4 p.m. - 5 p.m.
Gabriel Picioroaga (USD)
C* Dynamical Systems
Abstract: A classical dynamical system consists of a compact Hausdorff space X together with a homeomorphism σ : X → X. The study of the iterates σ◦σ…◦σ often leads to the existence of an attractor A on which σ displays "chaotic" behavior (e.g. Julia sets). There are other ways to generate attractors for example by means of an iterated function system (IFS) where the IFS are contractions: a theorem of Hutchinson provides the attractor. While appealing from the point of view of (fractal) geometry (and quite esthetic) these attractors are ill-behaved. Many a times one studies a space by means of the real or complex (continuous or smooth) valued functions on it. It may seem like that for fractals such study would bring nothing to the table, due to their "monstrous " geometry : every function could be continuous and/or smoothness may make no sense.
In my talk I will give an introduction to C* dynamical systems and justify why it provides a comfortable setting to incorporate fractals into mainstream (Functional) Analysis. In this setting the "ill behavior" of the attractors will mean that "non-commutativity" is at play. In the particular case when A is a Cantor set I will talk about the quantum differential df=[F,f] where F is a Fredholm module over the algebra of real valued functions on A thought of as multiplication operators.