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Mathematics

Colloquia 2022-23

The department colloquia will be held nearly every Tuesday (except holidays) throughout the fall and spring semesters. Check back to this site for more information. Events are held at 3:35 p.m. in SC 323. Refreshments are served in SC 313F beginning at 3:15 p.m., unless otherwise noted. All are invited to attend.

Graduate Students: The mathematics colloquium is a valuable resource and you should make every effort to attend regularly.

For more detailed information, or if you wish to give a talk, please contact Muhammad Usman

Check back for Fall 2022 semester listings

Past Colloquia Events

Spring 2022

January

 

Jan. 20: Kyle Helfrich, Ohio Wesleyan University; Orthogonal Recurrent Neural Networks and Batch Normalization in Deep Neural Networks

Abstract: Despite the recent success of various machine learning techniques, there are still numerous obstacles that must be overcome. One obstacle is known as the vanishing/exploding gradient problem. This problem refers to gradients that either become zero or unbounded. This is a well-known problem that commonly occurs in Recurrent Neural Networks (RNNs). In this talk, we will describe how this problem can be mitigated, establish three different architectures that are designed to avoid this issue and derive update schemes for each architecture. Another portion of this talk will focus on the often used technique of batch normalization. Although found to be successful in decreasing training times and in preventing overfitting, it is still unknown why this technique works. 


Jan. 25: Kelly Buch, University of Tennessee, Knoxville; Multi-Disciplinary Research at the Interface of Mathematics and Biology

Abstract: Mathematical models of real-life situations are powerful tools that can be used in a variety of disciplines when research questions cannot be answered with experiments or field study alone. The process of creating and interpreting mathematical models of real-world systems is a multi-disciplinary effort. It requires collaboration across disciplines in all steps: translating relevant information about the system into mathematical objects, performing mathematical analysis on the model, and translating the results of the analysis back into the original discipline. As a mathematical modeler, I love this translation process and I collaborate with scientists to model biological phenomena. In this talk, I will present two of my recent multi-disciplinary modeling projects to display both my approach to mathematical modeling and the breadth of applications I’m interested in. In both projects, I will highlight model development of the model and the utility of model analysis in the application discipline. We will begin with an application in ecology, introducing a mathematical model for vector-borne tree diseases and interpret it to make recommendations for wildlife managers attempting to eradicate such diseases. We will also discuss an application in physiology, introducing a mathematical model for Reactive Scope, a conceptual framework for the long-term impacts of short-term stress responses. While in its infancy, this modeling approach shows promise in its ability to produce testable outcomes to advance experimental physiology.


Jan. 27: Anataska Dobreva, Arizona State University; Studying vision and immune processes with mathematical modeling

Abstract: This talk will consist of two main parts, showcasing my work in applying mathematics in retina and immunology research. Photoreceptors, rods and cones are the cells of the eye responsible for vision. Photoreceptors mainly use glucose to create energy and to renew their light-absorbing outer segments (OS). In the first part of the talk, I will present the development and analysis of the first mathematical model for the metabolic dynamics of a cone that accounts for energy generation from external lactate and fatty acids oxidation of OS. With multiple parameter bifurcation analysis, we investigate how interactions among key mechanisms affect the cone’s metabolic vitality under glucose shortage, and with in-silico experiments we explore the possibility for recovery. Time-varying global sensitivity analysis is applied for both normal and nutrient stress conditions to assess in each case the dynamic impact of different processes to the model outputs of interest. Our work provides insight into the role of metabolites under glucose starvation conditions, which may elucidate pathways and disruptions resulting in degenerative retinal diseases such as age-related macular degeneration and retinitis pigmentosa whose progression has been linked to glucose deprivation and disruptions in cellular metabolism. In the second part of the talk, I will present my work on developing and analyzing the first mathematical models for the autoimmune hair loss disease alopecia areata (AA). In AA, the immune system attacks hair follicles and disrupts their natural cycle through phases of growth, regression, and rest. The disease manifests with distinct hair loss patterns, and what causes it and how to treat it are open questions. I will first present our ODE model for AA in follicles in stage of growth. Next, I will explain how we incorporate follicle cycling into the model and explore what processes have the greatest impact on the duration of hair growth in healthy versus diseased follicles. Finally, I will highlight the global and marginal linear stability analysis results from our PDE model, which captures the patterns that characterize hair loss in AA.


February

 

Feb. 1: Sougata Dhar, University of Connecticut; Lyapunov-type inequalities for third-order linear and half-linear difference equations and extensions

Abstract: In this talk, we will focus on the Lyapunov-type inequalities for third-order difference equations, the discreet version of differential equations. Unlike their counterparts, these inequalities for difference equations were limited only to even-order cases prior to this work. The resulting inequalities utilize positive and negative parts of a function rather than the traditional absolute value of the function. We first discuss the linear case and then establish the subsequent results for the quasilinear case. In this process, we introduce a new approach to tackle these inequalities as the techniques for even order difference equations are not applicable to odd order difference equations. Moreover, we will discuss a few additional results for linear difference equations as which are further extended to more general linear equations. We will conclude after a brief discussion for the third order backward difference equations and dynamic equations on time scales.


Feb. 3: Sabrina Streipert, McMaster University; Discrete Delay Population Models

 

Abstract: The continuous Hutchinson model is a delay logistic growth model, where a delay was introduced in the per-capita growth rate. Despite its popularity, this delay differential equation exhibits some questionable behavior as the population persists independent of the delay. One of its discretizations, the so-called Pielou model, can be criticized for the same reason. To formulate an alternative discrete delay population model of logistic growth, we first distinguish the growth and decline processes before introducing a delay solely in the growth term. The obtained model differs from existing discrete delay population models and exhibits realistic behaviour. If the delay exceeds a certain critical threshold, then the population goes extinct. On the other hand, if the delay is below that threshold, then the population survives and converges to a positive asymptotically stable equilibrium that decreases as the delay increases. As the next step toward extending our discrete delay population model to interacting species, we derived a discrete predator-prey model without delay. The analysis of this predator-prey model led us to the formulation of a discrete phase plane approach that has been deemed ineffective for planar maps. By considering the direction field, the corresponding nullclines, and our “next iterate root curves associated with the nullclines”, the global dynamics of the discrete predator-prey model are discussed.


Feb. 8: Yulong Li, University of Nevada, Reno; Hello, fractional ODEs!

 

Abstract: The fractional-order ordinary differential equations (in short, fractional ODEs) may be considered an old and yet novel topic, which is an emerging interdiscipline, intertwined with fractional-order calculus, fractional power operators, modeling, singular integral equations and special functions. In this presentation, we will:

  1. Introduce some open problems arising from the subject of fractional ODEs and use the double-sided fractional diffusion-advection reaction ordinary differential equation as the main example to present our recent accomplishments toward those open questions.
  2. Illustrate how fractional ODEs can attract collaborations from faculties who are doing classic ODEs, numerical analysis, integral equations and how it can produce many interesting research projects for our undergraduate and graduate students.

Feb. 22: Dr. Youssef Raffoul, Department of Mathematics, University of Dayton; Introduction to Time Scales with Applications to Stability and Boundedness

Abstract: Lately, there have been few talks on Time Scales by candidates that we interviewed to fill one of our positions. In this talk, we present an introduction to Time Scales and then provide some recent materials related to the stability of the zero solution and boundedness of solutions of general Dynamical Systems. 


March

March 1: Dr. Youssef Raffoul, Department of Mathematics, University of Dayton; The Case for Large Contraction

Abstract: We start our talk by displaying an example to motivate our motive for the need for Large Contraction. We will look at the existence of a periodic solution for a totally nonlinear functional delay differential equation by utilizing a modified version of the Krasnoselsski fixed point theorem in which regular Contraction is replaced with Large Contraction. Then, we prove a topological theorem that classifies functions that are Large Contraction. 


March 8: Dr. Jacob Shapiro, Department of Mathematics, University of Dayton; Semiclassical resolvent bounds for compactly supported radial potentials

Abstract: We employ separation of variables to prove weighted resolvent estimates for the semiclassical Schrödinger operator $-h^2 \Delta + V(|x|) - E$  in dimension $n \ge 2$, where, $h, \, E > 0$ and $V : [0, \infty) \to \mathbb{R}$ is $L^\infty$ and compactly supported. We show that the weighted resolvent estimate grows no faster than $\exp(Ch^{-1})$, and prove an exterior weighted estimate which grows $\sim h^{-1}$ . The analysis at small angular momenta proceeds by a Carleman estimate and the WKB approximation, while for large angular momenta we use Bessel function asymptotics. This is joint work with Kiril Datchev (Purdue University) and Jeffrey Galkowski (University College London).


March 10: Mohammad Niksirat, University of Alberta; Topological approach to the Doi-Onsager equation

Abstract: The Doi-Onsager equation describes the behavior of rigid-like molecules in liquid crystals @f@t  rf + div (f rr U(f))where f: Sn! R is the directional density function in the direction r 2Sn, Z f(r)  = 1and SSnjr   r0j f(r0) d ; U(f)(r) = for > 0. The equation is sometimes called the Smoluchowski or a non-linear Fokker-Planck Equation. It turns out that the stationary solutions of the equation satisfy the Onsager equation proposed in 1949. Experiments show that the phase of solutions changes between isotropic and nematic based on the intensity of the molecules. The problem in its original form with the Onsager kernel remained open until recently, despite some partial results developed for the problem with Maier Saupe potential. In this talk, we introduce an innovative topological method for the problem. This method can not only reproduce all previous results in a unified way, but also solves the equation with more general potentials than the one studied by Onsager. 


March 29: Mathew Wascher, University of Dayton, Department of Mathematics; A mechanistic framework for estimating SARS-CoV-2 prevalence from dust

Abstract: As we enter the third year of the pandemic and transition to strategies for managing endemic SARS-CoV-2, we will need to move away from mass testing and consider passive methods for monitoring potential outbreaks. One such avenue is observing viral RNA shed into the environment by infectious individuals. We develop a mechanistic modeling framework using Poisson processes to relate the amount of viral RNA observed at a particular location to the number of infectious individuals in that location. Our model is flexible enough to account for interindividual variation in viral shedding, and we demonstrate several useful theoretical properties. We fit our model to viral RNA observed in dust collected from vacuuming isolation rooms at The Ohio State University during the Fall 2020 semester using a Markov chain Monte Carlo algorithm. We further investigate the performance of our model on synthetic data. Although our example data consists of viral RNA collected from environmental dust, our modeling framework is general and can be applied to other modes of environmental shedding. This is joint work with Colin Klaus, Joe Tien, Ashleigh Bope. and Karen Dannemiller.


April

April 5: Steve Rosenberg, Boston University; hosted by Andre Larrain-Hubach; Geometric Aspects of Machine Learning

Abstract: From a mathematical viewpoint, machine learning involves gradient flow of a loss function on an infinite dimensional manifold, a situation familiar to geometers from gauge theory and Floer theory.  The loss function usually involves an error measurement term and a regularization term, which keeps the function from rapidly oscillating.  Regularization terms that reflect the geometry of the loss function seem to work well.  In a related direction, we can try to fit a data set in a high dimensional Euclidean space to a lower dimensional submanifold: this is so-called manifold learning.  Finding the best submanifold involves gradient flow on an infinite dimensional space of embeddings, and the geometry again controls how long the flow stays in the space of embeddings. 


April 26: Xiangzhou Song; Advisor, Dr. Liu; How technical analysis improves stock performance

Abstract: In technical analysis, the trader assumes that the past trading activities in a market and the past prices changes provide adequate information to show future price movements that are more likely. To determine the impact of technical analysis on traders’ stock portfolio performance, in this research project we use the historical price and volume data from the Dow Jones Industrial Average index (DJIA). The DJIA comprises the 30 largest companies in the USA which include IBM, Microsoft, Walmart, Apple, etc.  We apply different strategies and back-test the data to determine how the strategies affect the market portfolio performance. In our analysis and back-testing, we use a few indicators to chart the performance of the companies’ data over time and forecast the portfolio’s future returns.


April 26: Chris Bingman, Advisor, Dr. Peter Hovey; Logistic regression and classification trees in special forces selection

Abstract: Regression is commonly used to predict outcomes in various fields of study and industry based on a number of predictor variables often called regressors. The type of response, among other factors, determines the type of regression: linear or non-linear. In non-linear regression, logistic regression can be used to predict the probability of a qualitative response. Some of the numerous methods used to model regression are forward selection, backward elimination, and stepwise regression. Classification and Regression Trees are also a tool that can aid in identifying correlations between response and predictor variables. Using a dataset from the U.S. Army Special Operations Forces, we will investigate the effectiveness of using information gained from classification trees to supplement a logistic model, hopefully improving accuracy and predictability.


Fall 2021

September

Sept. 28: Dr. Ayse Sahin, Wright State University. More details >

Sept. 21: Dr. Paul Eloe, University of Dayton. More details >


November

Nov. 9: Dr. Sam Brensinger, University of Dayton. More details >

Nov. 16: Jonah Reeger, Senior Research Mathematician with AFRL. More details >


 


Spring 2021

February

Feb. 12: Jeffrey Lyons, The Citadel; Smoothness of Solutions to Third Order Conjugate Boundary Value Problem

Abstract: Under certain conditions, the solution to the third order conjugate boundary value problem consisting of the differential equation y’’’=f(x,y,y’,y’’) and conjugate boundary conditions y(x_1)=y_1, y(x_2)=y_2, y(x_3)=y_3 may be differentiated with respect to the boundary points and values. The resulting function solves the associated variational equation. This work extends that which has been attributed to Peano for initial value problems to boundary value problems and relies upon a continuous dependence result connecting the two. The proof of the main result ties together topics from calculus, differential equations, and linear algebra.


Feb. 19: Sougata Dhar, University of Connecticut; Lyapunov type inequalities and applications

Abstract: In this talk, we will discuss Lyapunov-type inequalities for several integer and fractional order differential equations for both linear and quasilinear cases. We will primarily concentrate on the third-order case and briefly mention the structure of the higher order case. Most of these inequalities utilize the integrals of the positive and negative parts of a function rather than the traditional absolute value of the function as compared to the existing results in the literature. Furthermore, we discuss the extensions of these inequalities to the multivariate case for radially symmetric functions. Finally, we use them to study the nonexistence, uniqueness, and existence-uniqueness criteria for several classes of boundary value problems. We will conclude the discussion with some open problems in this area.


Feb. 26: Bo Li, The Citadel; Simultaneous confidence intervals of estimable functions based on quasi-likelihood for over-dispersed data

Abstract: Two major problems besetting count data analysis in multiple comparisons are over-dispersion and violation of distributional assumptions of real data. In this talk, we describe the simultaneous confidence interval method to inference a collection of estimable functions in generalized linear models based on quasi-likelihood estimation. We assume that the independent observations have the variance proportional to a given function of the mean. We define the pivotal quantities in an asymptotic sense. We derive the joint limiting distribution of the pivotal quantities and the asymptotic distribution of the maximum modulus statistic. In the presence of over-dispersion, large-sample approximation method is shown to be liberal in multiple comparisons. We propose a percentile-t bootstrap method based on Pearson residuals as a robust alternative. It shows that the proposed method outperforms large-sample approximation method in the spirit of attaining the overall coverage probability, even when the working variance-mean structure moderately deviates from the real structure of the underlying distribution.


March

March 5: Steve Szabo, Eastern Kentucky University; A Taxonomy of Rings and Related Minimal Examples

Abstract: Many types of rings are defined using zero divisors or nilpotent elements. These ring classes fit nicely into a hierarchy which will be explored in this talk. Examples differentiating the classes will be given. Where possible, the example will be minimal with respect to order.


March 12: Ying-Ju Chen, University of Dayton; Bias Reduction of the Gini Index Estimation Based on Grouped Data using a computational approach

Abstract: Many government agencies still rely on the grouped data as the main source of information for calculation of the Gini index. Previous research showed that the Gini index based on the grouped data suffers the first and second-order correction bias compared to the Gini index computed based on the individual data. Since the accuracy of the estimated correction bias is subject to many underlying assumptions, we propose a new method, D-Gini, which reduces the bias in Gini coefficient based on grouped data. We investigate the performance of the D-Gini method on an open-ended tail interval of the income distribution. The results of the simulation study showed that our method is very effective in minimizing the first and second order-bias in the Gini index and outperforms other methods previously used for the bias-correction of the Gini index based on grouped data. Three data sets are used to illustrate the application of this method. I will talk about some ongoing work based on this study as well.


March 19: Edward Timko, University of Manitoba; Some Noncommutative Extensions of the F. and M. Riesz Theorem

Abstract: In this talk, we develop operator theoretic analogues of the F. and M. Riesz Theorem. We first re-cast the classical theorem as one relating ‘anti-analytic’ bounded linear functionals to a distinguished $*$-representation of the continuous functions on the unit circle. Next, we establish an analogous result relating similarly ‘anti-analytic’ bounded linear functionals to ‘completely non-singular’ $*$-representations of the Cuntz algebra and highlight notable differences. We then explore conditions for the existence of weak$^*$-continuous extensions of the aforementioned bounded linear functionals. We again find significant differences between the noncommutative setting and the classical, and we establish necessary and sufficient conditions for when weak ∗ -continuous extensions can be obtained. This is joint work with R. Clouâtre and R. Martin.


March 26: Jacob Shapiro, University of Dayton; Semiclassical resolvents estimates for long range Lipschitz potentials

Abstract: We give an elementary proof of weighted resolvent estimates for the semiclassical Schrödinger operator $-h^2 \Delta + V(x) - E)$ in dimension $n \neq 2$, where $h, E > 0$. The potential is real-valued and $V$ and $\partial_rV$ exhibit long range decay. The resolvent norm grows exponentially in $h^{-1}$, but near infinity it grows linearly. When V is compactly supported, we obtain linear growth if the resolvent is multiplied by weights supported outside a ball of radius $CE^{-1/2}$ for some $C > 0$. This $E$-dependence is sharp and answers a question of Datchev and Jin. This talk is based on joint work with Jeffrey Galkowski.


April

April 1: Matthew Wascher (Statistics) Modeling epidemics with behavioral considerations: two problems

Abstract: SIR-type models, where individuals are assumed to take on states, most commonly susceptible, infectious, and removed, that change over time due to infection, recovery, or behavioral events, are among the most common frameworks used for quantitative modeling of infectious disease epidemics. I am particularly interested in how behavior, including behavior taken by individuals and actions taken by authorities, affect epidemics and the tools we use to model them. I will discuss two such problems. The first is a probabilistic study of an agent-based network model. The second is a statistical approach inspired by COVID-19 data.

In the first problem, we consider an SIS epidemic modified to include avoidance behavior on an explicit network. In this model, each infected individual infects each of its healthy neighbors at rate λ, each infected individual recovers at rate 1, and each healthy individual avoids each of its infected neighbors at rate α by deactivating the edge from the infected neighbor to itself until the neighbor recovers. We study this process on the networks Z,Zn, and the star graph. We show that on Z and Zn, the asymptotic behavior of the epidemic changes qualitatively depending on α and λ, a phenomenon called a phase transition. On the star graph, we derive explicit bounds for the asymptotic survival time of the infection and show they differ substantially from the behavior of the SIS epidemic without avoidance on the star graph. This is joint work with Shirshendu Chatterjee and David Sivakoff.

In the second problem, we consider modeling an epidemic when data come from a population where all individuals in the population are tested at regular intervals. Such a strategy has been used by universities, including Ohio State, to attempt to mitigate the effects of COVID-19 among student populations. If the interval between repeated tests is smaller than the natural recovery time of the infection, then we expect that most infections will be observable in the data. However, this data will be interval censored: we know that an individual who tests positive must have become infected between the time of a positive test and the time that individual’s previous negative test but not the exact date of the infection. We develop a method we refer to as Interval Dynamic Survival Analysis (IDSA) that leverages this feature of the data and discuss its performance. This is joint work with Patrick Schnell, Greg Rempala, and Wasuir Rahman KhudaBukhsh.


April 6: William Worden, Rice University (Topology) Hyperbolic 3-manifolds, polyhedral decompositions, and hidden symmetries

Abstract: In the early 1980s William Thurston revolutionalized the field of low-dimensional topology with his hyperbolization theorem and geometrization conjecture. His work brought to the forefront the study of hyperbolic 3-manifolds, and made possible computational tools like SnapPy that have led to further insight through experimentation. I will survey some of this history, explore some families of hyperbolic 3-manifolds that can be understood through their decompositions into polyhedra, and discuss some of my own work that leverages the combinatorial and geometric structure of such polyhedral decompositions.


April 8: Andrew Richards (Statistics) New Species Tree Inference Methods Under the Multispecies Coalescent Model

Abstract: Inference of the evolutionary histories of species, commonly represented by a species tree, is complicated by the divergent evolutionary history of different parts of the genome. Different loci on the genome can have different histories from the underlying species tree (and each other) due to processes such as incomplete lineage sorting (ILS), gene duplication and loss, and horizontal gene transfer. The multispecies coalescent is a commonly used model for performing inference on species and gene trees in the presence of ILS. (Li)kelihood-based assemb(ly), or Lily, is a new method for species tree inference under the multispecies coalescent. The method is presented and compared to two frequently used methods, SVDQuartets and ASTRAL, using simulated and empirical data. Generalizing the procedure to allow for differing mutation rates is briefly discussed.


April 9: George Todd, University of Dayton; Power Moments of Character Sums

Abstract: Character sums are ubiquitous in number theory. Kloosterman sums, for example, are character sums closely related to the fourier coefficients of modular forms. Due to a result of Katz, Kloosterman sums are asymptotically equidistributed with respect to Sato-Tate measure, suggesting that exact calculations are unlikely. One direction is to study power moments of Kloosterman sums. So far, the most successful method of computing these power moments is to calculate a related quantity realized as the trace of a symmetric power of the Kloosterman sheaf. This method, however, is quite involved. We discuss recent work on computing these power moments in a simpler way using supercharacters, as well as obstructions to further work on the topic. Along the way, we hope to show the utility of power moments of character sums more generally. This work is joint with Stephan Ramon Garcia, Ángel Chávez, and Brian Lorenz.


April 13: Won Chul Song (Statistics) Group Feature Screening via F-test

Abstract: Feature screening is crucial in analysis of ultrahigh dimensional data, where the number of variables (features) is exponentially larger than the number of observations. In various ultrahigh dimensional data, variables are naturally grouped with correlation structures within groups. In this article, we propose a group screening method via the F-test. The new method is in contrast with the existing literature on feature screening, which screens variables one by one. Under certain regularity conditions, we prove that the proposed group screening procedure possesses a sure screening property that selects all active groups with probability approaching to one at an exponential rate. We use simulations to demonstrate the advantages of the proposed method and show its application in a genome-wide association study. We conclude that grouping method is very effective in large-scale inference for high dimensional data and is a good choice, as an optimal test can detect true signals with desired properties.


April 15: Jun Li, University of Michigan (Topology) Symplectic mapping class groups in dimension 4

Abstract: Symplectic manifolds arise naturally in abstract formulations of classical mechanics, while symplectic topology is an interesting mixture of the “soft” and the “rigid.” In this talk, we will focus on rigidity phenomena in symplectic topology. In particular, we will discuss recent developments for the mapping class groups of 4- dimensional symplectic manifolds, and how these root in dynamics and topology in dimension 2. 


April 20: Christoforos Neofytidis, Ohio State University (Topology) Topology, Geometry and Dynamics of aspherical manifolds

Abstract: The Borel conjecture asserts that the homeomorphism type of closed aspherical manifolds is determined by their fundamental groups. Manifolds satisfying the Borel conjecture are called topologically rigid. In this talk, we generalize in all dimensions (and give a new, uniform proof of) a rigidity theorem on aspherical fibered 3-manifolds, due to Gromov and Wang. A key ingredient for this new, mostly algebraic, approach is the non-vanishing of the Euler characteristic of the fiber (which is a hyperbolic surface in dimension three). We then explain how the Euler characteristic is expected to determine the topology of aspherical manifolds with respect to the Borel conjecture, as well as other long-standing problems, such as the Hopf problem (Topology) and the Anosov-Smale conjecture (Dynamics).


Fall 2020

September

Sept. 4: Joe Mashburn, University of Dayton; Microhomogeneous Spaces

Abstract: Since the 1960s the topological property of homogeneity has been useful in the study of cardinal bounds in topological spaces. We recently rediscovered a weaker and little known property called microhomogeneity which can be used in the place of homogeneity in many of these cardinal bounds. In this talk we will see how microhomogeneity can be used and compare the behavior of microhomogeneous spaces with that of homogeneous spaces.


Sept. 11: Paul Eloe, University of Dayton; Two point boundary value problems for ordinary differential equations, uniqueness implies existence

Abstract: We consider a family of two point $n-1 ,1$ boundary value problems for $n$th order nonlinear ordinary differential equations and obtain conditions in terms of uniqueness of solutions that imply existence of solutions. A standard hypothesis that has proved effective in uniqueness implies existence type results is to assume uniqueness of solutions of a large family of $n-$point boundary value problems. Here, we shall replace that standard hypothesis with one in which we assume uniqueness of solutions of a large family of two point boundary value problems. We then obtain readily verifiable conditions on the nonlinear term that in fact imply the uniqueness of solutions of the large family of two point boundary value problems.


Sept. 18: Jeffrey Neugebauer, Eastern Kentucky University; Positive Solutions of a Boundary Value Problem at Resonance

Abstract: In this talk, we will employ a shift method to study a boundary value problem that is at resonance. By proving the associated differential operator satisfies a maximum principle, we show the Green’s function of the shifted BVP is nonpositive. Upper and lower solutions and fixed point methods are used to show the existence of solutions of the shifted BVP.


Sept. 25: Johnny Henderson, Baylor University; Existence of local solutions for fractional difference equations with left focal boundary conditions

Abstract: For $1 < \nu \leq 2$ a real number and $T\geq 3$ a natural number, conditions are given for the existence of solutions of the $\nu$th order At{\i}c{\i}-Eloe fractional difference equation, $\Delta^\nu y(t) + f(t+ \nu -1, y(t+ \nu-1)) =0,$ $t \in \{0,1,\ldots, T\},$ and satisfying the left focal boundary conditions $\Delta y(\nu-2) = y(\nu +T) = 0$. The conditions involve growth conditions on $f$ and constraints on the size of $T$.


October

Oct. 2: Saleh Almuthaybiri, Qassim University; Sharper existence and uniqueness results for solutions to third-order boundary value problems

Abstract: The purpose of this talk is to present new results where we sharpen Smirnov's recent work on existence and uniqueness of solutions to third-order ordinary differential equations that are subjected to two-and three-point boundary conditions. The advancement is achieved in the following ways. Firstly, we provide sharp and sharpened estimates for integrals regarding various Green's functions. Secondly, we apply these sharper estimates to problems in conjunction with Banach's fixed point theorem. Thirdly, we apply Rus's contraction mapping theorem in a metric space, where two metrics are employed. Our new results improve those of Smirnov by showing that a larger class of boundary value problems admit a unique solution.


Oct. 9: Lynne Yengulalp, Wake Forest University; Topological completeness and the role of G-delta subsets

Abstract: We start with the Baire Category Theorem for complete metric spaces: The intersection of any countable sequence of open dense subsets of a complete metric space is dense in the space. The countable intersection of open sets is called a G-delta set. In this talk, we discuss some topological properties more general than complete metrizability and the role of G-delta sets in the study of such properties.


Oct: 16: Paul Eloe, University of Dayton; Three point boundary value problems for ordinary differential equations, uniqueness implies existence

Abstract: This is a continuation of the September 11 presentation in which uniqueness implies existence results for a family of two point $n-1 ,1$ boundary value problems for $n$th order nonlinear ordinary differential equations were presented. In this talk we move to a family of $n-2 ,1,1$ boundary value problems; again, an abstract result is obtained and again, a result with verifiable hypotheses, a monotonicity condition in the nonlinear term, is obtained.


Oct. 30: Kathryn McCormick, California State University Long Beach; Twisted Steinberg Algebras

Abstract: A groupoid is an algebraic object encompassing both groups and equivalence relations. For many years, algebras offunctions on groupoids, such as Steinberg algebras and groupoid C*-algebras, have provided diverse and tractable models for algebraists and analysts alike. Thirty years prior to the introduction of Steinberg algebras, Renault initiated the study of twisted groupoid C*-algebras, which have been valuable in modeling an even broader class of C*-algebras and in providing an inroad to difficult problems in C*-algebras such as the UCT problem. In this talk, I will describe twisted Steinberg algebras on ample Hausdorff groupoids, introduced by myself and coauthors, and some results on describing the ideal structure of a twisted Steinberg algebra when the underlying groupoid is effective. 


November

Nov. 13: Benjamin F. Akers, Air Force Institute of Technology; Wave resonances: existence, analyticity and numerics

Abstract: Nonlinear waves occur in a wide variety of applications, including laser propagation, oceanography, combustion, and more. In special circumstances these waves resonate, resulting in bifurcatingsolution branches in the nonlinear problem. In this talk we consider the asymptotics, existence, andanalyticity of these solution branches. Two distinct proofs of existence are discussed: the first isbased on a perturbation series, the second is a contraction mapping argument. Both proofs spawnnumerical methods. The numerical methods are compared, and results from each are presented. The application of these methods to the spectral stability problem, where resonances occur ateigenvalue collisions, is discussed.


Nov. 20: Nathan Carlson, California Lutheran University; Cardinality bounds on topological spaces with a focus on homogeneous and microhomogeneous spaces

Abstract: The theory of cardinality bounds on topological spaces has played a prominent role in the field of set-theoretic topology. Early work by Alexandroff and Urysohn showed that the cardinality of a compact, perfectly normal space is at most c, the cardinality of the continuum. In 1969 Arhangel’skii answered a 50-year old question of Alexandroff and Urysohn by showing the cardinality of a compact, first countable, Hausdorff space is also at most c. In the 1970s it was noticed by van Douwen, Arhangel’skii and others that if a space is additionally homogeneous then bounds on the cardinality of the space can be improved. Roughly speaking, a space is topologically homogeneous if the topology acts the same at any point. Formally, X is homogeneous if for every x and y in X there exists a homeomorphism h from X onto X such that h(x) = y. We will survey results in this area, notably a result of Carlson and Ridderbos, as well as de la Vega’s Theorem, which states that the cardinality of a compact, homogeneous, Hausdorff space is at most 2^{t(X)}. t(X) is known as the tightness of X. We will also show that this result extends to the broader class of microhomogeneous spaces. This builds upon recent work by Anderson, Mashburn, and Yengulalp on cardinality bounds on microhomogeneous spaces.


December

Dec. 4: Jacob Shapiro, University of Dayton; Semiclassical resolvent estimates and wave decay in low regularity

Abstract: We study weighted resolvent bounds for semiclassical Schr\"{o}dinger operators. When the potential function is Lipschitz with long range decay, the resolvent norm grows exponentially in the inverse semiclassical parameter $h$. When the potential is merely bounded and has compact support, the resolvent still grows exponentially but with an extra polynomial loss in $h$. This extends the works of Burq and Cardoso-Vodev in the smooth case. Our main tool is a global Carleman estimate. We apply the resolvent estimates along with the resonance theory for blackbox perturbations to show local energy decay for the wave equation with a wavespeed that is an $L^\infty$ perturbation of unity.


Dec. 11: Alan Veliz-Cuba, University of Dayton; Designing multistability with AND gates

Abstract: Systems of differential equations have been used to model biological systems such as gene and neural networks. A problem of particular interest is to understand and control the number of stable steady states. Here we propose conjunctive networks (systems of differential equations equations created using AND gates) to achieve any desired number of stable steady states. Our approach uses combinatorial tools to easily predict the number of stable steady states from the structure of the wiring diagram.


Spring 2020

APRIL

April 30: Yaoxing Yong and Adja Ba, University of Dayton. More details >

April 23: John Luebking and Christina Farwick, University of Dayton. More details >

FEBRUARY

Feb. 11: Dr. Shixu Meng, Department of Mathematics, University of Michigan. Wave Propagation and Inverse Problems. More details >

Feb. 6: Dr. Katelyn Leisman, J.L. Doob Research Assistant Professor, University of Illinois. The Abnormally Normal Behavior of the Nonlinear Schrödinger Equation. More details >

JANUARY

Jan. 28: Dr. Jacob Shapiro, Australian National University. Decay of waves in rough media. More details >

Fall 2019

DECEMBER

Dec. 5: Mona Almutari, University of Dayton. The existence of a unique solution of a Caputo fractional differential equation. Wenfeng Wu, University of Dayton. A Computational Study of Option Pricing Models. More details >

NOVEMBER

Nov. 21: Jace Robinson, Tenet3. The need for strategic cyber systems analysis. More details >

Nov. 14: Ben Linowitz, Oberlin College. Can you hear the shape of a drum? More details >

Nov. 7: Paul Eloe, University of Dayton. Nonlinear interpolation, week 3. More details >

OCTOBER

Oct. 31: Paul Eloe, University of Dayton. More on nonlinear interpolationMore details >

Oct. 24: Paul Eloe, University of Dayton. On uniqueness of solutions implies existence of solutions More details >

Oct. 17: R. Gerald Keil, University of Dayton. Oh that’s easy, just do a transformationMore details >


Spring 2019

MARCH

March 7: Gu Wang, Worcester Polytechnic Institute. Sharing Profits in the Sharing Economy.  Abstract and more details >

March 21: Aurel Stan, Ohio State University Marion. Semi-quantum operators and Meixner random variables.  Abstract and more details >

March 28: Sarah Burke, Air Force Institute of Technology. Optimal Multi-Response Designs.  Abstract and more details >

APRIL

April 4: Abigail Kramer, University of Dayton. Numerical Solution of Coupled Diffusion Systems for Spatial Pattern Formations.  Abstract and more details >

April 11: Limin Jin, University of Dayton, A tree-based method to price European and American options with stochastic volatility or stochastic interest rate and Lijun Lin, University of Dayton, A Comparison of Numerical Solutions of the Black-Scholes Model.  Abstracts and more details >

April 25: Hind Alasmari, Stability in Volterra Integro-differential Equations, and Nouf Alsomali, A hybrid tree method using Heston-Hull-White type models, University of Dayton Abstracts and more details >

April 26 (Friday): Sean Cleary, The odd world of Thompson's groups, The City College of New York Abstract and more details >

MAY

May 1 (Wednesday): Ruiqi Wang, Analysis of Hedge Fund Crash Risk and Xichen Yan, Analysis of Mutual Funds Performance Persistence Using Alternative Performance Measurements, University of Dayton Abstracts and more details >

May 2: Johnathon Spilker, Comparison of Hidden Markov Model Algorithms and their Applications and Peter Kawiecki, Optimal Stopping in Stock Price Bubbles: an alternative method, University of Dayton Abstracts and more details >

Fall 2018

SEPTEMBER

Sept. 27: Jeffrey Neugebauer, Eastern Kentucky University. An Avery Fixed Point Theorem Applied to a Hammerstein Integral Equation.  Abstract and more details >

OCTOBER

Oct. 11: Yang Liu, Wright State University.  Abstract and more details >

NOVEMBER

Nov. 1: Anup R. Lamichhane, Ohio Northern University.  Abstract and more details >

Nov. 6: Pinju Lee, University of Dayton. Portfolio Formation, Crash Risk and Stock Synchronicity.  Abstract and more details >

Nov. 8: Youssef Raffoul, University of Dayton. Stability And Boundedness In Nonlinear Neutral Differential Equations using New Variation of Parameters Formula And Fixed Point Theory.  Abstract and more details >

Nov. 15: Valentin Deaconu, University of Nevada, Reno. Crossed product correspondences and applications.  Abstract and more details >

Nov. 29: Didier Hirwantwari (Bootstrapping Transfer Function Models) and Ebtsam Alrasheedi (Applications of fixed point theorems to boundary value problems at resonance), University of Dayton.  Abstracts and more details >

DECEMBER

Dec. 6: Maha Reshedi (A comparison of numerical and analytical solutions of differential equations and systems) and Teng Zhaopu (Numerical solution of 2D Vasicek PDE model), University of Dayton.  Abstract and more details >


Summer Term 2018

JULY

Omid Shirdelan will present his mathematics clinic research on Tuesday July 24 at 10:30 a.m. in SC 310. All are invited to attend. For more information >

Spring Term 2018

APRIL

April 26: (1) Forecasting Using Logistic Regression and Box–Jenkins (ARIMA) Models, Amal Alsomali, University of Dayton. (2) Bootstrapping a Moving Average Time Series Data, Ashley Mailloux, University of Dayton. Abstracts and more >

April 19: Boundedness and stability of solutions in nonlinear difference equation Qasim Alharbi and Mohammed Alharthi, University of Dayton. Abstract and more >

April 12: Uniqueness and Existence of Solutions of Boundary Value Problems at Resonance for Ordinary Differential Equations. Jabr Aljedani, University of Dayton.  Abstract and more >

April 5: Torsion invariants in operator algebras and K-theory. Joseph Migler, Ohio State University. Abstract and more >

MARCH

March 22: Residuals and diagnostics for ordinal regression models: A surrogate approach. Dungang Liu, University of Cincinnati Lindner College of Business.  Abstract and more >

March 15: A Method for Data De-Grouping and its Impact on Curve Fitting. Tatjana Miljkovic, Miami University.  Abstract and more >

March 8: Outputs of Generalized Trigonometric Functions. Ian Hogan, Central State University. Abstract and more >

FEBRUARY

February 22: Finite Products of Nowhere Real Linearly Ordered Sets. Tetsuya Ishiu,  Miami University.  Abstract and more >

February 15: Fractional Differential Equations. Muhammad Islam, University of Dayton. Abstract and more >

February 8: Idealized Models of Insect Olfaction. Pamela Pyzza, Ohio Wesleyan University. Abstract and more >

February 1: Jackknife Empirical Likelihood Method for the Comparison of Mean Residual Life Functions. Ying-Ju Tessa Chen, University of Dayton. Abstract and more >

JANUARY

January 25: The Role of the Group Inverse in the Ergodicity of Level-Dependent Quasi-Birth-and-Death Processes (LDQBDs). James Cordeiro, University of Dayton.  Abstract and more >

Fall Term 2017

DECEMBER

December 7: (1) The Search for an Improved Estimator in Determining the Probability of Jet Engine Failure. Kaity Jones, University of Dayton. (2) Optimal stopping problems for a Brownian motion with a disorder on a finite interval, Runze Hu, University of Dayton  Abstracts and more >

NOVEMBER

November 30: Spread option pricing with two underlying assets in a regime-switching model. Ying Ding, University of Dayton.  Abstract and more >

November 9: The Clay Institute Millennium Prize Problem on Navier-Stokes and its Probabilistic and Compressible Counterparts. Sivaguru Sritharan, Air Force Institute of Technology. Abstract and more >

November 2: Set theory and automorphisms of corona algebras. Paul McKenney, Miami University. Abstract and more >

OCTOBER

October 26: Visualizing & Validating CO$T Optimization (with JMP as your Analytic Hubs. Tom Filloon, Stat.i.m llc. Abstract and more >

October 19: Algebras having Bases Consisting Solely of Strongly Regular Elements. Daniel Bossaller, Ohio University. Abstract and more >

October 12: A combinatorial approach to minimal free resolutions of path ideals and domino ideals. Shelley Bouchat, Indiana University of Pennsylvania. Abstract and more >

SEPTEMBER

September 28:  Quasilinearization and Boundary Value Problems at Resonance for Caputo Fractional Differential Equations. Saleh Almuthaybiri, University of Dayton. Abstract and more >

September 21:  Discretization Scheme in Volterra Integro-differential Equations that Preserves Stability and Boundedness. Youssef Raffoul, University of Dayton. Abstract and more >

September 7:  An exact numerical scheme for curves with corners in 2D, Dr. Catherine Kublik,  University of Dayton. Abstract and more >


Summer 2017

JULY 2017

July 25:  A Nonlinear Analysis of an Oscillator Equation with Damping and External Forcing Using a Perturbation Method, Eman Alassaf,  University of Dayton, Advisor: Muhammad Usman. Abstract and more >

JUNE 2017

June 23:  Lyapunov functionals and stability in nonlinear infinite delay Volterra discrete systems, Budar and Sarah Alshammari,  University of Dayton, Advisor: Youssef Raffoul. Abstract and more >

June 15:  Decomposition of Varies Complete Graph into Isomophic Copies of 4-cycle with Three Pendant Edges, Rabab Alzahrani,  University of Dayton, Advisor: Atif Abueida. Abstract and more >

Spring 2017

APRIL 2017

April 28:  The Impact of Data Breaches on Firms’ Stock Price, Kaili Chen,  University of Dayton,  Advisor: Dr. Chen. Abstract and more >

April 27: First presentation: Reduction of truncation error for a finite difference scheme for the Black Scholes equation, Thanadol Sukjitnittayakarn,  University of Dayton, Advisor: Ruihua Liu; Second presentation: Optimal investment, consumption and life insurance, Chenwei Liu, University of Dayton, Advisor: Dan Ren. Abstracts and more >

April 20: Optimal Investment and Consumption in Regime-Switching Jump Diffusion ModelsRodrigue Nguimfack, University of Dayton, Advisor: Ruihua Liu. Abstract and more >

April 7A Classification of n-tuples of Commuting isometries, Edward Timko,  Indiana University, Host: Paul Eloe. Abstract and more >

April 6: Existence and Nonexistence of Positive Solutions of Two Point Fractional Boundary Value Problems, Jeffrey Neugebauer, Eastern Kentucky University, Host:  Muhammad Islam. Abstract and more >

MARCH 2017

March 31: (Friday at 12:20 p.m.): Solvability by Radicals, Ananth Hariharan, I.I. T. Bombay, Host: Lynne Yengulalp. Abstract and more >

March 30: An Optimal Investment Problem Using Regime-Switching Model with Stochastic Interest Rate, Cheng Ye, University of Dayton, Advisor: Ruihua Liu. Abstract and more >

March 23: Some Implications of Neighborhood Homogeneity. Nick Harner, University of Dayton, Advisor: Joe Mashburn. Abstract and more >

March 16: Bootstrapping General ARIMA Models, Seth Gannon, University of Dayton. Abstract and more >

March 9: Asymptotically Periodic Solution of a Quantum Volterra Equation, Muhammad Islam, University of Dayton. Abstract and more >

FEBRUARY 2017

February 21: A semiparametric regression under biased sampling and random censoring: a local pseudo-likelihood approach, Yassir Rabhi, University of Sherbrooke. Abstract and more >

February 14: Empirical Likelihood Based Detection Procedure for Change Point in Mean Residual Life Functions under random censorship, Ying-Ju Chen, Miami University. Abstract and more >

February 9: Mean Field Games for Stochastic Growth with Relative Utility, Son Nguyen, University of Puerto Rico. Abstract and more >

February 7: Price Dynamics in a Limit Order Book under time-dependent order flow, Jonathan Chavez Casillas, University of Calgary. Abstract and more >

February 2: Fast Alternating Minimization Algorithms for Inverse Problems in ImagingDr. Maryam Yashtini, Georgia Institute of Technology.  Abstract and more >

JANUARY 2017

January 24: A Markov-Modulated M/M/1 Retrial Queue with Unreliable Server, Dr. James D. Cordeiro, MediaDyne Systems Engineering.  Abstract and more >

Fall 2016

DECEMBER 2016

December 14A numerical study of an option pricing model using Radial Basis Functions collocation method, Walaa Alharbi, University of Dayton. Abstract and more >

December 9: First presentation - Quasilinearization and Boundary Value Problems at Resonance, Kareem Alanazi and Meshal Alshammari, University of Dayton. Second presentation - Packings of Various Complete Graphs with Isomorphic Copies of the 4-Cycle with a Pendant Edge, Badriah Alrashadi, University of Dayton. Abstracts and more >

December 1: Selling stock with long/short term taxes, Hang Gu, University of Dayton.

NOVEMBER 2016

November 17: Existence of a Positive Solution of Boundary Value Problems Theorems, Ahlam Abid, University of Dayton. Abstract and more >

November 10: Spectral Properties of Jacobi Matrices, Joanne Dombrowski, Wright State University, hosted by Jon Brown. Abstract and more >

November 3: Green's functions as convolutions of Green's functions for lower order fractional differential equationsPaul Eloe, University of Dayton. Abstract and more >

OCTOBER 2016

October 27: (Regular) Graded Skew Clifford Algebras of Low Global Dimension, Dr. Manizheh Nafari, Central State University, hosted by Muhammad Usman. Abstract and more >

October 20: Tyler Masthay, University of Dayton. 

SEPTEMBER 2016

September 29: Boundary Value Problems at Resonance and Fixed Point Theorems, Paul Eloe, University of Dayton. Abstract and more >

September 22: The Nahm Transform, Dr. Andres Larrain-Hubach, University of Dayton. Abstract and more >

SUMMER 2016

August 3: Comparison Theorems and Free Boundary Value Problems for Ordinary Differential Equations, Alaa Alharbi, University of Dayton

July 1: Almost 2-perfect Maximum Packing and Minimum Covering of Complete Graphs with 6-cycles, Meshail Alharbi and Maram Almazmumi, University of Dayton.


Spring 2015

MARCH 2015

March 24: Patrick Chadowski, University of Dayton:  "Existence and Uniqueness of Solutions in Nonlinear Differential Equations"  Read abstract (pdf)>>

March 19: Carl Mummert, Marshall University: "What is 'reverse' mathematics?"  Read abstract (pdf)>>

FEBRUARY 2015

February 2: Gabriela Martinez, Cornell University: "Augmented Lagrangian Methods for Solving Optimization Problems with Stochastic-Order Constraints." Read abstract (pdf) >>

February 4: Mark Tomforde, University of Houston: "Using Results from Dynamical Systems to Classify Algebras and C* -algebras." Read abstract (pdf) >>

February 5: Kevin McGoff, Duke University: "Statistical Inference for Dynamical Systems." Read abstract (pdf) >>

February 10: Alan Veliz-Cuba, University of Houston: "Practical and theoretical aspects of modeling gene networks." Read abstract (pdf) >>

February 19: Alaa Almansour, University of Dayton: "Boundary Value Problems at Resonance for Ordinary Differential Equations." Read abstract (pdf) >>

February 26: May Mei, Denison University: "Modeling Quasicrystals with Dynamical Systems." Read abstract (pdf) >>

Fall 2014

DECEMBER 2014

December 4: Jing Dan Zhang, University of Dayton:  "Pricing Options Using the Tree Method in a Switching Model with State Dependent Switching Rates." Read abstract (pdf) >>

December 4: Zhiyang Zhang, University of Dayton:  "Pricing Options in Jump Diffusion Models Using the Fast Fourier Transform." Read abstract (pdf) >>

December 9: Jing Nie, University of Dayton:  "Efficiency Comparison of Moody's KMV Model and Altman's Z-score Model Predicting Corporate Default with Empirical U.S. Data."  Read abstract (pdf) >>

December 11: Hanan Aljubran, University of Dayton:  "Asset Pricing in Policy Uncertainty Periods."  Read abstract (pdf) >>

December 11: Mohammed Aldandani, University of Dayton:  "A Green's Function for a Two-Term Second Order Differential Operator.:  Read abstract (pdf) >>

NOVEMBER 2014

November 6: Zhifeng Kuang, Universal Technology Corporation & Air Force Research Laboratory:  "Solving a Class of NP-Hard Optimization Problems Using Coupled Monte Carlo and Molecular Dynamics Simulations."  Read abstract (pdf) >>

November 11: Tracy Hwang, Risk Manager in Residence

November 20: Michael A. Radin, Rochester Institute of Technology:  "Dynamics of a discrete population model for extinction and sustainability in ancient civilizations."

November 25: Chenyu Qiu, University of Dayton:  "An Analysis of American Companies (1990-2000) Using the KMV Model." Read abstract (pdf)>>

OCTOBER 2014

October 2: Dr. Lance Lijian Chen, Department of MIS, OM and Decision Sciences, University of Dayton: "Two Topics on the Stochastic Programming and their Applications." Read Abstract (pdf) >>

October 16: Dr. Eloe, Department of Mathematics, University of Dayton:  "Multi-term Linear Fractional Nabia Difference Equations with Constant Coefficients."  Read Abstract (pdf) >>

October 23: Jireh Loreaux, University of Cincinnati:  "Extracting Hidden Information:  The Interplay Between Operators and their Diagonal Sequences."  Read Abstract (pdf) >>

October 30: Dr. Gang Yu, Kent State University:  "Sequences with Bounded Auto-Correlations."  Read Abstract (pdf) >>

SEPTEMBER 2014

September 18: Jonathan Brown, University of Dayton: "Determining if C*-algebras are simple." Read Abstract (pdf) >>

September 24: Jonathan Brown, University of Dayton: "Simplicity of the Irrational Rotation Algebra." Read Abstract (pdf) >>


Spring 2013

MARCH 2014

March 13: Muhammad Islam, University of Dayton:  "Bounded, asymptotically stable and L1 solutions of Caputo fractional differential equations." Read Abstract (pdf) >>

March 20: Paul Eloe, University of Dayton:  "A boundary value problem for a fractional differential equation." Read Abstract (pdf) >>

March 27: Tamer Oraby, University of Cincinnati: "Modeling parental acceptance of vaccination for paediatric infectious diseases."  Read Abstract (pdf) >>

 FEBRUARY 2014

February 6: Paul Eloe, University of Dayton: "Variation of parameters and fractional difference equations." Read abstract (pdf) >>

February 13: Jonathan Brown, Kansas State University: "The center of rings associated to directed graphs."  Read abstract (pdf) >>

February 18: Edward Hanson, Williams College: "Characterization of Leonard Pairs." Read abstract (pdf) >>

February 20: Jean Nganou, University of Oregon: "A Stone type duality between profinite MV-algebras and multisets." Read abstract (pdf) >>

JANUARY 2014

January 23: Matthew DeVilbiss, University of Dayton: "Finding the Grundy Number of line graphs." Read abstract (pdf) >>

January 30: Charlie Suer, University of Louisville: "Extending the PC-Tree Algorithm to the Torus." Read abstract (pdf) >>

Fall 2013

DECEMBER 2013

December 3: Abdulmohsen Alruwaili, University of Dayton: "Boundedness and Decay of Solution in Delay Difference Equation with Unbounded Forcing Terms."  Read abstract (pdf) >>

December 3: Norah Alnami, University of Dayton: "Asymptotically Stable Solutions of a System of Coupled Nonlinear Differential Equations."  Read abstract (pdf) >>

December 5: Salah Alsahafi and Abdualrazaq Sanbo, University of Dayton: "Boundedness of Solutions in Volterra Systems of Difference Equations."  Read abstract (pdf) >>

December 5: Pei Zhang, University of Dayton: "Idiosyncratic Risk and the Cross-Section of Expected Stock Return a Threshold Regress Approach."  Read abstract (pdf) >>

NOVEMBER 2013

November 7: David Freeman, University of Cincinnati: "Invertible Carnot Groups."  Read abstract (pdf) >>

November 14: Asmaa Alharbi and Hadiah Esmaiel, University of Dayton: "Exponential Smoothing."  Read abstract (pdf) >>

November 21: Nujud Alshehri, University of Dayton: "Forced Monotone Methods." Read abstract (pdf) >>

November 21: Ahmad Alhamed, University of Dayton: "Multivariate Time Series Models." Read abstract (pdf) >>

OCTOBER 2013

October 3: Paul Eloe, University of Dayton: "A solution algorithm for three term linear fractional difference equations with constant coefficients."

October 14: Willy Hereman, Colorado School of Mines: "Symbolic computation of conservation laws of nonlinear partial differential equations." (Electro-Optics and Mathematics Joint Seminar)

October 17: Catherine Kublik, University of Dayton: "Coarsening in high order, discrete, ill-posed diffusion equations."

October 24: Richard Kublik, Materials Resources LLC: "An Algorithm for Locally Adaptive Time Stepping."

October 31: Michael Radin, Rochester Institute of Technology: "Eventually periodic solutions & patterns of unbounded solutions of a second order delayed max-type difference equation."

SEPTEMBER 2013

September 12: Dan Ren, University of Dayton: "Optimal stopping time for the last passage time and last maximum time."

September 19: Lynne Yengulalp, University of Dayton: "Topological completeness."

September 26: Amanda Keck Criner, University of Dayton Research Institute: "Thermal nondestructive evaluation of porous materials."


CONTACT

Department of Mathematics

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