Analysis and Applied Math Seminar

The Analysis and Applied Mathematics (AAM) Seminar is intended for Kennesaw State faculty working in the various areas of analysis and applied mathematics to get together to discuss their current work or related questions. Seminars often involved advanced mathematical knowledge. However, the seminars are open to anyone who is interested in attending.

Upcoming Events

No events currently scheduled


Past Events

Friday, September 20, 2019

  • SPEAKER: Sara Motlaghian, Georgia State University
  • TITLE: "Topological Properties of J-Orthogonal Matrices"
  • TIME/LOCATION: 2:00-3:00pm, D-249, Marietta campus
  • ABSTRACT: Link to pdf abstract

Friday, October 11, 2019

  • SPEAKER: Guihong Fan, Columbus State University
  • TITLE: "Persistence, global stability, and global Hopf bifurcation in a staged tick population model with delays"
  • TIME/LOCATION: 2:00-3:00pm, D-249, Marietta campus
  • ABSTRACT: Link to pdf abstract

Friday, November 8, 2019

  • SPEAKER: Lingju Kong, University of Tennessee at Chattanooga
  • TITLE: "On the principal eigenvalue of a biharmonic system"
  • TIME/LOCATION: 2:00-3:00pm, D-249, Marietta campus
  • ABSTRACT: Link to pdf abstract

Friday, November 15, 2019

  • SPEAKER: Jeremy Harris, Emory University
  • TITLE: "Cellular co-infection increases the rate of influenza A virus production and shapes the immune response to infection"
  • TIME/LOCATION: 2:00-3:00pm, D-249, Marietta campus
  • ABSTRACT: During viral infection, the number of virions infecting individual cells can vary significantly over time and space. While this variation in the cellular multiplicity of infection (MOI) may have important phenotypic consequences, the relationship between cellular phenotypes (output) in response to viral infection and the cellular MOI (input) remains poorly understood. To study these cellular input/output relationships, our experimental collaborators performed bulk cell culture infection experiments, in which they infected ∼2 million cells with influenza A virus (IAV) at various bulk MOI treatments. They measured several cellular response outcomes during a single round of replication (from 0–18 hours post infection): cell death kinetics, viral infection distribution, virus production, interferon induction, and superinfection exclusion. To determine how these cellular responses change as a result of cellular coinfection, we developed several mathematical models that include single-cell level input/output relationships. Using an appropriate viral infection distribution across cells, we can 'scale' these single-cell relationships up to the bulk cell culture level. By fitting these models to the bulk cell culture data, we were able to determine which infection outcomes were sensitive to cellular coinfection. For instance, we found that virus production increases and saturates at high levels of viral input. We also found that infected cell death rates and type I interferon expression are independent of viral input while type III interferon induction is sensitive to viral input, identifying a role for cellular co-infection in shaping the host immune response to IAV infection. Our results suggest that, the extent of cellular co-infection by influenza viruses may play a critical role in determining viral fitnesses, cellular response phenotypes, and overall infection outcomes during the viral infection.

Wednesday, October 21, 2020

  • SPEAKER: Dr. Doug Pfeffer, Berry College
  • TITLE: "Invertibility of a Class of Toeplitz Operators"
  • TIME/LOCATION: 3:30-4:30pm online in Zoom
  • ABSTRACT: Link to pdf abstract

Thursday, October 29, 2020

  • SPEAKER: Dr. Yaqin Feng, Department of Mathematics, Ohio University
  • TITLE: "Stability and Instability of Steady States for a Branching Random Walk"
  • TIME/LOCATION: 2:00-3:00pm online in Zoom
  • ABSTRACT: We consider the time evolution of a lattice branching random walk with local perturbations. Under certain conditions, we prove the Carleman type estimation for the moments of a particle subpopulation number and show the existence of a steady state.

Friday, April 9, 2021

  • SPEAKER: Dr. Nsoki Mavinga, Swarthmore College
  • TITLE: "Delay Differential Equations with Applications to the Analysis of the Spread of Vector-Borne Diseases"
  • TIME/LOCATION: 2:30-3:30pm online in Zoom
  • ABSTRACT: Many problems in applied science give rise to delay differential equations. These are differential equations in which the current rate of change of the system depends not only on the current state but also on the history of the system; i.e. the system has memory. In this talk, we will discuss the stability of equilibrium solutions for a two-lag delay differential equation which models the spread of infectious diseases; namely, vector-borne diseases where the lags are incubation periods in humans and vectors. We show that there are some values of the transmission and recovery rates for which either the disease dies out or it spreads into an endemic state. The approach is based on the linearization method and the analysis of roots of transcendental equations.

Friday, April 23, 2021

  • SPEAKER: Dr. Eric Stachura, Kennesaw State University
  • TITLE: "Quantitative estimates for solutions of the Maxwell system in Lipschitz Domains"
  • TIME/LOCATION: 1:00-2:00pm online in Zoom
  • ABSTRACT: The effects of rough surfaces on scattering are important in many applications, ranging from radar surveillance to radio communication. One natural question is the following: precisely how do the rough surfaces affect the various scattering problems? I will address this problem for electromagnetic scattering, and discuss how to obtain various estimates with a precise dependence on the Lipschitz character of the underlying scatterer. Special attention is needed for trace and extension operators over certain Sobolev spaces. In particular, I will discuss a weak formulation of the scattering problem and obtain explicit bounds for the solution in terms of the incident fields and the Lipschitz character of the domain. This is joint work with Niklas Wellander.

Monday, June 28, 2021

  • SPEAKER: Dr. Larry Wang, Kennesaw State University
  • TITLE: "Construction of Finite Tight Frames"
  • TIME/LOCATION: 3:00-4:00pm online in Zoom
  • ABSTRACT: Finite tight frames are used widely for many applications including signal processing, internet coding, wireless communication, and quantum detection theory. One important problem in these applications is the construction of finite tight frames with a prescribed norm for each vector in the tight frame. Another important problem is the construction of finite tight frames containing specified elements as needed in real-world applications. We present two algorithms that address these problems. As one of the applications of tight frames in quantization, Pulse Code Modulation (PCM) quantization will be discussed. This is based on joint work with Jun Ji, Yang Wang, Dejun Feng, and David Jimenez.

Friday, October 29, 2021

  • SPEAKER: Dr. Ghan S Bhatt, Tennessee State University
  • TITLE: "Finite Equiangular Tight Frames"
  • TIME/LOCATION: 2:30-3:30pm, online in Zoom
  • ABSTRACT: Frames in Hilbert spaces are a generalization of bases, and they are used to construct a given vector in a Hilbert space. Frames with a minimum coherence (absolute value of the dot product) are desired for several applications. The lowest coherence occurs when the frame is an equiangular frame. Although such frames are known to exist in some selected dimensions, their construction is still a very challenging problem. In this talk, we will discuss the challenges and constructions in some particular cases. The talk will be accessible to senior undergraduate and graduate students.

Thursday, November 4, 2021

  • SPEAKER: Dr. Wandi Ding, Middle Tennessee State University
  • TITLE: "Optimal control applied to mosquito-borne diseases: Malaria and WNV"
  • TIME/LOCATION: 3:30-4:30pm, online in Zoom
  • ABSTRACT: We present some optimal control work on mosquito-borne diseases: Malaria and West Nile Virus. First, a malaria transmission model with SEIR (susceptible-exposed-infected-recovered) classes for the human population, SEI (susceptible-exposed-infected) classes for the wild mosquitoes, and an additional class for sterile mosquitoes is formulated. We derive the basic reproduction number of the infection. We formulate an optimal control problem in which the goal is to minimize both the infected human populations and the cost to implement two control strategies: the release of sterile mosquitoes and the usage of insecticide-treated nets to reduce malaria transmission. Adjoint equations are derived and the characterization of the optimal controls are established. Finally, we quantify the effectiveness of the two interventions aimed at limiting the spread of Malaria. A combination of both strategies leads to more rapid elimination of the wild mosquito population that can suppress Malaria transmission.

    Secondly, we consider a West Nile Virus transmission model that describes the interaction between bird and mosquito populations (eggs, larvae, adults) and the dynamics for larvicide and adulticide, with impulse controls. We derive the basic reproduction number of the infection. We reformulate the impulse control problems as nonlinear optimization problems to derive adjoint equations and establish optimality conditions. We formulate three optimal control problems which seek to balance the cost of insecticide applications (both the timing and application-level) with (1) the benefit of reducing the number of mosquitoes, (2) the benefit of reducing the disease burden, or (3) the benefit of preserving the healthy bird population. Numerical simulations are provided to illustrate the results of both models.

Thursday, February 24, 2022

  • SPEAKER: Dr. Lingju Kong, University of Tennessee at Chattanooga
  • TITLE: "Modeling User Adoption and Abandonment Dynamics of Online Social Networks Using Compartment Models"
  • TIME/LOCATION: 3:30-4:30pm, online in Zoom
  • ABSTRACT: Link to pdf abstract

Wednesday, October 19, 2022

  • SPEAKER: Dr. Tyler Bongers, Harvard University
  • TITLE: "Using energies to study the geometry of a set"
  • TIME/LOCATION: 1:00-2:00pm, online in Zoom
  • ABSTRACT: The energy of a measure is a tool which detects structure in a set at different dimensions. Energies are defined by generalizing the (physical) potential in an electric field and help us understand how concentrated a set is on different scales; this gives a useful tool in the study of fractal sets and their geometry. In this talk we will explore the motivations for defining energies, see how they can be used to estimate the sizes of sets and their shadows, and discuss an open problem involving the four-corner Cantor set and numerical linear algebra. This last part is joint work with Krystal Taylor.

Wednesday, November 2, 2022

  • SPEAKER: Joshua McGinnis, Drexel University
  • TITLE: "Rigorous justification for macroscopic waves in a two-dimensional lattice with random masses"
  • TIME/LOCATION: 1:15-2:15pm, online in Zoom
  • ABSTRACT: Link to pdf abstract