Department of Mathematical Sciences
Colloquium Series, 2018 - 2019
Purpose: To discuss mathematical research and interdisciplinary problems in all areas of mathematics and applied mathematics. Talks are welcome from faculty, graduate students, and outside speakers from academia and industry. Talks should be at a level accessible to graduate students. Students and faculty at all levels and from all departments are welcome to attend.
Date/Time | Speaker | Title/Abstract |
Friday, September 14
3:00-4:00pm The MAC |
Dr. Ugur G. Abdulla Department of Mathematical Sciences Florida Institute of Technology |
Title: Breast Cancer Detection through Electrical Impedance Tomography and Optimal Control of Elliptic PDEs -- Invitation to Research Abstract: In this talk I am going to discuss the inverse Electrical Impedance Tomography (EIT) problem or Calderon problem on recovering electrical conductivity tensor and potential in the body based on the measurement of the boundary voltages on the electrodes for a given electrode current. The inverse EIT problem presents an effective mathematical model of breast cancer detection based on the experimental fact that the electrical conductivity of malignant tumors of the breast is significantly different from conductivity of the normal tissue. I am going to introduce a mathematical model of the inverse EIT problem as a PDE constrained optimal control problem in a Sobolev-Besov spaces framework, where the electrical conductivity tensor and boundary voltages are control parameters, and the cost functional is the norm declinations of the boundary electrode current from the given current pattern and boundary electrode voltages from the measurements. The state vector is a solution of the second order elliptic PDE in divergence form with bounded measurable coefficients under mixed Neumann/Robin type boundary condition. Some recent results on the existence of the optimal control, Frechet differentiability in the Besov space setting, derivation of the he formula for the Frechet gradient, optimality condition, and extensive numerical analysis in the 2D case through implementation of the gradient method in Banach spaces will be presented. Talk will end with the formulation of some major open problems and the perspectives of future advance. |
Friday, October 5
3:00-4:00pm The MAC |
Dr. Yalchin Efendiev Department of Mathematics Texas A&M University |
Title: Data Integration in Multiscale Simulations Abstract: In this talk, I will discuss several data integration techniques in multiscale simulations. I will give a brief overview of multiscale simulation concepts that will be used. These multiscale techniques are designed for problems when the coarse grid does not resolve scales and contrast. I will describe the relation between multiscale and upscaling methods. I will describe three data integration techniques. The first one, Bayesian multiscale modeling, will sample basis functions and incorporate available data. In the second approach, we will use deep learning techniques to design and modify existing multiscale methods in the presence of data and nonlinearities. |
Friday, October 12
3:00-4:00pm The MAC |
Dr. Alexandru Tamasan Department of Mathematics University of Central Florida |
Title: Current Density based Impedance Imaging (CDII) Abstract: In this talk I will present the inverse hybrid problem of CDII, where the electrical conductivity of body is to be recovered from of the magnitude of one current density field. Physically we use a connection between the current density field generated from the boundary, with interior measurements of the magnetization in a MRI machine. The basic idea is to first recover the voltage potential, which solves a generalized 1-Laplacian. Mathematical methods involved in solving this problem combines ideas from Riemannian geometry with geometric measure theory, and touch on some algebraic topology. |
Friday, November 16
3:00-4:00pm The MAC |
Roqia Jeli Department of Mathematical Sciences Florida Institute of Technology |
Title: On the Qualitative Theory of the Nonlinear Parabolic p-Laplacian Type Reaction-Diffusion Equations Abstract: This dissertation presents full classification of the evolution of the interfaces and asymptotics of the local solution near the interfaces and at infinity for the nonlinear second order parabolic p-Laplacian type reaction-diffusion equation of non-Newtonian elastic filtration. Nonlinear partial differential equation is a key model example expressing competition between non-linear diffusion with gradient dependent diffusivity in either slow (p > 2) or fast (1 < p < 2) regime and nonlinear state dependent reaction (b > 0) or absorption (b < 0) forces. If interface is finite, it may expand, shrink, or remain stationary as a result of the competition of the diffusion and reaction terms near the interface, expressed in terms of the parameters p; β, sign b, and asymptotics of the initial function near its support. In the fast diffusion regime strong domination of the diffusion causes infinite speed of propagation and interfaces are absent. In all cases with finite interfaces we prove the explicit formula for the interface and the local solution with accuracy up to constant coefficients. We prove explicit asymptotics of the local solution at infinity in all cases with infinite speed of propagation. The methods of the proof are generalization of the methods developed in U.G. Abdulla & J. King, SIAM J. Math. Anal., 32, 2(2000), 235-260; U.G. Abdulla, Nonlinear Analysis, 50, 4(2002), 541-560 and based on rescaling laws for the nonlinear PDE and blow-up techniques for the identification of the asymptotics of the solution near the interfaces, construction of barriers using special comparison theorems in irregular domains with characteristic boundary curves. |
Friday, April 19
3:00-4:00pm The MAC |
Dr. Robert Talbert Department of Mathematics Grand Valley State University |
Title: Flipped learning in theory and practice for mathematics Abstract: Flipped learning is a pedagogical model in which learners get first contact with new ideas through guided and structured self-learning activities prior to group meetings, allowing significantly more attention to be paid during class meetings to more advanced topics through challenging active learning tasks done collaboratively. Flipped learning combines the best traditions of tutorial and case study methods with modern technologies and evidence-based teaching practices, to help create highly effective learning environments for all learners. In this talk, we will trace the origins of flipped learning, present a framework for flipped learning based in self-determination theory, and illustrate real-life examples from applications to mathematics courses. |
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