Mathematics Department Colloquium Series 

The Mathematics Department established the Mathematics Department Colloquium Series through a Faculty Development Grant in 1999 to provide a place to discuss new research in Mathematics. Speakers for the series come from both inside the UTC Department of Mathematics as well as guest speakers from other institutions. The Colloquium Series meets periodically throughout the year.

Upcoming Colloquium Series Talks

Time: 3:00PM - 4:00PM

Date: Friday, February 22, 2019

Place: SimCenter Auditorium (Rm. 105) 

Speaker: Mahboub Baccouch

University of Nebraska at Omaha

Title: Discontinuous Galerkin methods for solving differential equations:

Superconvergence, error estimation, and adaptivity

Abstract: Discontinuous Galerkin (DG) nite element methods are becoming important techniques for the computational solution of many real-world problems describe by differential equations. They combine many attractive features of the nite element and the nite volume methods.

These methods have been successfully applied to many important PDEs arising from a wide range of applications. DG methods are highly accurate numerical methods and have considerable advantages over the classical numerical methods available in the literature. The main advantages include: they (i) handle problems having discontinuities such as those arising in hyperbolic problems (e:g: shocks), (ii) handle problems having sharp transition layers such as those arising in convection-diffusion problems, (iii) handle problems with complex geometries, (iv) suitable for long time simulation (e:g:; they maintain the phase and shape of the waves accurately), (v) produce efficient parallel solution procedures, (vi) exhibit optimal convergence rate, and (vii) achieve very nice superconvergence results, which can be used to design asymptotically exact a posteriori estimates of discretization errors. Error estimators are essential to steer adaptive schemes where either the mesh is locally rened (h-renement) or the polynomial degree is raised (p-renement). Furthermore, DG methods can easily handle meshes with hanging nodes, elements of various types and shapes, and local spaces of different orders. Finally, DG methods provide accurate and efficient simulation of physical and engineering problems, especially in settings where the solutions exhibit poor regularity. For these reasons, they have attracted the attention of many researchers working in diverse areas, from computational uid dynamics, solid mechanics and optimal control, to nance, biology and geology.

In this talk, we give an overview of the main features of DG methods and their extensions such as the local DG (LDG) methods, which are natural extension of the DG methods aimed at solving higher-order equations. We rst introduce the DG method for solving nonlinear ODEs and present several properties that render them so attractive such as convergence, superconvergence phenomena, a posteriori error estimation, and mesh adaptivity. Then, we extend the methods to other PDEs such as convection, convection-diffusion, wave, KdV, Euler-Bernoulli equations. Furthermore, we present a stochastic analogue of the DG and LDG methods for stochastic equations. Some open problems and future research directions will be mentioned.  

This talk is appropriate for the students with serious interest in research.

Time: 3:00PM-3: 50PM

Date: Tuesday, February 26, 2019

Place: EMCS 218

Speaker: Jonathan Troup 

Department of Mathematics 

University of Oklahoma

Title: Students’ Development of Geometric Reasoning about the Derivative of Complex-Valued Functions

Abstract: In this paper, I share results of a case study describing the development of two undergraduate students’ geometric reasoning about the derivative of a complex-valued function with the aid of Geometer’s Sketchpad (GSP). My participants initially had difficulty reasoning about the derivative as a rotation and dilation. Without the aid of GSP, they could describe the rotation and dilation aspect of the derivative for linear complex-valued functions, but were unable to generalize this to non-linear complex-valued functions. Participants’ use of GSP, speech, and gesture assisted with discovering function behavior, generalizing how the derivative describes the rotation and dilation of an image with respect to its pre-image for non-linear complex-valued functions, and recognizing that the derivative is a local property.

This talk may be appropriate for all students with a strong interest in Math Education.

Time: 2:15PM-3:05PM

Date: Friday, March 01, 2019

Place: SimCenter Auditorium (Rm. 105) 

Speaker: K.B. Kulasekera

Department of Bioinformatics and Biostatistics

University of Louisville, Louisville, Kentucky

Title: Selection of the Optimal Personalized Treatment from Multiple Treatments with Multivariate Outcome Measures

Abstract: In this work we propose a novel method for individualized treatment selection when the treatment response is multivariate. For the K treatment ($K>2$)  scenario we compare quantities that are suitable indexes based on outcome variables for each treatment conditional on patient specific scores constructed from collected covariate measurements. Our method covers any number of treatments and outcome variables, and it can be applied for a broad set of models. The proposed method uses a rank aggregation technique to estimate an ordering of treatments based on ranked lists of treatment performance measures such as smooth conditional means and conditional probability of a response for one treatment dominating others. The method has the flexibility to incorporate patient and clinician preferences to the optimal treatment decision on an individual case basis. A simulation study demonstrates the performance of the proposed method in finite samples. We also present data analyses using HIV and Diabetes clinical trials data to show the applicability of the proposed procedure for real data.

This talk may be appropriate for all students with a strong interest in research.

Most Recent Colloquium Series Talk 

Time: 2:30PM-3:20PM

Date: Friday, February 01, 2019

Place: SimCenter Auditorium (Rm. 105)

Speaker: John Gounley

Oak Ridge National Laboratory

Title: Scalable Simulations of Blood Flow

Abstract: Computational simulations of blood flow offer the means to study a wide range of phenomena, from cardiovascular disease to the metastatic progression of cancer. However, performing large-scale and high-resolution simulations of blood flow requires a scalable computational framework to run efficiently on high-performance computing resources. In this talk, we discuss the development of such a framework using HARVEY, a parallel hemodynamics solver. We focus on the implementation of two numerical schemes, the lattice Boltzmann and immersed boundary methods, for a distributed memory environment and assess their scalability. This work is in collaboration with Amanda Randles (Duke) and Erik Draeger (LLNL)

This talk is appropriate for the students with serious interest in research.