Weekly Colloquium

Dr. Benjamin Fine discusses public-key cryptographyThe Department hosts a weekly colloquium on Fridays at 2pm, usually in Southern Hall, room 303. If you would like to present, please contact Dr. Huiqing Zhu with a title and abstract. Please see our tips on abstracts below. You can also find links to previous years' titles and abstracts below.

DatePresenter, AffiliationTitle, Abstract
9 Dec 2016Dr. Runchang Lin

Ultraconvergence of Finite Element Method by Richardson Extrapolation

In this talk, two novel Richardson extrapolation operators are proposed to investigate local \(2k\)th order ultraconvergence properties of the \(k\)th order Lagrange finite element method for the second order elliptic problems. We show that, for both tensor product \(Q_k\) element and simplicial \(P_k\) element, the post-processed displacement and gradient both have \(2k\)th order ultraconvergence at interior mesh nodes away from the boundary. Numerical results are provided to demonstrate the theoretical findings.

2 Dec 2016Dr. Dhruba Adhikari

Maximal Monotonicity and Existence of Nonzero Solutions

 

The theory of maximal monotone operators in Banach spaces plays an important role in the solvability of a large class of partial differential equations, particularly the ones in divergence form. The talk will begin with an introduction to maximal monotone operators in Hilbert spaces. An extension of the notion to Banach spaces will then be discussed. Among others, examples of maximal monotone operators which appear as the subdifferentials of certain convex functions will be given. Finally, an existence theorem for nonzero solutions of operator equations in Banach spaces will be presented.

4 Nov 2016Dr. Benjamin Fine, Fairfield University

CRYPTOGRAPHY - SECURITY and HOW TO STEAL CREDIT CARD NUMBERS

Because of the increasing power of computing machinery, cryptosystems, both public key and classical, are becoming less secure. At the same time there is an increasing need for secure cryptosystems. This is clear from the increasing use of internet shopping, electronic financial transfers and so on.

 

The first part of this talk will introduce the basic techniques and terminology of cryptology. It then proceeds to public key methods. Finally, the increasing power of computing machinery has created some unease with the security of the standard number theoretic methods, leading to the development of cryptographic methods using noncommutative objects. This is presently a lively area of research. At the end of the talk we will give a very brief introduction to this field that has now been dubbed noncommutative algebraic cryptography.

7 Oct 2016Dr. Michael Starbird, University of Texas at Austin

Geometric Gems

Plain, plane geometry contains some of the most beautiful proofs ever—-some dating from ancient times and some created by living mathematicians. This talk will include some of my favorites including an incredibly clever way to see that a plane intersects a cone in an ellipse, a non-calculus method--developed by a living mathematician--for computing areas under challenging curves, and many more. Geometry provides many treats!

16 Sep 2016Dr. Iliyan Iliev, USM

Social Science Applications of Bayesian Structural VAR Models and Natural Language Processing

Computerized text analysis and structural time series models have been underutilized in Social Science research despite their many applications. This project studies the dynamic interactions of energy sector campaign contributions to members of the U.S. Senate and their reactions. Congressional rhetoric is segregated from the database of Committee hearings using a Java script, and then analyzed using a Bayesian natural language processing algorithm. The categorized rhetoric over time is then linked to the campaign contributions data, and analyzed using a Bayesian time-series model. Conditioning on party and Senate class, I find strong evidence for a fully dynamic model, where rhetoric and contributions engage in a complex system of leads, lags, and contemporaneous interactions.

15 Sep 2016Dr. John Travis, Mississippi College

Webwork

WeBWorK is an open-source online homework system delivering individualized assessment problems. Immediate feedback encourages students to persist until they succeed. Instructors receive real-time statistics that indicate how to better serve students.

An Open Problem Library of over 35,000 refereed and catalogued problems covers nearly the entire mathematics curriculum. Most problems utilize a robust checking engine which allows almost any type of formula-like answer.

More than 1000 institutions utilize WeBWorK, most in the USA, but also in Canada and Mexico, as well as Europe, Asia, and Africa.

This talk gives an overview of WeBWorK's features, including recent improvements and a summary of how to utilize WeBWorK in the classroom. Participants are encouraged to bring an internet-capable device and participate in real-time.
29 Apr 2016Dr. Sung Lee, USM

TBA

22 Apr 2016Dr. Raymond Atta-Fynn, University of Texas at Arlington

Materials Modeling via Dynamics

Sampling rare events and reconstructing the free energy along a path from an initial to a final state of physical and chemical processes is one of the principal goals of materials modeling. This can be achieved with a computational technique known as metadynamics, which allows efficient sampling and permits an accurate reconstruction of the free energy landscape with the aid of a small set of collective variables. This talk will provide a brief overview of the metadynamics method and how it is applied to molecular and solid state systems. Specific applications in the context of metal ion structure and hydrolysis in aqueous environments, and the generation of atomistic structures of amorphous semiconductors will be presented.

15 Apr 2016Dr. Paula Smithka, USM (Philosophy and Religion)

Dr. Who and Philosophy 101

Philosophy begins in wonder! (Aristotle said that). And Doctor Who certainly creates a sense of wonder in its companions. In this talk, I will provide a brief introduction to what philosophy is, the various areas of philosophical inquiry, and why Doctor Who is so very philosophical.

1 Apr 2016Dr. Carmen Wright, Jackson State University

The Generalized and Symmetric Spaces in \(\textrm{SL}_2(\mathbb F_q)\) and \(\textrm{GL}_2(\mathbb F_q)\)

We will discuss the generalized symmetric spaces for \(\textrm{SL}_2(\mathbb F_q)\) and \(\textrm{GL}_2(\mathbb F_q)\). Specifically, we will characterize the structure of these spaces, and prove that when the characteristic of \(\mathbb F_q\) is not equal to two, the extended generalized symmetric space is equal to the generalized symmetric space for \(\textrm{SL}_2(\mathbb F_q)\) and nearly equal for \(\textrm{GL}_2(\mathbb F_q)\).

11 Mar 2016Dr. Maarten Buijsman, USM (Marine Science)

The Propagation and Dissipation of Tidal Internal Gravity Waves in Numerical Simulations

As the surface tide propagates over underwater topography, energy is transferred to internal gravity waves that can propagate thousands of kilometers through an eddying ocean. Underway, these low-mode internal waves may scatter into high modes at steep topography, be affected by wave-wave interaction, and they may nonlinearly interact with the mesoscale eddy field. Their dissipation causes the mixing of water masses, sustaining the overturning circulation and affecting climate. It is not yet clear what their ultimate fate is. Do they dissipate their energy along the way or when they break on the continental shelves? In this talk I will address these questions with idealized numerical simulations and with the realistically forced Hybrid Coordinate Ocean Model, the operational forecast model of the US Navy.

4 Mar 2016Dr. Ras Pandey, USM (Physics and Astronomy)

Random walk, polymer chain, and protein by computer simulation experiments

Random walks are a classical mechanism for analyzing phenomena as diverse as stock market trends and information in cell phone chips. They give a starting point for exploring the structure and dynamics of systems with string-like constituents, such as polymer chains and proteins. While polymer chains' structure and dynamics are relatively well understood, the structure and dynamics of a protein remain an open problem. Issues include atomic scale structures, first principle force-fields, structure-based constraints, etc. We discuss protein folding, self-assembly, and network formation with specific examples (e.g. histone H3.1, lysozyme, alpha-synuclein), using a coarse-grained approach involving large-scale computer simulations.

12 Feb 2016Dr. Jiu Ding, USM

A Piecewise Quadratic Interpolation Method for the Computation of Stationary Densities

We propose a piecewise quadratic interpolation method that can be efficiently used to approximate a stationary density of Frobenius-Perron operators associated with interval mappings. The convergence of the method for the Lasota-Yorke class of piecewise stretching mappings is proved, and numerical results are also presented.
5 Feb 2016Dr. Bernd Schröder, USM

Every order-preserving self map of the \(L^p\) unit ball has a fixed point

This talk will give a brief introduction why fixed points are important, why \(L^p\) spaces are important and then proceed to prove that every order-preserving self map of the \(L^p\) unit ball has a fixed point. We will then talk about how this result is applied and how it could be extended.

Tips on abstracts

Dear speaker: We like to maintain a list of titles, topics, and abstracts, so that we (and you) have a record of who has visited and talked about which topic.

  • The topic should be short, similar to the headlines in the AMS subject classifications.
  • Please aim for no more than 100 words in your abstract. We're not fanatically rigorous about this, but an abstract should summarize the essence of a presentation, not give every detail. It’s a sales pitch, not a business plan. Keeping the abstract at 100 words also is a good preparatory step for a concise and informative talk that communicates the salient points of your work.
  • You may notice that we are MathJax-enabled, so feel free to use \(\mathrm{\LaTeX}\) markup in your abstract when appropriate.

Previous years' seminars

2015 · 2014 · 2013 · 2011-2013