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Mathematics

Mathematics Graduate Seminar - Spring 2021

The seminar is scheduled from 2:00 pm - 3:00 pm on Tuesday afternoon. If you are not a member of the Math Department and would like to attend the seminar please email us at MathDept@tntech.edu for a link to the virtual meeting. 
 
DATE   SPEAKER TITLE/Abstract
February 2    
February 9 Dr. Amy Chambers Introduction to Wavelets    
February 16          
February 23 Steven Buchanan Big Numbers - We explore the limits of computers and logic on a quest to define larger and larger numbers.
March 2 Prosper Aime Tchoumo Robust Estimation of Lognormal Severity ModelsInsurance companies often model severity using parametric distributions such as Lognormal, Gamma, exponential and others. Insurance data contain outliers very often. The Maximum Likelihood Estimator (MLE) is the most efficient method of estimating parameters but presents some limitations when data are contaminated by outliers. It is therefore crucial to find out a method that addresses such limitations. To overcome such limitations, the Method of Trimmed Moment (MTM) is a better alternative. In this presentation, we study both methods using lognormal and conduct simulations to show that MTM is a better alternative.
March 9 Jacob Copeland TBD
March 23 Sydney Clere An Audio Application of the Fourier Transform - In music, it is often desirable to alter the sound of voices or instruments by analog or digital means. These manipulations, when performed digitally, fall into the sect of computer science known as digital signal processing. If a signal is distorted, one way of returning the signal to its original state is by means of the Fourier Transform. This presentation will explore digital signal processing in an audio application using Octave, specifically that of guitar distortion effects and noise cancellation using the Fourier transform.  Both the continuous and discrete Fourier transforms will be introduced as well as the fast Fourier transform Octave function. 
March 30 Caleb Gilmore Noether Strongly Primary Ideals - 
In the study of primary ideals in ring theory, there exists the concept of a (Noether) strongly primary ideal, that is a primary ideal which contains a power of its radical. This talk will explore the relationships between this ideal and other special types of primary ideals. We will also consider strongly Laskerian rings, or rings in which every ideal can be expressed as an intersection of finitely many Noether strongly primary ideals, and an interesting equivalence for such rings.
April 6 Seth Agee Generalizations of the Black-Scholes Model -
Fischer Black and Myron Scholes derived their famous options pricing formula in 1973 under the assumption that the stock price follows a geometric Brownian motion with constant volatility term. In this talk, we discuss an alternative derivation of this formula and give similar results under a generalized model.
April 13 Chris McDonald N-Absorbing Ideals of Commutative Rings
April 20 Padmini Veerapen Deformations and Hochschild Cohomology -
A deformation can be viewed as the definition of a new multiplicative structure on an associative algebra over a field. In this talk, we explore the connection between this new multiplicative structure and Hochschild (co)homology.
FALL 2020 SEMINARS  
September 4 Amy Chambers Introduction to Graph C*-Algebras https://web.microsoftstream.com/video/273437c5-bb0b-4897-9563-46c5216c7c76
September 11 Michael Allen An Introduction to Statistical (Machine) Learning - Machine Learning and Artificial Intelligence are hot, hot topics today. In fact, over 80% of current NSF funding goes toward these two fields. Financial institutions, baseball teams, and game shows are all using AI or neural networks in one way or another. So, what is Artificial Intelligence and Machine Learning? This talk will give an introduction to Machine Learning and AI, discuss their roots in mathematics and statistics, and give some demonstrations of their use. https://web.microsoftstream.com/video/9a6b645c-0a09-4f47-ae33-f5b145b048b2
September 18 Seth Agee The Black-Scholes equation, which earned Scholes and Merton their 1997 Nobel Memorial Prize in Economics, revolutionized the way options were traded, and is still a commonly used equation for options pricing. In this presentation, we examine an alternative way to derive the Black-Scholes equation without solving any partial differential equations, and apply results from real analysis to provide a more elegant solution. This gives a fantastic example of how a purely abstract idea can be applied to the real world. 
https://web.microsoftstream.com/video/b49d5679-3a90-42ef-97ea-f0746ab09707
September 25  Amy Chambers Examples of Graph C*-Algebras - In this talk, we will look at some concrete examples of Graph C*-Algebras. Particularly, we will choose a particular Hilbert space H and view certain Graph C*-Algebras as C*-subalgebras of B(H).
https://web.microsoftstream.com/video/24f6dbe1-b310-4271-94c8-44501401e7f3
October 2 Menassie Ephrem, Coastal Carolina University Finite-dimensional Labeled Graph C*-Algebras - Given a directed graph E and a labeling L, one forms the labeled graph C*-algebra by taking a set of subsets of vertices and considering a generating family of partial isometries and projections.   

In this talk, we will discuss the basics of graph C*-algebras and how to form C*-algebras from labeled graphs  We will compute some such algebras.  Focusing on finite algebras we will formulate a process to compute these algebras.  We will present results that are obtained from experiments and eventually proven.
October 9 Motoya Machida Brownian motions, coupling, Pitman theorem and beyond.  A sample path of Brownian motion is continuous, nowhere differentiable, moving everywhere from negative to positive, and it can be viewed forward or backward in time. Pitman (1975) showed that a sample path of Brownian motion conditioned on positive values (or, simply a three-dimensional Bessel process) can be constructed and coupled with Brownian motion. In the talk we present the construction of Pitman as an intertwining dual. In general, we can show that (a) an intertwining dual can be constructed via Liggett dual, and (b) a coupled realization becomes bivariate Markovian. We will discuss possible applications beyond Pitman theorem.
October 16    
October 23 Damian Kubiak The Daugavet property in Banach spaces.  https://web.microsoftstream.com/video/1e59d38a-f5b8-4eb1-bdba-f363705a95be
October 30    
November 6 Padmini Veerapen An Intro to Poisson Algebras.
https://web.microsoftstream.com/video/fc8ef206-eac3-4ca1-88fa-8584018f3e55
November 13 Chudamani Poudyal Truncated and Censored Parametric Lognormal Severity Models.
https://web.microsoftstream.com/video/ff4a7ebb-c026-41de-b4cf-953d3f3e3061
November 20 Alexander Shibakov  

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