Mathematics Graduate Seminar - Fall 2023

The seminar is scheduled from 2:00 pm - 2:45 pm on Tuesday afternoon in Bruner Hall 126. 

11/7/2023 Dr. Motoya Machida

Title: Langevin diffusions and Monte Carlo methodology.


 Abstract: Gradient descent is a method of iterative optimization to minimize an objective function f(x). When a noise is added and a step size converges to zero, this iterative algorithm is viewed as a Langevin diffusion. It eventually reaches equilibrium in distribution proportional to exp(-f(x)). In this talk we introduce a notion of ``stochastic flow'' of sample path and ``duality'' of stochastic processes. A dual process, called an ``intertwining dual,'' will play a pivotal role in determining a stopping time (of algorithm) so that we can sample ``exactly'' from the stationary distribution in a finite steps. Thus, it will enable us to perform Monte Carlo simulations. [Demonstration code (bm.R) for this talk and more can be found at]


10/31/2024 Patrick Bartol

Title: Feynman-Kac Formulation of Black-Scholes Option Pricing.

Abstract:  Financial institutions have the ability to sell to buyers derivatives and options. Typical contracts that sell to the buyer the right to purchase stock for a strike price at a future time regardless of the stocks value at that time are called European call options. These institutions rely on the Black-Scholes option pricing to set contract price for European call options. The primary result we investigate is what the Black-Scholes model is and how it can be derived.  We will explore its foundation to understand stochastic differential equations starting with probability theory and Ito calculus. From there, infinitesimal generators are introduced along with related results to deduce the Feynman-Kac formula in order to solve the Black-Scholes option pricing problem. Once this has been examined, we move onto relating the Feynman-Kac formula to the partial differential equation associated to asset portfolio. The solution to this equation via the Feynman-Kac formula becomes the Black-Scholes option pricing.


10/24/2023 Dr. Padmini Veerapen

Title:  Looking Ahead with Hope Amidst the Trials and Tribulations of Graduate
School in Mathematics

Abstract:  In this talk, I will address questions graduate students often pose to me when I am either
in attendance at a conference or when I am teaching a class. The questions center around
themes such as survival in graduate school, developing good research writing skills, being
ready for life after graduate school, and establishing collaborations. At conferences or in
classes, my focus is often on the delivery of the mathematics and my goal in this talk, is
to elaborate on some of the tricky non-mathematical issues that come along as we focus
on the mathematics.

10/17/2023 Dr. Kehelwala Dewage Maduranga Title: NCQS: Nonlinear Convex Quadrature Surrogate Hyperparameter Optimization
: Ever wanted a taste of the latest in artificial intelligence, without the hefty travel bill to France? Deep learning, a cornerstone of modern artificial intelligence, necessitates optimized hyperparameters as models evolve in complexity. Traditional optimization strategies, with their reliance on smooth loss functions, are often suboptimal for advanced models. To bridge this gap, we introduce the Nonlinear Convex Quadrature Surrogate (NCQS) method for hyperparameter optimization. NCQS employs a data-driven approach, utilizing a convex quadrature surrogate to determine optimal hyperparameters, validated across various benchmarks and datasets. Our method showcases versatility in tasks like automatic target recognition, pushing the boundaries in resource-efficient deep learning and addressing pivotal challenges like computational memory and latency.
10/3/2023 Shelly Forgey Title: Instant Feedback in the Classroom through Learning Catalytics
: Are you using a Pearson product this semester, or do you plan on teaching with a Pearson text in the near future? Included in their platform is a versatile product called Learning Catalytics, which utilizes something almost every student has all-too-close at hand: their phone, computer, or tablet. Create your own questions that connect seamlessly to your presentation and give you an immediate snapshot of your students’ understanding. With 18 different question types, including pencil-paper style graphing as well as the usual multiple-choice and numeric, keep your students engaged throughout the lecture with easy-to-prepare modules so that you can deliver questions exactly when you need feedback. You can even deliver a question on-the-fly without being derailed by the blank looks and uncomfortable silence we often experience during lectures. 
(Bring laptop, tablet, or other device for participation)
9/26/2023 Isaac Gyasi Title:  Estimation Comparison of the AR (1) Model Using the Box Jenkin Method and Multilayer Perceptron 
  Forecasting Time Series data has been an important subject in many fields today. The traditional models used in forecasting time series have gained popularity over the past decades. In this paper, a 1000 AR (1) samples of size 100 was created and the next value (prediction) for each sample was predicted using the AR (1) model and an artificial neural network (multilayer perceptron). The density plot for the predictions of both models was plotted and their variances was computed. Using the Uniformly Minimum variance unbiased estimator (UMUVE), the AR (1) model predictions had a less variability as compared to the variability of the predictions for the multilayer perceptron. This speaks well of the conditional maximum likelihood estimator for the AR (1) model, making it more likely to make an estimate which will be close to the true parameter. 
9/19/2023 Jeremy Carew Title: Induction of Diversity in Classifier Ensembles
: The issue of predicting the class of an object is common in the machine learning world.  Today, we will briefly discuss the random forest algorithm, one of the most popular algorithms in machine learning.  After, we will discuss a newly proposed method, the "Krypteia" method, and compare/contrast this with the random forest.
9/5/2023 Dr. Damian Kubiak Title: Extreme Diameter 2 Properties in Banach Spaces
Abstract: In this talk we will present extreme version of diameter 2 properties in Banach spaces as well as some related properties.  A Banach space has a diameter 2 property if all members of a class of certain subsets of the unit ball have diameter 2, it has an extreme diameter 2 property if the diameter of 2 is attained.  We will present examples of spaces which possess and do not possess these properties.
8/29/2023 Dr. Amy Chambers Title: Intro to C* - Algebras with Examples

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