Mathematics Graduate Seminar - Spring 2023

The seminar is scheduled from 2:00 pm - 2:45 pm on Tuesday afternoon in Bruner Hall 308. 

DATE	SPEAKER	TITLE/Abstract
4/18/2023	Dr. Christopher Davis	Title: A partition of unity method for a plate frictional contact problem  Abstract: In this work, we consider the use of a flat-top partition of unity method to solve a plate frictional contact problem.  Under the assumption that the solution is smooth enough, optimal error estimates are made in the energy norm.  Numerical examples are given to demonstrate the effectiveness of the proposed method.
4/12/2023	Benjamin Vannozzi	Title: The Tangent Space and 3 Ways to Define a Tangent Vector Abstract: Moving from ordinary analysis on R^n to Analysis on n-dimensional manifolds, we seek a generalization of the classical tangent to a curve in the plane or a surface in space at a point. This generalization is known as the Tangent Space to the manifold at a point. A vector space, the Tangent Space's elements are called tangent vectors, and these concepts have three distinct (but equivalent) definitions. We show in what sense these separate definitions are equivalent, and then we use this newly-defined Tangent Space to define the Differential of a map between manifolds at a point to be a linear map between a tangent space of each manifold.
4/11/2023	Nengenen Shadrach Mbativga	Title: Interpolation and L2 Projection in 1D Abstract: The brief content of this presentation forms a firm foundation and introduces us to the Finite Element Methods (FEM) for solving Partial Differential Equations(PDEs). We shall review the concepts of Linear Interpolation and L2 Projection and then apply them as useful techniques for approximating functions. The scope of this talk only covers Piecewise Polynomial Approximation in 1D that can be used to approximate other more general functions. We will compare the two techniques to see which is better. Finally, we will employ the use of computer software for the implementation of these ideas.
4/4/2023	Jeremy Carew	Title: Building a Random Forest Abstract: In this discussion, we'll talk about the machine learning task of classifying, decision trees, ensemble methods, and putting all of it together to get a popular learning algorithm: the random forest.
3/28/2023	Isaac Gyasi	Title: Application of Survival Model to Analyse Default Rates of Personal Bank Loans.  Abstract: The high levels of non-performing loans over the past few years reduced the profitability of the banking industry, which have caused bank failures that have adversely affected economic development. The study identifies the predictors for the risk of default of personal bank loans using data from a local bank . A sample of 196 personal loan borrowers was examined. The number of dependents, educational level, type of employer, gender, age, and marital status were noted. The Cox Proportional Hazard model was fitted using the sample data. Educational level, gender, age, and marital status were found to be non-significant predictors of default. However, the number of dependents and employer type were significant predictors of hazard. It was observed that hazard increased by 21.025% for an additional dependent a borrower takes on. The risk of default is 84.118% higher for a borrower whose employer is not government as compared to a government employee.
3/21/2023	David Rowinn	Title: Probabilistic Techniques In Zero Knowledge Proof Systems Abstract: In this presentation, we will explore a notion of zero-knowledge in verifying results through randomized algorithms and interactive proof systems. We will then build upon this notion to introduce probabilistic techniques in the proof systems. We will examine the mechanism to verify that a statement is true without yielding any additional knowledge about the statement itself and demonstrate it in the example of whether two graphs are isomorphic or not.
3/7/2023	Patrick Bartol	Title: Feynman-Kac and Black-Scholes Formulas Abstract: This seminar was inspired by Dr. Pechmann's talk back in January, which introduced the Feynman-Kac Formula and its applications in finance. In this presentation, we will discuss the concept of infinitesimal generators and their connection to stochastic differential equations, allowing us to describe the Feynman-Kac formula.  Then we will discuss option pricing in the stock market, and how they are associated with partial differential equations. Finally, we construct the Black-Scholes formula by way of Feynman-Kac.
2/28/2023	Dr. Kehelwala Dewage Gayan Maduranga	Title: Symmetry Structured Convolutional Neural Networks Abstract: We consider Convolutional Neural Networks (CNNs) with 2D structured features that are symmetric in the spatial dimensions. Such networks arise in modeling pairwise relationships for a sequential recommendation problem, as well as secondary structure inference  problems of RNA and protein sequences. We develop a CNN architecture that generates and preserves the symmetry structure in the network’s convolutional layers. We present parameterizations for the convolutional kernels that produce update rules to maintain symmetry throughout the training. We apply this architecture to the sequential recommendation problem, the RNA secondary structure inference problem, and the protein contact map prediction problem, showing that the symmetric  structured networks produce improved results using fewer numbers of machine parameters.
2/21/2023	Alizza Schremp	Title: The Matrix Tree Theorem Abstract: In graph theory, Kirchhoff's matrix tree theorem gives a way to calculate the total number of spanning trees of a graph. In this talk we will discuss two different proofs of the matrix tree theorem.
2/14/2023	Angus Bryant	Title:  How to Share a Secret Abstract: Secret-sharing is an area of mathematics focused on efficiently distributing ‘shares’ to participants who can construct an unknown secret by pooling their shares together. The challenge is to arrange these shares in such a way that only certain groups of participants can construct the secret, and no information can be gained from other groups of participants combining their shares. Many methods are used to create these so-called ‘schemes’, but the most popular way is to use matrices and matroids and to leverage their properties to create optimal schemes.
2/7/2023	Dr. Damian Kubiak	Title: On Some Geometric Properties in Banach Spaces Abstract: In this talk we will present some new properties of Banach spaces related to the geometry of the unit ball.