Graduate Student Seminars

COSAM Departments Mathematics & Statistics Research Seminars Graduate Student Seminar

Upcoming Graduate Student Seminar Seminars

Past Graduate Student Seminar Seminars

DMS Graduate Student Seminar
Apr 17, 2024 03:00 PM
161 ACLC

jessica

Speaker: Dr. Jessica McDonald

Title: What is Discrete Mathematics (Combinatorics)?

Abstract: This talk aims to give an idea of what research in discrete mathematics (combinatorics) is all about. I will attempt to define the field and its many sub-fields, and we will discuss some example problems. I will also talk about our discrete group at Auburn – what the research interests of the faculty in our group are, and what graduate courses we offer.

DMS Graduate Student Seminar
Apr 03, 2024 03:00 PM
161 ACLC

Speaker: Profesor Hal Schenck (Auburn)

Title: Combinatorics and Commutative Algebra

Abstract: This talk will give an overview of the spectacular success of algebraic methods in studying problems in discrete geometry and combinatorics. First, we'll discuss the face vector (number of vertices, edges, etc.) of a convex polytope and recall Euler's famous formula for polytopes of dimension 3. Then, we'll discuss graded rings, focusing on polynomial rings and quotients. Associated with a simplicial polytope P (every face is "like" a triangle) is a graded ring called the Stanley-Reisner ring, which "remembers" everything about P and gives a beautiful algebra/combinatorics dictionary. I will sketch Stanley's solution to a famous conjecture using this machinery and touch on connections between P and objects from algebraic geometry (toric varieties). No prior knowledge of the terms above will be assumed or needed for the talk.

DMS Graduate Student Seminar
Feb 28, 2024 03:00 PM
161ACLC

Speaker: Professor Nedret Billor

Title: A Journey from Program Overview to Capstone Projects and Beyond

Abstract: In this seminar, we'll explore our statistics and data science programs, from foundational learning to capstone applications, and their role in advancing Ph.D. research. We will also discuss the diverse research areas within our statistics and data science programs. Further, we will delve into the advantages that a background in data science brings to traditional statistics and mathematics education, particularly through the lens of a PhD student who has been navigating both fields simultaneously.

DMS Graduate Student Seminar
Jan 24, 2024 03:00 PM
161 ACLC

Speaker: Professor Junshan Lin

Title: Overview of Computational Mathematics: Algorithms, Theory, and Applications

This semester, we will only have four talks at the designated time.

DMS Graduate Student Seminar
Nov 29, 2023 03:00 PM
108 ACLC

Speaker: Rui Shi, Auburn University

Title: Outlier Detection with Cluster Catch Digraphs (CCDs)

Abstract: Outlier detection is one of the most popular research topics and also a challenging task. Many outlier detection approaches based on different techniques have been developed. We propose approaches that are based on Cluster Catch Digraphs (CCDs).

CCDs are a family of clustering algorithms. The CCD algorithms are graph-based, density-based, and distribution-based approaches. They construct a certain number of hyperspheres to capture latent cluster structures. There are two main versions of CCDs: KS-CCDs and RK-CCDs. The latter ones are especially appealing as they do not require parameter input.

We develop two outlier detection algorithms that first utilize RK-CCDs to build hyperspheres for each cluster structure. Then, by constructing a Mutual Catch Graph (MCG) from the KS-CCD, outliers can be identified among those points that are not in any of the hyperspheres. We called these two approaches the Mutual catch graph with Cluster Catch Digraph (M-CCD) algorithm and the Fast Mutual catch graph with Cluster Catch Digraph (Fast M-CCD) algorithm. However, due to some shortcomings of RK-CCDs, they perform poorly with high dimensionality. To resolve this issue, we propose a new version of CCDs with the Nearest Neighbor Distance (NND) and refer to it as NN-CCD. Subsequently, we proposed another outlier detection algorithm based on NN-CCDs, which has much better performance with high dimensionality; we call this approach the Mutual catch graph with Nearest Neighbor Cluster Catch Digraph (M-NNCCD) algorithm. We also propose ways to adapt the above algorithm to the cases when the shapes of clusters are arbitrary; we call those approaches the Mutual catch graph with Flexible Cluster Catch Digraph (M-FCCD) algorithm and the Mutual catch graph with Flexible Nearest Neighbor Cluster Catch Digraph (M-FNNCCD) algorithm. Additionally, we offer an approach to calculate the outlying-ness scores for all the CCD-based algorithms.

Keywords: Outlier detection, Graph-based clustering, Cluster catch digraphs, \(k\)-nearest neighborhood, Mutual catch graphs, Nearest neighbor distance, Outlying-ness score.

DMS Graduate Student Seminar
Nov 15, 2023 03:00 PM
108 ACLC

Speaker: Pete Johnson, Auburn University

Title: Meme Theory in Mathematics: Early Days

Abstract: The term “meme,” meaning any idea, notion, or system thereof, that can exist in the human mind and be communicated, was first mentioned in print (so far as I know) by Richard Dawkins, in one of the later chapters of The Selfish Gene. He credits a colleague for the idea. Dawkins is a Darwinian theorist; he was fascinated by his colleague’s idea because it dawned on him that memes can evolve and mutate and be acted upon by natural selection just as living organisms can. It has long seemed to me that mathematics is a great area in which to study meme evolution, due to the relative simplicity and recognizability of the relations among mathematical memes; mathematics might be to meme theory as our solar system has been to physics. I’ll give a few examples of what you might look for, and of what you might ask.

DMS Graduate Student Seminar
Nov 08, 2023 03:00 PM
108 ACLC

Speaker: Narendra Govil, Auburn University

Title: Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials

Abstract: The Inequalities of Markov and Bernstein Type are fundamental in Approximation Theory, because of their use in proofs of Inverse Theorems in Approximation Theory. Quite often, further progress in Inverse Theorems has depended on first obtaining a corresponding generalization or analogue of Markov’s and Bernstein’s inequalities.

In this talk we plan to make a brief introduction and development of this subject. The talk will also include some new results and open problems in this direction.

DMS Graduate Student Seminar
Nov 01, 2023 03:00 PM
108 ACLC

Speaker: Le Chen, Auburn University

Title: Disorderly Surface Growth

Abstract: In this talk, we will introduce the surface growth phenomenon in a disordered system. Examples include the wetting, burning, and rupture of paper, the accumulations of snowflakes, as well as the growths of crystal and tumor. Despite the apparent diversity in these processes, their surface fluctuations exhibit some universal characteristics. Stochastic partial differential equations (SPDEs), in particular, the Kardar-Parisi-Zhang (KPZ) equation, are the main mathematical tool to capture these universal features, which then provide the universality classes that go beyond the central limit theorem. The significance of this field of research is underscored by the prestigious accolades awarded to its pioneers, including Giorgio Parisi (the Nobel Prize in Physics in 2021) and Martin Hairer (the Fields Medal in 2014), among many others. This talk aims to serve as both an overview of SPDEs in the context of disordered surface growth and as a source of inspiration for students considering a Ph.D. in this exciting field. The main reference of this talk is the book by two physicists Barabási and Stanley, Fractal Concepts in Surface Growth, Cambridge University Press, 1995.

DMS Graduate Student Seminar
Oct 25, 2023 03:00 PM
108 ACLC

Speaker: Joanie Morris, Auburn University,

Title: Benefits of Interdisciplinary Mathematics – Graphs & Ideals

Abstract: When choosing research projects, students can often get siloed into one research group. However, many interesting problems can arise at the intersection of several mathematical areas and looking at a mathematical object from different research perspectives can provide useful tools and insights. In this talk, I'll briefly discuss my experience working in between Graph Theory and Combinatorial Commutative Algebra. I'll discuss some of the connections between these fields and some results produced by exploring those connections.

DMS Graduate Student Seminar
Oct 18, 2023 03:00 PM
108 ACLC

Speaker: Hewan Shemtaga, Auburn University

Title: Chemotaxsis Model on Compact Graph

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