Nevada State University Mathematics Colloquium is held monthly on the second or third Tuesday of each month. Typically, colloquium talks are given immediately following our Math Tea. For inquiries, please contact Sungju Moon or Nandita Sahajpal.
Spring 2025
Apr 15: Eva Goedhart (Bryn Mawr/Kimberton Waldorf School)
A Visualization of Happy Numbers
Abstract. After defining happy numbers, we will look at which numbers are happy in various bases and exponents. Then using the graphical structure of a tree, we will explore what placing happy numbers into a tree form can show us about the happy numbers.
Apr 8: Gabriel Elvin (CSU-San Bernardino)
Quantifying Order Within Chaos: An Exploration of Results and Unsolved Problems in Ramsey Theory
Abstract. Ramsey theory is often described as the study of finding order within chaos. In this talk, we will explore two different types of structures: graphs (i.e. networks) and solutions sets, and we will compare and contrast their behavior. In both settings, we can quantify how much of a certain substructure we should see within a larger structure. This presentation will reveal some of the mysteries of Ramsey theory, including unexpected results and unsolved problems.
Mar 11: Ritvik Ramkumar (Cornell)
Steiner’s Conic Problem
Abstract. A conic in $\mathbb{R}^{2}$ is the zero set of a quadratic polynomial in two variables. This includes many familiar examples, such as circles, parabolas, and hyperbolas, as well as some degenerate cases, like the union of two lines. A classical problem in enumerative geometry is Steiner’s conic problem, which asks: How many conics are tangent to five given conics? I will discuss the history of this problem, its solution, and how it is a special instance of more general problems in algebraic geometry.
Fall 2024
Dec 10: Capstone Student Presentations
Rose Reasons: Duals of Multi-edge Cycle Graphs
Abstract. In graph theory, each planar graph has an associated graph, called its dual. We will be examining complexes from DNA self-assembly, namely multi-edge cycle graphs, and discussing their duals.
Jason Rice: Connectivity of DNA Self Assembled Complexes with One-Armed Tiles
Abstract. It is of interest to study the connectedness of tile based DNA nanostructures. Here we will demonstrate the use of adjacency matrices of weighted digraphs representing such structures to show properties of connectivity for varying tile distributions.
Josh Miller (‘25): Minimum Orders of Realized DNA Complexes Given a Specified Pot
Abstract. We explore the minimum order of a DNA complex such that every order greater can be realized by the same pot.
In addition, Andrew will give a 5 minute introduction to the overarching topic of DNA self-assembly so that the speakers don’t have to introduce terminology over and over again.
Oct 15: Jason Rice (NV State)
Lean Chops by Proving Props
Abstract. Lean is a programming language designed specifically for proving mathematical theorems in the most rigorous way imaginable—by explaining it to a computer. No case left behind. Specifically, we will start with modelling basic propositional logic. For example, negation and contradiction have very interesting implementations that may provide a more profound understanding of fundamental concepts. We will also cover more advanced topics such as inductive types, type classes, proof tactics, decidability, and the coup de gras shall be, unironically, the idea of proof irrelevance. Anyone who is familiar with the idea of functions and types in any programming language should be able to follow along.
Oct 8: Sean Breckling (NNSS)
Nevada National Security Sites Undergraduate/MSI Internship Recruitement and Ongoing Research
Sep 17: Dan Graybill (Fort Lewis College)
An Introduction to Classifying All Possible Juggling Patterns with Siteswap
Abstract. Toss juggling currently lives in an interesting place. While it is the subject intense research as a field of recreational mathematics it seems relegated to the circus tent to most mathematicians. This talk aims to present the developments made in the rigorous mathematical analysis of juggling. Through the work of countless amateur and recreational mathematicians this subject has developed into a highly approachable yet rich mathematical topic with far reaching connections. We will explore and juxtapose two ways of classifying all possible juggling patterns. One by establishing isomorphisms to the braid groups, and the other through a notation developed withing the social juggling community known as Siteswap.
Summer 2024
Mathematical Epidemiology Seminar
Click here to view recordings of the summer seminar series.
June 12: Alice Oveson (Maryland), Toward a Novel Behavior - Epidemiology Modeling Framework for Pandemics of Respiratory Pathogens
June 5: Elisha Are (Simon Fraser), COVID-19 Modelling and Analysis with SIR-Type Frameworks
May 29: Idriss Sekkak (Université de Montréal), Stochastic Epidemic Modeling: An Introduction
May 14: Michael Wolfson (uOttawa), Toward a Digital Twin for Canadian Infectious Disease Epidemiology
Spring 2024
Apr 16: Rachel Petrik (Rose-Hulman)
Close Encounters of the $K$-KInd: Navigating the Neighborhoods of KNN Classifiers and Regressors
Abstract. In this talk, we’ll dive into the world of $K$-Nearest Neighbors (KNN), a straightforward yet powerful machine-learning algorithm that relies on the concept of proximity for both classification and regression tasks. ``Close Encounters of the $K$-Kind’’ takes you on a journey to decode the essentials of KNN and understand how `neighborly’ data points contribute to predictions. In addition, we’ll offer strategies to overcome common pitfalls like the curse of dimensionality and differing feature units.
Mar 12: Julie Vega (Maret School)
Braid Group Cryptography
Abstract. Think briefly about braiding hair or a friendship bracelet. While forming your beautiful creation you are changing the position of each string (or piece of hair) in the process. Intuitively, the braid group is a set of elements that comes from recording the position of strings throughout the braiding process. The braid group is a fascinating group and can be found in many contexts including quantum physics, robotics, and on the surface of the sun! This talk will introduce the braid group and investigate some group properties. We will end the talk with a look at how the braid group can be used in cryptography, a field interested in sending and receiving private encrypted messages.
Feb 13: Andrew Lavengood-Ryan (NV State)
Emergence of Linear Diophantine Equations in DNA Self-Assembly
Abstract. In this talk, we’ll explore the fundamentals of DNA self-assembly and see how graph theory can be used to model this biological process. As we explore the structure of the complexes that can be produced from this process, we will see how a number-theoretic structure - in particular, linear diophantine equations - emerge naturally. We will also see how this structure makes predicting the size of the DNA complexes a simple gcd computation.
Fall 2023
Nov 21: Xinyu Zhao (McMaster U.)
Instability of the 2D Euler Equations
Abstract. Hydrodynamic stability is a well-established but still highly active research area in fluid dynamics, with pioneering work by Helmholtz, Kelvin, Rayleigh and Reynolds during the nineteenth century. To develop an understanding of how “small” perturbations grow and modify fluid flows, one usually linearizes the governing equations, and investigates the eigenvalues and eigenvectors of the linearized operator. The flow is considered linearly unstable if the operator possesses an eigenvalue with a positive real part. In this talk, we will present a numerical study of the instability of the 2D Taylor-Green vortex, which is a steady solution of the 2D Euler equations. This is based on a joint work with Bartosz Protas and Roman Shvydkoy.
Nov 14: Taylor McAdam (Pomona College)
Chaos on the Circle
Abstract. Rotate a circle by a fixed angle, then repeat again and again. Where will a single point travel? Will it come back to where it started and how does the answer depend on the rotation angle? Despite their simplicity, rotations and other transformations of the circle teach us a lot about many processes like planets orbiting a sun, coffee stirred in a cup, and about the very nature of numbers themselves. In this talk, I will discuss a variety of ways that mathematicians think about how “complicated" or chaotic such a process becomes. Along the way we find surprising connections to other areas of math such as (ir)rationality of real numbers and binary sequences.
Oct 10: Emily A. Robinson (Cal Poly San Obispo)
Human Perception of Statistical Charts: An Introduction to Graphical Testing Methods
Abstract. In a world full of data, we all consume graphics on a regular basis in order to inform our decisions and aid in making discoveries about the information presented. With the continuous relevance of graphics, it is important for statisticians in any specialty area to understand what makes a chart good or bad. Through testing, we can better inform and establish fundamental principles for creating and displaying graphics. In this presentation, I will first motivate the talk with a brief history of graphics and established data visualization studies. I will then introduce recent methods used for testing graphics and share my work on establishing guidelines for the use of logarithmic scales.
Click here to view recordings of the past colloqium talks.