Mina Rees 

Schedule (ET):

10:00 am - 10:15 am: Welcome

10:15 am - 11:15 am: Keynote Speaker:  Moira Chas (Stony Brook University)

Title: What do you mean by a Möbius strip? And by a Klein bottle? Where do these surfaces exist?

Abstract: Certain mathematical objects have achieved Internet fame, among them the Möbius strip, the Klein bottle, and the fourth dimension.

In this age of short attention spans, brief descriptions are repeated everywhere, but their frequency is often inversely proportional to their accuracy. For instance, we may read that the Klein bottle has no inside or outside and can only exist in the fourth dimension—wrong on both counts. In this talk, I will explain what mathematicians actually mean by a Möbius strip and a Klein bottle, how these objects were discovered, and highlight some of their lesser-known representations. 

11:30 - 12:30:  Contributed talks

12:30 - 1:30: Lunch (on your own)

1:30 - 3:30: Contributed Talks
Please showcase your research for a general audience of mathematicians.

3:30 pm - 5:00 pm: Wine and Cheese Social 

Speakers, Titles, Abstracts

 Speaker: Nkechi Agwu (BMCC, CUNY)
Title:  Mathematical Storytelling Based on the Carnegie African Diaspora Project 
Abstract:  The Ethnomathematics Research Group (ERG) of the National Mathematical Centre (NMC), Abuja and Prof. Nkechi Agwu, BMCC, CUNY, and Carnegie African Diaspora Fellow (CADF), are partnering on a joint project to develop curriculum on the use of Culture, History and Women's Stories in the teaching and learning of mathematics. This presentation will share with the audience some of curriculum developed from a Mathematical storytelling perspective that is currently being used to teach Discrete Mathematics, Mathematical Reasoning and Quantitative Literacy courses at BMCC, CUNY. This work has resulted in several presentations, publications, honors and awards, including memorialization of Prof. Agwu as a notable woman of Mathematics in Serie 1 of the Even Quads Playing cards of the Association of Women in Mathematics and a book series by the NMC on Ethnomathematics based on selected Nigerian Cultures.

Speaker: Erin Carmody (SUNY Delhi)
Title: Killing Primes
Abstract: What makes primes so special and intriguing? Prime numbers have two major features: they are creative and they are unique. Primes are unique because a prime number p > 1 has only two positive integer factors, namely 1 and p. Primes are also very creative. The fundamental theorem of arithmetic says that every positive integer can be written as a product of primes. Thus, the creativity of the primes gives us of all the rest of the natural numbers. In M, we see what happens when we pause or mute the creative ability of a prime number.

Speaker: Caroline Davis (Stony Brook University)
Title: Combinatorics and Degenerations of Special Curves
Abstract:  We’ll give a brief overview (with plenty of pictures!) about moduli spaces of rational maps over C. The moduli space of all degree d maps is 2d-2 complex dimensional and studying lower dimensional subspaces (known as Critical Orbit Relation varieties) provides a technique of studying the full moduli space. The 1 dimensional setting is accessible not just by arithmetic tools but also classic analytic and topological tools from complex dynamics. The simplest example of a COR curve is the moduli space of quadratic polynomials, popularized by the Mandelbrot set, and other COR curves generalize this already rich theory in interesting new ways. Natural questions include: given COR curve, what is its global topology? Is it connected? Does it have genus? What are boundary elements and how many such punctures are there? What Mandelbrot-like structure exists in it? In this talk, we’ll give an intuitive account of these topics.

Name: Aihua Li (Montclair State University)
Title: Design of Strips with Geometry Shapes and Mathematical Analysis
Abstract:  In this research, we investigate different methods to create geometric designs for textile strips and to explore the geometric properties of the involved shapes. Three designs that contain circles, squares, and golden spiral pieces with repeating patterns and certain tangencies are developed. We provide relationships between geometry and the considered textile designs and examine the mathematics used to characterize the geometrical shapes. These are good examples demonstrating how mathematics can be visualized in textile design and how it can help student learners to experience real world applications and connections between mathematics and arts.

Speaker: Lucy Koch-Hyde (CUNY Graduate Center)
Title:  Counting subgroups of free groups using graphs
Abstract: I will give an introduction to free groups and show how to count certain kinds of subgroups of free groups using a straightforward argument about graphs.

Speaker: Sarita Nemani (Georgian Court University)
Title: Stability of Polynomials under Uniform Perturbation
Abstract: A conjecture on robustness of stable transfer polynomials has been solved in negative. In this work, we formulate a characterization of stable transfer polynomials, which will be used to identify a class of polynomials satisfying the conjecture. Further results will be derived as variations of the conjecture.

Speaker: Siobhan O'Connor (CUNY Graduate Center)
Title: Fun with Free Group Automorphisms
Abstract:  I'll provide a simple introduction to the action of free group automorphisms on elements of the free group on two generators through exploring a puzzle game about patterns of colored beads. A freely reduced word in a free group is called positive if it does not contain inverse generators. We say a word is potentially positive if there is an automorphism of the free group which sends it to a positive word. I’ll discuss some of my and my collaborators' recent research results, such as a quadratic time algorithm for deciding whether a word in F2 is potentially positive, the exact growth rate of potentially positive words of length n in F2, and new lower bounds for the growth rates of potentially positive words in higher ranks of free group. I’ll also explain some implications of potential positivity in the study of one-relator groups, and some other puzzles you can do with free group automorphisms.

Speaker: Lauren Rose (Bard College)
Title:  Quads: A SET-like game with a twist,
Abstract:  Quads is a SET-like card game published by the AWM under the name EvenQuads. The goal is to find quads, which are sets of four cards that satisfy a simple pattern. Each card can be viewed as a binary vector, leading naturally to interpretations in finite geometry, coding theory, and cryptography. A central question is to find large collections of cards that do not contain a quad, analogous to the celebrated Cap Set problem for SET. We will describe known results for Quads and explore the related question: How many cards must be laid out to guarantee that a quad appears?

Speaker: Chenlu Yu (Bard College)
Title: Eye-Dentification: A Deep Learning-Based Ocular Disease Classification Tool
Abstract:  Ocular diseases are the leading cause of blindness globally, yet diagnosis often depends on access to ophthalmologists and specialized equipment. Machine learning offers a promising approach to automating detection of retinal images. Our tool classifies medical fundus screenings. Our goals were to compare the performance of multiple CNN architectures (EfficientNet, ResNet, DenseNet). We deploy the trained models in an interactive web app, allowing real-time uploads and classification(educational usage only).

Organizing Committee: Siobhan O'Connor (Chair), Sandra Kingan, Tamara Kucherenko, Azita Mayeli, Giovanna Ricevuto, John Terilla. 

Sponsored by the Graduate Center's Mathematics Department
and the GC AWM Student Chapter.