Simon's Rock/BHSEC Math Seminar

Together with the Bard High School Early Colleges across the country, the Simon's Rock Math faculty host a monthly seminar live at Simon's Rock, livestreamed and made available across the Bard Network (see https://bhsec.bard.edu/ for more information on the BHSEC network). This seminar is intended to give opportunities for a diverse range of undergraduate and high school students to see and hear about the work of Mathematicians beyond their classrooms, and inspire a new view of Mathematics as a vibrant, interesting and dynamic field of study. We are also committed to giving a platform to early career BIPOC and Latinx Mathematicians to give talks about their work to a large audience, and help build an inclusive and diverse Mathematical community with these young scholars.

Unless otherwise noted, the seminar will occur at 4PM (Eastern) in the Lecture Center at Simon's Rock.

BHSEC students should consult with their teachers for locations.

To watch video recordings of past talks, you can access the seminar's YouTube playlist at: https://www.youtube.com/playlist?list=PLLKRp11HSZyOHGsAX8lRqLT5Xgitt8d8k.

Spring 2022 Schedule

Previous Semesters

Abstracts

Spring 2022

Emma Hasson and Yolanda Zhu (February 11): Much work has been done on Latin squares finite case, including the study of uniquely completable and critical subsets. A partial Latin Square is said to be uniquely completable if it only has one possible completion. A critical subset is a uniquely completable partial Latin Square with the property that if any one entry is removed, the partial Latin square is no longer uniquely completable. In this talk, we will introduce two main examples of infinite Latin squares -- the integer square L_ℤ and the set of Fractal squares -- and the unique implications of their infinite structure. Our discussion will focus on critical sets which we have found on these squares and their properties, such as density and diversity. We will also discuss our further attempts to construct critical sets on these squares.

Chassidy Bozeman (March 31): Zero forcing on a simple graph is an iterative coloring procedure that starts by initially coloring vertices white and blue and then repeatedly applies the following color change rule: if any vertex colored blue has exactly one white neighbor, then that neighbor is changed from white to blue. Any initial set of blue vertices that can color the entire graph blue is called a zero forcing set. The zero forcing number is the cardinality of a minimum zero forcing set. A well-known result is that the zero forcing number of a simple graph is an upper bound for the maximum nullity of the graph (the largest possible nullity over all symmetric real matrices whose ij^th entry (for i ≠ j) is nonzero whenever {i,j} is an edge in G and is zero otherwise).

A variant of zero forcing, known as power domination (motivated by the monitoring of the electric power grid system), uses the power color change rule that starts by initially coloring vertices white and blue and then applies the following rules:

1) In step 1, for any white vertex w that has a blue neighbor, change the color of w from white to blue.

2) For the remaining steps, apply the color change rule.

Any initial set of blue vertices that can color the entire graph blue using the power color change rule is called a power dominating set.

We present results on the power domination problem of a graph by considering the power dominating sets of minimum cardinality and the amount of steps necessary to color the entire graph blue.

Angela Robinson (April 14): Modern cryptography is used to secure the global digital communication infrastructure of today. The security of all widely-deployed public key cryptographic (PKC) systems are based on the difficulty in solving variations of the integer factorization and discrete logarithm problems. In this talk, we will look at the revolutionary cryptosystems that emerged in the 1970's based on these two number theoretic problems: RSA Encryption and Diffie-Hellman Key Exchange. We will look at the historical significance of these schemes, some cryptanalytic attacks against them, and where these algorithms are found today.

Joy Wang (May 5): The 2021 Nobel Prize in Physics was awarded with one half jointly to two scientists "for the physical modelling of Earth's climate, quantifying variability and reliably predicting global warming". Their work laid the foundation for the development of current climate models and our knowledge of humanity's influence on the climate. In this talk, we will visualize climate change, risks and impact. Through building a radiation balance climate model, we will understand how increased levels of carbon dioxide in the atmosphere can lead to increased temperatures at Earth's surface. We will examine the complexity of climate models, dynamics of the climate system, climate projections, and climate justice.

This seminar is supported by the National Science Foundation through grant award DMS-2137608.