Student Seminars will be held on Thursdays in Bailey 207 (unless otherwise noted) 12:50pm, during common hour throughout fall term. We will have a pizza lunch at 12:30pm in Bailey 204.
See you in the Fall '25 Semester!
Previous Seminars Spring '25:
May 22nd 2025- Union College Professor of Mathematics, Brenda Johnson Presents:
Title: Fixed Points and Fermat
Abstract: If you pick an integer a and a prime number p, the difference a^p-a will be divisible by p. This fact is known as Fermat's Little Theorem and is a standard result in number theory courses. There are many ways to prove this theorem, often involving ideas from number theory and abstract algebra. A less standard approach uses functions one might see in a first-year calculus course together with basic results from the field of dynamical systems. In this talk, we will see how to prove Fermat's Little Theorem and some related results in number theory from this dynamical systems perspective.
May 15th- Special Guest Speaker: Professor Moon Duchin (Cornell University, Math)
Thursday, May 1st- Professor Matthew Lamoureux, University of Connecticut's College of Engineering's School of Computing
Presents: A Gentle Introduction to Text Mining
Abstract: Many of the tools we use to analyze information rely on structure, so we often see data provided neatly in rows and columns (think Excel spreadsheets). That said, lots of data is unstructured yet still valuable; specifically, there is no shortage of written text in our world—books in our libraries, message boards on Reddit, customer feedback on products. This presentation will provide a quick overview of common techniques used in processing unstructured text data.
Thursday, April 24th- Assistant Professor of Mathematics, Junqing Qian presents: An Introduction to complex numbers and conformal maps
Abstract: Conformal mappings - angle-preserving mappings - have many real-life applications. To name a few, it has applications in Cartography (map-making), Aerodynamics, Electrostatics & Fluid Dynamics, Medical Imaging, etc. In today's talk, we will start from the basics of complex numbers to complex differentiation. Then we will present how being differentiable in the complex sense is equivalent to being an angle-preserving mapping. A concrete example of the conformal map cos(z) will be presented at the end.
Thursday, April 10th-Union College Assistant Professor of Mathematics, Phanuel Mariano presents: The isoperimetric inequality and its connection to probability
Abstract: The isoperimetric inequality is a geometric result relating the square of the circumference of a closed plane curve to the area it encloses, along with various generalizations of this relationship. There is a connection between inequalities that come up in probability and the classical isoperimetric inequality. The connection is through Brownian motion, which is a mathematical model for the random movement of a particle. It was first observed by Robert Brown in 1827 while looking at pollen grains through a microscope. I will discuss some classical isoperimetric problems related to the expected lifetime of Brownian motion from a domain.
Student Seminars for Winter '25:
Thursday, March 6th-Union College Math Professor Leila Khatami presents: A Game of Commuting Matrices
Abstract: One of the first things we learn about matrix multiplication is that it is not commutative; that is, if A and B are two square matrices of the same size, in general AB is not equal to BA. However, some pairs of matrices do commute. For example, if one of the matrices is the identity or zero matrix, or if A and B are the same, then AB = BA. This leads to a natural question: which pairs of matrices commute? More specifically, given a matrix, can we characterize matrices that commute with it? In this talk, we explore this question through the lens of a mathematical game, which can help us understand some key tools used in studying this problem.
Thursday, February 13th-Union College Emeritus Professor, Julius Barbanel Ph.D. Presents: The Euclidean Algorithm and Irrational Numbers
Abstract: The Euclidean Algorithm is a procedure for determining the greatest common divisor of two positive integers. Irrational numbers are real numbers that cannot be expressed as the ratio of two integers. These two ideas certainly do not seem to be related, but we shall explore a rather surprising historical connection between them. This exploration will include a quick tour of ancient Greek mathematics.
Thursday, February 6th- It is Movie Time! Union College Mathematics Department Presents: The Proof
The Proof: This documentary produced by Nova uses the search for a proof of Fermat's famous theorem to
provide a better understanding of the quest for knowledge. It is this quest that apparently motivates
mathematicians to attempt to solve what many feel is the unsolvable. For those of you unfamiliar with Fermat's Last Theorem, it states that for all natural numbers n greater than 2, 𝑥^𝑛 + 𝑦^𝑛 = 𝑧^𝑛 has no solutions for natural numbers x, y, and z. Over 300 years ago, Fermat stated that he had a proof of this result, but the margin of the paper was too small to include it. Because this problem had an obvious link with the Pythagorean Theorem (and because Fermat stated that he had a proof) mathematicians felt the argument would be found immediately. But for centuries people struggled to uncover the proof, and it was not until the mid 1990s that Andrew Wiles of Princeton University finally succeeded. For further information on the documentary, see https://www.pbs.org/wgbh/nova/proof/