The Colloquium

The BU Society of Mathematics Colloquium is a venue for students studying (and interested in) mathematics to give talks on topics of their choice to a general math audience. We will have colloquia bi-weekly on Tuesdays at 6:30. There will be a 15-minute tea (and snacks) before the talks begin. We ask that talks will be in the range of 30-60 minutes, but this is by no means strict (of course don't go too far over/under). Speakers will be asked to provide notes for their talk typeset in LaTeX to be included in a proceedings-style publication at the end of the semester.

We ask that topics of talks be accessible to, say, a student who has taken the calculus sequence and seen some linear algebra. However, this is not a strict requirement and will consider colloquium talk proposals on a case-by-case basis. If you're interested in presenting, please contact Zach in our discord or email him at zzobair@bu.edu.

Upcoming Talks

Recent Talks

An Invitation to Algebraic Geometry

Skyler Marks

In high school algebra 1 and 2, we study the theory of single variable polynomial equations. In linear algebra, we study systems of linear equations, or polynomial equations with no exponents greater than 1. Algebraic Geometry combines these disciplines to study polynomial equations (in particular, their solutions) in many variables. This theory is useful as it is specific enough that we can compute with it, yet general enough that it applies to many problems we care about. The promised invitation will be extended by way of plane conics and cubics. After some definitions and preliminaries, we will review a family of classical results regarding plane conics (quadratic polynomials in two variables.

We will begin by classifying conics into families who’s members are “alike”. We will then leverage this classification to study the intersections of two conics. Our conclusion to this first act will be a detailed discussion of the number of conics passing through n points in the plane.
A follow up talk may consist of an attempt to generalize this theory to the case of plane cubics; polynomials of degree three in two variables. Through this endeavor we will introduce results from classical algebraic geometry; these may (if time permits) include Bézout’s theorem, intersection theory, and blowups; of course, for these developments, we must introduce projective geometry and some more advanced language. Finally, our third act will discuss in vague terms the position of stacks and moduli spaces in the picture, together with the categorical and algebraic foundation they necessitate.

Root Systems and Lie Groups

Zoe Siegelnickel


A root system is a collection of vectors definied over a Euclidian vector space with certain geometric properties. Some of the isometries generated by these roots form a group called a Weyl group. These groups are used extensively to study various symmetries. We will do a brief introduction to Euclidean space, isometries, and root systems before discussing Weyl groups and Weyl chambers and how they appear in Lie Theory.

Elliptic Curve Cryptography

Skyler Marks

The digital world is kept secure by cryptography. The idea behind most modern cryptographic systems is that if I have a public number (some sort of seed) and a secret number (usually called a private key) I can perform some operation with them to generate a third number (which usually called a public key). The public key is easy to generate by combining a seed and a private key, but hard to generate any other way; this allows us to verify the authenticity of a private key very easily. One such operation involves finding collinear points on an elliptic curve, giving rise to elliptic curve cryptography. This talk introduced elliptic curves over finite fields, explained how we can use their geometry to define an appropriate operation, and touched on why this operation is appropriate for cryptography. Slides for the talk can be found here.