Kiddie Colloquium

The history of cryptography is filled with brilliant mathematical insights and technological breakthroughs, but it is also a history ██████████████████████████████████████████████████. I will give an account of two ████████ incidents from the past quarter-century in which powerful organizations…

You are probably familiar with the classification of simple Lie groups. Some of them are special linear, some are orthogonal, and some are symplectic. Some of them are over R, and some are over C. Slightly less known is the fact that the weirder real forms can all be represented over H. You…

We will ponder the following question: Suppose we have a finite group of order between n and 2n. How large of an abelian subgroup must it have? This question will lead us to some strange proofs and wild constructions, and to another fairly natural group theory problem…

A universal cover in ℝⁿ is a convex set that can cover every set of diameter 1. Lebesgue asked in 1914 what the minimum area of a universal cover in ℝ² is. I shall present my study of the minimum volume V of a universal cover in ℝ³, showing that 0.545 < V < 0.656, improving a previous…

In this talk I’ll present one of the most fundamental results in Random Matrix Theory: the convergence in distribution of the empirical law of the eigenvalues of a Wigner matrix to the semicircle distribution. This is a classical result dating to the founding of the subject. The proof is…

In this interactive talk you will be introduced to pencil puzzles, which are types of logic puzzles that can be described and solved on paper. (The most famous examples being sudoku and slitherlink.) We will explore multiple different genres of puzzles, introduce some key logical ideas…

Classification theorems in mathematics always have the form: "Any X belongs either to one of n infinite series of classical objects, or is one of the m exceptions". For example:

- A regular polyhedron in R^n is either a regular simplex, cube, or cocube, or it is an isocahedron, a…

In a quassical quaotic system, the space average and the time average of a function are equal. What about the quantum quase? In this talk, we’ll introduce the notion of quantum ergodicity, describe what it means, prove some things about it, and discuss applications.

Karma is a never ending cycle, unless there's a singularity. We will introduce Grothendieck's nearby and vanishing cycle functors, which detect singularities of algebraic varieties.