Kiddie Colloquium

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.

Let P = A_0 A_1 ... A_n be a convex polygon on the plane. Define for all 1 <= k <= n-1 the operation f_k which replaces P with a new polygon f_k(P) = A_0 ... A_{k-1} A_k' A_{k+1} ... A_n where A_k' is the reflection of A_k across the perpendicular bisector of A_{k-1}A_{k+1}. Prove that (…

Similarities between Galois theory and the theory of covering spaces are so striking that algebraists use geometric language to talk of field extensions whereas topologists talk of Galois covers. I will explain A. Grothendieck's formulation of abstract Galois theory, which builds a bridge…

A Cayley graph G is a highly symmetric graph whose vertex set is a finite group Gamma. A rather surprising theorem, due to Payan, shows that, if Gamma is (Z/2Z)^n, then G cannot have chromatic number exactly 3. (In other words, if G is 3-colorable then G is also 2-colorable.) I'll show you…

Ergodic theory has applications to many different fields of mathematics, and it tends to look very different in each of these places. One of these fields is additive combinatorics. With an aim to demonstrate what ergodic theory looks like in this setting, I will present an ergodic-theoretic…