Past Events

A plane tree is a rooted tree where each node's children have a left-to-right order. Classically, the number of plane trees with n+1 vertices is equal to the nth Catalan

We study adversarially robust algorithms for insertion-deletion (turnstile) streams, where future updates may depend on past algorithm outputs. While robust algorithms exist for insertion-only streams with only a polylogarithmic overhead

Randomly packed Z-pentominoes on the square lattice are known numerically to undergo a disorder-order phase transition as the packing fraction increases; see the attached images by Barnes (2010). I will

The standard approach to studying the liquid-vapor phase transition uses the Maxwell double-tangent construction. Whereas this construction is easily justified physically, deriving it mathematically has proved to be more difficult.

We use SAT solvers to improve bounds of the celebrated Hales-Jewett Numbers, one of the most important numbers in Ramsey Theory.

Abstract: Is maze-solving parallelizable? Can you find a short path, without a map? These two algorithmic questions can be rigorously formalized (via competitive analysis) and analyzed (using convex regularization). In

You're driving on a two lane road, approaching a stoplight. Shortly after the light, the left lane merges into the right lane. Do you stay in the right lane for

Hadwiger's conjecture, first formulated in 1943, is a vast generalization of the four-color theorem, and remains one of the central open problems in graph theory. An even stronger statement, known

How should one design unprecedented democratic processes capable of handling enormous sets of alternatives like all possible policies, bills, or statements? I argue that this challenge can be addressed through

How many coin tosses would it take until reaching for the first time either n Heads or m Tails?. Although this setup is related to the classical Problem of points,

I will present an n^2 time algorithm for single-source shortest paths with negative real weights, building on the breakthrough work of Fineman (STOC 2024). The talk will be entirely self-contained,

A lot can be said about Tangles in graphs. Some will say that "Tangles describe highly connected regions in a graph" and others say "Tangles of graphs are ways of

We describe two unexpected applications of game theory to recreational mathematics. The first, which is joint work with Scrabble expert Nick Ballard, is a Scrabble position in which the best

Suppose that a continuous-time, stochastic diffusion (i.e., the Susceptible-Infected process) spreads on an unknown graph. We only observe the time at which the diffusion reaches each vertex, i.e., the set

Understanding the random graph threshold for "containing H as a subgraph" is not hard when H is a fixed graph. In contrast, when H is a spanning subgraph, the question

The classical EKR theorem states that the largest intersecting family of k-uniform subsets of an n-element set consists of all k-sets through a fixed element. More generally, it is known

In this talk we study a counting problem that originated on Mathematics Stack Exchange: How many ways can a rectangular grid be partitioned into a prescribed number of connected polyominoes

Consider n independent, biased coins, each with a known probability of heads. Presented with an ordering of these coins, flip (i.e., toss) each coin once, in that order, until we

How large can the gap between consecutive primes be relative to their magnitude? We will discuss some heuristics and prove a result of Westzynthius, who showed that prime gaps can

I will discuss several recent results on the Turán density of long cycle-like hypergraphs. These results (due to Kamčev–Letzter–Pokrovskiy, Balogh–Luo, and myself) all follow a similar framework, and I will