Previous Conferences & Workshops

I will explore two questions about projections of geometric objects in 4-dimensional spaces:

(1) Let $A$ be a convex body in $\mathbb{R}^4$, and let $(p_{12}, p_{13}, p_{14}, p_{23}, p_{24}, p_{34})$ be the areas of the six coordinate projections of...

One way to define a matroid is via its base polytope.  From this point of view, some matroid invariants easily have geometric interpretations: e.g., the number of bases is the number of vertices of the polytope.  It turns out that most interesting...

We will present recent applications of enumerative algebra to the study of stationary states in physics. Our point of departure are classical Newtonian differential equations with nonlinear potential. It turns out that the study of their stationary...

The Bergelson conjecture from 1996 asserts that the multilinear polynomial ergodic averages with commuting transformations converge pointwise almost everywhere in any measure-preserving system. This problem was recently solved affirmatively for...

TBD

Hindman’s Theorem states that whenever the natural numbers are finitely coloured there exists an infinite sequence all of whose finite sums are the same colour. By considering just powers of 2, this immediately implies the corresponding result for...

Gromov--Witten invariants and Welschinger invariants count curves over the complex and real numbers. In joint work with J. Kass, M. Levine, and J. Solomon, we gave arithmetically meaningful counts of rational curves on smooth del Pezzo surfaces over...

The Prékopa-Leindler inequality (PL) and its strengthening, the Borell-Brascamp-Lieb inequality, are functional extensions of the Brunn-Minkowski inequality from convex geometry, which itself refines the classical isoperimetric inequality. These...

Q1: A fundamental result in coding theory, known as the Plotkin bound, suggests that a binary code can tolerate up to ¼ fraction of adversarial corruptions. Can we design codes that handle more errors if we allow interaction between the sender and...