Past Events

Supracellular actomyosin cables often drive morphogenesis in development. The origin of these cables is poorly understood. We show theoretically and computationally that under external loading, cell-cell junctions capable of mechanical feedback could...

The property |z||w| = |zw| of complex numbers leads naturally to the following question concerning sums of squares: in the polynomial ring R = Z[x_1,...,x_r, y_1,... y_s], what is the minimal n such that [(x_1)^2 + ... +(x_r)^2] [(y_1)^2 + ... +(y_s)...

Hermitian, pluriclosed metrics with vanishing Bismut-Ricci form give a natural extension of Calabi-Yau metrics to the setting of complex, non-Kahler manifolds, and arise independently in mathematical physics. We reinterpret this condition in terms of...

In this talk we will give an exact characterization for the asymptotic distribution of quadratic forms in IID random variables with finite second moment, where the underlying matrix is the adjacency matrix of a graph. In particular we will show that...

Humans have been discussing the benefits and drawbacks of democratic vs. authoritarian governance for millennia, with perhaps the earliest and most famous discussion favoring enlightened authoritarian rule contained in Plato's 'Republic'. The...

In 1900, Hilbert posed the following problem: “Given a Diophantine equation with integer coefficients: to devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in (rational)...

A basic example of a family of curves with level structure is the Hesse pencil of elliptic curves: $$x^3+y^3+z^3+ \lambda xyz = 0,$$ which gives a family of elliptic curves with labelled 3-torsion points. The parameter $\lambda$ is a parameter on the...

This talk will introduce the topic of graph product structure theory. I will show that many graphs with bounded treewidth can be described as subgraphs of the strong product of a graph with smaller treewidth and a bounded-size complete graph. To this...

It is well known that a line can intersect at most 2n-1 cells of the n x n chessboard. What happens in higher dimensions: how many cells of the d-dimensional [0,n]^d box can a hyperplane intersect? We also prove the integer analogue of the following...

What happens to a progressively dilating body when folding the space in which it lives? For a start, we shall examine the problem in a Euclidean context, surveying results of Randol and Strichartz through the quantitative, fractal-geometric viewpoint...