Past Events

It is a classical problem to understand the set of Jacobians of curves among all abelian varieties, i.e., the image of the map Mg→Ag which sends a curve X to its Jacobian JX. In characteristic p, Ag has interesting filtrations, and we can ask how the...

Many geometry processing tasks can be performed by solving partial differential equations (PDEs) on surfaces. These PDEs usually involve boundary conditions (e.g., Dirichlet or Neumann) defined anywhere on the surface, not just on the physical...

Suppose Alice can send a quantum message to Bob in a quantum system modeled as a finite graph. But, imagine there is an eavesdropper which can attach an infinite-dimensional quantum system to the finite graph used by Alice and Bob. Can Alice still...

Geometric mechanics describes Lagrangian and Hamiltonian mechanics geometrically, and information geometry formulates statistical estimation, inference, and machine learning in terms of geometry. A divergence function is an asymmetric distance...

Usage-Based Insurance (UBI) is one of the most recent innovations by auto insurance companies that links the premium rates of customers to their actual driving performance. In this program, drivers’ behaviours are monitored directly while they drive...

The classical obstacle problem consists of finding the equilibrium position of an elastic membrane whose boundary is held fixed and which is constrained to lie above a given obstacle. By classical results of Caffarelli, the free boundary is smooth...

A collection of families $(\F_{1}, \F_{2} , \cdots , \F_{k}) \in \mathcal{P}([n])^k$ is \emph{cross-Sperner} if there is no pair $i \not= j$ for which some $F_i \in \F_i$ is comparable to some $F_j \in \F_j$. Two natural measures of the `size' of...

Chebyshev's bias is the surprising phenomenon that there is usually more primes of the form 4n+3 than of the form 4n+1 in initial intervals of the natural numbers. More generally, following work from Rubinstein and Sarnak, we know Chebyshev's bias...

Random interlacements is a Poissonian soup of doubly-infinite random walk trajectories on Z^d, with a parameter u > 0 controlling the intensity of the Poisson point process. In a natural way, the model defines a percolation on the edges of Z^d with...

Left-right symmetry of the anatomy of vertebrate bodies is crucial for proper physiological function and requires active mechanisms throughout embryonic development. The somites, which give rise to the vertebrae and rib cage, appear as highly...