Past Events

A point-line incidence is a point-line pair such that the point is on the line. The Szemer\'edi-Trotter theorem says the number of point-line incidences for n (distinct) points and lines in R^2 is tightly upperbounded by O(n^{4/3}). We advance the...

I will present some classes of fully nonlinear PDEs on: complex hermitian and Riemannian manifolds which are motivated (respectively) by hypercomplex and quaternionic geometry. In particular, I will formulate the generalization of the conjecture of...

A momentous legacy of twentieth-century mathematics is the realisation that deterministically evolving systems frequently exhibit, when observed for sufficiently extended periods of time, a statistical behaviour akin to the limiting behaviour of...

The classification of 2-dimensional TQFTs was obtained by cutting up surfaces into disks, cylinders, and pairs of pants. In higher dimension, such a decomposition of n-manifolds is not available. We need to cut up manifolds not only along codimension...

Membrane-enclosed fluid objects, or capsules, are everywhere in natural and industrial processes, from red blood cells and circulating tumor cells in the life sciences to encapsulated substances in the pharmaceutical, food and cosmetic industries. A...

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...