Simon Fraser University

Fano varieties are projective algebraic variety with “positive curvature”. Recently, using the notion of K-stability which originates in differential geometry, projective moduli spaces for Fano varieties have been constructed. In this talk I will...

I will briefly introduce the notion of formality for differential graded Lie algebras, and the role it plays in deformation theory. I will then discuss some geometric applications obtained in a joint work with Claudio Onorati.

Variational phase-field models of fracture have been at the center of a multidisciplinary effort involving a large community of mathematicians, mechanicians, engineers, and computational scientists over the last 25 years or so. I will start with a...

Particles with diameters of nanometres to micrometres form the building blocks of many of the materials around us, and can be designed in a multitude of ways to form new ones. Such particles commonly live in fluids, where they jiggle about randomly...

Shared rides, which pool individual riders into a single vehicle, are essential for mitigating congestion and promoting more sustainable urban transportation. However, major ridesharing platforms have long struggled to maintain a healthy and...

A basic question about an algebraic variety X is how similar it is to projective space. One measure of similarity is the minimum degree of a rational map from X to projective space, the "degree of irrationality". This number, not to mention the...

Stochastic gradient descent (SGD) is the standard optimization method for training machine learning (ML) models. SGD requires a step-size that depends on unknown problem-dependent quantities, and the choice of this step-size heavily influences the...

The rational points of an abelian variety form a finitely generated group and computing the rank of this group is a hard and central problem in arithmetic geometry. One method, which follows the original proof of Mordell and Weil of the finiteness of...

Skeletal muscle is the motor that drives human and animal movement; however, our understanding of how muscle performs this function is limited because of challenges in directly measuring muscle deformation and force output in living beings. In this...

Partial differential equations (PDEs) on surfaces arise throughout the natural and applied sciences. The solution of such equations poses a big challenge for rather general surfaces, where no parametrization is possible. In this talk, we will give an...