Francis Bischoff

A standard way of presenting a group is to choose a collection of generators and then to specify a list of relations that must be satisfied. These are not always optimal: sometimes there are non-trivial identities among the relations. For example...

Abstract: Functional data such as time series and images are ubiquitous in applications and are equipped with natural concatenation operations. For machine learning applications, it is often helpful to build structured representations of such data...

This is the second part of an introduction to Poisson geometry. In this part, I will discuss the geometry of Poisson manifolds, such as their symplectic leaves, through the use of illustrative examples. I will also briefly discuss the quantization of...

I will give an introduction to Poisson geometry, starting with its role in the dynamics of physical systems and its relationship to symplectic geometry. Through the use of illustrative examples, I will highlight some of the basic features of Poisson...

In this talk, I will explain the concepts of limits and colimits in the context of infinity categories. As a warm-up, I will start by recalling these notions in the setting of ordinary categories. I will also compare these concepts with homotopy (co...

A common theme in homotopy theory is to record not just whether two objects are equivalent, but also *how* they are equivalent. For instance, we can consider maps between spaces, homotopies between maps, homotopies between homotopies, and so on. An...

I will start by giving a broad overview of our seminar so far, outlining the way in which characteristic classes arise from the cohomology of classifying spaces. When the coefficients for cohomology are the real numbers, the characteristic classes...

Can you embed the real projective plane in three-dimensional space? Motivated by this and similar questions, I will introduce the correspondence between real line bundles and hypersurfaces, the first Stiefel-Whitney class, and Poincare duality. In...

In this seminar, we have seen that problems in deformation theory are often controlled by differential graded Lie algebras (dgla). For example, in Martin's talk, we saw how the deformations of an associative algebra are controlled by a dgla structure...

In this seminar, we have seen that problems in deformation theory are often controlled by differential graded Lie algebras (dgla). For example, in Martin's talk, we saw how the deformations of an associative algebra are controlled by a dgla structure...