Past Events

Quillen-Barr-Beck (co)homology is a theory which studies the objects of a category where we can make sense of such notions as “modules” and “derivations”. More precisely, in his thesis, Beck defined a general notion of modules and derivations in a...

In this talk, we introduce some recent regularity results of free boundary in optimal transportation. Particularly for higher order regularity, when densities are Hölder continuous and domains are C^2, uniformly convex, we obtain the free boundary is...

Categorical Message Passing Language (CaMPL) is a functional style concurrent programming language with a categorical semantics. In this talk, we explore the categorical semantics, programming syntax, and proof theory representations for CaMPL. This...

A classical Electrical Engineering problem is to determine whether two networks of resistors are equivalent. The standard solution is to use a process of eliminating internal nodes (the star/mesh transformation) which may be seen as a rewriting...

Topological insulators are materials that exhibit unique physical properties due to their non-trivial topological order. One of the most notable consequences of this order is the presence of protected edge states as well as closure of bulk spectral...

A linear conic programming problem aims at minimizing a linear objective over the intersection of an affine set and a closed convex cone. The conic feasibility problems we study in this talk naturally arise from the optimality conditions of linear...

The classical notion of symmetry can be formalized by actions of groups. Quantum symmetry is a generalization of the notion of symmetry to the quantum setting, where symmetries can no longer be completely described by the actions of groups. In this...

Diophantine geometry is a modern-day incarnation of mathematicians' perennial interest in solving algebraic equations in integers. Its fundamental idea is to study the geometric objects defined by algebraic equations in order to understand their...

The Zariski closure of the central path (which interior point algorithms track in convex optimization problems such as linear and semidefinite programs) is an algebraic curve, called the central curve. Its degree has been studied in relation to the...

The locally symmetric diffusions, also known as Brownian motions, on generalized Sierpinski carpets were constructed by Barlow and Bass in 1989. On a fixed carpet, by the uniqueness theorem (Barlow-Bass-Kumagai-Teplyaev, 2010), the reflected...