Stable commutator length (scl) is a well established invariant of group elements g  (write scl(g)) and  has both geometric and algebraic meaning.

It is a phenomenon that many classes of non-positively curved groups have a gap in stable commutator length: For every non-trivial element g, scl(g) > C for some C>0. Such gaps may be found in hyperbolic groups, Baumslag-solitair groups, free products, Mapping class groups, etc. 
However, the exact size of this gap usually unknown, which is due to a lack of a good source of “quasimorphisms”.

In this talk I will construct a new source of quasimorphisms which yield optimal gaps and show that for Right-Angled Artin Groups and their subgroups the gap of stable commutator length is exactly 1/2. I will also show this gap for certain amalgamated free products.

Today, everyone knows everything: with only a quick trip through WebMD or Wikipedia, average citizens believe themselves to be on an equal intellectual footing with doctors and diplomats. All voices, even the most ridiculous, demand to be taken with equal seriousness, and any claim to the contrary is dismissed as undemocratic elitism. Tom Nichols argues that in this climate, democratic institutions themselves are in danger of falling either to populism or to technocracy- or in the worst case, a combination of both.

Tom Nichols is Professor of National Security Affairs at the US Naval War College, an adjunct professor at the Harvard Extension School, and a former aide in the U.S. Senate. His latest book is The Death of Expertise: The Campaign Against Established Knowledge and Why it Matters. This lecture is based on that book.

All welcome. No need to book.

A theorem of Gromov states that the number of generators of the fundamental group of a manifold with nonnegative 
curvature is bounded by a constant which only depends on the dimension of the manifold. The main ingredient 
in the proof is Toponogov’s theorem, which roughly speaking says that the triangles on spaces with positive 
curvature, such as spheres, are thick compared to triangles in the Euclidean plane. In the talk I shall explain 
this more carefully and deduce Gromov’s result.

Numerical methods for SDEs typically use only the discretized increments of the driving Brownian motion. As one would expect, this approach is sensible and very well studied.

In addition to generating increments, it is also straightforward to generate time integrals of Brownian motion. These quantities give extra information about the Brownian path and are known to improve the strong convergence of methods for one-dimensional SDEs. Despite this, numerical methods that use time integrals alongside increments have received less attention in the literature.

In this talk, we will develop some underlying theory for these time integrals and introduce a new numerical approach to SDEs that does not require evaluating vector field derivatives. We shall also discuss the possible implications of this work for multi-dimensional SDEs.