I will report on joint work with Michael Weiss (https://arxiv.org/pdf/1503.00498.pdf):

Let K be a subset of a smooth manifold M. In some cases, functor calculus methods lead to a homotopical formula for M \ K in terms of the spaces M \ S,  where S runs through the finite subsets of K. This is for example the case when K is a smooth compact sub manifold of co-dimension greater or equal to three.

Abstract: We define the Hochschild complex and cohomology of a monoid in an Ab-enriched monoidal category. Then we interpret some of the lower dimensional cohomology groups and discuss when the cohomology ring happens to be graded-commutative.

The smooth representation theory of a p-adic reductive group G

with characteristic zero coefficients is very closely connected to the

module theory of its (pro-p) Iwahori-Hecke algebra H(G). In the modular

case, where the coefficients have characteristic p, this connection

breaks down to a large extent. I will first explain how this connection

can be reinstated by passing to a derived setting. It involves a certain

differential graded algebra whose zeroth cohomology is H(G). Then I will

report on a joint project with

R. Ollivier in which we analyze the higher cohomology groups of this dg

algebra for the group G = SL_2.

There are several classes of random function that appear naturally in mathematical physics, probability, number theory, and other areas of mathematics. I will give a brief overview of some of these random functions and explain what they are and why they are important. Finally, I will explain how I use chebfun to study these functions.
 

In Soft Matter, octupolar order is not just an exotic mathematical curio. Liquid crystals have already provided a noticeable case of soft ordered materials for which a (second-rank) quadrupolar order tensor may not suffice to capture the complexity of the condensed phases they can exhibit. This lecture will discuss the properties of a third-rank order tensor capable of describing these more complex phases. In particular, it will be shown that octupolar order tensors come in two separate, equally abundant variants. This fact, which will be given a simple geometric interpretation, anticipates the possible existence of two distinct octupolar sub-phases. 

Following the spirit of Grothendieck’s Esquisse d’un Programme, the Ihara/Oda-Matsumoto conjecture predicted a combinatorial description of the absolute Galois group of Q based on its action on geometric fundamental groups of varieties. This conjecture was resolved in the 90’s by Pop using anabelian techniques. In this talk, I will discuss some satronger variants of this conjecture, focusing on the more recent solutions of its pro-ell and mod-ell two-step nilpotent variants.