We are getting better at predicting things about our environment - the impact of climate change for example. But what about predicting our collective effect on ourselves? We can predict the small things, but we fail miserably when it comes to many of the big things. The financial crisis cost the world trillions, yet our ability to forecast and mitigate the next economic crisis is very low. Is this inherently impossible? Or perhaps we are just not going about it the right way?
Occupants of Manifolds
Abstract
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.
Hochschild cohomology of monoids
Abstract
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.
Derived Hecke algebras
Abstract
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.
14:30
Random plane waves and other classes of random functions
Abstract
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.
Octupolar Order Tensors
Abstract
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.