The University of Oxford’s Ashmolean Museum is not only an exhibitor of art, but home to vital artistic research. The museum’s collections are investigated by some of the world’s leading historians, archaeologists, anthropologists and… mathematicians?
Throughout November 2016, the Ashmolean Museum and Oxford Mathematics proudly present Random Walks, a series of short films that present the historical world through mathematical eyes.
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?
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.
