One can ask whether the fundamental groups of 3-manifolds are distinguished by their sets of finite quotients. I will discuss the recent solution of this question for Seifert fibre spaces.
I will illustrate how to build families of expanders out of 'very mixing' actions on measure spaces. I will then define the warped cones and show how these metric spaces are strictly related with those expanders.
Science is giving us unprecedented insight into the big questions that have challenged humanity. Where did we come from? What is the ultimate destiny of the universe? What are the building blocks of the physical world? What is consciousness?
‘What We Cannot Know’ asks us to rein in this unbridled enthusiasm for the power of science. Are there limits to what we can discover about our physical universe? Are some regions of the future beyond the predictive powers of science and mathematics? Are there ideas so complex that they are beyond the conception of our finite human brains? Can brains even investigate themselves or does the analysis enter an infinite loop from which it is impossible to rescue itself?
To coincide with the launch of his new book of the same title, Marcus du Sautoy will be answering (or not answering) those questions. He will also be signing copies of the book before and after the lecture.
To book please email @email
In quite an elementary, hands-on talk, I will discuss some Ax-Lindemann type results in the setting of modular functions. There are some very powerful results in this area due to Pila, but in nonclassical variants we have only quite weak results, for a rather silly reason to be discussed in the talk.
In algebraic and arithmetic geometry, there is the ubiquitous notion of a moduli space, which informally is a variety (or scheme) parametrising a class of objects of interest. My aim in this talk is to explain concretely what we mean by a moduli space, going through the functor-of-points formalism of Grothendieck. Time permitting, I may also discuss (informally!) a natural obstruction to the existence of moduli schemes, and how one can get around this problem by taking a 2-categorical point of view.
We outline some concepts and issues around decidability in valued fields of positive characteristic.
For full details please visit:
http://blogs.bodleian.ox.ac.uk/adalovelace/files/2015/10/Ada-Lovelace-S…
Starting from Hilbert's 10th problem, I will explain how to characterise the set of integers by non-solubility of a set of polynomial equations and discuss related challenges. The methods needed are almost entirely elementary; ingredients from algebraic number theory will be explained as we go along. No knowledge of first-order logic is necessary.
Let $G(n,d)$ be a random $d$-regular graph on $n$ vertices. In 2004 Kim and Vu showed that if $d$ grows faster than $\log n$ as $n$ tends to infinity, then one can define a joint distribution of $G(n,d)$ and two binomial random graphs $G(n,p_1)$ and $G(n,p_2)$ -- both of which have asymptotic expected degree $d$ -- such that with high probability $G(n,d)$ is a supergraph of $G(n,p_1)$ and a subgraph of $G(n,p_2)$. The motivation for such a coupling is to deduce monotone properties (like Hamiltonicity) of $G(n,d)$ from the simpler model $G(n,p)$. We present our work with A. Dudek, A. Frieze and A. Rucinski on the Kim-Vu conjecture and its hypergraph counterpart.