Mon, 24 Oct 2016

16:00 - 17:00
C3

On sets of irreducible polynomials closed by composition

Giacomo Micheli
(Oxford)
Abstract

Let S be a set of monic degree 2 polynomials over a finite field and let C be the compositional semigroup generated by S. In this talk we establish a necessary and sufficient condition for C to be consisting entirely of irreducible polynomials. The condition we deduce depends on the finite data encoded in a certain graph uniquely determined by the generating set S. Using this machinery we are able both to show examples of semigroups of irreducible polynomials generated by two degree 2 polynomials and to give some non-existence results for some of these sets in infinitely many prime fields satisfying certain arithmetic conditions (this is a joint work with A.Ferraguti and R.Schnyder). Time permitting, we will also describe how to use character sum techniques to bound the size of the graph determined by the generating set (this is a joint work with D.R. Heath-Brown).

Mon, 10 Oct 2016
16:00
C3

The large sieve

Aled Walker
(Oxford)
Abstract

The large sieve is a powerful analytic tool in number theory, with many beautiful and diverse applications. In its most general form it resembles an approximate Bessel's inequality, and this clear modern theory rests on the combined effort of countless mathematicians in the mid-twentieth century -- Linnik, Roth, Selberg, Montgomery, Vaughan, and Bombieri, to name a few. However, it is hardly obvious to the beginner why this rather abstract inequality should be called 'large', or 'sieve'. In this introductory talk, aimed particularly at new graduate students, we discuss the rudimentary theory of the large sieve, some particular applications to sieving problems, and (at least one) proof. 

Fri, 02 Dec 2016
14:15
C3

Wetropolis flood demonstrator

Onno Bokhove
(School of Mathematics, University of Leeds)
Abstract

The mathematical design of the table flood demonstrator Wetropolis will be presented. Wetropolis illustrates the concepts of extreme rainfall and flooding.

It shows how extreme rainfall events  can cause flooding of a city due to groundwater and river flood peaks. Rainfall is supplied randomly in space using four outcomes (in a reservoir, on a moor, at both places or nowhere) and randomly in time using four rainfall intensities (1s, 2s, 4s, or 9s during a 10s Wetropolis day), including one extreme event, via two skew-symmetric discrete probability distributions visualised by two Galton boards. Wetropolis can be used for both public outreach and as scientific testing environment for flood mitigation and data assimilation.

More information: https://www.facebook.com/resurging.flows

Fri, 18 Nov 2016
14:15
C3

Analogue models of hydraulic fracturing

Finn Box
(University of Oxford)
Abstract

The spreading of a viscous fluid in between a rigid, horizontal substrate and an overlying elastic sheet is presented as a simplified model of the hydraulic fracturing process. In particular, the talk will focus on the case of a permeable substrate for which leak-off arrests the propagation of the fluid and permits the development of a steady state. The different regimes of  gravitationally-driven and elastically-driven flow will be explored, as will the cases of a stiff and flexible sheet, before a discussion of the influence that particles included in the fluid have on the fracture propagation. 

Thu, 16 Jun 2016

11:00 - 15:45
C3

'Around quantum j-mappings (model theory and sheaves)'.

Andres Villaveces
(Bogota)
Abstract
Abstract: finding a "non-commutative limit" of the j-invariant (to real numbers, in a way that captures reasonably well the connection with extensions of number fields) has prompted several approaches (Manin-Marcolli, Castaño-Gendron). I will describe one of these approaches in a brief way, and I will make some connections to the model theory of sheaves.
Mon, 16 May 2016
16:00
C3

Curves and their fundamental groups

Junghwan Lim
((Oxford University))
Abstract

I will describe a sketch of the proof of Grothendieck conjecture on fundamental groups.
 

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