### Construction of 2-adic integral canonical models of Hodge-type Shimura varieties

## Abstract

varieties to p=2, using Dieudonné display theory.

Thu, 08 May 2014

16:00 -
17:00

L5

Wansu Kim

(University of Cambridge)

We extend Kisin's construction of integral canonical models of Hodge-type Shimura

varieties to p=2, using Dieudonné display theory.

Tue, 11 Mar 2014

13:15 -
14:00

C4

Stanley Strawbridge

(University of Cambridge)

Pluripotency is a key feature of embryonic stem cells (ESCs), and is defined as the ability to give rise to all cell lineages in the adult body. Currently, there is a good understanding of the signals required to maintain ESCs in the pluripotent state and the transcription factors that comprise their gene regulatory network. However, little is known about how ESCs exit the pluripotent state and begin the process of differentiation. We aim to understand the molecular events associated with this process via an experiment-model cycle.

Tue, 15 Oct 2013

14:30 -
15:30

C2

Andrew Thomason

(University of Cambridge)

An independent set in an $r$-uniform hypergraph is a subset of the vertices
that contains no edges. A container for the independent set is a superset
of it. It turns out to be desirable for many applications to find a small
collection of containers, none of which is large, but which between them
contain every independent set. ("Large" and "small" have reasonable
meanings which will be explained.)

Applications include giving bounds on the list chromatic number of
hypergraphs (including improving known bounds for graphs), counting the
solutions to equations in Abelian groups, counting Sidon sets,
establishing extremal properties of random graphs, etc.

The work is joint with David Saxton.

Thu, 24 Oct 2013

12:00 -
13:00

L6

Dr. Shiwu Yang

(University of Cambridge)

We study the nonlinear wave equations on a class of asymptotically flat Lorentzian manifolds $(\mathbb{R}^{3+1}, g)$ with time dependent inhomogeneous metric g. Based on a new approach for proving the decay of solutions of linear wave equations, we give several applications to nonlinear problems. In particular, we show the small data global existence result for quasilinear wave equations satisfying the null condition on a class of time dependent inhomogeneous backgrounds which do not settle to any particular stationary metric.

Mon, 04 Nov 2013

14:15 -
15:15

Oxford-Man Institute

Nathanael Berestycki

(University of Cambridge)

The coalescing Brownian flow on $\R$ is a process which was introduced by Arratia (1979) and Toth and Werner (1997), and which formally corresponds to starting coalescing Brownian motions from every space-time point. We provide a new state space and topology for this process and obtain an invariance principle for coalescing random walks. The invariance principle holds under a finite variance assumption and is thus optimal. In a series of previous works, this question was studied under a different topology, and a moment of order $3-\eps$ was necessary for the convergence to hold. Our proof relies crucially on recent work of Schramm and Smirnov on scaling limits of critical percolation in the plane. Our approach is sufficiently simple that we can handle substantially more complicated coalescing flows with little extra work -- in particular similar results are obtained in the case of coalescing Brownian motions on the Sierpinski gasket. This is the first such result where the limiting paths do not enjoy the non-crossing property.

Joint work with Christophe Garban (Lyon) and Arnab Sen (Minnesota).

Mon, 28 Oct 2013

15:45 -
16:45

Oxford-Man Institute

Alan Sola

(University of Cambridge)

With F. Johansson Viklund (Columbia) and A. Turner (Lancaster), we have studied a regularized version of the Hastings-Levitov model of random Laplacian growth. In addition to the usual feedback parameter $\alpha>0$, this regularized version of the growth process features a smoothing parameter $\sigma>0$.

We prove convergence of random clusters, in the limit as the size of the individual aggregating particles tends to zero, to deterministic limits, provided the smoothing parameter does not tend to zero too fast. We also study scalings limit of the harmonic measure flow on the boundary, and show that it can be described in terms of stopped Brownian webs on the circle. In contrast to the case $\alpha=0$, the flow does not always collapse into a single Brownian motion, which can be interpreted as a random number of infinite branches being present in the clusters.

Fri, 29 Nov 2013

14:00 -
15:00

L5

Fri, 14 Jun 2013

14:30 -
15:30

DH 3rd floor SR

Dr. Anthony Anderson

(University of Cambridge)

Colloidal suspensions do not freeze uniformly; rather, the frozen phase (e.g. ice) becomes segregated, trapping bulk regions of the colloid within, which leads to a fascinating variety of patterns that impact both nature and technology. Yet, despite the central importance of ice segregation in several applications, the physics are poorly understood in concentrated systems and continuum models are available only in restricted cases. I will discuss a particular set of steady-state ice segregation patterns that were obtained during a series of directional solidification experiments on concentrated suspensions. As a case study, I will focus of one of these patterns, which is very reminiscent of ice lenses observed in freezing soils and rocks; a form of ice segregation which underlies frost heave and frost weathering. I will compare these observations against an extended version of a 'rigid-ice' model used in previous frost heave studies. The comparison between theory and experiment is qualitatively correct, but fails to quantitatively predict the ice-lensing pattern. This leaves open questions about the validity of the assumptions in 'rigid-ice' models. Moreover, 'rigid-ice' models are inapplicable to the study of other ice segregation patterns. I conclude this talk with some possibilities for a more general model of freezing colloidal suspensions.

Fri, 03 May 2013

14:30 -
15:30

DH 3rd floor SR

Duncan Hewitt

(University of Cambridge)

Convection in a porous medium plays an important role in many geophysical and industrial processes, and is of particular current interest due to its implications for the long-term security of geologically sequestered CO_2. I will discuss two different convective systems in porous media, with the aid of 2D direct numerical simulations: first, a Rayleigh-Benard cell at high Rayleigh number, which gives an accurate characterization both of the convective flux and of the remarkable dynamical structure of the flow; and second, the evolution and eventual `shut-down' of convection in a sealed porous domain with a source of buoyancy along only one boundary. The latter case is also studied using simple box models and laboratory experiments, and can be extended to consider convection across an interface that can move and deform, rather than across a rigid boundary. The relevance of these results in the context of CO_2 sequestration will be discussed.

Thu, 25 Apr 2013

14:00 -
15:00

Rutherford Appleton Laboratory, nr Didcot

Dr Tobias Berka

(University of Cambridge)

Very-large scale data analytics are an alleged golden goose for efforts in parallel and distributed computing, and yet contemporary statistics remain somewhat of a dark art for the uninitiated. In this presentation, we are going to take a mathematical and algorithmic look beyond the veil of Big Data by studying the structure of the algorithms and data, and by analyzing the fit to existing and proposed computer systems and programming models. Towards highly scalable kernels, we will also discuss some of the promises and challenges of approximation algorithms using randomization, sampling, and decoupled processing, touching some contemporary topics in parallel numerics.

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