Thu, 24 Jan 2019

16:00 - 17:00
L6

### Hida families of Drinfeld modular forms

Giovanni Rosso
(University of Cambridge)
Abstract

Seminal work of Hida tells us that if a modular eigenform is ordinary at p then we can always find other eigenforms, of different weights, that are congruent to our given form. Even better, it says that we can find q-expansions with coefficients in p-adic analytic function of the weight variable k that when evaluated at positive integers give the q-expansion of classical eigenforms. His construction of these families uses mainly the geometry of the modular curve and its ordinary locus.
In a joint work with Marc-Hubert Nicole, we obtained similar results for Drinfeld modular forms over function fields. After an extensive introduction to Drinfeld modules, their moduli spaces, and Drinfeld modular forms, we shall explain how to construct Hida families for ordinary Drinfeld modular forms.

Fri, 22 Feb 2019

14:00 - 15:00
C2

### The viscosities of partially molten materials undergoing diffusion creep

John Rudge
(University of Cambridge)
Abstract

Partially molten materials resist shearing and compaction. This resistance

is described by a fourth-rank effective viscosity tensor. When the tensor

is isotropic, two scalars determine the resistance: an effective shear and

an effective bulk viscosity. In this seminar, calculations are presented of

the effective viscosity tensor during diffusion creep for a 3D tessellation of

tetrakaidecahedrons (truncated octahedrons). The geometry of the melt is

determined by assuming textural equilibrium.  Two parameters

control the effect of melt on the viscosity tensor: the porosity and the

dihedral angle. Calculations for both Nabarro-Herring (volume diffusion)

and Coble (surface diffusion) creep are presented. For Nabarro-Herring

creep the bulk viscosity becomes singular as the porosity vanishes. This

singularity is logarithmic, a weaker singularity than typically assumed in

geodynamic models. The presence of a small amount of melt (0.1% porosity)

causes the effective shear viscosity to approximately halve. For Coble creep,

previous modelling work has argued that a very small amount of melt may

lead to a substantial, factor of 5, drop in the shear viscosity. Here, a

much smaller, factor of 1.4, drop is obtained.

Wed, 27 Feb 2019

18:00 - 21:00

### OCIAM Dinner at Christ Church, Oxford

Keynote: Professor Grae Worster
(University of Cambridge)
Further Information

Here's a quick note about the location and dress code for Wednesday's OCIAM event at Christ Church.

The Lecture will take place in the Michael Dummett Lecture Theatre, which is in Blue Boar Quad at 6pm. Please enter via the lodge and ask for directions.

Pre-dinner drinks at 7:15pm and dinner at 7:45pm itself will take place in the Lee Building (in the Freind room = SCR dining room. Yes, e before i.)

Given that we will be in the SCR dining room, please dress smartly (Jacket and tie for the gents, please. No jeans.)

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Thu, 31 Jan 2019

16:00 - 17:30
L3

### Poroelastic propagation and pancakes: understanding why supraglacial lakes spread but Venutian lava domes stop

Dr. Jerome Neufeld
(University of Cambridge)
Abstract

Many fluid flows in natural systems are highly complex, with an often beguilingly intricate and confusing detailed structure. Yet, as with many systems, a good deal of insight can be gained by testing the consequences of simple mathematical models that capture the essential physics.  We’ll tour two such problems.  In the summer melt seasons in Greenland, lakes form on the surface of the ice which have been observed to rapidly drain.  The propagation of the meltwater in the subsurface couples the elastic deformation of the ice and, crucially, the flow of water within the deformable subglacial till.  In this case the poroelastic deformation of the till plays a subtle, but crucial, role in routing the surface meltwater which spreads indefinitely, and has implications for how we think about large-scale motion in groundwater aquifers or geological carbon storage.  In contrast, when magma erupts onto the Earth’s surface it flows before rapidly cooling and crystallising.  Using analogies from the kitchen we construct, and experimentally test, a simple model of what sets the ultimate extent of magmatic intrusions on Earth and, as it turns out, on Venus.  The results are delicious!  In both these cases, we see how a simplified mathematical analysis provides insight into large scale phenomena.

Fri, 19 Oct 2018

14:00 - 15:00
C2

### Plumes in heterogeneous porous formations

Duncan Hewitt
(University of Cambridge)
Abstract

Plumes are a characteristic feature of convective flow through porous media. Their dynamics are an important part of numerous geological processes, ranging from mixing in magma chambers to the convective dissolution of sequestered carbon dioxide. In this talk, I will discuss models for the spread of convective plumes in a heterogeneous porous environment. I will focus particularly on the effect of thin, roughly horizontal, low-permeability barriers to flow, which provide a generic form of heterogeneity in geological settings, and are a particularly widespread feature of sedimentary formations. With the aid of high-resolution numerical simulations, I will explore how a plume spreads and flows in the presence of one or more of these layers, and will briefly consider the implications of these findings in physical settings.

Fri, 15 Jun 2018

12:00 - 13:00
C6

### Character correspondences for symmetric and complex reflection groups.

Eugenio Giannelli
(University of Cambridge)
Abstract

Abstract: In 2016 Ayyer, Prasad and Spallone proved that the restriction to
S_{n-1} of any odd degree irreducible character of S_n has a unique irreducible
constituent of odd degree.
This result was later generalized by Isaacs, Navarro Olsson and Tiep.
In this talk I will survey some recent developments on this topic.

Thu, 22 Nov 2018

16:00 - 17:30
L3

### Variational models and partial differential equations for mathematical imaging

Carola Schönlieb
(University of Cambridge)
Abstract

Images are a rich source of beautiful mathematical formalism and analysis. Associated mathematical problems arise in functional and non-smooth analysis, the theory and numerical analysis of partial differential equations, harmonic, stochastic and statistical analysis, and optimisation. Starting with a discussion on the intrinsic structure of images and their mathematical representation, in this talk we will learn about variational models for image analysis and their connection to partial differential equations, and go all the way to the challenges of their mathematical analysis as well as the hurdles for solving these - typically non-smooth - models computationally. The talk is furnished with applications of the introduced models to image de-noising, motion estimation and segmentation, as well as their use in biomedical image reconstruction such as it appears in magnetic resonance imaging.

Tue, 30 Apr 2019

17:00 - 18:00
L1

### Julia Wolf - The Power of Randomness

Julia Wolf
(University of Cambridge)
Further Information

Far from taking us down the road of unpredictability and chaos, randomness has the power to help us solve a fascinating range of problems. Join Julia Wolf on a mathematical journey from penalty shoot-outs to internet security and patterns in the primes.

Julia Wolf is University Lecturer in the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge.

5-6pm
Mathematical Institute
Oxford

Please email @email to register.

Watch live:
https://livestream.com/oxuni/wolf

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

Thu, 03 May 2018

16:00 - 17:00
L6

### Irreducibility of random polynomials

Péter Varjú
(University of Cambridge)
Abstract

Let $P$ be a random polynomial of degree $d$ such that the leading and constant coefficients are 1 and the rest of the coefficients are independent random variables taking the value 0 or 1 with equal probability. Odlyzko and Poonen conjectured that $P$ is irreducible with probability tending to 1 as $d$ grows.  I will talk about an on-going joint work with Emmanuel Breuillard, in which we prove that GRH implies this conjecture. The proof is based on estimates for the mixing time of random walks on $\mathbb{F}_p$, where the steps are given by the maps $x \rightarrow ax$ and $x \rightarrow ax+1$ with equal probability.

Thu, 08 Mar 2018
16:00
C5

### TBA

Lawrence Barrott
(University of Cambridge)
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