Mon, 18 Jan 2016

16:00 - 17:00
L3

4th moment of quadratic Dirichlet L-functions in function fields

Alexandra Florea
(Stanford University)
Abstract

We discuss moments of $L$-functions in function fields, in the hyperelliptic ensemble, focusing on the fourth moment of quadratic Dirichlet $L$-functions at the critical point. We explain how to obtain an asymptotic formula with some of the secondary main terms.

Fri, 29 Apr 2016
12:00
L6

Prandtl equations in Sobolev Spaces

Tong Yang
(City University of Hong Kong)
Abstract
The classical result of Oleinik and her collaborators in 1960s on the Prandtl equations shows that in two space dimensions, the monotonicity condition on the tangential component of the velocity field in the normal direction yields local in time well-posedness of the system. Recently, the well-posedness of Prandtl equations in Sobolev spaces has also been obtained under the same monotonicity condition. Without this monotonicity condition, it is well expected that boundary separation will be developed. And the work of Gerard-Varet and Dormy gives the ill-posedness, in particular in Sobolev spaces, of the linearized systemaround a shear flow with a non-degenerate critical point under when the boundary layer tends to the Euler flow exponentially in the normal direction. In this talk, we will first show that this exponential decay condition is not necessary and then in some sense it shows that the monotonicity condition is sufficient and necessary for the well-posedness of the Prandtl equations in two space dimensions in Sobolev spaces. Finally, we will discuss the problem in three space dimensions.

Questioning the credibility of financial stress tests

The Mathematical Finance Group in Oxford has long been a leader in research on financial mathematics. In recent years a number of research areas have become key focal points within the Group, notably behavioural finance and financial big data, robust pricing and machine learning. In particular, research has focused on financial stability, an area that became critical after the Financial Crisis in 2008. 

Tue, 02 Feb 2016

12:00 - 13:15
L4

Cutkosky rules and Outer Space

Dirk Kreimer (Berlin)
(HU Berlin)
Abstract

Amplitudes in quantum field theory have discontinuities when regarded as
functions of
the scattering kinematics. Such discontinuities can be determined from
Cutkosky rules.
We present a structural analysis of such rules for massive quantum field
theory which combines
algebraic geometry with the combinatorics of Karen Vogtmann's Outer Space.
This is joint work with Spencer Bloch (arXiv:1512.01705).

Martin Bridson

Symmetry, Spaces and Undecidability - Public Lecture now online

When one wants to describe the symmetries of any object or system, in mathematics or everyday life, the right language to use is group theory. How might one go about understanding the universe of all groups and what kinds of novel geometry might emerge as we explore this universe?

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Ada Lovelace Symposium 9-10 December - live streaming

When you think about the founders of computing you may think Alan Turing, you may even think Charles Babbage. But you should definitely think about Ada Lovelace. Ada Lovelace is not only the link between Babbage and Turing, but a woman of fierce originality and intellectual interests whose ideas went beyond Babbage’s ideas of computers as manipulating numbers, and focused on their creative possibilities and their limits, the very issues with which we are wrestling today.

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