Everyone knows that Moore’s law says that computers get cheaper at an exponential rate. What is not as well known is that many other technologies that have nothing to do with computers obey a similar law. Costs for DNA sequencing, some forms of renewable energy, chemical processes and consumer goods have also dropped at an exponential rate, even if the rates vary and are typically slower than for computers.
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
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.
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).
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?