Past Forthcoming Seminars

13 July 2018

In the Boussinesq framework, velocity couples to density fluctuations whereas in magnetohydrodynamic turbulence, the velocity field is coupled to the magnetic field. Both systems support waves (inertia-gravity in the presence of rotation, or Alfvén), with anisotropic dispersion relations. What kind of turbulence regimes result from the interactions between waves and nonlinear eddies in such flows? And what is delimiting these regimes?

I shall sketch the phenomenological framework for rotating stratified turbulence within which one is led to scaling laws in terms of the Froude number, Fr=U/[LN], which measures the relative celerity of gravity waves and nonlinear eddies, with U and L characteristic velocity and length scale, and N the Brunt-V\"ais\"al\"a frequency. These laws apply to the mixing efficiency of such flows, indicating the relative roles of the buoyancy flux due to the waves, and of the measured kinetic and potential energy dissipation rates. Various measures of mixing are found to follow power laws in terms of the Froude number, and may differ for the three regimes that can be identified, namely the wave-dominated, wave-eddy balance and eddy-dominated domains [1]. In particular, in the intermediate regime, the effective dissipation varies linearly with Fr, in agreement with simple wave-turbulence arguments. This analysis is inspired by and corroborates results from a large parametric study using direct numerical simulations (DNS) on grids of 1024^3 points, as well as from atmospheric and oceanic observations.

Such scaling laws can be related to previous DNS results concerning the existence for the energy of bi-directional constant-flux cascades to both the small scales and to the large scales, due to the presence of rotation in such flows, as measured for example in the ocean. These dual energy cascades lead to an alteration, and a decrease, of the mixing and available energy to be dissipated in the small scales [2]. Some perspectives might also be given at the end of the talk.


[1] A. Pouquet, D. Rosenberg, R. Marino & C. Herbert, Scaling laws for mixing and dissipation in unforced rotating stratified turbulence. J. Fluid Mechanics 844, 519, 2018.
[2] R. Marino, A. Pouquet & D. Rosenberg, Resolving the paradox of oceanic large-scale balance and small-scale mixing. Physical Review Letters 114, 114504, 2015.

  • Mathematical Geoscience Seminar
4 July 2018
Paul Arne Østvær

Motivic homotopy theory gives a way of viewing algebraic varieties and topological spaces as objects in the same category, where homotopies are parametrised  by the affine line.  In particular, there is a notion of $\mathbb A^1$ contractible varieties.  Affine spaces are $\mathbb A^1$ contractible by definition.  The Koras-Russell threefold KR defined by the equation $x + x^2y + z^2 + t^3 = 0$ in $\mathbb A^4$ is the first nontrivial example of an $\mathbb A^1$ contractible smooth affine variety.  We will discuss this example in some detail, and speculate on whether one can use motivic homotopy theory to distinguish between KR and $\mathbb A^3$.

  • Algebraic Geometry Seminar
2 July 2018
Lauren Williams

The tree amplituhedron A(n, k, m) is a geometric object generalizing the positive Grassmannian, which was introduced by Arkani-Hamed and Trnka in 2013 in order to give a geometric basis for the computation of scattering amplitudes in N=4 supersymmetric Yang-Mills theory. I will give a gentle introduction to the amplituhedron, and then describe what it looks like in various special cases. For example, one can use the theory of sign variation and matroids to show that the amplituhedron A(n, k, 1) can be identified with the complex of bounded faces of a cyclic hyperplane arrangement. I will also present some conjectures relating the amplituhedron A(n, k, m) to combinatorial objects such as non-intersecting lattice paths and plane partitions. This is joint work with Steven Karp, and part of it is additionally joint work with Yan Zhang.

2 July 2018
Cyril Closset

As we have learned over the last 10 years, many exact results for various observables in three-dimensional N=2 supersymmetric theories can be extracted from the computation of "supersymmetric partition functions" on curved three-manifold M_3, for instance on M_3= S^3 the three-sphere. Typically, such computations must be carried anew for each M_3 one might want to consider, and the technical difficulties mounts as the topology of M_3 gets more involved. In this talk, I will explain a different approach that allows us to compute the partition function on "almost" any half-BPS geometry. The basic idea is to relate different topologies by the insertion of certain half-BPS line defects, the "geometry-changing line operators." I will also explain how our formalism can be related to the Beem-Dimofte-Pasquetti holomorphic blocks. [Talk based on a paper to appear in a week, with Heeyeon Kim and Brian Willett.]

  • String Theory Seminar
28 June 2018
Fernando Vega-Redondo

Poor economies not only produce less; they typically produce things that involve fewer inputs and fewer intermediate steps. Yet the supply chains of poor countries face more frequent disruptions - delivery failures, faulty parts, delays, power outages, theft, government failures - that systematically thwart the production process.

To understand how these disruptions affect economic development, we model an evolving input-output network in which disruptions spread contagiously among optimizing agents. The key finding is that a poverty trap can emerge: agents adapt to frequent disruptions by producing simpler, less valuable goods, yet disruptions persist. Growing out of poverty requires that agents invest in buffers to disruptions. These buffers rise and then fall as the economy produces more complex goods, a prediction consistent with global patterns of input inventories. Large jumps in economic complexity can backfire. This result suggests why "big push" policies can fail, and it underscores the importance of reliability and of gradual increases in technological complexity.

26 June 2018
Richard James

The World population is growing at about 80 million per year.  As time goes by, there is necessarily less space per person. Perhaps this is why the scientific community seems to be obsessed with folding things.  In this lecture Dick James presents a mathematical approach to “rigid folding” inspired by the way atomistic structures form naturally - their features at a molecular level imply desirable features for macroscopic structures as well, especially 4D structures.  Origami structures even suggest an unusual way to look at the Periodic Table.

Richard D. James is Distinguished McKnight University Professor at the University of Minnesota.

Please email to register.

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

26 June 2018
Prof Abhay Ashtekar

Over 50 years ago, Bondi, Sachs, Newman, Penrose and others laid down foundations for the theory of gravitational waves in full non-linear general relativity. In particular, numerical simulations of binary mergers used in the recent discovery of gravitational waves are based on this theory. However, over the last 2-3 decades, observations have also revealed that the universe is accelerating in a manner consistent with the presence of a positive cosmological constant $\Lambda$. Surprisingly, it turns out that even the basic notions of the prevailing theory of gravitational waves --the Bondi news, the radiation field, the Bondi-Sachs 4-momentum-- do not easily generalize to this context, {\it no matter how small $\Lambda$ is.} Even in the weak field limit, it took a hundred years to find an appropriate generalization of Einstein's celebrated quadrupole formula to accommodate a positive cosmological constant. I will summarize the main issues and then sketch the current state of the art.