Since the double helical structure of DNA was discovered in 1953, decades of research into the behaviour of DNA have revealed many other fascinating phenomena about of the molecule of life. In 1965, Jerome Vinograd discovered that DNA in the polyoma virus is naturally found in a circular form. This work opened the gates to a new interdisciplinary field that studies the topology of DNA and its biological implications for the functionality of the molecule.

In this talk I will introduce topological aspects of

(i) bacterial site-specific recombination – an important cellular reaction that exchanges segments of DNA and is capable of creating (topological) knots and links;

(ii) developmental genome rearrangements in ciliates – organisms whose genome, during specialisation, has a complex spatial structure that can be measured by the genus; and

(iii) the organisation of the kinetoplast DNA in trypanosomes – whose kinetoplast genome (the `energy power-house’ of the cell) consists of thousands of DNA circles that are chained to each other, forming a non-trivial link that resembles a medieval mailchain armour.

Sketched out in 1992, selected by ESA in 1996, launched in 2009, Planck delivered on March 21st its first full sky maps of the millimetric emission at 9 frequencies, as well as those which follow from them, and in particular Planck map of the anisotropies of the Cosmic Microwave Background (CMB). The later displays minuscule variations as a function of the observing direction of the temperature of the fossile radiation around its mean temperature of 2.725K. I will briefly describe how these high resolution maps with a precision of a few parts in a million have been obtained, from collection to analysis of the first 500 billion samples of our HFI instrument.

CMB anisotropies reveal the imprint of the primordial fluctuations which initiate the growth of the large scale structures of the Universe, as transformed by their evolution, in particular during the first 370 000 years, i.e. till the Universe became transparent and the forming of the image we record today. The statistical characteristics of these anisotropies allow constraining jointly the physics of the creation of the primordial fluctuations and that of their evolution. They teach us the possible value of the parameters of the models which we confront to data. I will describe Planck estimates of the density of the constituents of the Universe (usual matter, cold dark matter or CDM, dark energy…), and their implication in terms of derived quantities like the expansion rate or the spatial curvature. I will review what we learnt on the generation of the fluctuation, and wil discuss extensions of the standard cosmological model, so called « Lambda-CDM », both in term of non minimal physical models — multi-field inflation for instance, or additional constituents – like cosmic strings or a fourth neutrino.

Finally, it will briefly describe other promising results on the matter distribution which is travelled through by the CMB image on its long 13.7 billion years trip towards us. I will mention in particular what we can learn on the dark matter distribution – which is detected through its distorting effet of the CMB image by gravitationnal lensing, or that of hot gaz, which is revealed by the spectral distortion it induces.

I will discuss joint work with Peter Scholze on the pro-étale topology of schemes. The main goal of this work is to give an intuitive perspective on the foundations of l-adic cohomology. After giving the basic definitions, I will explain the local contractibility of the pro-étale site of a scheme (and its homological consequences). Using this, we will see why the category of locally constant sheaves on the pro-étale topology gives rise to a fundamental group that is rich enough to detect all lisse l-adic sheaves through its representation theory (which fails for the groups constructed in SGA1 and SGA3 on non-normal schemes).

Crossovers are formed between homologous chromosomes in meiosis, the sex-specific cell division process during which a diploid cell gives rise to four gametes. In most species, nearby crossovers are rarer than if they were to arise independently. Such a phenomenon, discovered in 1913 by Sturtevant, has been coined « interference ».

In this talk I first review how mathematical modeling has been used to describe interference. Then I provide recent results based on analysing state of the art experimental data, giving novel insights into what new features must be included hereafter in improved modeling approaches. Last but not least, I will consider what happens in « recombinant inbred lines » where meiosis is repeated over many generations. By working within the framework of quantum field theory equations, I will provide a mathematical solution to an open problem going back to 1931, namely how to generalize to any number of loci the 2-locus formula of Haldane and Waddington.

The « very good » property for algebraic stacks was introduced by Beilinson and Drinfeld in their paper « The Quantization of Hitchin’s Integrable System and Hecke Eigensheaves ». They proved that for a semisimple complex group G, the moduli stack of G-bundles over a smooth complex projective curve X is « very good » as long as X has genus g > 1. We will introduce the « very good » property in the context of a group action on an algebraic variety, and prove it for a moduli space of parabolic bundles on P1 arising from quiver representations. As a special case, we will consider the « very good » property for the diagonal action of the group PGL(n) on a product of partial flag varieties and its relationship with the space of solutions to the additive Deligne-Simpson problem.

The principal approximation methods used to compute the inspiral of compact binary systems are the post-Newtonian (pN) expansion, in which an orbital angular velocity MΩ serves as the expansion parameter; and the self-force or extreme-mass-ratio-inspiral approach, in which the small parameter is the mass ratio m/M of the binary’s two components. We work in an overlapping regime where both approximations are valid and find numerical values of pN coefficients at orders beyond the reach of current analytical work. In this talk we present a novel analytic extraction of high-order pN parameters that govern quasi-circular binary systems using ultra-high accuracy numerical computations.

The problem reads: Is there a general principle(s) that underlies the processes of human learning the following?

1. Native languages.

2. Mathematics.

3. Bipedal locomotion.

We shall bring (speculative) evidence for the existence of such principle(s) and indicate a possible direction of (quasi)mathematical modeling of (conjectural) universal learning.

Starting from the known unfaithful spinorial representations of the compact subalgebra KE(10) of the hyperbolic Kac Moody algebra E(10), new fermionic `higher spin’ representations are constructed in a second quantized framework.

Alternative Splicing is an important source of variety in the process of protein expression. It is deregulated in human diseases including cancer. The precise mechanism through which a splicing variant is selected for expression is not known at present. Here, we demonstrate that alternative splicing involves the RNA interference protein machinery, previously discovered as important for gene regulation at a distinct step, i. e. at the translational level.