Much of black hole thermodynamics is limited to systems with a high degree of symmetry. In this talk, I will discuss a non-stationary, non-axisymmetric black hole spacetime that nevertheless admits a standard thermodynamics: a black hole corotating with an orbiting moon. More precisely, we consider a Kerr black hole perturbed by a particle on the circular orbit whose frequency matches that of the event horizon. The key point is that the spacetime has a helical Killing vector that generates the event horizon, allowing the surface gravity to be defined in the standard way. The surface gravity is uniform on the horizon and should correspond to the Hawking temperature of the black hole. We calculate the change in surface gravity/temperature, finding it negative: the moon has a cooling effect on the black hole. We also calculate the area/entropy of the perturbed black hole, finding no change from the background Kerr value.

I will present an overview of the work that has gone into formulating a theory of tidal deformations and dynamics of black holes in general relativity. This includes a description of the tidal environment around a black hole, a description of the tidal deformation in terms of the intrinsic geometry of the event horizon, and a description of how the black hole can exchange energy and angular momentum with its tidal environment.

I will review the state-of-the-art analytic effective one body (EOB) approach to the general-relativistic two-body dynamics and its completion using numerical relativity (NR) simulations. I will discuss in detail three cases: i) coalescence of (spinning) black hole binaries (BBHs); ii) tidal effects in coalescing neutron star binaries and the EOS-universality at merger; iii) the BBH scattering problem and the determination of the scattering angle in EOB and NR. I will present several examples about how NR simulations can inform the EOB model so to build a comprehensive EOBNR model of the two-body dynamics and waveforms in general relativity. Implications for gravitational wave data analysis are discussed.

It is found a change of variables transforming A2 elliptic one-parametric Hamiltonian (in other words, 3-body elliptic Calogero Hamiltonian, or two-dimensional Lame operator) into algebraic differential operator with polynomial coefficients. It is shown the A2 elliptic model is equivalent to gl(3) quantum top and its parameter is determined by spin of gl(3) representation. It is found the discrete values of the parameter for which two-dimensional Lame operator has polynomial eigenfunctions.

We investigate how deeply nested are the loops in the O(n) model on random maps. In particular, we find that the number P of loops separating two points in a planar map in the dense phase with V >> 1 vertices is typically of order c(n) ln V for a universal constant c(n), and we compute the large deviations of P. The formula we obtain shows similarity to the CLE_{kappa} nesting properties for n = 2cospi(1 – 4/kappa). The results can be extended to all topologies using the topological recursion.

This is based on a joint ongoing work with J. Bouttier

 

Locally analytic representations of p-adic Lie groups are of interest in several branches of arithmetic algebraic geometry, notably the p-adic local Langlands program. I will discuss some work in progress towards a Beilinson-Bernstein style localisation theorem for admissible locally analytic representations of semisimple compact p-adic Lie groups using equivariant formal models of rigid analytic flag varieties.

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The four billion years old genetic code is quasi-universal among living organisms. Mathematical insights into the genetic code can be gained by studying its symmetries. Symmetries by base substitutions were identified for the 2' and 3' sets of aminoacyl-tRNAs with Soulé in 2007. Half a century ago, Rumer described symmetries by base substitutions for degeneracy, the number of base triplets coding for each of the twenty canonical amino acids found in natural proteins. Apart from base substitutions, another class of mutations consists of frameshift mutations. The most frequent frameshift mutations are single-base deletions which are highly deleterious within genes as they alter the reading frame. The central role of mutations which are errors induced by biological catalysts, will be analyzed in the context of the minimization of their deleterious effects, the codon assignment of amino acids and chain termination signals in the genetic code and molecular evolution.
 

The central axis of the famous DNA double helix is often constrained or even circular.   The topology of this axis can influence which proteins interact with the underlying DNA. Subsequently, in all cells there are proteins whose primary function (type II topoisomerases)  is to change the DNA axis topology — for example converting a torus link into an unknot. Additionally, there are several protein families (most importantly, site-specific recombinases) that change the axis topology as a by-product of their interaction with DNA.

This talk will describe some typical DNA conformations, and the families of proteins that change these conformations. I'll present a few examples illustrating how 3-manifold topology (including Dehn surgery and Heegaard Floer homology) have been useful in understanding certain DNA-protein interactions, and discuss the most common techniques used to attack these problems.

Une des définitions possibles des nombres de Hurwitz est qu'ils comptent certaines cartes étiquetées. De même que les cartes planaires sont en bijection avec des arbres plans (ou ordonnés), ces cartes étiquetées sont en bijection avec des arbres étiquetés de type Cayley. Le but de l'exposé sera de montrer comment l'étude de ces arbres permet de d'obtenir de nouvelles formules pour les nombres de Hurwitz doubles ainsi que des propriétés de polynomialité.

Considérons une marche aléatoire simple sur un arbre de Galton-Watson critique conditionné à avoir une hauteur supérieure à $n$. La loi du point d'atteinte de la hauteur $n$ par la marche aléatoire s'appelle la mesure harmonique au niveau $n$. Il est bien connu que le cardinal de l'ensemble des sommets de l'arbre au niveau $n$ est de l'ordre de $n$. En 2013 Curien et Le Gall ont prouvé qu'il existe une constante $beta=0.78…$ telle que la mesure harmonique est portée, à un ensemble de masse arbitrairement petite près, par un ensemble de cardinal de l'ordre de $n^beta$. Dans cet exposé, nous présentons l'existence d'une nouvelle constante universelle $lambda=1.21…$ telle que, avec grande probabilité, la mesure harmonique portée par un sommet typique à la hauteur $n$ est de l'ordre $n^{-lambda}$.