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.
 

In 1999, C Sonnenschein and AM Soto proposed the tissue organization field theory (TOFT). The TOFT posits 1) that cancer is a tissue-based disease whereby carcinogens (directly) and germ-line mutations (indirectly) alter normal interactions between the stroma and adjacent epithelium; and 2) the default state of all cells is proliferation with variation and motility. This later premise is relevant to and compatible with evolutionary theory, and is diametrically opposed to that of the somatic mutation theory.

This theoretical change is incompatible with the reductionist genocentric perspective generated by the molecular biology revolution. Rather than forcing a “bricolage” we decided to frontally attack the problem by joining efforts with philosophers, mathematicians and theoretical biologists to search for principles upon which to build a theory of organisms .While the theory of evolution has provided an increasingly adequate explanation of phylogeny, biology still lacks a theory of organisms that would encompass ontogeny and life cycles, and thus phenomena on a conception to death time-scale.

To achieve this goal we propose that theoretical extensions of physics are required in order to grasp the living state of matter. Such extensions will help to describe the proper biological observables, i.e. the phenotypes. Biological entities must also follow the underlying principles used to understand inert matter. However, these physical laws and principles may not suffice to make the biological dynamics intelligible at the phenotypic level. By analogy with classical mechanics, where the principle of inertia is the default state of inert matter, we are proposing two aspects of the default state in biology, and a framing principle, namely: i) Default state: cell proliferation with variation as a constitutive property of the living. Variation is generated by the mere fact that cell division results in two overall similar, but not identical cells. ii) Default state: motility, which encompasses cell and organismic movements as well as movement within cells. iii) Framing principle: life phenomena exhibit never identical iterations of a morphogenetic process. Organisms are the consequence of the inherent variability generated by proliferation, motility and auto-organization which operate within the framing principle. From these basic premises, we will elaborate on the generation of robustness, the structure of theoretical determination, and the identification of biological proper observables.

The "geodetic light-cone gauge" is a convenient coordinate system for the observation of light-like signals by a geodetic observer.
 
After introducing it I will give two examples on how it can be applied to physically interesting problems: i)  the precision determination of dark-energy parameters;  ii) the description of strong gravitational lensing. If time allows I will also mention some very recent work on gravitational bremsstrahlung from massless particle collisions.

The process of blood coagulation and clot formation in vivo is not yet completely understood. One of the main questions related to haemostasis is why the clot stops growing in normal conditions before it completely obstructs the flow in the vessel, whereas, in pathologic cases, it can continue to grow, often with fatal consequences. Hence, revealing the mechanisms by which the clot grows and stops growing in the flow remains of great importance. In order to study this topic we have developed a hybrid DPD-PDE method where Dissipative Particle Dynamics (DPD) is used to model plasma flow and platelets, while the protein regulatory network is described by a system of partial differential equations. The model describes interactions between the platelet aggregation and the coagulation cascade. As a result of modelling we propose a new mechanism of clot growth and growth arrest in flow.

The developed model and its parts can be used as a base to modelling of different physiological phenomena related to cell-cell interactions and blood flows. In this context we discuss some prospects of this modelling approach (e.g. modelling of morphogenesis, atherosclerosis), as well as some ongoing modelling projects (e.g. cell deformation in a narrow flow, spontaneous blood coagulation).

A (strict) categorical group is a (strict) monoidal category with an additional operation of 'inversion' under monoidal product. It has an equivalent description in terms of crossed modules. In order to study the representations/actions of categorical groups, we introduce a notion of semi-direct product of categories. It turns out that there are many interesting examples of semi-direct product of categories. In particular I will give some examples where one of the category is a (strict) categorical group. We use the notion of semi direct product of categories to define a kind of 'twisted action' of a categorical group. If time permits I will discuss a version of Schur's lemma in this context.
 

Reference:Twisted actions of categorical groups, S Chatterjee, A Lahiri, A Sengupta, Theory and Applications of Categories, Vol. 29, 2014, No. 8, pp 215-255

I will describe general ideas that lead to the explicit constructions of models of emergent space. In particular, I will solve a pre-geometric quantum mechanical model for D-particles in a presence of a large number of background D4 branes, and show that it is equivalent to the classical motion of the particles in the ten dimensional geometry sourced by the D4 branes. If time allows, other cases will be briefly discussed as well.

In 1958, Kolmogorov defined the entropy of a probability measure preserving transformation. Entropy has since been central to the classification theory of measurable dynamics. In the 70s and 80s researchers extended entropy theory to measure preserving actions of amenable groups (Kieffer, Ornstein-Weiss). My recent work generalizes the entropy concept to actions of sofic groups; a class of groups that contains for example, all subgroups of GL(n,C). Applications include the classification of Bernoulli shifts over a free group. This answers a question of Ornstein and Weiss.

Résumé : En 1948 H.S. Wall a publié ses résultats sur la théorie analytique des fractions continues. Dans la première partie de cet exposé nous présentons une classe remarquable de fractions continues introduite par Wall et appelées g-fractions. Nous montrerons comment elles peuvent être utilisées pour approcher certaines applications analytiques bornées réelles.
La deuxième partie de l’exposé sera consacrée aux applications de cette méthode. Nous discuterons de la conjecture de Ramanujan portant sur la convergence d’une des fractions continues, la théorie de renormalisation des applications unimodales (l’approche herglotzien de H. Epstein), et la sommabilité de séries de Poincaré-Sundman dans le problème des 3 corps.

Abstract: In 1948 Hubert Wall introduced the particular class of analytic continued fractions called g-fractions. In the first part of this talk we describe briefly the definition and its principal properties. We show how g-fractions arise naturally in some problems related to dynamical systems theory and random walks. We introduce then the Ramanujan conjecture from the theory of limit periodic continued fractions and its solution given with help of g-fractions. The g-fractions can be effectively used in approximation theory. Here we explain how the anti-Herglotz functions approach of Henri Epstein can inspire us to use g-fractions in approximation of fixed points of renormalization operators in functional spaces. Finally, some applications of g-fractions to Sundman-Poincaré series from celestial mechanics are discussed.