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

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.

In 1960, Higman asked whether the number f(n,q) of conjugacy classes of n x n unitriangular matrices U(n,q) over the finite field with q elements, is polynomial in q for every n.  I will survey what is known about this problem, explain the connections to realization spaces of matroids, enumerative combinatorics and group representation theory.  I will then describe our recent efforts to prove the conjecture for small n and disprove it for large n.

Joint work with Andrew Soffer.

I will show a simple example of fast-slow partially hyperbolic systems in which the fast variable acts similarly to a Gaussian  noise and will obtain, for such a deterministic setting, results similar to the one obtained in Freidlin–Wentzell theory. In particular, I will show conditions under which there exists a unique SRB measure with exponential decay of correlations.
 
(Work in collaboration with Jacopo de Simoi).

 

Information plays a critically important role in ecology and evolution but is very often subjective or analog or both. This is a problem because most information theory has been developed for objective and discrete information. Can information theory be extended this theory to incorporate multiple forms of information, each with its own (physical) carriers and dynamics? Here I will not review all the possible roles information can play, but rather what conditions an appropriate theory should satisfy.
 

Séminaire Laurent Schwartz — EDP et applications

According to a widely held opinion, Life corresponds to a physical state far from equilibrium. Thus, whereas such fundamental notion of equilibrium physics as ‘ground state’ is widely used to describe the properties of biological macromolecules or even macromolecular complexes, it is considered of no use for the description of a whole living cell. I would like to challenge this preconception, by discussing how the idea of a cell in a ground state is possible, and what could be the nature of the forces responsible for its stability. Strikingly, this line of inquiry leads to a novel justification of the self-organization principle, as the action of the restoring forces responsible for the stability of the ground state amounts to “optimization without natural selection of replicators”. Unlike the statistical-mechanical approaches to self-organization, our approach does not encounter the problem of ‘tradeoff between stability and complexity’ at the level of individual cell.
 

The infrared structure of quantum gravity is explored by solving a lattice version of the Wheeler-DeWitt equations. For this talk, first, the case of 2+1 dimensions is presented. The wavefunction solutions only depend on the geometric quantities indicating preservation of diffeomorphism. Properties of the lattice vacuum are consistent with the existence of an ultraviolet fixed point in G located at the origin, thus precluding the existence of a weak coupling perturbative phase. The correlation length exponent is determined exactly and found to be nu=6/11. The results obtained lend support to the claim that the Lorentzian and Euclidean formulations belong to the same field-theoretic universality class. I then discuss some results in 3+1 dimensions. Investigations of the vacuum wave functional further indicate that for weak enough coupling, G < Gc, a pathological ground state with no continuum limit appears, where configurations with small curvature have vanishingly small probability.

Motivated by the 32-dimensional extension of the spin representation of the compact Lie algebra so(10) to the ‘maximal compact’ subalgebra of the real Kac-Moody Lie algebra of type E10 described by Damour et al. and Henneaux et al. Hainke and myself introduced the concept of a generalized spin representation that allows similar constructions for the ‘maximal compact’ subalgebras of real Kac-Moody Lie algebras of arbitrary simply laced type.

By work of Ghatei, Horn, Weiss and myself, integration of these representations leads to two-fold spin covers of the ‘maximal compact’ subgroups of the corresponding split real Kac-Moody groups. The problem that semisimple elements generally do not have a locally finite action and therefore obstruct integration is circumvented by an amalgamation method using the Iwasawa decomposition and the theory of buildings. The existence of these spin covers has been conjectured by Damour and Hillmann; it contains an extended Weyl group, which in the E10 case is relevant to fermionic billards.

We construct simply laced semisimple Lie algebras L with structure constants built into the Lie bracket. This also gives structure constants for the simply connected Chevalley group associated to the Lie algebra L. For infinite dimensional simply laced Kac-Moody algebras and their associated Kac-Moody groups, we obtain a complete description of the structure constants for root vectors corresponding to real roots whose sum is real. This is joint work with Pierre Cartier.