Let K be a CDVF of mixed characteristic (0,p) and G the absolute Galois group of K. When the residue field of K is perfect, Laurent Berger constructed a p-adic differential equation NdR(V) for any de Rham representation V of G. In this talk, we will generalize his construction when the residue field of K is not perfect. We also explain some ramification properties of our NdR , which are due to Adriano Marmora in the perfect residue field case.

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Computational anatomy has emerged as a new subject focusing on the quantitative analysis of the variability of biological shapes with interesting challenges both from the mathematical and computational point of view. In this talk I will explain how a geometrical point of view based on the idea of shapes as structured spaces, actions of groups of diffeomorphisms and (sub)-Riemannian geometry provide nice vehicles to build a full processing framework called here diffeomorphometry.

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

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