Each living animal or human originates from a single cell, which divides several times, then cells differentiate and robustly self-organize into tissues and organs. This talk will discuss mechanisms governing such tissue development. Forces, shapes, movements, shape changes, all obey the laws of mechanics. But cellular materials (made of cells tiling the space) have peculiar mechanical properties.Our example is the Drosophila metamorphosis: within a few days, the fly strikingly changes from a rather simple maggot shape to a refined adult shape with wings, legs, antennas, waist, neck, and compound eyes. We film the fly’s dorsal structure (the thorax, see Figure), and its wing. We characterize quantitatively each geometrical or topological change at cell scale: cell divisions, cell neighbour changes, cell size and shape changes, and programmed cell deaths. Our unified description respects tensorial symmetry and is thus built to be valid in any dimension. It enables us to coarse-grain the discrete description, at the cell scale, to link it with a continuum mechanics description, which encompasses the information useful at the tissue scale. Such rigorous multi-scale
approach applies to a large class of disordered systems, including aggregates of living cells, or collectively migrating cells.In addition, measuring mechanical stresses in situ in the developing tissues evidences unexpected interplays between patterns of tissue elongation, cell division and mechanical stress. The complex regulation of tissue morphology, based on feedbacks betwen physics and genetics, is the subject of active researches: open questions and perspectives will be presented.

 

In 1970 Matiyasevich, building on earlier work of Davis–Putnam–Robinson, proved that every enumerable subset of $mathbb{Z}$ is Diophantine, thus showing that Hilbert’s 10th problem is undecidable for $mathbb{Z}$. The problem of extending this result to the ring of integers of number fields (and more generally to finitely generated infinite rings) has attracted significant attention and, thanks to the efforts of many mathematicians, the task has been reduced to the problem of constructing, for certain quadratic extensions of number fields $L/K$, an elliptic curve $E/K$ with $rk(E(L))=rk(E(K))>0$.  In this talk I will explain joint work with Peter Koymans, where we use Green–Tao to construct the desired elliptic curves, settling Hilbert 10 for every finitely generated infinite ring.
 
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Atttention : La première Leçon aura lieu à l’IMO, Amphithéâtre Yoccoz, le 11 mars de 10h à 12h
Retrouvez toutes ces informations sur le site de la Fondation Mathématique Jacques Hadamard :
https://www.fondation-hadamard.fr/fr/evenements/cours-avances/
Abstract:
We will discuss some recent work around the geometric Langlands program. Specific topics will depend on audience interest, but I hope to introduce the subject generally, discuss some parts of the proof of geometric Langlands in characteristic 0, give partial results in characteristic p, and discuss some arithmetic applications.
 

Atttention : La première Leçon aura lieu à l’IMO, Amphithéâtre Yoccoz, le 11 mars de 10h à 12h
Retrouvez toutes ces informations sur le site de la Fondation Mathématique Jacques Hadamard :
https://www.fondation-hadamard.fr/fr/evenements/cours-avances/
Abstract:
We will discuss some recent work around the geometric Langlands program. Specific topics will depend on audience interest, but I hope to introduce the subject generally, discuss some parts of the proof of geometric Langlands in characteristic 0, give partial results in characteristic p, and discuss some arithmetic applications.
 

Atttention : La première Leçon aura lieu à l’IMO, Amphithéâtre Yoccoz, le 11 mars de 10h à 12h
Retrouvez toutes ces informations sur le site de la Fondation Mathématique Jacques Hadamard :
https://www.fondation-hadamard.fr/fr/evenements/cours-avances/
Abstract:
We will discuss some recent work around the geometric Langlands program. Specific topics will depend on audience interest, but I hope to introduce the subject generally, discuss some parts of the proof of geometric Langlands in characteristic 0, give partial results in characteristic p, and discuss some arithmetic applications.
 

Atttention : La première Leçon aura lieu à l’IMO, Amphithéâtre Yoccoz, le 11 mars de 10h à 12h
Retrouvez toutes ces informations sur le site de la Fondation Mathématique Jacques Hadamard :
https://www.fondation-hadamard.fr/fr/evenements/cours-avances/
Abstract:
We will discuss some recent work around the geometric Langlands program. Specific topics will depend on audience interest, but I hope to introduce the subject generally, discuss some parts of the proof of geometric Langlands in characteristic 0, give partial results in characteristic p, and discuss some arithmetic applications.
 

Atttention : La première Leçon aura lieu à l’IMO, Amphithéâtre Yoccoz, le 11 mars de 10h à 12h
Retrouvez toutes ces informations sur le site de la Fondation Mathématique Jacques Hadamard :
https://www.fondation-hadamard.fr/fr/evenements/cours-avances/
Abstract:
We will discuss some recent work around the geometric Langlands program. Specific topics will depend on audience interest, but I hope to introduce the subject generally, discuss some parts of the proof of geometric Langlands in characteristic 0, give partial results in characteristic p, and discuss some arithmetic applications.
 

Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
In the first part of my talk, I will discuss the distinction between (i) the conservativeenergy, which is conserved under the conservative equations of motion, and (ii) the binding energy, which enters the flux-balance laws. The difference between these two energies is called a Schott term and was historically expected to vanish for circular orbits. But I will show that at 4PN, the Schott term does not vanish due to a hereditary piece in the dissipative equations of motion. I will explain how the Schott term can link the notions of orbital and waveform frequencies and properly ensure the absence of arbitrary constants in physical observables within the post-Newtonian formalism.
In the second part of my talk, I will present the derivation of the action-angle 4PN conservative Hamiltonian for bound eccentric systems, including the 4PN tail term. The latter appears as an enhancement function of the eccentricity, which takes the form of a well-controlled infinite sum, which is resummed in a simple form such as to maintain a 10-5 relative accuracy for any eccentricity. It is then immediate to deduce the 4PN links between the conservative constants of motion (energy and angular momentum) and the fundamental (radial and azimuthal) orbital frequencies. From there, I obtain the 4PN redshift, which is in perfect agreement with analytical self-force.
 
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Running Seminar
The argument–shift method constructs maximal Poisson-commutative subalgebras of the symmetric algebra $S(mathfrak g)$ of a Lie algebra $mathfrak g$ with respect to the Lie–Poisson bracket. Their quantizations—known as quantum argument–shift subalgebras—form maximal commutative subalgebras of the universal enveloping algebra $U(mathfrak g)$ and play a fundamental role in quantum integrable systems. Although existence and uniqueness of these quantizations have been established in many cases, the underlying argument–shift procedures, realized as derivations of $S(mathfrak g)$, had not previously been quantized. Recently, Yasushi Ikeda and I defined quantized argument–shift procedures for $mathfrak{gl}_n$ and proved that they generate the associated quantum argument–shift subalgebras.
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Running Seminar
In my talk, I will introduce several sets of central elements in the universal enveloping algebra U(glN) and explain the relationships between them using average value of the gl-weight system as an example. As a consequence, we obtain a proof of the M. Kazarian, E. Krasilnikov, S. Lando, and M. Shapiro conjecture that the mean value of the gl-weight system is a tau function of the KP hierarchy.
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Séminaire de géométrie arithmétique
Hurwitz moduli spaces of covers of curves of degree $d$ are classical and well studied objects if one assumes that $d!$ is invertible and hence no wild ramification phenomena occur. There were very few attempts to study the wild case. In the most important one Abramovich and Oort started with the classical space $H_{2,1,0,4}$ of double covers of $P^1$ ramified at four points and (following an idea of Kontsevich and Pandariphande) described its schematic closure $H$ in the space of stable maps over $Z$. The result over $F_2$ was both strange and informative, but lacked a modular interpretation.
In the main part of my talk I will describe the example of Abramovich-Oort and then tell about a work in progress of Hippold, where a (logarithmic) modular version of Hurwitz space of degree $p$ is constructed when only $(p-1)!$ is invertible. In particular, it conceptually explains phenomena observed by Abramovich-Oort. In the second part I will briefly describe another outcome of the same ideas. It was observed by Abramovich-Ollson-Vistoli that $H$ is the blowing up of the modular curve $X(2)$. This is not a coincidence, and the same ideas can be used to refine the wild level structures of Drinfeld and construct modular interpretation of the minimal modifications of the curves $X(p^n)$ which separate ordinary branches at any supersingular point. This is a work in progress and I’ll only indicate the basic idea and some examples. 
 
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The magic triangle due to Cvitanovic and Deligne-Gross is an extension of the Freudenthal-Tits magic square of semisimple Lie algebras. In a recent work with Kimyeong Lee, we identify all 2d rational conformal field theories associated to the magic triangle. These include various Wess-Zumino-Witten models, Virasoro minimal models, compact bosons and their non-diagonal modular invariants. At level one, we find a two-parameter family of modular linear differential equation of fourth order whose solutions produce the affine characters of all elements in the magic triangle. We find a universal coset relation for the whole triangle which generalizes the dual pairs with respect to (E8)_1 in the Cvitanovic-Deligne exceptional series. At level two, we find a special row of the triangle – the subexceptional series has novel N=1 supersymmetry, and the super characters satisfy a one-parameter family of fermionic modular linear differential equations. Moreover, we find many new coset constructions involving WZW models at higher levels.
 
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