We shall try to assign  mathematical meaning to the language used by biologists for describing   basic structures and processes in  living organisms, from the   (sub)cellular level up to  evolutionary dynamics of populations. 
In particular, we shall elucidate  the mathematical as well as biological meaning of the following concepts.
● biological (non-Shannon) information,● descriptional (non-Kolmogorov) complexity,● biological structure,● biological function (performed by a particular structure), ● biological purpose (of a function),● information/program encoded and stored by a material structure (DNA, RNA),● information/signal transmitted by a matter/energy process/flow, ● information/program, which controls such a « flow »,● biological structures build by (networks of) matter/energy flows, e.g transcription –> translation –>  protein folding.
Also we indicate a potential use of formalisation of  biological language  in genetic engineering, e.g. in the analysis/applications of CRISPR and of  phage assisted continuous evolution.

We shall try to assign  mathematical meaning to the language used by biologists for describing   basic structures and processes in  living organisms, from the   (sub)cellular level up to  evolutionary dynamics of populations. 
In particular, we shall elucidate  the mathematical as well as biological meaning of the following concepts.
● biological (non-Shannon) information,● descriptional (non-Kolmogorov) complexity,● biological structure,● biological function (performed by a particular structure), ● biological purpose (of a function),● information/program encoded and stored by a material structure (DNA, RNA),● information/signal transmitted by a matter/energy process/flow, ● information/program, which controls such a « flow »,● biological structures build by (networks of) matter/energy flows, e.g transcription –> translation –>  protein folding.
Also we indicate a potential use of formalisation of  biological language  in genetic engineering, e.g. in the analysis/applications of CRISPR and of  phage assisted continuous evolution.

We shall try to assign  mathematical meaning to the language used by biologists for describing   basic structures and processes in  living organisms, from the   (sub)cellular level up to  evolutionary dynamics of populations. 
In particular, we shall elucidate  the mathematical as well as biological meaning of the following concepts.
● biological (non-Shannon) information,● descriptional (non-Kolmogorov) complexity,● biological structure,● biological function (performed by a particular structure), ● biological purpose (of a function),● information/program encoded and stored by a material structure (DNA, RNA),● information/signal transmitted by a matter/energy process/flow, ● information/program, which controls such a « flow »,● biological structures build by (networks of) matter/energy flows, e.g transcription –> translation –>  protein folding.
Also we indicate a potential use of formalisation of  biological language  in genetic engineering, e.g. in the analysis/applications of CRISPR and of  phage assisted continuous evolution.

We shall try to assign  mathematical meaning to the language used by biologists for describing   basic structures and processes in  living organisms, from the   (sub)cellular level up to  evolutionary dynamics of populations. 
In particular, we shall elucidate  the mathematical as well as biological meaning of the following concepts.
● biological (non-Shannon) information,● descriptional (non-Kolmogorov) complexity,● biological structure,● biological function (performed by a particular structure), ● biological purpose (of a function),● information/program encoded and stored by a material structure (DNA, RNA),● information/signal transmitted by a matter/energy process/flow, ● information/program, which controls such a « flow »,● biological structures build by (networks of) matter/energy flows, e.g transcription –> translation –>  protein folding.
Also we indicate a potential use of formalisation of  biological language  in genetic engineering, e.g. in the analysis/applications of CRISPR and of  phage assisted continuous evolution.

Probability and analysis informal seminar
In this talk, we will briefly review the main ideas for solving singular SPDEs with the use of Regularity Structures. After presenting the main symmetries known, we will focus on some recent progress concerning the chain rule symmetry in the full subcritical regime. These symmetries allow us to restrict the space of solutions.
 
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
In this talk, it will be shown that the Kerr metric describes a pair of self-dual and anti-self-dual Taub-NUT instantons, like the N and S poles of a bar magnet. The implications of this fact will be discussed. Firstly, it derives the Newman-Janis algorithm without an ambiguity: a mathematical procedure that generates spinning black hole solutions from non-spinning ones by means of a complex transformation, previously believed as merely a formal construct. Secondly, it uniquely determines the effective point-particle Lagrangian of Kerr black hole in post-Minkowskian gravity, based on the topological nature of the gravitational Dirac string (Misner string) associated with the NUT charges. This off-shell construction resolves the longstanding struggle that the gravitational dynamics of Kerr black holes at the second post-Minkowskian order is not uniquely, or easily, determinable from the scattering amplitudes methods. The gravitational Compton amplitude for Kerr black hole will be presented, which achieves correct factorizations without spurious poles in a simple manner. Finally, a new chapter of relativity will be proposed, in which spin is intrinsically unified into spacetime: « spinspacetime”.
 
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Kadanoff’s block idea pioneers the renormalization group (RG) theory and clarifies the scaling hypothesis in critical phenomena. Nevertheless, it has difficulty as a quantitatively reliable RG method due to uncontrolled approximations when formulated in the spin language. Reformulated in a modern tensor-network language, the block idea is equipped with a natural measure of RG errors. In 2D, the RG errors are typically smaller than 1% and decrease systematically when more coupling constants are retained in the RG map. The relative error of the estimated free energy of the 2D Ising model can easily go down to about 10-9 using a personal computer.
In 3D, due to the linear growth of entanglement entropy, the RG errors are too large for the block-tensor map to be reliable. For the 3D Ising model, the RG errors grow to more than 10% just after one RG step, and then keep growing to more than 30% near the critical fixed point. Even worse, the estimated scaling dimensions fail to converge with respect to the RG step. We propose an entanglement filtering (EF) scheme to cleanse the redundant entanglement. Enhanced by the proposed EF, the RG errors near the critical fixed point goes down to 6%; they decrease slowly to 2% when more couplings are retained. The estimated scaling dimensions become stable respect to the RG step. The relative errors of the first two relevant fields are 0.4% and 0.1% in the best case. The proposed RG is promising as a systematically-improvable real space RG method in 3D.
 
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The most universal kind of linear algebra is based not on abelian groups, but on homotopy-theoretic objects known as spectra. According to chromatic homotopy theory, one can systematically organize spectra into periodic families.  On the other hand, a natural source of spectra is provided by algebraic K-theory, a highly refined cohomological invariant of rings (or schemes, etc).  This leads to the subject of this course: the interaction of the chromatic theory with algebraic K-theory.  The story begins with classical theorems of Thomason, Mitchell, and Hesselholt-Madsen.  Bold generalizations of these theorems were conjectured by Rognes and Ausoni-Rognes, under the umbrella term of « redshift ».  Several of these conjectures are now theorems due to recent work of many people.  Remarkably, this work has applications to « pure » chromatic homotopy theory: Burklund-Hahn-Levy-Schlank used it to settle (in the negative) the « telescope conjecture », the last of Ravenel’s conjectures.
Lecture 1: Introduction to chromatic homotopy theory.Lecture 2: Descent and « soft redshift ».
 Lecture 3: « Hard redshift », a.k.a. the Lichtenbaum-Quillen property.
 Lecture 4: The telescope conjecture.

The most universal kind of linear algebra is based not on abelian groups, but on homotopy-theoretic objects known as spectra. According to chromatic homotopy theory, one can systematically organize spectra into periodic families.  On the other hand, a natural source of spectra is provided by algebraic K-theory, a highly refined cohomological invariant of rings (or schemes, etc).  This leads to the subject of this course: the interaction of the chromatic theory with algebraic K-theory.  The story begins with classical theorems of Thomason, Mitchell, and Hesselholt-Madsen.  Bold generalizations of these theorems were conjectured by Rognes and Ausoni-Rognes, under the umbrella term of « redshift ».  Several of these conjectures are now theorems due to recent work of many people.  Remarkably, this work has applications to « pure » chromatic homotopy theory: Burklund-Hahn-Levy-Schlank used it to settle (in the negative) the « telescope conjecture », the last of Ravenel’s conjectures.
Lecture 1: Introduction to chromatic homotopy theory.Lecture 2: Descent and « soft redshift ».
 Lecture 3: « Hard redshift », a.k.a. the Lichtenbaum-Quillen property.
 Lecture 4: The telescope conjecture.

The most universal kind of linear algebra is based not on abelian groups, but on homotopy-theoretic objects known as spectra. According to chromatic homotopy theory, one can systematically organize spectra into periodic families.  On the other hand, a natural source of spectra is provided by algebraic K-theory, a highly refined cohomological invariant of rings (or schemes, etc).  This leads to the subject of this course: the interaction of the chromatic theory with algebraic K-theory.  The story begins with classical theorems of Thomason, Mitchell, and Hesselholt-Madsen.  Bold generalizations of these theorems were conjectured by Rognes and Ausoni-Rognes, under the umbrella term of « redshift ».  Several of these conjectures are now theorems due to recent work of many people.  Remarkably, this work has applications to « pure » chromatic homotopy theory: Burklund-Hahn-Levy-Schlank used it to settle (in the negative) the « telescope conjecture », the last of Ravenel’s conjectures.
Lecture 1: Introduction to chromatic homotopy theory.Lecture 2: Descent and « soft redshift ».
 Lecture 3: « Hard redshift », a.k.a. the Lichtenbaum-Quillen property.
 Lecture 4: The telescope conjecture.

The most universal kind of linear algebra is based not on abelian groups, but on homotopy-theoretic objects known as spectra. According to chromatic homotopy theory, one can systematically organize spectra into periodic families.  On the other hand, a natural source of spectra is provided by algebraic K-theory, a highly refined cohomological invariant of rings (or schemes, etc).  This leads to the subject of this course: the interaction of the chromatic theory with algebraic K-theory.  The story begins with classical theorems of Thomason, Mitchell, and Hesselholt-Madsen.  Bold generalizations of these theorems were conjectured by Rognes and Ausoni-Rognes, under the umbrella term of « redshift ».  Several of these conjectures are now theorems due to recent work of many people.  Remarkably, this work has applications to « pure » chromatic homotopy theory: Burklund-Hahn-Levy-Schlank used it to settle (in the negative) the « telescope conjecture », the last of Ravenel’s conjectures.
Lecture 1: Introduction to chromatic homotopy theory.Lecture 2: Descent and « soft redshift ».
 Lecture 3: « Hard redshift », a.k.a. the Lichtenbaum-Quillen property.
 Lecture 4: The telescope conjecture.

I will explain how convex projective geometry over non-Archimedean ordered fields may be used to study large scale properties of individual real Hilbert geometries and degenerations of convex projective actions, using a projective geometry version of ultralimits. Non-Archimedean convex subsets have a naturally associated quotient Hilbert metric space. In the case of ultralimits, we show that it is the ultralimit of the real Hilbert metric spaces under a natural non-degeneracy condition. I will present some examples and give a full description of the Hilbert metric space for non-Archimedean polytopes defined over R, which correspond to the asymptotic cones of a fixed real polytope. This is joint work with Xenia Flamm.