### Isoperimetry with density

Frank Morgan
In 2015 Chambers proved the Log-convex Density Conjecture, which says that for a radial density f on $R^n$, spheres about the origin are isoperimetric if and only if log f is convex (the stability condition). We discuss recent progress and open questions for other densities, unequal perimeter and volume densities, and other metrics.

### A minimaxmax problem for improving the torsional stability of rectangular plates

Filippo Gazzola
We introduce a new function which measures the torsional instability of a partially hinged rectangular plate. By exploiting it, we compare the torsional performances of different plates reinforced with stiffening trusses. This naturally leads to a shape optimization problem which can be set up through a minimaxmax procedure.

### Finite dimensional Hilbert space: spin coherent, basis coherent and anti-coherent states

Karol Zyczkowski
Among the set of all pure states living in a finite dimensional Hilbert space $\mathcal{H}_N$one distinguishes subsets of states satisfying some natural condition. One basis independent choice, consist in selecting the spin coherent states, corresponding to the $SU(2)$ group, or generalized, $SU(K)$ coherent states. Another often studied example is basis dependent, as states coherent with respect to a given basis are distinguished by the fact that the moduli of their off-diagonal elements (called 'coherences') are...

### Spacetime replication of continuous-variable quantum information

Barry Sanders
Combining the relativistic speed limit on transmitting information with linearity and unitarity of quantum mechanics leads to a relativistic extension of the no-cloning principle called spacetime replication of quantum information. We introduce continuous-variable spacetime-replication protocols, expressed in a Gaussian-state basis, that build on novel homologically constructed continuous-variable quantum error correcting codes. Compared to qubit encoding, our continuous-variable solution requires half as many shares per encoded system. We show an explicit construction for the five-mode case...

### New applications of coherent states in quantum information theory

Giulio Chiribella
Coherent states have been long known for their applications in quantum optics and atomic physics. In recent years, a number of new applications have emerged in the area of quantum information theory. In this talk I will highlight two such applications. The first is the comparison between classical and quantum strategies to process information. Byproducts of this comparison are benchmarks that can be used to certify quantum advantages in realistic experiments, fundamental relations between quantum...

### Les codes correcteurs

Christophe Ritzenthaler
A l'occasion du centenaire de la naissance de Claude Shannon, la SMF, la SMAI et le CIRM organisent, à l'issue de la conférence SIGMA, une après-midi d'exposés grand public autour de l'oeuvre scientifique de Claude Shannon, de la théorie de l'information et de ses applications.

### La compression des données

A l'occasion du centenaire de la naissance de Claude Shannon, la SMF, la SMAI et le CIRM organisent, à l'issue de la conférence SIGMA, une après-midi d'exposés grand public autour de l'oeuvre scientifique de Claude Shannon, de la théorie de l'information et de ses applications.

### Transferring information across image and shape collections

Niloy Mitra
Large image and 3D model repositories of everyday objects are now ubiquitous and are increasingly being used in computer graphics and computer vision, both for analysis and synthesis. However, images of objects in the real world have a richness of appearance that these repositories do not capture, largely because most existing 3D models are untextured. In this work we develop an automated pipeline capable of linking the two collections, and transporting texture information from images...

### Mutually enriching connections between ergodic theory and combinatorics - part 8

Vitaly Bergelson
² The early results of Ramsey theory : Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres. ² Three main principles of Ramsey theory : First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always...

### Mutually enriching connections between ergodic theory and combinatorics - part 7

Vitaly Bergelson
² The early results of Ramsey theory : Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres. ² Three main principles of Ramsey theory : First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always...

### Mutually enriching connections between ergodic theory and combinatorics - part 4

Vitaly Bergelson
² The early results of Ramsey theory : Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres. ² Three main principles of Ramsey theory : First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always...

### Mutually enriching connections between ergodic theory and combinatorics - part 2

Vitaly Bergelson
² The early results of Ramsey theory : Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres. ² Three main principles of Ramsey theory : First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always...

### Mutually enriching connections between ergodic theory and combinatorics - part 1

Vitaly Bergelson
² The early results of Ramsey theory : Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres. ² Three main principles of Ramsey theory : First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always...

### Panorama des services numériques de la Pateforme en Ligne pour les Mathématiques

Damien Ferney
Un panorama des Services Numériques disponibles sur la Plateforme en Ligne pour les Mathématiques (PLM). Nous ferons un inventaire des services numériques accessibles à travers le Portail des Mathématiques et décrirons leur utilité dans un cadre collaboratif ou nomade et nous aborderons brièvement leur utilisation et leur configuration.

### Forcing theory for transverse trajectories of surface homeomorphisms - Part 3

Fabio Tal
Several recent papers on surface dynamics have used transverse foliations and maximal isotopies for homeomorphisms isotopic to the identity as a main tool in their work. In this mini-course we will introduce the basic concepts behind this tool and show a new way o deriving useful dynamical information by means of a forcing procedure. The applications involve ways of obtaining existence of non-contractible periodic points with consequences for rotation sets of toral homeomorphisms, exponential growth...

### Forcing theory for transverse trajectories of surface homeomorphisms - Part 2

Patrice Le Calvez
Several recent papers on surface dynamics have used transverse foliations and maximal isotopies for homeomorphisms isotopic to the identity as a main tool in their work. In this mini-course we will introduce the basic concepts behind this tool and show a new way o deriving useful dynamical information by means of a forcing procedure. The applications involve ways of obtaining existence of non-contractible periodic points with consequences for rotation sets of toral homeomorphisms, exponential growth...

### Forcing theory for transverse trajectories of surface homeomorphisms - Part 1

Patrice Le Calvez
Several recent papers on surface dynamics have used transverse foliations and maximal isotopies for homeomorphisms isotopic to the identity as a main tool in their work. In this mini-course we will introduce the basic concepts behind this tool and show a new way o deriving useful dynamical information by means of a forcing procedure. The applications involve ways of obtaining existence of non-contractible periodic points with consequences for rotation sets of toral homeomorphisms, exponential growth...

### Sur la conjecture de Hodge entière pour les solides réels

Olivier Wittenberg
Nous formulons un analogue de la conjecture de Hodge entière pour les variétés réelles. Celui-ci possède des liens étroits avec des propriétés classiques: existence d'une courbe réelle de genre pair, algébricité de l'homologie du lieu réel. Comme dans le cas complexe, la conjecture de Hodge entière réelle peut tomber en défaut mais est plausible pour les 1-cycles sur les variétés dont la géométrie est assez simple. Nous l'établissons pour plusieurs familles de solides uniréglés. Il...

### Algebraic multigrid and subdivision

Maria Charina
Multigrid is an iterative method for solving large linear systems of equations whose Toeplitz system matrix is positive definite. One of the crucial steps of any Multigrid method is based on multivariate subdivision. We derive sufficient conditions for convergence and optimality of Multigrid in terms of trigonometric polynomials associated with the corresponding subdivision schemes. (This is a joint work with Marco Donatelli, Lucia Romani and Valentina Turati).

### The unitary extension principle on LCA groups

Ole Christensen
The unitary extension principle (UEP) by Ron & Shen yields a convenient way of constructing tight wavelet frames in L2(R). Since its publication in 1997 several generalizations and reformulations have been obtained, and it has been proved that the UEP has important applications within image processing. In the talk we will present a recent extension of the UEP to the setting of generalized shift-invariant systems on R (or more generally, on any locally compact abelian...

### Fourier-Mukai partners of canonical covers in positive characteristic

Sofia Tirabassi
We show that surfaces arising as canonical covers of Enriques and bielliptic surfaces do not have any non-trivial Fourier–Mukai partner, extending result of Sosna for complex surfaces. This is a joint work with K. Honigs and L. Lombardi.

### The non-archimedean SYZ fibration and Igusa zeta functions - Part 2

Johannes Nicaise
The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its relations with the Minimal Model Program and Igusa's p-adic zeta functions. No prior knowledge of non-archimedean geometry is assumed. These lectures are based on joint work with Mircea Mustata and Chenyang Xu.

### Catching ghosts with a coarse net: real and imaginary effects in ecological monitoring routine based on sparse sampling

Natalia Petrovskaya
Data collection and subsequent interpretation plays an important role in many ecological problems. Quantities such as the total population size and/or average population density are often evaluated based on data collected as a result of a sampling procedure. Accurate evaluation of the above quantities is crucial in ecological applications where they are used for making decision about means of control. Examples include management of pest insects in agricultural fields, prevention of plant diseases and control...

### Evolutionary branching: trade-offs and magic traits

Eva Kisdi
Adaptive dynamics has shaped our understanding of evolution by demonstrating that, via the process of evolutionary branching, ecological interactions can promote diversification. The classical approach to study the adaptive dynamics of a system is to specify the ecological model including all trade-off functions and other functional relationships, and make predictions depending on the parameters of these functions. However, the choice of trade-offs and other functions is often the least well justified element of the model,...

### Quiver Grassmannians of Dynkin type

Giovanni Cerulli-Irelli
Given a finite-dimensional representation M of a Dynkin quiver Q (which is the orientation of a simply-laced Dynkin diagram) we attach to it the variety of its subrepresentations. This variety is strati ed according to the possible dimension vectors of the subresentations of M. Every piece is called a quiver Grassmannian. Those varieties were introduced by Schofield and Crawley Boevey for the study of general representations of quivers. As pointed out by Ringel, they also...

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