### Stochastic modeling for population dynamics: simulation and inference - Part 3

Benoîte De Saporta
The aim of this course is to present some examples of stochastic models suitable for population dynamics. The first part will introduce a class of continuous time models called piecewise deterministic Markov processes (PDMPs). Their trajectories are deterministic with jumps at random times. They are especially suitable to model phenomena with different time scales: a fast time-sacla corresponding to the deterministic behaviour and a slow time-scale corresponding to the jumps. I'll present different biological systems...

### Stochastic modeling for population dynamics: simulation and inference - Part 2

Benoîte De Saporta
The aim of this course is to present some examples of stochastic models suitable for population dynamics. The first part will introduce a class of continuous time models called piecewise deterministic Markov processes (PDMPs). Their trajectories are deterministic with jumps at random times. They are especially suitable to model phenomena with different time scales: a fast time-sacla corresponding to the deterministic behaviour and a slow time-scale corresponding to the jumps. I'll present different biological systems...

### Stochastic modeling for population dynamics: simulation and inference - Part 1

Benoîte De Saporta
The aim of this course is to present some examples of stochastic models suitable for population dynamics. The first part will introduce a class of continuous time models called piecewise deterministic Markov processes (PDMPs). Their trajectories are deterministic with jumps at random times. They are especially suitable to model phenomena with different time scales: a fast time-sacla corresponding to the deterministic behaviour and a slow time-scale corresponding to the jumps. I'll present different biological systems...

### Sup-norm estimates for $\overline{\partial}$ in $\mathbb{C}^{3}$

Berit Stensønes
I will talk about recent joint work with Dusty Grundmeier and Lars Simon. We have proved sup-norm estimates for dbar on a wide class of pseudoconvex domains in $\mathbb{C}^{3}$, including all known examples of bounded, pseudoconvex domains with real-analytic boundary of finite D’Angelo type.

### Unique ergodicity for foliations on compact Kähler surfaces

Nessim Sibony
How to study the dynamics of a holomorphic polynomial vector field in $\mathbb{C}^{2}$? What is the replacement of invariant measure? I will survey some surprising rigidity results concerning the behavior of these dynamical system. It is helpful to consider the extension of this dynamical system to the projective plane. Consider a foliation in the projective plane admitting a unique invariant algebraic curve. Assume that the foliation is generic in the sense that its singular points...

### Birational transformations preserving codimension one foliations

Jorge Vitório Pereira
I will report on a work in progress with Federico Lo Bianco, Erwan Rousseau, and Frédéric Touzet about the structure of codimension one foliations having an infinite group of birational symmetries.

### Symplectic Carleman approximation on co-adjoint orbits

Erlend Fornæss Wold
For a complex Lie group $G$ with a real form $G_{0}\subset G$, we prove that any Hamiltionian automorphism $\phi$ of a coadjoint orbit $\mathcal{O}_{0}$ of $G_{0}$ whose connected components are simply connected, may be approximated by holomorphic $O_{0}$-invariant symplectic automorphism of the corresponding coadjoint orbit of $G$ in the sense of Carleman, provided that $\mathcal{O}$ is closed. In the course of the proof, we establish the Hamiltonian density property for closed coadjoint orbits of all...

### Projective rational manifolds with non-finitely generated discrete automorphism group and infinitely many real forms

Keiji Oguiso
We show, among other things, one way to construct a smooth complex projective rational variety of any dimension n ≥ 3, with discrete non-finitely generated automorphism group and with infinitely many mutually non-isomorphic real forms. This is a joint work in progress with Professors Tien-Cuong Dinh and Xun Yu.

### Spatial search using lackadaisical quantum walks

Thomas G. Wong
The coined quantum walk is a discretization of the Dirac equation of relativistic quantum mechanics, and it is a useful model for developing quantum algorithms. For example, many quantum spatial search algorithms are based on coined quantum walks. In this talk, we explore a lazy version of the coined quantum walk, called a lackadaisical quantum walk, which uses a weighted self-loop at each vertex so that the walker has some amplitude of staying put. We...

### Problems with continuous quantum walks

Chris Godsil
Continuous quantum walks are of great interest in quantum computing and, over the last decade, my group has been studying this topic intensively. As graph theorists, one of our main goals has been to get a better understanding of the relation between the properties of a walk and the properties of the underlying graph. We have had both successes and failures. The failures lead to a number of interesting open questions, which I will present...

### Time-multiplexed quantum walks

Christine Silberhorn
Photonic quantum systems, which comprise multiple optical modes, have become an established platform for the experimental implementation of quantum walks. However, the implementation of large systems with many modes, this means for many step operations, a high and dynamic control of many different coin operations and variable graph structures typically poses a considerable challenge. Time-multiplexed quantum walks are a versatile tool for the implementation of a highly flexible simulation platform with dynamic control of the...

### How to compute using quantum walks

Vivien Kendon
Quantum walks are widely and successfully used to model diverse physical processes. This leads to computation of the models, to explore their properties. Quantum walks have also been shown to be universal for quantum computing. This is a more subtle result than is often appreciated, since it applies to computations run on qubit-based quantum computers in the single walker case, and physical quantum walkers in the multi-walker case (quantum cellular automata). Nonetheless, quantum walks are...

Stefanie Barz

### Interview at CIRM: Martin Hairer

Martin Hairer
Martin Hairer KBE FRS (born 14 November 1975 in Geneva, Switzerland) is an Austrian mathematician working in the field of stochastic analysis, in particular stochastic partial differential equations. As of 2017 he is Regius Professor of Mathematics at the University of Warwick, having previously held a position at the Courant Institute of New York University. He was awarded the Fields Medal in 2014, one of the highest honours a mathematician can achieve.

### Correlation spectrum of Morse-Smale flows

Gabriel Rivière
I will explain how one can get a complete description of the correlation spectrum of a Morse-Smale flow in terms of the Lyapunov exponents and of the periods of the flow. I will also discuss the relation of these results with differential topology. This a joint work with Nguyen Viet Dang (Université Lyon 1).

### Simulation of kinetik electrostatic electron nonlinear (KEEN) waves with variable velocity resolution grids and high-order time-splitting

Michel Mehrenberger
KEEN - Vlasov plasmas - acoustic waves - semi-Lagrangian scheme - Vlasov-Poisson equation; - BGK mode

### On the Hall-MHD equations

Dongho Chae
In this talk we present recent results on the Hall-MHD system. We consider the incompressible MHD-Hall equations in $\mathbb{R}^3$. $\partial_tu +u \cdot u + \nabla u+\nabla p = \left ( \nabla \times B \right )\times B +\nu \nabla u,$ $\nabla \cdot u =0, \nabla \cdot B =0,$ $\partial_tB - \nabla \times \left (u \times B\right ) + \nabla \times \left (\left (\nabla \times B\right )\times B \right ) = \mu \nabla B,$ \$u\left (x,0...

### Tracing the dark matter web

Sergei Shandarin
Dark matter (DM) constitutes almost 85% of all mass able to cluster into gravitationally bound objects. Thus it has played the determining role in the origin and evolution of the structure in the universe often referred to as the Cosmic Web. The dark matter component of the Cosmic Web or simply the Dark Matter Web is considerably easier to understand theoretically than the baryonic component of the web if one assumes that DM interacts only...

### Polariton graph simulators

Natalia Berloff
We propose a platform for finding the global minimum of XY Hamiltonian with polariton graphs. We derive an approximate analytic solution to the spinless complex Ginzburg-Landau equation that describes the density and kinetics of a polariton condensate under incoherent pumping. The analytic expression of the wavefunction is used as the building block for constructing the XY Hamiltonian of two-dimensional polariton graphs. We illustrate examples of the quantum simulator for various classical magnetic phases on some...

### Recent progress in the classification of torsion subgroups of elliptic curves

Alvaro Lozano-Robledo
This talk will be a survey of recent results and methods used in the classification of torsion subgroups of elliptic curves over finite and infinite extensions of the rationals, and over function fields.

### Signature morphisms from the Cremona group

Susanna Zimmermann
The plane Cremona group is the group of birational transformations of the projective plane. I would like to discuss why over algebraically closed fields there are no homomorphisms from the plane Cremona group to a finite group, but for certain non-closed fields there are (in fact there are many). This is joint work with Stéphane Lamy.

### On low temperature kinetic theory; spin diffusion, anyons, Bose Einstein condensates

Leif Arkeryd
To illustrate specifically quantum behaviours, the talk will consider three typical problems for non-linear kinetic models evolving through pair collisions at temperatures not far from absolute zero. Based on those examples, a number of differences between quantum and classical Boltzmann theory is discussed in more general term.

Anne Mangeney

### Fusion rings from quantum groups and DAHA actions

Catharina Stroppel
In this talk I will give a short overview about fusion rings arising from quantum groups at odd and even roots of unities. These are Grothendieck rings of certain semisimple tensor categories. Then I will study these rings in more detail. The main focus of the talk will be an expectation by Cherednik that there is a certain DAHA action on these rings which can be used to describe the multiplication and semisimplicity of these...

Omer Offen

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