### Geometric recursion

Jorgen Ellegaard Andersen
Geometric Recursion is a very general machinery for constructing mapping class group invariants objects associated to two dimensional surfaces. After presenting the general abstract definition we shall see how a number of constructions in low dimensional geometry and topology fits into this setting. These will include the Mirzakhani-McShane identies, mapping class group invariant closed forms on Teichmüller space (including the Weil-Petterson symplectic form) and the Goldman symplectic form.

### Was the Russian theory of cycles a mathematical theory?

Irina Konovalova-Peaucelle
Cournot Centre session devoted to the transformations that took place in mathematical economics during the interwar period.

### Steady states and long range correlations in driven systems - Lecture 1

David Mukamel
In these three lectures steady states and dynamical properties of nonequilibrium systems will be discussed. Systems driven out of thermal equilibrium often reach a steady state which under generic conditions exhibits long-range correlations. This is very different from systems in thermal equilibrium where long-range correlations develop only at phase transition points. In some cases these correlations even lead to long-range order in d=1 dimension, of the type occurring in traffic jams. Simple examples of such...

### Entropy and entanglement bounds for reduced density matrices of fermionic states

Elliott H. Lieb
One of the important aspects of many-body quantum mechanics of electrons is the analysis of two-body density matrices. While the characterization of one-body density matrices is well known and simple to state, that of two-body matrices is far from simple – indeed, it is not fully known. In this talk I will present joint work with Eric Carlen in which we study the possible entropy of such matrices. We find, inter alia, that minimum entropy...

### Combination therapies and drug resistance in heterogeneous tumoral populations

Marcello Delitala
How combination therapies can reduce the emergence of cancer resistance? Can we exploit intra-tumoral competition to modify the effectiveness of anti-cancer treatments? Bearing these questions in mind, we present a mathematical model of cancer-immune competition under therapies. The model consists of a system of differential equations for the dynamics of two cancer clones and T-cells. Comparisons with experimental data and clinical protocols for non-small cell lung cancer have been performed. In silico experiments confirm that...

Dongho Chae

### Forward and backward simulation of Euler scheme

Emmanuel Gobet
We analyse how reverting Random Number Generator can be efficiently used to save memory in solving dynamic programming equation. For SDEs, it takes the form of forward and backward Euler scheme. Surprisingly the error induced by time reversion is of order 1.

### Bandits in auctions (& more)

Vianney Perchet
In this talk, I will introduce the classical theory of multi-armed bandits, a field at the junction of statistics, optimization, game theory and machine learning, discuss the possible applications, and highlights the new perspectives and open questions that they propose We consider competitive capacity investment for a duopoly of two distinct producers. The producers are exposed to stochastically fluctuating costs and interact through aggregate supply. Capacity expansion is irreversible and modeled in terms of timing...

### Privacy and statistical minimax: quantitative tradeoffs

Martin Wainwright
privacy mechanism#local differential privacy#discolure risk#Laplacian mechanism#statistical minimax with privacy#location estimation#total variation contraction#non-parametric density estimation#Sobolev smoothness class#nonparametric deconvolution#metric entropy#mutual information and Fano's inequality#mutual information contraction

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948
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192
• 2019
48

• Audiovisual
1,187