The particularity of the nonlinear processes is that they satisfy some stochastic differential equations where there is no linearity (with respect to the associated partial differential equation). The linear stochastic processes had been well known for decades. But, the nonlinear ones are the subject of intense researchs in the domain of the probability, in the partial differential equations but also in the applications of the mathematics.
However, real phenomena are more often nonlinear processes than linear one.
Let us give some examples of nonlinear processes that we are interested in:

- The self-stabilizing diffusion. This diffusion can be obtained as a limit of mean-field particles interacting system. It has been initially constructed to modelize the plasmas. However, it now is used to study chemical or biological species in interaction or in the contraction of the muscular cells.
- The diffusion of Dreyer et al. This diffusion is of McKean-Vlasov type. It is used to count the proportion of Lithium atoms in a Lithium-battery. By assuming that the charge is slow, an hysteresis phenomenon appears. Nevertheless, this phenomenon (obtained by some authors by analytical techniques) is not well understood in the probabilistic view point.
- The Delarue Inglis Rubenthaler and Tanré diffusion. It is used to modelise the potential of the membrane of a neuron in a neuronal system with a large number of neurons. Some metastability questions occurs for this model which well-posedness has been obtained in 2015.
- The self-interacting diffusion. In addition to its use to modelise some polymers, it can also be used in stochastic algorithms. Indeed, the classical method of gradient descending has a default: the slowness if the cost potential that we search the minimum (which is classical when we do a maximum of likelihood) is nonconvex. So, we used the simulated anneahiling. By using the self-interacting diffusion, one expect to reduce the exit-time so that the method would be faster.
- The Cucker-Smale diffusion. This diffusion is a stochastic version of the classical Cucker-Smale model. This model is used to understand the flocking. It is of McKean-Vlasov type with also the position.

- Romain Ravaille, Institut Camille Jordan
- Julian Tugaut, Institut Camille Jordan
- Pascale Villet, Institut Camille Jordan

- Alessandra BIANCHI, Padova (Italy)
- Paul-Eric CHAUDRU DE RAYNAL, Chambéry (France)
- Quentin CORMIER (INRIA Nice)
- François DELARUE, Nice (France)
- Gonçalo DOS REIS, Edinburgh (United Kingdom)
- Hong DUONG, Birmingham (United Kingdom)
- Jean-François JABIR, Moscow (Russia)
- Aline KURTZMANN, Nancy (France)
- Michela OTTOBRE, Edinburgh (United Kingdom)
- Grigorios PAVLIOTIS, London (United Kingdom)
- William SALKELD, Edinburgh (United Kingdom)
- Lukasz SZPRUCH, Edinburgh (United Kingdom)
- Etienne TANRÉ, Nice (France)
- Milica TOMASEVIC, Polytechnique (France)

- Oumaima BENCHEIKH, (École des Ponts ParisTech)
- Quentin CORMIER (INRIA Nice)
- Paul DOBSON (Heriott-Watt University, Edinburgh)
- William HAMMERSLEY (University of Edinburgh)
- Romain RAVAILLE (Université Jean Monnet, Saint-Étienne)
- William SALKELD (University of Edinburgh)

Talk of Alessandra BIANCHI

Talk of Paul-Eric CHAUDRU DE RAYNAL

Talk of Quentin CORMIER

Talk of François DELARUE

Talk of Gonçalo DOS REIS

Talk of Hong DUONG

Talk of Jean-François JABIR

Talk of Aline KURTZMANN

Talk of Michela OTTOBRE

Talk of Grigorios PAVLIOTIS

Talk of William SALKELD (to appear soon)

Talk of Lukasz SZPRUCH

**Talk of Etienne TANRÉ was in blackboard.**

**Talk of Milica TOMASEVIC was in blackboard.**

Poster of Oumaima BENCHEIKH

Poster of Quentin CORMIER

Poster of Paul DOBSON

Poster of William HAMMERSLEY

Poster of Romain RAVAILLE

Poster of William SALKELD

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We are thankful to Université Jean Monnet, Institut Camille Jordan, Labex MiLyon and Fédération de Recherche en Mathématiques Auvergne Rhône-Alpes.