## Construction of geometric rough paths

Abstract: This talk is based on a joint work in progress with L. Zambotti (UPMC). First, I will give a brief introduction to the theory of rough paths focusing on the case of Hölder regularity between 1/3 and 1/2. After this, I will address the basic problem of construction of a geometric rough path over a given ɑ-Hölder path in a finite-dimensional vector space. Although this problem was already solved by Lyons and Victoir in 2007, their method relies on the axiom of choice and thus is not explicit; in exchange the proof is simpler. In an upcoming paper, we provide an explicit...

Read More## 3 SESIONES SEMINARIO OPTIMIZACION Y EQUILIBRIO

Expositores 16:00–16:30hrs Prof. Boulmezaoud, Tahar Zamene, Laboratoire de Mathématiques de Versailles, Université de Versailles, France Title: On Fourier transform and weighted Sobolev spaces Astract: We prove that Fourier transform defines a simple correspondance between weighted Sobolev spaces. As a consequence, we display a chain of nested invariant spaces over which Fourier transform is an isometry. &&&&& 16:30–17:00 hrs Prof. Lev Birbrair, Federal Univerisity of Ceara, Brazil Title: Resonance sequences. Differential equations meet Number Theory....

Read More## Limits of sequences of maximal monotone operators.

Abstract: We consider a sequence of maximal monotone operators on a reflexive Banach space. In general, the (Kuratowski) lower limit of such a sequence is not a maximal monotone operator. So, what can be said? In the first part of the talk, we show that such a limit is a representable monotone operator while its Mosco limit, when it exists, is a maximal monotone operator. As an application of the former result, we obtain that the variational sum of two maximal monotone operators is a representable monotone operator. In the second part of the talk, we consider a sequence of representative...

Read More## Non-Parametric Bayesian Techniques for Spatial Temporal Models, Optimisation and Decision Making

Abstract: The use of Bayesian techniques for modelling spatial temporal phenomena has extensively increased over the last decade, providing flexibility and uncertainty quantification for inference and prediction. This talk focuses on how to place Gaussian Process models over complex phenomena and explores how the information from these models can be used for flexible uncertainty aware decision making. This talk provides examples of the application and advantages of using these techniques for environmental monitoring, quantitative social sciences, criminology and human behaviour. (Esta...

Read More## The KPZ fixed point

Abstract: I will describe the construction and main properties of the KPZ fixed point, which is the scaling invariant Markov process conjectured to arise as the universal scaling limit of all models in the KPZ universality class, and which contains all the fluctuation behavior seen in the class. The construction follows from an exact solution of the totally asymmetric exclusion process (TASEP) for arbitrary initial condition. This is joint work with K. Matetski and J. Quastel.

Read More## The Contact Process on Evolving Scale-Free Networks

Resumen: In this talk we present some results on the contact process running on large scale-free networks, where nodes update their connections at independent random times. We will show that depending on the parameters of the model we can observe either slow extinction for all infection rates, or fast extinction if the infection rate is small enough. This differs from previous results in the case of static scale-free networks where only the first behaviour is observed. We will also show that the analysis of the asymptotic form of the metastable density of the process and its dependency on...

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