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Geometry of Laplacian growth models

Grant number: 18/07857-8
Support Opportunities:Regular Research Grants
Duration: September 01, 2018 - August 31, 2019
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics - Probability
Convênio/Acordo: Texas A&M University
Mobility Program: SPRINT - Projetos de pesquisa - Mobilidade
Principal Investigator:Luiz Renato Gonçalves Fontes
Grantee:Luiz Renato Gonçalves Fontes
Principal researcher abroad: Eviatar B. Procaccia
Institution abroad: Texas A&M University, United States
Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:17/10555-0 - Stochastic modeling of interacting systems, AP.TEM


The project addresses various questions at the interface of probability, geometry and statistical mechanics, whose common feature is novel assertion of physical phenomenon in natural probabilistic models. The specific problems are concerned with complex systems, that are generated by diffusion, or the harmonic measure, such as aggregation processes, in an attempt to grasp the nature of a physical phenomenon, which is resisting proof in more classical models in the field, such as DLA. The problems concentrate around the Hastings-Levitov model, which is a continuous off lattice version of many of the known lattice aggregation models. The methods to be employed borrow ideas and tools from various mathematical disciplines e.g. complex analysis, harmonic analysis, differential equations, ergodic theory and geometric measure theory. The project contains problems whose difficulty ranges from graduate to full research level. It therefore offers a great opportunity to get graduate students and postdocs involved in top-notch research in probability and mathematical physics. The project will also aid to continue the tradition of the PIs' collaborative involvement with the international community. (AU)

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