My name is Lucas Lacasa.
I received a MSc in Theoretical Physics from Universidad Complutense de Madrid (UCM) back in 2004 and a MSc and PhD in Physics of Complex Systems from Universidad Politénica de Madrid (UPM) in 2006 and 2009 respectively, under the supervision of Dr. Bartolo Luque.
During my thesis, I worked mainly on three slightly separated areas within what we could call Complex Systems science. First, we developed some graph theoretical based methods for nonlinear time series analysis, a concept initially borrowed from graph theory called visibility graphs. While the theory as a whole is still on its infancy, we have already described a few properties of the method, and applied to several problems in time series, such as the estimation of fractal dimension in self-similar series, or the discrimination between stochastic (either with or without correlations) and chaotic processes. Currently I'm still working on the topic, mainly trying to push forward the theoretical foundations of the method (essentially, this means that I try to analytically relate specific time series structures with their visibility graph counterpart ).
Another part of my thesis dealt with number theoretical systems showing some kind of 'complex' behavior (scaling, phase transitions, self-organized criticality). We tried to establish connections between statistical physics and number theory, and mainly this was done by approaching number theoretical or combinatorial problems through a stat phys perspective.
Finally, the third part of the thesis addressed several applications of statistical mechanics to complex social and biological problems (such as agent based models of hierarchy formation, complex network embedded models of aircraft diffusion, and so on).
After this, in 2009 I spent a year working in several research centers. At the Brazilean Center for Physics Research (department of Theoretical Physics), I worked with prof. Evaldo Curado in some generalized Heisenberg algebras that describe quantum mechanical systems whose energy spectra spacings shows chaotic fluctuations.
Right after this I went to the Santa Fe Institute (CSSS '09 fellow), just before making a stay at the Center for Mathematical Research (CRM, Complex Systems Group), where I worked with prof. Alvaro Corral in developing mathematical models to describe the universal statistical properties of written texts.
This was followed by a postdoc position at IFISC in 2010. There I worked with prof. Raúl Toral in some problems of visibility graph theory and with him and Dr. Niko Komin we worked on the physics of a Ginzburg-Landau model with diversity (that can be mapped to a phi-4 random field model).
Currently I'm an assistant professor at the department for applied mathematics and statistics, in the Universidad Politécnica de Madrid (school of Aeronautics).
During my thesis, I worked mainly on three slightly separated areas within what we could call Complex Systems science. First, we developed some graph theoretical based methods for nonlinear time series analysis, a concept initially borrowed from graph theory called visibility graphs. While the theory as a whole is still on its infancy, we have already described a few properties of the method, and applied to several problems in time series, such as the estimation of fractal dimension in self-similar series, or the discrimination between stochastic (either with or without correlations) and chaotic processes. Currently I'm still working on the topic, mainly trying to push forward the theoretical foundations of the method (essentially, this means that I try to analytically relate specific time series structures with their visibility graph counterpart ).
Another part of my thesis dealt with number theoretical systems showing some kind of 'complex' behavior (scaling, phase transitions, self-organized criticality). We tried to establish connections between statistical physics and number theory, and mainly this was done by approaching number theoretical or combinatorial problems through a stat phys perspective.
Finally, the third part of the thesis addressed several applications of statistical mechanics to complex social and biological problems (such as agent based models of hierarchy formation, complex network embedded models of aircraft diffusion, and so on).
After this, in 2009 I spent a year working in several research centers. At the Brazilean Center for Physics Research (department of Theoretical Physics), I worked with prof. Evaldo Curado in some generalized Heisenberg algebras that describe quantum mechanical systems whose energy spectra spacings shows chaotic fluctuations.
Right after this I went to the Santa Fe Institute (CSSS '09 fellow), just before making a stay at the Center for Mathematical Research (CRM, Complex Systems Group), where I worked with prof. Alvaro Corral in developing mathematical models to describe the universal statistical properties of written texts.
This was followed by a postdoc position at IFISC in 2010. There I worked with prof. Raúl Toral in some problems of visibility graph theory and with him and Dr. Niko Komin we worked on the physics of a Ginzburg-Landau model with diversity (that can be mapped to a phi-4 random field model).
Currently I'm an assistant professor at the department for applied mathematics and statistics, in the Universidad Politécnica de Madrid (school of Aeronautics).
