--- - categoria: Plenarias charlas: - titulo: Diversity of statistical behavior in dynamical systems abstract: For chaotic dynamical systems, it is unfeasible to compute long-term orbits precisely. Nevertheless, we may be able to describe the statistics of orbits, that is, to compute how often an orbit will visit a prescribed region of the phase space. Different orbits may or may not follow different statistics. I will explain how to measure the statistical diversity of a dynamical system. This diversity is called emergence, is independent of the traditional notions of chaos. I will begin the talk by discussing classic problems of discretization of metric spaces and measures. Then I will apply these ideas to dynamics and define two forms of emergence. I will present several examples, culminating with new dynamical systems for which emergence is as large as we could possibly hope for. This talk is based on joint work with Pierre Berger (Paris). pdf: '' speaker: nombre: Jairo Bochi afiliacion: Universidad Católica de Chile web: http://www.mat.uc.cl/~jairo.bochi/ - titulo: TBA abstract: '' pdf: '' speaker: nombre: Mónica Clapp afiliacion: UNAM web: https://www.matem.unam.mx/fsd/mclapp - titulo: TBA abstract: '' pdf: '' speaker: nombre: Alicia Dickenstein afiliacion: Universidad de Buenos Aires web: http://mate.dm.uba.ar/~alidick/ - titulo: Entropy methods and sharp convergence of Markov Chains. abstract: We describe how entropy methods can be used to derive quantitative versions of various scaling limits of Markov chains. We will focus on the the description of non-equilibrium states of interacting particle systems. pdf: '' speaker: nombre: Milton Jara afiliacion: Instituto de Matemática Pura e Aplicada web: https://impa.br/page-pessoas/milton-jara/ - titulo: Measuring the complexity of countable objects abstract: Computability theory is the sub-area of mathematical logic that studies ways to measure the complexity of objects, constructions, theorems, and mathematical proofs related to countably infinite objects. On one hand, the natural objects seem to be linearly ordered from simpler to more complex, while, on the other hand the general objects are ordered in a chaotic way. This dichotomy between natural objects and objects in general is hard to study mathematically, as we don't have a formal definition of "natural object." The objective of this talk is to introduce Martin's conjecture (open for more than 40 years) and see how it explains this dichotomy. pdf: '' speaker: nombre: Antonio Montalbán afiliacion: University of California, Berkeley web: https://math.berkeley.edu/~antonio/ - categoria: Semiplenarias charlas: - titulo: Eigenfunction concentration via geodesic beams abstract: '' pdf: '' speaker: nombre: Yaiza Canzani afiliacion: University of North Carolina web: https://canzani.web.unc.edu/ - titulo: Unconditional discriminant lower bounds exploiting violations of the generalized riemann hypothesis abstract: | In the 1970’s Andrew Odlyzko proved good lower bounds for the discriminant of a number field. He also showed that his results could be sharpened by assuming the Generalized Riemann Hypothesis. Some years later Odlyzko suggested that it might be possible to do without GRH. I shall explain Odlyzko’s ideas and sketch how for number fields of reasonably small degree (say up to degree 11 or 12) one can indeed improve the lower known bounds by exploiting hypothetical violations of GRH. This is joint work with Karim Belabas, Francisco Diaz y Diaz and Salvador Reyes, extending unpublished results of Matías Atria. pdf: '' speaker: nombre: Eduardo Friedman afiliacion: Universidad de Chile web: http://www.uchile.cl/portafolio-academico/impresion.jsf?username=friedman - titulo: Estimates for spherical averages abstract: '' pdf: '' speaker: nombre: Luz Roncal afiliacion: UBCAM -Basque Center for applied mathematics web: https://sites.google.com/view/luzroncal - titulo: Characterizations of Nonnegative polynomials of some varieties abstract: | I will describe some recent results on the characterization of those polynomials that are nonnegative on a variety \(X\) in \(R^n\). In the first part of the talk I will explain why this is an interesting problem it turns out to have a wealth of applications ranging from nonconvex optimization to stochastic control. In the second part of the talk I will explain how this problem can be approached on algebraic curves and surfaces, presenting ongoing joint work with G. Blekherman (GA Tech), R. Sinn (U. Lepizig) and G.G. Smith (Queen's U). pdf: '' speaker: nombre: Mauricio Velasco afiliacion: Universidad de los Andes web: http://wwwprof.uniandes.edu.co/~mvelasco/Velasco.html - titulo: TBC abstract: '' pdf: '' speaker: nombre: Nicolás Andruskiewitsch afiliacion: Universidad Nacional de Córdoba web: https://www.famaf.unc.edu.ar/~andrus/ - titulo: TBC abstract: '' pdf: '' speaker: nombre: Andrea Rotnizky afiliacion: School of Public Health Harvard T.H. CHAN web: https://www.hsph.harvard.edu/andrea-rotnitzky/ - titulo: TBA abstract: '' pdf: '' speaker: nombre: Helena Nussensveig afiliacion: Universidad Federal de Rio de Janeiro web: http://www.im.ufrj.br/hlopes/ - titulo: Unique Continuation for some Nonlinear Dispersive Models abstract: | We shall study unique continuation properties (UCP) of solutions to some time evolution eq’s. We are interested in the following two questions: (1) local : if \(u_1\), \(u_2\) are solutions of the eq. which agree in an open set Ω, do they agree in the whole domain? (2) asymptotic at infinity : if \(u_1\), \(u_2\) are solutions of the eq. such that at two different times \(t_1\), \(t_2\) $$ ||| u_1(·, t_j ) − u_2(·, t_j )||| < \infty,\quad j = 1, 2, $$ do they are equal in the whole domain? (\(|||\ ·\ |||\) represents an appropriate "norm") We shall concentrate on these questions for solutions of (i) the Kortewegde Vries eq., the Benjamin-Ono eq., (iii) the Intermediate Long Wave eq., (iv) the Camassa-Holm eq. and (v) related models. These are integrable models and the last three are non-local. pdf: '' speaker: nombre: Gustavo Ponce afiliacion: University of California web: http://web.math.ucsb.edu/~ponce/ - titulo: Transfer operators and atomic decomposition abstract: Since the groundbreaking contributions of Ruelle, the study of transfer operators has been one of the main tools to understand the ergodic theory of expanding maps, that is, discrete dynamical systems that locally expand distances. Questions on the existence of interesting invariant measures, as well the statistical properties of such dynamics system, as exponential decay of correlations and Central Limit Theorem, can be answered studying the spectral properties of the action of these operators on suitable spaces of functions. Using the method of atomic decomposition, we consider new Banach spaces of functions (that in some cases coincides with Besov spaces) that have a remarkably simple definition and allows us to obtain very general results on the quasi-compactness of the transfer operator acting in these spaces, even when the underlying phase space and expanding map are very irregular. Joint work with Alexander Arbieto (UFRJ-Brazil). pdf: '' speaker: nombre: Daniel Smania afiliacion: Universidade de São Paulo web: http://conteudo.icmc.usp.br/pessoas/smania/ - categoria: Cursos charlas: - titulo: TBA abstract: '' pdf: '' speaker: nombre: Roberto Imbuzeiro afiliacion: IMPA web: https://impa.br/page-pessoas/roberto-imbuzeiro-oliveira/ - titulo: TBA abstract: '' pdf: '' speaker: nombre: Sebastian Hurtado afiliacion: University of Chicago web: https://math.uchicago.edu/~shurtados/ - titulo: TBA abstract: '' pdf: '' speaker: nombre: Isabel Hubard afiliacion: UNAM web: https://www.matem.unam.mx/fsd/hubard - categoria: Públicas charlas: - titulo: TBA abstract: '' pdf: '' speaker: nombre: Eduardo Saez de Cabezón afiliacion: Universidad de la Rioja web: https://belenus.unirioja.es/~esaenz-d/ - titulo: TBA abstract: '' pdf: '' speaker: nombre: Ingrid Daubechis afiliacion: DUKE University web: https://ece.duke.edu/faculty/ingrid-daubechies