{"id":16,"date":"2014-12-30T17:48:50","date_gmt":"2014-12-30T20:48:50","guid":{"rendered":"http:\/\/eventos.cmm.uchile.cl\/escuelappe2015\/?page_id=16"},"modified":"2018-01-22T17:47:30","modified_gmt":"2018-01-22T20:47:30","slug":"programa","status":"publish","type":"page","link":"https:\/\/eventos.cmm.uchile.cl\/escuelappe2018\/programa\/","title":{"rendered":"Programa"},"content":{"rendered":"

 <\/p>\n\n\n\n\n\n\n\n\n\n\n\n
<\/td>\nMi\u00e9rcoles<\/strong><\/td>\nJueves<\/strong><\/td>\nViernes<\/strong><\/td>\n<\/tr>\n
10:00-11:00<\/td>\nRivero<\/td>\nCabezas<\/td>\nKyprianou<\/td>\n<\/tr>\n
11:00-11:30<\/td>\nCaf\u00e9<\/em><\/td>\nCaf\u00e9<\/em><\/td>\nCaf\u00e9<\/em><\/td>\n<\/tr>\n
11:30-12:30<\/td>\nKyprianou<\/td>\nRivero<\/td>\nRivero<\/td>\n<\/tr>\n
12:30-15:00<\/td>\nAlmuerzo<\/em><\/td>\nAlmuerzo<\/em><\/td>\nAlmuerzo<\/em><\/td>\n<\/tr>\n
15:00-16:00<\/td>\nCabezas<\/td>\nKyprianou<\/td>\nCabezas<\/td>\n<\/tr>\n
16:00-16:30<\/td>\nCaf\u00e9<\/em><\/td>\nCaf\u00e9<\/em><\/td>\nCaf\u00e9<\/em><\/td>\n<\/tr>\n
16:30-17:30<\/td>\nMena<\/td>\nTapia<\/td>\nLopes<\/td>\n<\/tr>\n
<\/td>\n<\/td>\nCena<\/em><\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Mini-Cursos:<\/h2>\n

Andreas Kyprianou<\/strong>, University of Bath<\/h5>\n

Exploration of R^d by the isotropic \u03b1-stable process<\/em><\/strong>
\nIn this mini-course we will review some very recent work on isotropic stable processes in high dimension. The recent theory of self-similar Markov and Markov additive processes gives us new insights into their trajectories. Combining this with classical methods, we revisit some old results, as well as offering new ones.<\/p>\n

[su_button url=\u00bbhttp:\/\/eventos.cmm.uchile.cl\/escuelappe2018\/wp-content\/uploads\/sites\/52\/2018\/01\/kryprianou_escuelappe2018_beijing_stable.pdf\u00bb target=\u00bbblank\u00bb style=\u00bbdefault\u00bb background=\u00bb#EE3124″ color=\u00bb#FFFFFF\u00bb size=\u00bb3″ wide=\u00bbno\u00bb center=\u00bbno\u00bb radius=\u00bbauto\u00bb icon=\u00bbicon:file-pdf-o\u00bb icon_color=\u00bb#FFFFFF\u00bb text_shadow=\u00bbnone\u00bb desc=\u00bb\u00bb onclick=\u00bb\u00bb rel=\u00bbnofollow\u00bb title=\u00bb\u00bb id=\u00bb\u00bb class=\u00bb\u00bb]Descargar slides[\/su_button]<\/p>\n

V\u00edctor Rivero<\/strong>,\u00a0Centro de Investigaciones Matem\u00e1ticas, Guanajuato<\/h5>\n

Excursion theory and fluctuation theory for L\u00e9vy and Markov additive processes<\/strong>
\n<\/em>Fluctuation theory of L\u00e9vy and Markov additive processes aims at obtaining path properties by decomposing the paths at the instants were it reaches a new suprema, respectively a new minimum. Most of the applications of these processes are based in results from fluctuation theory. The purpose of this course is to give an introduction of fluctuation theory for these processes based on the techniques from excursion theory from the supremum, respectively from the infimum. In order to explain the key ideas, we will start by the simplest case of a real valued random walk or a discrete time Markov additive process, where many technicalities arising in the continuous time case are avoided. Then we will tackle the continuous time case and we will make some connections with the course of Pr. Kyprianou.<\/p>\n

[su_button url=\u00bbhttp:\/\/eventos.cmm.uchile.cl\/escuelappe2018\/wp-content\/uploads\/sites\/52\/2018\/01\/rivero_escuelappe2018_curso-chile_02.pdf\u00bb target=\u00bbblank\u00bb style=\u00bbdefault\u00bb background=\u00bb#EE3124″ color=\u00bb#FFFFFF\u00bb size=\u00bb3″ wide=\u00bbno\u00bb center=\u00bbno\u00bb radius=\u00bbauto\u00bb icon=\u00bbicon:file-pdf-o\u00bb icon_color=\u00bb#FFFFFF\u00bb text_shadow=\u00bbnone\u00bb desc=\u00bb\u00bb onclick=\u00bb\u00bb rel=\u00bbnofollow\u00bb title=\u00bb\u00bb id=\u00bb\u00bb class=\u00bb\u00bb]Descargar slides[\/su_button]<\/p>\n

Manuel Cabezas<\/strong>, Pontificia Universidad Cat\u00f3lica de Chile<\/h5>\n

The ant in the labyrinth: Random walks on critical high-dimensional graphs<\/strong>
\n<\/em>The ant in the labyrinth is a term coined in 1976 by Pierre-Gilles de Gennes to refer to the simple random walk on a critical percolation cluster of $\\mathbb{Z}^d$.
\nHe proposed to study this model since it is the canonical example of diffusion in critical environments.
\nThe goal of this mini-course is to present the history of this model and to communicate some of the recent progress towards understanding this model in the high-dimensional case. In particular, we will present a very detailed result obtained for the simple random walk on critical branching random walks in $\\mathbb{Z}^d$. This simplified model is strongly believed to share a common scaling limit with the critical percolation case, a behaviour that is expected to be universal in high dimension.
\nPresenting this topic will lead us to discuss a wide variety of subjects: random walks in random environments, critical trees, critical graphs, the super-brownian motion \u2026<\/p>\n

Charlas invitadas:<\/h2>\n
Fabio Lopes<\/strong>, Pontificia Universidad Cat\u00f3lica de Valpara\u00edso<\/h5>\n

Cows on the move<\/strong>
\n<\/em>Consider an epidemic that spread in a population of moving particles on Z^d. The particles may infect each other upon direct contact, but may also be infected via contaminated locations. We formulate a simple model incorporating this phenomenon and demonstrate that the presence of site contamination may have an impact on the epidemic spread. Specifically, site contamination can cause a subcritical model to become supercritical, and measures aimed at controlling site contamination thereby has the potential to suppress large outbreaks. We also discuss some open problems regarding this model. (joint work with M. Deijfen and T. Britton.)<\/p>\n

Gonzalo E. Mena<\/strong>, Columbia University<\/h5>\n

Optimal transport and applications to Data Science<\/strong><\/em>
\nOptimal transport (OT) provides rich representations of the discrepancy between probability measures supported on geometric spaces. Recently, thanks to the development of computational techniques, OT has been used to address problems involving massive datasets, as an alternative to usual KL-divergence based approaches. In this talk I will introduce the OT problem and comment on its elementary duality properties. Then, I will present the entropy regularized problem and its (fast) solution via Sinkhorn iterations. Finally, I will overview two applications to Data Science: first, dimensionality reduction via Wasserstein Barycenters and Wasserstein PCA. Second, parameter inference in generative models defined through complex nonlinear transformation of a noise distribution.<\/p>\n

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Nikolas Tapia<\/strong>, Universidad de Chile<\/h5>\n

Construction of geometric rough paths<\/strong><\/em>
\nThis 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 H\u00f6lder 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 \u0251-H\u00f6lder 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 result is more general. In an upcoming paper, we provide an explicit construction clarifying the connection between rough paths theory and free (nilpotent) Lie algebras. In particular, we use an explicit form of the Baker\u2013Campbell\u2013Hausdorff formula due to Loday in order to provide explicit expressions and bounds to achieve such a construction.<\/p>\n

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  Mi\u00e9rcoles Jueves Viernes 10:00-11:00 Rivero Cabezas Kyprianou 11:00-11:30 Caf\u00e9 Caf\u00e9 Caf\u00e9 11:30-12:30 Kyprianou Rivero Rivero 12:30-15:00 Almuerzo Almuerzo Almuerzo 15:00-16:00 Cabezas Kyprianou Cabezas 16:00-16:30 Caf\u00e9 Caf\u00e9 Caf\u00e9 16:30-17:30 Mena Tapia Lopes Cena Mini-Cursos: Andreas Kyprianou, University of Bath Exploration of R^d by the isotropic \u03b1-stable process In this mini-course we will review some very … Seguir leyendo Programa<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":14,"featured_media":0,"parent":0,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-16","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/eventos.cmm.uchile.cl\/escuelappe2018\/wp-json\/wp\/v2\/pages\/16","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/eventos.cmm.uchile.cl\/escuelappe2018\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/eventos.cmm.uchile.cl\/escuelappe2018\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/escuelappe2018\/wp-json\/wp\/v2\/users\/14"}],"replies":[{"embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/escuelappe2018\/wp-json\/wp\/v2\/comments?post=16"}],"version-history":[{"count":44,"href":"https:\/\/eventos.cmm.uchile.cl\/escuelappe2018\/wp-json\/wp\/v2\/pages\/16\/revisions"}],"predecessor-version":[{"id":197,"href":"https:\/\/eventos.cmm.uchile.cl\/escuelappe2018\/wp-json\/wp\/v2\/pages\/16\/revisions\/197"}],"wp:attachment":[{"href":"https:\/\/eventos.cmm.uchile.cl\/escuelappe2018\/wp-json\/wp\/v2\/media?parent=16"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}