{"id":134,"date":"2026-03-26T09:57:50","date_gmt":"2026-03-26T12:57:50","guid":{"rendered":"https:\/\/sbm.org.br\/coloquio-sudeste-5\/?page_id=134"},"modified":"2026-09-22T10:50:13","modified_gmt":"2026-09-22T13:50:13","slug":"palestras-plenarias","status":"publish","type":"page","link":"https:\/\/sbm.org.br\/coloquio-sudeste-5\/palestras-plenarias\/","title":{"rendered":"Palestras Plenarias"},"content":{"rendered":"\t\t
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Palestras Plenarias<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Deu caos na matem\u00e1tica?\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Ali Tahzibi<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Instituto de Ciencias Matem\u00e1ticas e de computa\u00e7\u00e3o<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Resumo: <\/strong>Quando Edward Lorenz recebeu seu McBee LGP-30 no MIT, teve que dedicar uma sala espec\u00edfica para deixar o monstro barulhento trabalhando. Talvez poucas pessoas saibam, mas Lorenz tinha colaboradoras como as pesquisadoras Margaret Hamilton (que depois foi uma pe\u00e7a-chave na miss\u00e3o de Apolo 11) e Ellen Fetter, que o ajudaram a domar aquele computador na realiza\u00e7\u00e3o de seus c\u00e1lculos. O artigo do Lorenz (com colabora\u00e7\u00e3o de Fetter) publicado em 1963 no Journal of Atmospheric Science com o t\u00edtulo “Deterministic non-periodic flow” criou um caos no mundo da matem\u00e1tica, tal como o bater de asas de uma borboleta. Entretanto, aquela borboleta matem\u00e1tica j\u00e1 tinha, de certa forma, come\u00e7ado a nascer, antes, talvez no formato de lavra ainda, presente nos trabalhos de Richardson, que podem ser conferidos no livro “Weather prediction with numerical process”.<\/p>

\u00a0<\/p>

O sucesso do efeito borboleta foi tamanho que sua fama alcan\u00e7ou at\u00e9 as salas de cinema. Seus efeitos foram sentidos no mundo dos n\u00fameros e se entrela\u00e7ou nos trabalhos de Joan Birman e Robert F. Williams, ganhando complexidade topol\u00f3gica. Hoje, as asas da borboleta dan\u00e7am ao longo de n\u00f3s, tecendo afinidades com a \u00e1rea de grupo modular em teoria de n\u00fameros (mostrado por E. Ghys). Foram os estudos desse grupo modular que geraram dan\u00e7as algo-ritmicas na pra\u00e7a XV de Novembro, em S\u00e3o Carlos, durante o festival Pint of Science, em 2024.<\/p>

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Scalable Bernoulli Factory MCMC for Intractable Marginalised Posteriors<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Fl\u00e1vio Bambirra Gon\u00e7alves<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Universidade Federal de Minas Gerais<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Resumo: <\/strong>Bernoulli factory MCMC} algorithms implement accept-reject Markov chains without explicit computation of acceptance probabilities, and are used to target posterior distributions associated with intractable likelihood models. Intractable likelihoods naturally arise in continuous-time models and mixture distributions, or from the marginalisation of a tractable augmented model. Bernoulli factory MCMC algorithms often mix better than alternatives that target a tractable augmented posterior. However, we show that their computational performance typically deteriorates exponentially with data size, as happens in naively implemented pseudo-marginal algorithms. To address this, we propose a simple divide-and-conquer Bernoulli factory MCMC algorithm and prove that it has polynomial complexity for factorising models, with the exact degree depending on the existence of efficient unbiased estimators of the intractable likelihood ratio. We demonstrate the effectiveness of our approach with applications to Bayesian inference in two intractable likelihood models, and observe respective polynomial cost of degree 1.2 and 1 in the data size.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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Tema da Palestra<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Hamid Hassanzadeh<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Universidade Federal do Rio de Janeiro<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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\n Resumo:<\/strong> Let h<\/mi><\/math> be a nonzero homogeneous polynomial of degree \n \n d<\/mi>\n ≥<\/mo>\n 1<\/mn>\n <\/math> \n in the polynomial ring \n \n \u2102<\/mi>\n [<\/mo>\n z<\/mi>0<\/mn><\/msub>\n ,<\/mo>\n …<\/mo>\n ,<\/mo>\n z<\/mi>n<\/mi><\/msub>\n ]<\/mo>\n <\/math>. \n Associated to h<\/mi><\/math> is the gradient map obtained from its partial derivatives\n <\/p>\n\n \n
\n \n grad<\/mtext>\n (<\/mo>\n h<\/mi>\n )<\/mo>\n :<\/mo>\n \u2119<\/mi>n<\/mi><\/msup>\n ⇢<\/mo>\n \u2119<\/mi>n<\/mi><\/msup>\n ,<\/mo>\n <\/mspace>\n z<\/mi>\n ↦<\/mo>\n \n (<\/mo>\n \n ∂<\/mo>h<\/mi><\/mrow>\n ∂<\/mo>z<\/mi>0<\/mn><\/msub><\/mrow>\n <\/mfrac>\n :<\/mo>\n . . . <\/mo>\n :<\/mo> \n \n ∂<\/mo>h<\/mi><\/mrow>\n ∂<\/mo>z<\/mi>n<\/mi><\/msub><\/mrow>\n <\/mfrac>\n )<\/mo>\n <\/mrow>\n .<\/mo>\n <\/math>\n <\/div>\n\n

\n The polar degree<\/span> of h<\/mi><\/math> is the degree of the gradient map of h<\/mi><\/math> (i.e., the number of points in the preimage of a general point). A polynomial h<\/mi><\/math> is called homaloidal<\/span> if the map grad<\/mtext>(<\/mo>h<\/mi>)<\/mo><\/math> is birational (an isomorphism on a nonempty open subset).\n <\/p>\n\n

\n Dolgachev showed in [?] that there are exactly three homaloidal plane curves, up to a linear change of homogeneous coordinates. June Huh in [?] showed that there are irreducible homaloidal hypersurfaces of any given degree \n \n d<\/mi>\n ≥<\/mo>\n 3<\/mn>\n <\/math> \n in the projective space of dimension \n \n n<\/mi>\n ≥<\/mo>\n 3<\/mn>\n <\/math>. \n Dimca and Papadima conjectured in [?, Section 3] that none of them has only isolated singular points:\n <\/p>\n\n \n
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\n Conjecture 3.<\/span> \n \n There are no homaloidal hypersurfaces of degree \n \n d<\/mi>\n ≥<\/mo>\n 3<\/mn>\n <\/math> \n with only isolated singular points in the projective space of dimension \n \n n<\/mi>\n ≥<\/mo>\n 3<\/mn>\n <\/math>.\n <\/span>\n <\/p>\n <\/div>\n\n

\n Dimca proved the conjecture for quasi-homogeneous singularities. The conjecture was later proved in full generality by June Huh [?] using topological methods to reduce the conjecture to the quasi-homogeneous case.\n <\/p>\n\n

\n In this talk, we present a commutative algebraic method to prove the conjecture and some of its generalizations in the case of quasi-homogeneous singularities.\n <\/p>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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Short wave vs. long wave interaction in the relativistic context.\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Hermano Frid<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Universidade de S\u00e3o Paulo - Ribeir\u00e3o Preto<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Resumo: <\/strong>We review some recent results concerning\u00a0short wave- long wave interactions in the relativistic context, including the application to relativistic isothermal gas dynamics.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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N\u00e3o-hiperbolicidade por coexist\u00eancia de diferentes hiperbolicidades <\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Katrin Gelfert<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Universidade Federal do Rio de Janeiro<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Resumo: <\/strong>Os sistemas din\u00e2micos hiperb\u00f3licos s\u00e3o caracterizados pela contra\u00e7\u00e3o uniforme nas dire\u00e7\u00f5es est\u00e1veis e pela expans\u00e3o uniforme nas dire\u00e7\u00f5es inst\u00e1veis, sendo a ferradura de Smale um exemplo cl\u00e1ssico. Nosso interesse, no entanto, est\u00e1 em sistemas n\u00e3o hiperb\u00f3licos, nos quais a contra\u00e7\u00e3o e a expans\u00e3o interagem de modo a produzir uma din\u00e2mica neutra.<\/p>

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Estudamos uma classe de produtos skew sobre uma ferradura, cujas aplica\u00e7\u00f5es nas fibras s\u00e3o dadas por dois difeomorfismos do c\u00edrculo. Uma fam\u00edlia particularmente importante surge das a\u00e7\u00f5es projetivas de matrizes em SL(2, \u211d)<\/strong>, especialmente quando uma das matrizes \u00e9 hiperb\u00f3lica e a outra \u00e9 el\u00edptica. Esse contexto combina naturalmente um sistema din\u00e2mico parcialmente hiperb\u00f3lico, com dire\u00e7\u00f5es est\u00e1vel, inst\u00e1vel e central, e um cociclo de matrizes.<\/p>

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O expoente de Lyapunov na dire\u00e7\u00e3o central coincide com a taxa de crescimento exponencial dos produtos de matrizes associados. Discutimos o espectro desses expoentes por meio do formalismo termodin\u00e2mico e da geometria do espa\u00e7o das medidas erg\u00f3dicas, destacando o papel das medidas n\u00e3o hiperb\u00f3licas e apresentando alguns resultados recentes.<\/p>

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Este \u00e9 um trabalho conjunto<\/strong> com L. J. D\u00edaz, M. Rams e J. Zhang.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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Efeitos Induzidos pela Rugosidade numa Equa\u00e7\u00e3o de Rea\u00e7\u00e3o-Difus\u00e3o em um Dom\u00ednio Fino<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Marcone Corr\u00eaa Pereira<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Universidade de S\u00e3o Paulo<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Resumo: <\/strong>Nesta apresenta\u00e7\u00e3o, analisamos um problema de rea\u00e7\u00e3o-difus\u00e3o formulado em um dom\u00ednio fino dotado de uma condi\u00e7\u00e3o de contorno do tipo Robin, modelando rea\u00e7\u00f5es catalisadas na fronteira. Motivados por aplica\u00e7\u00f5es em microflu\u00eddica, consideramos a rugosidade ressonante, na qual tanto a amplitude quanto o per\u00edodo das oscila\u00e7\u00f5es da fronteira s\u00e3o da mesma ordem de grandeza que a espessura do dom\u00ednio.<\/span><\/p>

A depender da intensidade do termo de rea\u00e7\u00e3o na condi\u00e7\u00e3o de Robin, identificamos tr\u00eas regimes distintos. Em particular, caracterizamos o regime cr\u00edtico no qual a influ\u00eancia da geometria do dom\u00ednio e todas as caracter\u00edsticas fisicamente relevantes do processo s\u00e3o totalmente capturadas. Este \u00e9 um trabalho conjunto com o Prof. Igor Pazanin (Universidade de Zagreb) e com o pesquisador de p\u00f3s-doutorado Jean Carlos Nakasato.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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Modeling Interaction Structure in High-Throughput Phenotyping in Tropical Forage Breeding Using Hidden Sparse Markov Random Fields<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Nancy Lopes Garcia<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Universidade Estadual de Campinas<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Resumo: <\/strong>High-throughput phenotyping via drone-based remote sensing offers a rapid, non-invasive framework for monitoring morphophysiological traits in agricultural crops, particularly forage species. Extracting precise metrics such as plant height, canopy density, and leaf cover from high-resolution aerial imagery requires robust statistical segmentation to separate plant structures from the background. We model these images using a Gaussian mixture driven by a hidden Markov Random Field (MRF). A central statistical challenge in this formulation is the joint estimation of the interacting neighborhood structure of the hidden MRF and the number of Gaussian mixture components. To address this, we propose a Bayesian Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm that explores subsets of a maximal interaction neighborhood. Model selection is performed using a marginal pseudoposterior distribution, effectively mitigating the computational burden of intractable normalization constants. This framework enables precise digital trait extraction, providing scalable insights into crop performance and supporting variety selection for agricultural management.<\/p>

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Joint work with Victor Freguglia, Guilherme Francio Niederauer and Mateus Figueiredo
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The Moduli Space of Metric Structures<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Pablo Carrasco<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Universidade Federal de Minas Gerais<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Resumo: In this talk I will introduce a metric geometry on the space of (weakly hyperbolic) metric structures on a closed surface of genus at least two. I will explain how this viewpoint offers a common perspective on familiar spaces such as Teichm\u00fcller space and Culler\u2013Vogtmann Outer space.<\/span>
<\/span>The guiding idea is to start from large-scale geometric data and use tools from thermodynamic formalism to study the local geometry of this space. The talk will be introductory, and no previous familiarity with dynamical systems will be assumed.<\/span>
<\/span>This is joint work with Stephen Cantrell (St Andrews), Emilio Corzo, and Federico Rodriguez-Hertz (Penn State).<\/span><\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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Da mec\u00e2nica hamiltoniana aos sistemas com v\u00ednculos: uma vis\u00e3o geom\u00e9trica<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Paula Balseiro<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Universidade Federal Fluminense<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Resumo: <\/strong>A mec\u00e2nica cl\u00e1ssica \u00e9 o ber\u00e7o de v\u00e1rias \u00e1reas da geometria diferencial, como as geometrias simpl\u00e9tica e de Poisson. Nesta palestra, revisitaremos essas motiva\u00e7\u00f5es iniciais e veremos como as estruturas simpl\u00e9ticas e de Poisson aparecem de forma natural para auxiliar na descri\u00e7\u00e3o intr\u00ednseca da din\u00e2mica de um sistema hamiltoniano, na busca por quantidades conservadas e nos processos de redu\u00e7\u00e3o por simetria via grupos de Lie. Em seguida, abordaremos o estudo dos sistemas mec\u00e2nicos com v\u00ednculos (sistemas n\u00e3o-hol\u00f4nomos) e veremos como novas ferramentas geom\u00e9tricas precisam ser desenvolvidas para o seu estudo. Discutiremos o problema da hamiltoniza\u00e7\u00e3o e os crit\u00e9rios geom\u00e9tricos que medem a obstru\u00e7\u00e3o para um sistema n\u00e3o-hol\u00f4nomo ser hamiltoniano, destacando o contexto geom\u00e9trico na formula\u00e7\u00e3o e an\u00e1lise desses problemas.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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Understanding Gender Parity in Mathematics: A Robust Bayesian Network Perspective<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Thais Fonseca<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Universidade Federal do Rio de Janeiro<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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Resumo: <\/strong>Gender disparities in mathematics and STEM education are shaped by complex interactions among educational, socioeconomic, labour-market, and demographic factors. In this talk, we focus on modeling the dependence structure among the multiple factors influencing gender parity in mathematics using Bayesian networks. In particular, we develop a robust quantile-based formulation that allows these relationships to be explored beyond traditional mean-based approaches, providing greater flexibility in the presence of outliers, heteroscedasticity, and departures from standard distributional assumptions. We also introduce a quantile-based criterion for robust network structure learning. The proposed framework is used to investigate gender parity in undergraduate mathematics and STEM education in Brazil, providing a multivariate perspective on how educational, economic, and social factors interact and contribute to regional differences in female participation.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

Palestras Plenarias Deu caos na matem\u00e1tica? Ali Tahzibi Instituto de Ciencias Matem\u00e1ticas e de computa\u00e7\u00e3o Resumo: Quando Edward Lorenz recebeu seu McBee LGP-30 no MIT, teve que dedicar uma sala espec\u00edfica para deixar o monstro barulhento trabalhando. Talvez poucas pessoas saibam, mas Lorenz tinha colaboradoras como as pesquisadoras Margaret Hamilton (que depois foi uma pe\u00e7a-chave […]<\/p>\n","protected":false},"author":12,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-134","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sbm.org.br\/coloquio-sudeste-5\/wp-json\/wp\/v2\/pages\/134","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sbm.org.br\/coloquio-sudeste-5\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sbm.org.br\/coloquio-sudeste-5\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sbm.org.br\/coloquio-sudeste-5\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/sbm.org.br\/coloquio-sudeste-5\/wp-json\/wp\/v2\/comments?post=134"}],"version-history":[{"count":46,"href":"https:\/\/sbm.org.br\/coloquio-sudeste-5\/wp-json\/wp\/v2\/pages\/134\/revisions"}],"predecessor-version":[{"id":570,"href":"https:\/\/sbm.org.br\/coloquio-sudeste-5\/wp-json\/wp\/v2\/pages\/134\/revisions\/570"}],"wp:attachment":[{"href":"https:\/\/sbm.org.br\/coloquio-sudeste-5\/wp-json\/wp\/v2\/media?parent=134"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}