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"Números Abstratos e de Medir na região do Diyala na antiga Mesopotânia: um exemplo de papéis flutuantes e sobrepostos" - Palestra EACH 27/08/2013
A história do conhecimento costuma considerar campos como a
matemática da Antiga Mesopotâmia como uma área homogênea e uma
espécie de unidade indivisível. Nos últimos anos, várias iniciativas
de pesquisa têm combatido essa imagem estática da matemática. Nesta
conferência, trataremos de um aspecto da matemática mesopotâmica que
permite estabelecer diferenças regionais. Trata-se da separação
entre números de medir (isto é, números acompanhados de unidades de
medidas e expressos dentro dos sistemas numéricos metrológicos) e
números assim chamados abstratos (isto é, números desacompanhados de
unidades de medidas e expressos no sistema sexagesimal posicional).
Nosso estudo de caso considerará os tabletes matemáticos
provenientes de escavações arqueológicas na região de um afluente do
rio Tigre, a saber, o região do rio Diyala, um pouco a nordeste de
Bagdá, onde no período paleo-babilônico consolidou-se o Reino de
Eshnunna.
Bacharel em Matemática Pura pela Universidade de São Paulo (1990), a Licenciatura em Matemática pela Universidade de São
Paulo (1997), o Doutorado em Educação Matemática pela Universidade
Estadual Paulista Júlio de Mesquita Filho (1997) e a Livre-Docência
em História da Ciência pela Universidade de São Paulo (2012). Sua
produção bibliográfica é na área de História, com trabalhos
publicados especialmente sobre os saberes na Antiguidade
mesopotâmica. É filiado às sociedades International Association for
Assyriology, Associação Nacional de História, Sociedade Brasileira
de História da Ciência, Sociedade Brasileira de História da
Matemática e Sociedade Brasileira de Matemática. Foi Research Fellow
junto à Universidade de Exeter, de 2003 a 2005. Visitou, em 2009,
como pós-doutorando, o Institut für Orientalistik da Universidade de
Viena. Visitou, em 2012, o laboratório SPHERE (Université
Paris-Diderot e CNRS). Foi contemplado, com vigência em 2013, com
bolsa de pesquisador estrangeiro pela Prefeitura de Paris. É membro
do conselho consultivo do Laboratório do Antigo Oriente-Próximo da
Universidade de São Paulo. É o representante nacional, pelo Brasil,
junto à International Commission on the History of Mathematics
(comissão conjunta da International Mathematical Union e da
International Union for the History and Philosophy of Science). É
membro do conselho editorial da Coleção História da Matemática da
Sociedade Brasileira de Matemática. É pesquisador associado
estrangeiro do Laboratório SPHERE - Sciences, Philosophie, Histoire
(CNRS e Paris 7).
Duração: 01:08:13
A correct programme to determine the exact interior of any discrete closed planar curve
In order to fill up interiors, drawing programmes usually resort to polynomial approximation. This leads to occasional flaws that are normally hidden by smoothing procedures. For instance, in Mathematical Morphology the grayscale dilation can smoke a picture and so cover up the sparse pixel flaws. However, for a binary environment this trick can harm the original contour. Herewith we present an exact filling procedure that works out for any discrete closed curve.
Duração: 01:07:00
Colóquio MAP - 07/06/2013 - Hydrodynamic Modelling of Pilot Wave-bouncing droplet coupling in a Faraday Problem
Recent experiments by two groups, Yves Couder (Paris) and John
Bush (MIT) have shown experimentally that droplets will bounce on the
surface of a vertically vibrated bath (instead of coalescing with it),
generating a Faraday-type wavefield at every bounce. From this state, a
pitchfork symmetry breaking bifurcation leads to a "walking" state whereby
the bouncing droplet is "guided" by the self-generated wavefield - the
droplet's pilot wave. Once this state is achieved a large array of
interesting dynamics ensues with surprising analogies to quantum
mechanical behaviour. We will present a coupled particle-fluid model that
can can be used simulate the dynamics of this problem. This is joint work
with John Bush, Andre Nachbin (IMPA) and Carlos Galeano (IMPA).
Duração: 01:04:25
Colóquio MAP - 23/08/2013 - École polytechnique fédérale de Lausanne* “RIEMANNIAN METRICS ON THE SPACE OF PLANE CURVES
Riemannian metrics on the space of curves are used in shape
analysis to describe deformations that take one shape to another and to
define a distance between shapes. The space of curves is an infinite
dimensional manifold and the Riemannian metrics that are of interest in
shape analysis are weak, i.e., interpreted as maps from the tangent bundle
to its dual, they are injective, but not surjective. One of the
consequences is that the geodesic distance induced by these metrics can
vanish. This talk will present examples, where this happens, and then show
how to modify the metric to prevent the vanishing of the distance. The
second part of the talk will focus on a particular class of metrics,
metrics of Sobolev type, and discuss their mathematical properties.
Duração: 00:57:19
Colóquio MAP 01/11/2013 - Qualitative Aspects of the Differential Equations of Principal Curvature Lines on Hypersurfaces of Euclidean 4-space and their Partially Umbilic Singularities
After a discussion of some historical landmarks for the study
of the differential equations as in the title, going back to Euler, Monge
and Darboux, for the case of surfaces in Euclidean 3-space, the results
of Gutierrez and Sotomayor (1982-3) on surfaces with Structurally Stable.
Configurations of principal curvature lines and umbilic singularities and
their Bifurcations will be reviewed and briefly compared with Peixoto’s
Theorem (1962) for Structurally Stable Differential Equations (Vector
Fields) and their Bifurcations (Sotomayor, 1974) on compact surfaces.
An extension of the results for surfaces to hypersurfaces in Euclidean
4-space will be presented in the form of an improved version of the
Genericity Theorem (of Kupka – Smale type) due to R. Garcia (1992). New
elements of this improvement include the stratified structure of the
partially umbilic singularities and the analysis of the heteroclinic partially
umbilic connections and attached separatrix surfaces.
Open problems and, old and present day, situations where the analysis of
Principal Structures, as those in the lecture, for modeling and
applications will be mentioned.
The mathematical ingredients of this lecture can be regarded as belonging
to the elusive boundary between Geometry, Analysis and Dynamical Systems.
Work in collaboration with R. Garcia (UFG) and D. Lopes (UFS).
Duração: 01:23:12
Colóquios do IFSC - Can a black hole have hair?
Black holes are one of the most fascinating predictions of the General Theory of Relativity. According to the conventional picture that emerged in the 1970s as a corollary of the uniqueness theorems, black holes are extremely constrained objects, determined by only a few global charges. For instance, two black holes with the same total mass and angular momentum must be precisely equal, in sharp contrast with stars. Such simplicity of black holes became immortalized in John Wheeler's mantra "Black holes have no hair". In this talk, I will start by reviewing the history and some key physical/mathematical properties of black holes in General Relativity. I will then discuss a novel mechanism that allows black holes to have 'hair' and challenges the standard paradigm. Some possible astrophysical consequences will be addressed. http://gravitation.web.ua.pt/herdeiro.
Duração: 02:37:13
Mathematical Intuitions and their Cerebral Bases
Mathematical Intuitions and their Cerebral Bases
<br><br>
Debatedor:<br>
Stanislas Dehaene (Collège de France)<br><br>
Data do Evento: 16 de Setembro de 2009 <br>
Local: Sala de Eventos – IEA<br>
Duração: 01:35:01
Maxwell (like) and Navier-Stokes (like) Equations Equivalent to Einstein Equation
Date: 04.05.2012 - 16 horas - Auditório Antônio Gilioli - IME USP - Bloco A
Speaker: Waldyr Alves Rodrigues Junior - IMECC-UNICAMP - (walrod@mpc.com.br).
Title: Maxwell (like) and Navier-Stokes (like) Equations Equivalent to Einstein Equation.
Abstract: In this lecture I am concerned to reveal that any space time structure < M, D, g, \tau_g, ^ > which is a model of gravitational field in General Relativity generated by a energy-moment tensor T - and which contains at least one Killing vector field A - is such that the 2-form Field F = dA (where A = g(A,)), satisfies a Maxwell like equation - with a well determined current that contains a term of superconducting type. Moreover, the Maxwell equations for F are straightforwardly shown to be equivalent to Einstein equation and to a Navier-Stokes equation as well. As a result, I exhibit a set of consisted of Einstein, Maxwell and Navier-Stokes equations that are completely equivalent from the mathematical point view, once some identifications about field variables are evince, as will be explained during the lecture.
I compare and emulate the results obtained with others on the same subject appearing in the literature.
More about the speaker:
http://www.ime.unicamp.br/noticias/docente-do-imecc-recebe-medalha-ouro
http://www.telesio-galilei.com/tg/images/stories/documents/Academy_News/wa%20rodrigues%20ups%20gold%20medal.pdf
http://en.wikipedia.org/wiki/Waldyr_Alves_Rodrigues_Jr.
Duração: 01:00:38
Metabiology: Life as Evolving Software_part001
Our goal is to prove mathematically that Darwinian evolution works by studying what physicists call a toy model, one that is much simpler than the real thing, but that hopefully preserves the essential features. DNA is digital software, so we study the evolution of randomly mutating software, a hill-climbing random walk in software space. This approach is starting to yield mathematical results, which we shall outline.
Duração: 01:54:35
Metabiology: Life as Evolving Software_part002
Our goal is to prove mathematically that Darwinian evolution works by studying what physicists call a toy model, one that is much simpler than the real thing, but that hopefully preserves the essential features. DNA is digital software, so we study the evolution of randomly mutating software, a hill-climbing random walk in software space. This approach is starting to yield mathematical results, which we shall outline.
Duração: 01:07:07
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