Floer Theory of Higher Rank Quiver 3-folds

We study threefolds Y fibred by $$A_m$$ A m -surfaces over a curve S of positive genus. An ideal triangulation of S defines, for each rank m, a quiver $$Q(\Delta _m)$$ Q ( Δ m ) , hence a $$CY_3$$ C Y 3 -category $$\mathcal {C}(W)$$ C ( W ) for any potential W on $$Q(\Delta _m)$$ Q ( Δ m ) . We show that for $$\omega $$ ω in an open subset of the Kähler cone, a subcategory of a sign-twisted Fukaya category of $$(Y,\omega )$$ ( Y , ω ) is quasi-isomorphic to $$(\mathcal {C},W_{[\omega ]})$$ ( C , W [ ω ] ) for a certain generic potential $$W_{[\omega ]}$$ W [ ω ] . This partially establishes a conjecture of Goncharov (in: Algebra, geometry, and physics in the 21st century, Birkhäuser/Springer, Cham, 2017) concerning ‘categorifications’ of cluster varieties of framed $${\mathbb {P}}GL_{m+1}$$ P G L m + 1 -local systems on S, and gives a symplectic geometric viewpoint on results of Gaiotto et al. (Ann Henri Poincaré 15(1):61–141, 2014) on ‘theories of class $${\mathcal {S}}$$ S ’.

VI encuentro nacional de semilleros de investigación en salud

El origen de la educación universitaria a partir de siete artes liberales reunidas en el Trívium (gramática, dialéctica y retórica) y el Quadrivium (aritmética, geometría, astronomía y música), marcan un cambio generacional irreversible en la edad media. El joven estudiante era formado en el uso del trívium como instrumento para el autoaprendizaje y posteriormente a través del quadrivium profundizaba en el conocimiento de las ciencias y las artes. Bajo este modelo se formaron científicos notables como Nicolás Copérnico, Isaac Newton, Marie Curie, Henri Poincare, Iván Pávlov e Iliá Méchnikov, entre muchos otros. Un elemento común en el proceso educativo de estos investigadores fue la formación y guía recibida en un momento determinante de sus vidas por su mentor; un profesional con experiencia y alta formación, pero ante todo un consejero, capaz de motivar y potenciar con disciplina y constancia las habilidades innatas del joven estudiante por el conocimiento, materializando así sus sueños en un proyecto de vida con vocación de servicio social.

Early Twentieth-Century Philosophy of Science

The pursuit of a definitive explanation of how scientists produce knowledge and what kinds of knowledge they produce became more urgent in the early twentieth century as science became increasingly important to society in the form of society-transforming technologies. As the century proceeded, philosophy of science emerged as a subdiscipline within philosophy, coordinate with the elusiveness of the goal of explaining science. By mid-century, philosophers, many trained in the physical sciences, had displaced scientists as the dominant figures in this effort. Henri Poincaré proposed a Mach-like relationalist theory of science, Bertrand Russell defended a logical atomism theory indebted to Ludwig Wittgenstein, and Percy Bridgman defended a theory he called operationalism. Concurrently, William James and John Dewey developed the pragmatism of Charles Sanders Peirce into an action- and belief-based explanation of science. But the dominant philosophy of science from the 1920s through the 1950s was logical positivism/empiricism.

Multivariate Normal Approximation on the Wiener Space: New Bounds in the Convex Distance

We establish explicit bounds on the convex distance between the distribution of a vector of smooth functionals of a Gaussian field and that of a normal vector with a positive-definite covariance matrix. Our bounds are commensurate to the ones obtained by Nourdin et al. (Ann Inst Henri Poincaré Probab Stat 46(1):45–58, 2010) for the (smoother) 1-Wasserstein distance, and do not involve any additional logarithmic factor. One of the main tools exploited in our work is a recursive estimate on the convex distance recently obtained by Schulte and Yukich (Electron J Probab 24(130):1–42, 2019). We illustrate our abstract results in two different situations: (i) we prove a quantitative multivariate fourth moment theorem for vectors of multiple Wiener–Itô integrals, and (ii) we characterize the rate of convergence for the finite-dimensional distributions in the functional Breuer–Major theorem.

Henri Poincare’s legacy for tipping points

<p>The science of Earth system and climate tipping points has evolved and matured as a disciplined approach to understanding anthropogenic and non-anthropogenic stresses on the Earth’s subsystems in the 21<sup>st</sup> century. However, tipping points is strongly interlinked with the science of bifurcations and dynamical systems, which received a seminal and resonant illumination by the great French mathematician Henri Poincare (1854-1912). Thus, quite a few historically minded tipping point scientists mention Poincare as the seminal, path-setting thinker for tipping point understandings.</p><p>Moreover, Poincare’s bifurcation and dynamical systems-pertinent science is also linked to his seminal role in chaos theory, which illuminates today’s understanding of climate stochasticity. Poincare famously said, "A very small cause which escapes us determines a considerable effect that we cannot see; so, we say this effect is random," which provided grounding for the chaos notion of critical sensitivity to initial conditions. Since Poincare, great strides in abrupt change understanding as linked to chaos (and within an examination of turbulence) have taken place in the science that informs tipping points, such as with the work of Ed Lorenz and David Ruelle. Additionally, the Russian mathematicians (e.g., Andronov and Arnold) have contributed greatly with the refining of differential equations for bifurcation understandings that Poincare began.  </p><p>This EGU presentation is a history of science presentation on Henri Poincare's commencement of bifurcation, dynamical system and chaos understandings as presented by a journalist who has done both interviews and general historical research. The presentation sets key points in Poincare’s biography and pertinent career and sketches the legacy of this Poincare focus up from Henri Poincare through Russian bifurcation scientists, catastrophe theorist Rene Thom, and ultimately Lorenz and current bifurcation theorists, such as Michael Ghil and Valerio Lucarini. It offers light on the ancestry of one of the most important examinations of the Anthropocene, climate change tipping points.  </p>

Felix Klein und Paul Koebe – „Durchführung eines im Grunde doch Kleinen Programms“

This article analyzes the relationship between the mathematicians Felix Klein and Paul Koebe. Inspired by Klein, Koebe provided the proofs for the uniformization theorems formulated by Klein and Henri Poincaré. In particular, Koebe was able to realize Klein’s original idea of a continuity proof, the possibility of which had been doubted by Poincaré. By analyzing Koebe’s letters to Klein and files from the Jena University Archives, new insights could be gained, which also concern Paul Koebe’s biography. Dieser Artikel analysiert die Beziehung zwischen den Mathematikern Felix Klein und Paul Koebe. Inspiriert von Klein lieferte Koebe die Beweise für die von Klein und Henri Poincaré formulierten Uniformisierungstheoreme. Insbesondere war Koebe in der Lage, Kleins ursprüngliche Idee eines Kontinuitätsbeweises zu realisieren, dessen Möglichkeit von Poincaré bezweifelt worden war. Durch die Analyse von Koebes Briefen an Klein und von Akten aus dem Jenaer Universitätsarchiv konnten neue Erkenntnisse gewonnen werden, die auch die Biographie Paul Koebes betreffen.

Frege, Poincaré, Carnap, Kripke: cuatro réplicas a un dogma kantiano

I present the replies that Gottlob Frege, Henri Poincaré, Rudolf Carnap, and Saul Kripke made to the assumption that apriority and necessity are interchangeable synonyms, an assumption that I take, together with the assumptions that there is a split between analytic truths and synthetic truths and that there is a dichotomy between our conceptual schemes and empirical content, as a Kantian dogma.