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Results and counter-examples concerning the (B)-conjecture
No full textIn 2003 Cordero-Erausquin, Fradelizi, and Maurey proved that the standard Gaussian measure
satisfies a certain concavity property known as the (B) property. This (B) property has two versions,
a weak version and a strong one. It is conjectured that any even log-concave measure satisfies at least
the weak (B)-property. We will show that strong (B) property can fail even for arbitrarily small
Gaussian perturbations on the standard Gaussian measure. We will also discuss some results and equivalent
formulations of the above conjecture regarding the weak (B) property.
Based on joint work with D.~Cordero-Erausquin.Non UBCUnreviewedAuthor affiliation: University of MinnesotaPostdoctora
Powers of convex bodies
No full textGiven a convex body and a real number , how should we define the convex body ? One way to answer this question is to write down a list of natural properties we expect from such a power, and then prove existence and uniqueness of a construction satisfying these properties.
In this talk we will explain why a natural power operation does not exist for , but does exist for . We will also discuss the uniqueness question, which is more delicate.
Based on joint work with Vitali Milman.Non UBCUnreviewedAuthor affiliation: University of MinnesotaPostdoctora
Liran Rotem: Algebraically inspired constructions in convex geometry
No full textNon UBCUnreviewedAuthor affiliation: Tel-Aviv UniversityGraduat
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Mixed volumes and mixed integrals
Get PDFIn recent years, mathematicians have developed new approaches to study convex sets: instead of considering convex sets themselves, they explore certain functions or measures that are related to them. Problems from convex geometry become thereby accessible to analytic and probabilistic tools, and we can use these tools to make progress on very difficult open problems. We discuss in this Snapshot such a functional extension of some “volumes” which measure how “big” a set is. We recall the construction of “intrinsic volumes”, discuss the fundamental inequalities between them, and explain the functional extensions of these results
Functional surface area measures
No full textIn 2013 Colesanti and Fragalà defined the surface area of a log-concave measure, and in 2015 Cordero-Erausquin and Klartag defined the moment measure of a convex function. These notions are basically the same. Comparing the results of the two papers raises some very natural questions about the surface area measure of log-concave functions. We will discuss the answers to a few of these questions.Non UBCUnreviewedAuthor affiliation: TechnionResearche
Geometric constructions and inequalities for α-concave functions
No full textNon UBCUnreviewedAuthor affiliation: Tel-Aviv UniversityGraduat
Characterization of self-polar convex functions
No full textAbstractIn a work by Artstein-Avidan and Milman the concept of polarity is generalized from the class of convex bodies to the larger class of convex functions. While the only self-polar convex body is the Euclidean ball, it turns out that there are numerous self-polar convex functions. In this work we give a complete characterization of all rotationally invariant self-polar convex functions on Rn
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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