Colloquium

Over the course of the last 15 years or so, Minhyong Kim has developed a method for making effective use of the fundamental group to bound sets of solutions to hyperbolic equations; his method opens a new avenue in the…
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Let C be a smooth projective curve (of genus g>1) over an algebraically closed field K. Let J(C) be the Jacobian of C. By Torelli’s theorem J(C), as a principally polarized Abelian variety determines C up to isomorphism. In 2010,…
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An affine action by a group G is a continuous action of G on a compact convex K set by affine transformations. Such actions arise in a natural way whenever G acts by homeomorphisms of a compact topological space X…
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Mapping class groups (and their cousins – automorphism groups of free groups) are some of the most ubiquitous groups in mathematics. Their representation theory is known to be very rich, but still remains very mysterious and many very basic questions…
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We recall some of the theory of modular forms starting with results of Jacobi on the theta function and sum of four squares. We will look at Ramanujan’s discriminant function, Hecke’s operators and the theory of new forms of Atkin…
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We study a notion of planar sectional curvature for polygonal complexes. These complexes are endowed with a collection of certain planar subcomplexes. The first part of the talk is devoted to a description of these objects. After that, we discuss…
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The subject of amenability essentially begins in 1900’s with Lebesgue. He asked whether the properties of his integral are really fundamental and follow from more familiar integral axioms.  This led to the study of positive, finitely additive and translation invariant…
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In the Euclidean space E of dimension n; an affine invariant point (resp. set) on the class of convex bodies of dimension $n$, endowed with the Hausdorff metric, is a continuous map from this class into  E (resp. into itself…
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Integral formulae on foliated Riemannian manifolds provide obstructions for the existence of foliations satisfying given geometric properties. Here, we shall  present a bit of history of this subject: from Reeb (1950) till Rovenski-Walczak (2012), and  brand new results obtained by…
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Tropicalization involves passing to an ordered group M, usually taken to be (R,+) or (Q,+), and viewed as a semifield. Although there is a rich theory arising from this viewpoint, idempotent semi-rings possess a restricted algebraic structure theory, and also…
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