Author Archive: raphy

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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