Colloquium

Non-Archimedean analytic spaces are analogues of complex manifolds when replacing the complex numbers by a non-Archimedean field, such as p-adic numbers or complex Laurent series. I will give several examples of situations involving degenerations in complex analysis and geometry that…
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Earlier and recent one-dimensional estimates and asymptotic relations for the cosine and sine Fourier transform of a function of bounded variation are refined in such a way that they become applicable for obtaining multidimensional asymptotic relations for the Fourier transform…
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What is the optimal way to cut a convex bounded domain K in Euclidean space R^n into two halves of equal volume, so that the interface between the two halves has least surface area? A conjecture of Kannan, Lovasz and…
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Given positive integers h and k, denote by r(h,k) the smallest integer n such that in any k-coloring of the edges of a tournament on more than n vertices, there is a monochromatic copy of every oriented tree on h…
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The family of high rank arithmetic groups is class of groups which is playing  an important role in various areas of mathematics. It includes SL(n,Z) for n>2, SL(n, Z[1/p]) for n>1, their finite index subgroups and many more. A number…
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  Consider a compact complex torus T, identified with the quotient C^n/L, where L is a lattice in C^n. Let p: C^n->T be the quotient map. Ullmo and Yafaev have recently asked the following question: Assume that X is an…
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Equivariant symplectic geometry is a meeting point for many areas of mathematics: it models symmetries of phase space in classical mechanics, extends algebraic-geometric phenomena, provides a geometric context for representations of Lie groups, and connects with geometry of convex polytopes….
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Topological dynamics studies behaviour of orbits under continuous transformations. Algebraic dynamics is the name attached to the study of automorphisms acting on a compact abelian group, from a “dynamical point of view”. In the 1970’s, motivated by the study of…
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We will give an overview of questions one might ask about the first-order theory of free groups and related groups: how much information can first-order formulas convey about these groups or their elements, what algebraic interpretation can be given for…
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Following Marty’s Theorem we present recent results about differential inequalities that imply (or not) some degree of normality. We deal with inequalities with reversed sign of inequality than that in Marty’s Theorem, i.e. |f^{(k)}(z)|> h(|f(z)|). Based on joined work with…
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