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Notes of Will Sawin first Hadamard lecture, 15-05-2023
Number theory over function fields 1. The classical theory Let us start with classical stuff. Theorem 1 (Dirichlet) a positive integer, an integer. There exist infinitely many prime numbers such that if and only if . A more precise statement … Continue reading
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Notes on Alexandros Eskenazis Rennes lectures january 26th 2023
When does embed into ? The question goes back to Banach. This will be an excuse to review some modern tools. Banach space theory has evolved into metric geometry. The leitmotiv will be: how does one prove non-embeddability? 1. Linear … Continue reading
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Notes of Maryna Viazovska’s Orsay lecture, january 2023
Sphere packings This lecture has been designed for an audience of 150 master’s students in Orsay, Universite Paris-Saclay. 1. The sphere packing problem 1.1. Density In Euclidean space, one tries to pack equal balls as densely as possible. Pack means … Continue reading
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Notes of Corinna Ulcigrai’s Hadamard Lectures, june 2022
Parabolic dynamics 1. Survey 1.1. What does hyperbolic, elliptic mean in dynamics? Let be a dynamical system. Even if deterministic, it can exhibit a chaotic behaviour. This has several characteristics. One of them is the Butterfly effect: sensitive dependence on … Continue reading
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Notes of Uri Bader IHES lectures october 5th, 2021
Algebraic representations of ergodic actions Based on joint work with Alex Furman, and earlier litterature. Thanks to Sami Douba for his help with notetaking. Today, we start with basics on measure spaces and algebraic varieties. Later on, we shall merge … Continue reading
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Notes of Karim Adiprasito’s Hadamard Lectures 2021-04-19
Karim Adiprasito I want to show how combinatorial tools can be used to prove results which previously came from algebraic geometry. Today, I give an 1. Overview of applications 1.1. Matroids and characteristic polynomials Example. The chromatic polynomial of a … Continue reading
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Notes of Mikolaj Fraczyk’s YGGT IX lecture, february 27th, 2020
Growth of mod- homology of higher rank lattices and mapping class groups 1. Homology growth Let be a finitely generated group, and a sequence of finite index subgroups. Let be some field. I am interested in the growth of Betti … Continue reading
Short presentations, YGGT IX, february 25th, 2020
5 minutes presentations 1. Anschel Schaffer-Cohen I am interested in big mapping class groups. Let such a group act continuously on a graph , with unbounded orbits. Assume the graph is hyperbolic, plus some kind of other property. Then is … Continue reading
Notes of Radhika Gupta’s YGGT IX lecture, february 25th, 2020
Non-uniquely ergodic arational trees in the boundary of Outer space With M. Bestvina and J. Tao. 1. Surface case 1.1. Laminations Let be a hyperbolic surface. A geodesic lamination is filling if the complement is made of discs or once-punctured … Continue reading
Notes of Yair Hartman’s YGGT IX lecture, february 25th, 2020
Which groups have bounded harmonic functions? Joint with Frisch, Tamuz and Vahidi-Ferdowsi. Familiar groups act on boundaries 1. Dirichlet’s problem Impose the temperature along the boundary of a domain , wait until equilibrium. What is the temperature inside? Temperature is … Continue reading
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