Dierk Schleicher (Université d'Aix-Marseille) посетил Лабораторию в ноябре 2019 г. по приглашению ассоциированного сотрудника Лаборатории, профессора факультета математики В.А. Тиморина.
13 ноября 2019 г. Dierk Schleicher выступил с докладом From Thurston’s vision in geometry, topology, and dynamics to current research in holomorphic dynamics на научном семинаре факультета математики
Since the 1980’s, Bill Thurston has done fundamental work in apparently quite different areas of mathematics: in particular, on the geometry of 3-manifolds, on automorphisms of surfaces, and on holomorphic dynamics. In all three areas, he proved deep and fundamental theorems that turn out to be surprisingly closely connected both in statements and in proofs.
In all three areas, the statements can be expressed that either a topological object has a geometric structure (the manifold is geometric, the surface automorphism has Pseudo-Anosov structure, a branched cover of the sphere respects the complex structure), or there is a well defined topological-combinatorial obstruction consisting of a finite collection of disjoint simple closed curves with specific properties. Moreover, all three theorems are proved by an iteration process in a finite dimensional Teichmüller space (this is a complex space that parametrizes Riemann surfaces of finite type).
I will try to relate these different topics and at least explain the statements and their context. I will also try to discuss current work with my dynamics team on Thurston theory in holomorphic dynamics.
15 ноября 2019 г. Dierk Schleicher выступил с докладом How to find roots of polynomials — and how university students can do successful research on a century-old problem семинаре «Геометрия и динамика»
Every polynomial of degree d has d roots over the complex numbers — this result has been known for centuries, and there are very old algorithms to find these roots. Especially since this is a problem that has substantial importance in many areas of science and engineering, it may come as a surprise that it is not so clear how to actually find all the roots of a given polynomial. We try to explain some of the difficulties, and how surprising progress has been made by a few young students. The moral of the story will be that mathematics is not finished, but provides challenges and opportunity for the next generation as well.
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