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Vasily Dolgushev, Temple University
I will introduce infinite Galois extensions and show that the automorphism group of an infinite Galois extension is naturally a topological group (with the Krull topology). If time will permit, I will talk about the fundamental theorem of infinite Galois theory.
Terrence Napier, Lehigh University
Joint work with Mohan Ramachandran on analogues of the Hartogs extension theorem (regarding the extension of a holomorphic function of several complex variables past a compact set) in the setting of Kaehler manifolds will be considered.
Ara Basmajian, CUNY Graduate Center
Abstract: In this talk we first describe some of the known results on the geometry and topology of infinite (topological) type surfaces and then we investigate the relationship between Fenchel-Nielsen coordinates and when the geodesic flow on such a surface is ergodic. Ergodicity of the geodesic flow is equivalent to the surface being of so called parabolic type (the surface does not carry a Green's function), and hence this problem is intimately connected to a version of the classical type problem in the study of Riemann surfaces. Specifically, we study so called tight flute surfaces -- (possibly incomplete) hyperbolic surfaces constructed by linearly gluing infinitely many tight pairs of pants along their cuffs -- and the relationship between their type and geometric structure. This is joint work with Hrant Hakobyan and Dragomir Saric.
Purvi Gupta, Rutgers University
Starting with the observation that every continuous complex-valued function on the unit circle can be approximated by rational combinations of one function and polynomial combinations of two functions, we will discuss analogous approximation phenomena for compact manifolds of higher dimensions. On a related note, we will discuss some questions regarding the minimum embedding (complex) dimension of real manifolds within the context of polynomial convexity. In the special case of even-dimensional manifolds, we will present a technique that improves previously known bounds. This is joint work with Rasul Shafikov.
There are no conferences next week.