Andrei Gabrielov (Purdue University, USA), Classification of spherical quadrilaterals

Oddział Warszawski Polskiego Towarzystwa Matematycznego, Instytut Matematyczny  Polskiej Akademii Nauk i Międzynarodowe Centrum Matematyczne im. Stefana Banacha

W dniu 31 lipca 2014 roku (CZWARTEK) o godz. 16:30 w sali 321, III piętro, w Instytucie Matematycznym PAN, ul. Śniadeckich 8
 

Prof. Andrei Gabrielov (Purdue University, USA)

wygłosi

WYKŁAD - KOLOKWIUM

pod tytułem

CLASSIFICATION OF SPHERICAL QUADRILATERALS

Streszczenie wykładu:   
 A spherical quadrilateral (membrane) is a bordered surface homeomorphic to a closed disc, with four distinguished boundary points called corners, equipped with a Riemannian metric of constant curvature 1, except at the corners, and such that the boundary arcs between the corners are geodesic. We discuss the problem of classification of these quadrilaterals and perform the classification up to isometry in the case that at most two angles at the corners are not multiples of Pi. This is a very old problem, related to the properties of solutions of the Heun's equation (an ordinary differential equation with four regular singular points). The corresponding problem for the spherical triangles, related to the properties of solutions of the hypergeometric equation, has been solved by Klein, with some gaps in Klein's classification filled in by Alexandre Eremenko in 2004. The quadrilateral case for small corners was treated in the thesis of Vladimir Smirnov (1918), but for arbitrary corners remains open.
This is joint work with Alexandre Eremenko (Purdue University, USA) and Vitaly Tarasov (Indiana University-Purdue University Indianapolis, USA).                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Andrei Gabrielov

Przed wykładem, od godz. 16:00, zapraszamy na spotkanie przy kawie i herbacie w sali klubowej IMPAN na IV piętrze.

Serdecznie zapraszamy
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