Every Tuesday, 1:45  3:20 pm with a 5minute break. Location: Seminar Hall Random Talks  Lecture Series A proof of uniformization  First Talk M.S. Raghunathan NCM, Mumbai. 160118 Abstract Prof. M. S. Raghunathan (NCM, Mumbai) will give a series of talks titled "Random Talks" starting Tuesday, January 16, 2018. The talks will be on diverse mathematical topics with a focus on an interesting theorem. The talks will be of 1.5hour duration with a 5minute break and will be given every Tuesday. Time: Every Tuesday, 1:45  3:20 pm with a 5minute break. Location: Seminar Hall Details for the first talk of the series are as follows. Date: Tuesday, January 16, 2018. Title: A proof of uniformization. Abstract: I will sketch a proof of the uniformzation theorem for Riemann surfaces. The theorem says in particular that any smooth surface carries a metric of constant curvature. There is no hope of proving any such result in higher dimensions. In fact even the question whether there exists a compact manifold of constant curvature is delicate. The answer (in the affirmative) employs some sophisticated arithmetic and this will be described in the second half of the talk.
