Abstract: The resolution of Geroch's conjecture states that the torus does not admit a metric positive scalar curvature and Bonnet-Myers' theorem implies that M x S^1 does not admit a metric of positive Ricci curvature. In this talk I'll show that M x T^m does not admit a metric of positive m-intermediate curvature. This is based upon joint work with Simon Brendle and Florian Johne.

Abstract: In the spirit of the celebrated Komlos theorem, we develop versions of the Weak and of the Hsu-Robbins-Erdos Laws of Large Numbers which are valid along appropriate (“lacunary”) subsequences of arbitrary sequences of random variables with bounded moments; as well as along all further (“hereditary”) subsequences of said subsequences. We review also the strong connections of this subject with lacunary trigonometric series. Joint work with Istvan Berkes, Budapest and Walter Schachermayer, Vienna.

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Abstract: We discuss some examples of deterministic and stochastic integrable systems, and compare the asymptotic phenomena that (should) underly their limiting behaviors.

Abstract: In this talk, I will give a very gentle introduction to certain questions studied in algebraic number theory. I will focus on modular forms and their associated Galois representations and explain Wiles’ original strategy for proving his celebrated modularity lifting theorem. I will conclude by briefly discussing how Wiles’ original strategy can be made to work with modern tools.