Friday, April 8, 2022
Time | Items |
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All day |
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9am |
04/08/2022 - 9:00am We discuss topics of common interest in the areas of geometry, probability, and combinatorics. Location: |
12pm |
04/08/2022 - 12:00pm The prime number theorem states that the number of primes of size at most T grows llike T/logT, proved by Hadamard and de la Vallee Poussin in 1896. For Gaussian primes, that is, prime ideals in Z[i], not only does the number of Gaussian primes of norm at most T grow like T/logT but also the angular components of Gaussian primes are equidistributed in all directions, as proved by Hecke in 1920. Geometric analogues of these profound facts have been of great interest over the years. We will discuss effective versions of these theorems for hyperbolic 3-manifolds and for rational maps. Both Kleinian groups and rational maps define dynamical systems on the Riemann sphere and they are expected to behave analogously in view of Sullivan’s dictionary. We will explain how our theorems fit in this dictionary. Location:
LOM 206
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2pm |
04/08/2022 - 2:00pm Abstract: In this talk, we will derive a priori interior Hessian estimates for the Lagrangian mean curvature equation under certain natural restrictions on the Lagrangian phase. As an application, we will use these estimates to solve the Dirichlet problem for the Lagrangian mean curvature equation with continuous boundary data on a uniformly convex, bounded domain. Location: |