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Penn Mathematics Colloquium

Wednesday, October 4, 2017 - 3:30pm

Ofer Zeitouni

Weizmann Institute and NYU


University of Pennsylvania


Tea before the talk at 3pm in the math lounge, 4th flood DRL

The solution to the one dimensional Fisher-KPP equation (1937) u_t=Delta u+u(1-u) starting from a step initial condition, converges after centering by 2t - 3/2 log t to a traveling wave. The logarithmic correction term, and in particular the coefficient 3/2,  was computed by Bramson (1978), through a connection with the maximum of branching Brownian motion. Recently, this computation proved crucial in the solution of a variety of problems: the law of the maximum of the critical Gaussian free field, the cover time of the 2-sphere by  Brownian sausage, the maxima of the characteristic polynomials of random unitary matrices, and even the  values of the Riemann zeta function on the critical line. These problems all share a hidden logarithmic (i.e., multiscale) correlation. In the talk I will describe these development and will emphasize the common philosophy in studying these very different models.