Thursday, October 27, 2022
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All day |
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4:00pm |
10/27/2022 - 4:00pm Sarnak’s M"obius disjointness conjecture asserts that for any zero entropy dynamical system $(X,T)$, any point $x$ in $X$ and any continuous function $f$ on $X$, the correlation of $f(T^n x)$ with the M"obius function tends to 0. We construct examples showing that this correlation can go to zero arbitrarily slowly. In fact, our methods yield a more general result, where in lieu of μ(n) one can put any bounded sequence such that the Cesàro mean of the corresponding sequence of absolute values does not tend to zero. This is a joint work with Amir Algom. Location:
LOM 206
10/27/2022 - 4:15pm A joint work with Andrew Lawrie (MIT) on the wave maps equation from the (1+2)-dimensional space to the 2-dimensional sphere, in the case of initial data having the equivariant symmetry. We prove that every solution of finite energy converges in large time to a superposition of harmonic maps (solitons) and radiation. It was proved by Côte, and Jia and Kenig, that such a decomposition is true for a sequence of times. Combining the study of the dynamics of multi-solitons by the modulation technique with the concentration-compactness method, we prove a “non-return lemma”, which allows to improve the convergence for a sequence of times to convergence in continuous time Location:
WLH 120
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