Dana Mendelson (Chicago) An infinite sequence of conserved quantities for the cubic Gross-Pitaevskii hierarchy on R Sponsored by the Meyer Fund

Thu, Nov. 30 3pm (MATH 350)

Probability

Rafael Frongillo (CU Boulder) Elicitation Complexity and Individual Sequences

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We consider the (de)focusing cubic Gross-Pitaevskii (GP) hierarchy on R, which is an infinite hierarchy of coupled linear non-homogeneous PDE which appears in the derivation of the cubic nonlinear Schrodinger (NLS) equation from quantum many-particle systems. Motivated by the fact that the cubic NLS on R is an integrable equation which admits infinitely many conserved quantities, we exhibit an infinite sequence of operators which generate analogous conserved quantities for the GP hierarchy. This is joint work with Andrea Nahmod, Natasa Pavlovic, and Gigliola Staffilani.

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In statistics, the term "elicitation" refers to the relationship between a loss function and its (expected) minimizer. The term arises from economics, where the loss is taken to be a monetary penalty, and one wishes to incentivize someone to truthfully report a desired statistic of some eventually observed random variable. Interestingly, not all statistics are elicitable, including simple measures of risk or deviation like the variance of a random variable. I will give a brief overview of elicitation, and mention a few interesting open questions in elicitation complexity, where we seek to indirectly elicit otherwise non-elicitable statistics. I will conclude with a connection to the notion of random individual sequences.