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2:00pm - 510R Rowland Hall - Combinatorics and Probability Stanislav Minsker - (USC) Concentration Inequalities and Moment Bounds for Self-Adjoint Operators with Heavy tails We present Fuk-Nagaev - type inequality for the sums of independent self-adjoint operators. This bound could be viewed as an extension of the well known “Matrix Bernstein” inequality to the case of operators with heavy-tailed norms. As a corollary, we deduce Rosenthal moment inequality that improves upon the previously known versions even in the scalar case. Finally, we will discuss applications of these bounds to the covariance estimation problem. |
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9:00am to 9:50am - Zoom - Inverse Problems Noemi Naujoks - (University of Vienna) Diffraction tomography and its application in ultrasound imaging |
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3:00pm to 4:00pm - RH 340P - Number Theory Kelly Isham - (Colgate University) Subring growth in Z^n Subgroups in $\mathbb{Z}^n$ are well-understood. For example, the growth rate of the number of subgroups in $\mathbb{Z}^n$ is known, and futher, for any $k$, a positive proportion of subgroups have corank $k$, though subgroups grow sparse as $k$ increases. Much less is known about subrings in $\mathbb{Z}^n$. There is not even a conjecture about what the growth rate of the number of subrings in $\mathbb{Z}^n$ should be. In this talk, we compare subgroup growth and subring growth. We then focus on subrings of corank $k$ and show that while the proportion of subgroups of any fixed corank is always positive, the proportion of subrings of any fixed corank is not. This is joint work with Nathan Kaplan. |