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# Events for 07/30/2019 from all calendars

## Texas A&M - Beihang Summer Program

## Workshop in Analysis and Probability Seminar

## Texas A&M - Beihang Summer Program

**Time: ** 1:30PM - 2:30PM

**Location: ** BLOC 220

**Speaker: **Irina Holmes, Texas A&M University

**Description: ****Title:** "Stochastic methods in harmonic analysis" **Abstract:**This talk is meant to introduce, through examples, the Bellman function method in harmonic analysis. Originating in the theory of stochastic processes, this clever method has been recently used to prove many sharp inequalities in harmonic analysis - some of which had been conjectures for a long time.

**Time: ** 3:00PM - 3:50PM

**Location: ** BLOC 605AX

**Speaker: **Khazhakanush Navoyan, University of Mississippi

**Title: ***$\xi$-completely continuous operators and $\xi$-Schur Banach spaces*

**Abstract: **For each ordinal $0\leqslant \xi\leqslant \omega_1$, we introduce the notion of a $\xi$-completely continuous operator and prove that for each ordinal $0< \xi< \omega_1$, the class $\mathfrak{V}_\xi$ of $\xi$-completely continuous operators is a closed, injective operator ideal which is not surjective, symmetric, or idempotent. We prove that for distinct $0\leqslant \xi, \zeta\leqslant \omega_1$, the classes of $\xi$-completely continuous operators and $\zeta$-completely continuous operators are distinct. We also introduce an ordinal rank $\textsf{v}$ for operators such that $\textsf{v}(A)=\omega_1$ if and only if $A$ is completely continuous, and otherwise $\textsf{v}(A)$ is the minimum countable ordinal such that $A$ fails to be $\xi$-completely continuous. We show that there exists an operator $A$ such that $\textsf{v}(A)=\xi$ if and only if $1\leqslant \xi\leqslant \omega_1$, and there exists a Banach space $X$ such that $\textsf{v}(I_X)=\xi$ if and only if there exists an ordinal $\gamma\leqslant \omega_1$ such that $\xi=\omega^\gamma$. Finally, prove that for every $0<\xi<\omega_1$, the class $\{A\in \mathcal{L}: \textsf{v}(A) \geqslant \xi\}$ is $\Pi_1^1$-complete in $\mathcal{L}$, the coding of all operators between separable Banach spaces. This is in contrast to the class $\mathfrak{V}\cap \mathcal{L}$, which is $\Pi_2^1$-complete in $\mathcal{L}$.

**URL: ***Event link*

**Time: ** 3:30PM - 4:30PM

**Location: ** BLOC 220

**Speaker: **Jay Walton, Texas A&M University

**Description: ****Title:** "On a Mathematical Model of a Genetic Engineering Approach to the Control of an Invasive Species: Analysis and Application" **Abstract:** One of the most important concerns in ecosystem management is the damage caused by invasive species. Discussed in this talk is a mathematical model for a recently proposed genetic engineering approach to controlling certain classes of invasive species. The primary mathematical tools employed in analyzing the feasibility and practical application of the biological control strategy are the theory of dynamical systems, both finite and infinite dimensional systems.