Dear all, The next Banach spaces webinar is on Friday June 5 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Denny Leung, National University of Singapore Title: Local convexity in $L^0$. Abstract. Let $(\Omega,\Sigma,\bP)$ be a nonatomic probability space and let $L^0(\Omega,\Sigma,\bP)$ be the space of all measurable functions on $(\Omega,\Sigma,\bP)$. We present some results characterizing the convex sets in $L^0$ that are locally convex with respect to the topology of convergence in measure. The work is motivated by results of Kardaras & Zitkovic (PAMS 2013) and Kardaras (JFA 2014) and is relevant to mathematical economics/finance. The talk is based on joint work with Niushan Gao and Foivos Xanthos: * A local Hahn-Banach Theorem and its applications, Arch. Math., 112(2019), 521-529. https://arxiv.org/abs/1809.01795 * On local convexity in $L^0$ and switching probability measures. https://arxiv.org/abs/1902.00992 * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule June 12: Noé de Rancourt, Kurt Gödel Research Center Thank you, and best regards, Bunyamin