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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Dmitriy Drusvyatskiy
University of Washington
Title: Slope and geometry in variational mathematics

Abstract: Various notions of the "slope" of a real-valued function pervade optimization, and variational mathematics more broadly. In the semi-algebraic setting - an appealing model for concrete variational problems - the slope is particularly well-behaved. This talk sketches a variety of surprising applications, illustrating the unifying power of slope. Highlights include error bounds for level sets, existence and regularity of steepest descent curves in complete metric spaces (following Ambrosio et al.), transversality and convergence of von Neumann's alternating projection algorithm, function approximation on singular domains with prescribed boundary behavior, and geometry of Moreau's sweeping process modeling contact dynamics. This talk will be self-contained, requiring no familiarity with variational analysis, optimization theory, or semi-algebraic geometry.

Date: Thursday, January 18, 2018
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  Ian Tice