BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Aris Daniilidis (University of Chile / Autonomous University of Ba rcelona) DTSTART:20201005T133000Z DTEND:20201005T143000Z DTSTAMP:20260423T035056Z UID:OWOS/20 DESCRIPTION:Title: As ymptotic Study of the Sweeping Process\nby Aris Daniilidis (University of Chile / Autonomous University of Barcelona) as part of One World Optim ization seminar\n\n\nAbstract\nLet $r\\mapsto S(r)$ be a set-valued mappin g with nonempty values and a closed semi-algebraic graph (or more generall y\, with a graph which is definable in some o-minimal structure). We shall be interested in the asymptotic behavior of the orbits of the so-called s weeping process $$\\dot x(r) \\in - N_{S(r)}\, \\quad r>0.\\hspace{2cm} (S PO)$$ \n\nKurdyka (Ann. Inst. Fourier\, 1998)\, in the framework of a grad ient dynamics of a $C^1$-smooth definable function $f$\, generalized the L ojasiewicz inequality and obtained a control of the asymptotic behavior of the gradient orbits in terms of a desingularizing function $\\Psi$ depend ing on $f$. We shall show that an analogous technique to the one used by K urdyka can be replicated to our setting for the sweeping dynamics. Our met hod recovers the aforementioned result of Kurdyka\, by simply considering the sweeping process defined by the sublevel sets of the function $f$: ind eed\, in this case setting $S(r) = [f \\leq r]$\, we deduce that the orbit s of (SPO) are in fact gradient orbits for $f$\, and\nthe nowadays called (smooth) Kurdyka-Lojasiwiecz inequality is recovered.\n\nThis talk is base d on a work in collaboration with D. Drusvyatskiy (Seattle).\n\nthe addres s and password of the zoom room of the seminar are sent by e-mail on the m ailinglist of the seminar one day before each talk\n LOCATION:https://researchseminars.org/talk/OWOS/20/ END:VEVENT END:VCALENDAR