BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Matthew Blair (New Mexico) DTSTART:20211027T163000Z DTEND:20211027T173000Z DTSTAMP:20260423T024446Z UID:HASS21/3 DESCRIPTION:Title: L p bounds for eigenfunctions at the critial exponent\nby Matthew Blair (New Mexico) as part of Harmonic Analysis and Symmetric Spaces 2021\n\n\nA bstract\nWe consider upper bounds on the growth of $L^pa$ norms of eigenfu nctions of the Laplacian on a compact Riemannian manifold in the high freq uency limit. In particular\, we seek to identify geometric or dynamical co nditions on the manifold which yield improvements on the universal $L^p$ b ounds of C. Sogge. The emphasis will be on bounds at the "critical exponen t"\, where a spectrum of scenarios for phase space concentration must be c onsidered. We then discuss a recent work with C. Sogge which shows that wh en the sectional curvatures are nonpositive\, there is a logarithmic type gain in the known $L^p$ bounds at the critical exponent.\n LOCATION:https://researchseminars.org/talk/HASS21/3/ END:VEVENT END:VCALENDAR