BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Vidit Nanda (Oxford) DTSTART:20201123T141500Z DTEND:20201123T151500Z DTSTAMP:20260423T024539Z UID:OxGeom/5 DESCRIPTION:Title: C omplex links and algebraic multiplicities\nby Vidit Nanda (Oxford) as part of Oxford Geometry and Analysis Seminar\n\n\nAbstract\nGiven a nested pair X and Y of complex projective varieties\, there is a single positive integer e which measures the singularity type of X inside Y. This is call ed the Hilbert-Samuel multiplicity of Y along X\, and it appears in the fo rmulations of several standard intersection-theoretic constructions includ ing Segre classes\, Euler obstructions\, and various other multiplicities. The standard method for computing e requires knowledge of the equations w hich define X and Y\, followed by a (super-exponential) Grobner basis comp utation. In this talk we will connect the HS multiplicity to complex links \, which are fundamental invariants of (complex analytic) Whitney stratifi ed spaces. Thanks to this connection\, the enormous computational burden o f extracting e from polynomial equations reduces to a simple exercise in c lustering point clouds. In fact\, one doesn't even need the polynomials wh ich define X and Y: it suffices to work with dense point samples. This is joint work with Martin Helmer.\n LOCATION:https://researchseminars.org/talk/OxGeom/5/ END:VEVENT END:VCALENDAR