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VERSION:2.0
PRODID:-//University of Liverpool Computer Science Seminar System//v2//EN
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DTSTAMP:20260413T115645Z
UID:Seminar-Maths-511@lxserverM.csc.liv.ac.uk
ORGANIZER:CN=Othon Michail:MAILTO:Othon.Michail@liverpool.ac.uk
DTSTART:20191118T140000
DTEND:20191118T150000
SUMMARY:Selected Topics in Mathematics Series
DESCRIPTION:Victor Goryunov: Vanishing cycles of matrix singularities\n\nThe talk is about holomorphic map germs M : (C^s , 0) ? M atn, where the target is the space of either square, or symmetric, or skew-symmetric n × n matrices. The target contains the set ? of all degenerate matrices, and our main object will be the vanishing topology of M?1(?). Our attention is on the singular Milnor fibre of M, that is, the local inverse image V of ? under a generic small perturbation of M. The variety V is highly singular, but, according to Le Dung Trang’s theorem, it is homotopic to a wedge of (s ? 1)-dimensional spheres.\n\nThe talk will start with introduction of local models for the spheres vanishing in the matrix context.\nWe will then prove the µ = ? conjecture formulated by Damon for corank 1 map-germs M with a generic linear part, and a generalisation of this conjecture\nto the matrix version of boundary function singularities.\n\nBifurcation diagrams of matrix singularities will also be discussed, and a rather unexpected appearance of the discriminants of certain Shephard-Todd\ngroups as such diagrams will be highlighted.\n\nIf time permits, possible approaches to the study of the monodromy will be mentioned\n\nhttps://www.csc.liv.ac.uk/research/seminars/abstract.php?id=511
LOCATION:MATH-103
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