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SUMMARY:Alex Suciu (Northeastern University)
DTSTART:20210413T160000Z
DTEND:20210413T170000Z
DTSTAMP:20260423T024545Z
UID:NUTopSem/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NUTopSem/4/"
 >Finiteness properties\, cohomology jump loci\, and tropical varieties</a>
 \nby Alex Suciu (Northeastern University) as part of Northeastern Topology
  Seminar\n\n\nAbstract\nThe Bieri--Neumann--Strebel--Renz invariants $\\Si
 gma^q(X)$ of a connected\, finite-type CW-complex $X$ are the vanishing lo
 ci for the Novikov--Sikorav homology of $X$ in degrees up to $q$.\nThese i
 nvariants live in the unit sphere inside $H^1(X\,\\mathbb{R})$\; this sphe
 re can be thought of as parametrizing all free abelian covers of $X$\, whi
 le the $\\Sigma$-invariants keep track of the geometric finiteness propert
 ies of those covers. On the other hand\, the characteristic varieties $\\V
 ^q(X) \\subset H^1(X\,\\mathbb{C}^{*})$ are the non-vanishing loci in degr
 ee $q$ for homology with coefficients in rank $1$ local systems. After exp
 laining these notions and providing motivation\, I will describe a rather 
 surprising connection between these objects\, to wit: each BNSR invariant 
 $\\Sigma^q(X)$ is contained in the complement of the tropicalization of $V
 ^{\\le q}(X)$. I will conclude with some examples and applications pertain
 ing to complex geometry\, group theory\, \nand low-dimensional topology.\n
LOCATION:https://researchseminars.org/talk/NUTopSem/4/
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