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SUMMARY:Algebraic geometry\, theory of singularities\, and convex geometry
DTSTART;VALUE=DATE-TIME:20150622T131500Z
DTEND;VALUE=DATE-TIME:20150622T140500Z
DTSTAMP;VALUE=DATE-TIME:20190619T130305Z
UID:indico-contribution-202-952@indico.math.cnrs.fr
DESCRIPTION:Speakers: Askold Khovanskii (University of Toronto)\nI will re
view some results which relate these areas of mathematics.\nNewton polyhed
ra connect algebraic geometry and the theory of singularities to the geome
try of convex polyhedra. This connection is useful in both direc- tions. O
n the one hand\, explicit answers are given to problems of algebra and the
theory of singularities in terms of the geometry of polyhedra. On the oth
er hand\, algebraic theorems of general character (like the Hirzebruch–R
iemann–Roch theorem) give significant information about the geometry of
polyhedra. In this way one obtains\, for example\, a multidimensional gene
ralization of the classical one-dimensional Euler–Mclaurin formula. Comb
inatorics related to the Newton polyhedra theory allows to prove that in h
yperbolic space of high dimension there do not exist discrete groups gener
ated by reflections with fundamental polyhedron of finite volume (it was a
longstanding conjecture).\nThe theory of Newton–Okounkov bodies relates
algebra\, singularities and geom- etry outside the framework of toric geo
metry. This relationship is useful in many directions. For algebraic geome
try it provides elementary proofs of intersection- theoretic analogues of
the geometric Alexandrov–Fenchel inequalities and far-reach- ing general
izations of the Fujita approximation theorem. The local version of the the
ory provides a new proof of the famous Teissier’s inequalities for the m
ultiplici- ties of primary ideals in a local ring. In geometry it suggests
a transparent analog of Alexandrov–Fenchel inequality for coconvex bodi
es.\n\nhttps://indico.math.cnrs.fr/event/202/contributions/952/
LOCATION:Centre Paul-Langevin AUSSOIS La Parrachée
URL:https://indico.math.cnrs.fr/event/202/contributions/952/
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SUMMARY:Families of isolated singularities and three inspirations from Ber
nard Teissier
DTSTART;VALUE=DATE-TIME:20150622T080000Z
DTEND;VALUE=DATE-TIME:20150622T085000Z
DTSTAMP;VALUE=DATE-TIME:20190619T130305Z
UID:indico-contribution-202-954@indico.math.cnrs.fr
DESCRIPTION:Speakers: Terence Gaffney (Northeastern University)\nPart of B
ernard Teisier¹s work is a substantial contribution to\nequisingularity t
heory. In this talk I will discuss three of the many\ninspirations his wor
k has given me\, and their role in my current approach\nto the equisingul
arity of isolated singularities. The talk will use\ndeterminantal singula
rities as an illustration of these ideas.\n\nhttps://indico.math.cnrs.fr/e
vent/202/contributions/954/
LOCATION:Centre Paul-Langevin AUSSOIS La Parrachée
URL:https://indico.math.cnrs.fr/event/202/contributions/954/
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SUMMARY:Milnor numbers of projective hypersurfaces and the chromatic polyn
omial of graphs
DTSTART;VALUE=DATE-TIME:20150622T120000Z
DTEND;VALUE=DATE-TIME:20150622T125000Z
DTSTAMP;VALUE=DATE-TIME:20190619T130305Z
UID:indico-contribution-202-956@indico.math.cnrs.fr
DESCRIPTION:Speakers: June Huh (Princeton)\nI will give an overview of a p
roof of a conjecture of Read that the coefficients of the chromatic polyno
mial of any graph form a unimodal sequence. There are two main ingredients
in the proof\, both coming from works of Bernard Teissier: The first is t
he idealistic Bertini for sectional Milnor numbers\, and the second is the
isoperimetric inequality for mixed multiplicities of ideals.\n\nhttps://i
ndico.math.cnrs.fr/event/202/contributions/956/
LOCATION:Centre Paul-Langevin AUSSOIS La Parrachée
URL:https://indico.math.cnrs.fr/event/202/contributions/956/
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SUMMARY:Local monomialization of analytic maps
DTSTART;VALUE=DATE-TIME:20150622T093000Z
DTEND;VALUE=DATE-TIME:20150622T102000Z
DTSTAMP;VALUE=DATE-TIME:20190619T130305Z
UID:indico-contribution-202-966@indico.math.cnrs.fr
DESCRIPTION:Speakers: Steven Dale Cutkosky (University of Missouri)\nWe pr
ove that germs of analytic maps of complex analytic varieties can be mad
e monomial by sequences of local blow ups of nonsingular analytic subvarie
ties in the domain and target along an arbitrary étoile. An étoile and t
he voûte étoilée is a generalization by Hironaka of valuations and the
Zariski Riemann manifold to analytic spaces.\n\nhttps://indico.math.cnrs.f
r/event/202/contributions/966/
LOCATION:Centre Paul-Langevin AUSSOIS La Parrachée
URL:https://indico.math.cnrs.fr/event/202/contributions/966/
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