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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:20170919T114421Z
UID:indico-contribution-202-12@cern.ch
DESCRIPTION:Speakers: Mr. KHOVANSKII\, Askold (University of Toronto)\nI w
ill review some results which relate these areas of mathematics.\nNewton p
olyhedra connect algebraic geometry and the theory of singularities to the
geometry of convex polyhedra. This connection is useful in both direc- ti
ons. On the one hand\, explicit answers are given to problems of algebra a
nd the theory of singularities in terms of the geometry of polyhedra. On t
he other hand\, algebraic theorems of general character (like the Hirzebru
ch–Riemann–Roch theorem) give significant information about the geomet
ry of polyhedra. In this way one obtains\, for example\, a multidimensiona
l generalization of the classical one-dimensional Euler–Mclaurin formula
. Combinatorics related to the Newton polyhedra theory allows to prove tha
t in hyperbolic space of high dimension there do not exist discrete groups
generated by reflections with fundamental polyhedron of finite volume (it
was a longstanding conjecture).\nThe theory of Newton–Okounkov bodies r
elates algebra\, singularities and geom- etry outside the framework of tor
ic geometry. This relationship is useful in many directions. For algebraic
geometry it provides elementary proofs of intersection- theoretic analogu
es of the geometric Alexandrov–Fenchel inequalities and far-reach- ing g
eneralizations of the Fujita approximation theorem. The local version of t
he theory provides a new proof of the famous Teissier’s inequalities for
the multiplici- ties of primary ideals in a local ring. In geometry it su
ggests a transparent analog of Alexandrov–Fenchel inequality for coconve
x bodies.\n\nhttps://indico.math.cnrs.fr/event/202/session/1/contribution/
12
LOCATION:Centre Paul-Langevin AUSSOIS La Parrachée
URL:https://indico.math.cnrs.fr/event/202/session/1/contribution/12
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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:20170919T114421Z
UID:indico-contribution-202-14@cern.ch
DESCRIPTION:Speakers: Mr. GAFFNEY\, Terence (Northeastern University)\nPar
t of Bernard Teisier¹s work is a substantial contribution to\nequisingula
rity theory. In this talk I will discuss three of the many\ninspirations h
is work has given me\, and their role in my current approach\nto the equi
singularity of isolated singularities. The talk will use\ndeterminantal s
ingularities as an illustration of these ideas.\n\nhttps://indico.math.cnr
s.fr/event/202/session/0/contribution/14
LOCATION:Centre Paul-Langevin AUSSOIS La Parrachée
URL:https://indico.math.cnrs.fr/event/202/session/0/contribution/14
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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:20170919T114421Z
UID:indico-contribution-202-16@cern.ch
DESCRIPTION:Speakers: Mr. HUH\, June (Princeton)\nI will give an overview
of a proof of a conjecture of Read that the coefficients of the chromatic
polynomial of any graph form a unimodal sequence. There are two main ingre
dients in the proof\, both coming from works of Bernard Teissier: The firs
t is the idealistic Bertini for sectional Milnor numbers\, and the second
is the isoperimetric inequality for mixed multiplicities of ideals.\n\nhtt
ps://indico.math.cnrs.fr/event/202/session/1/contribution/16
LOCATION:Centre Paul-Langevin AUSSOIS La Parrachée
URL:https://indico.math.cnrs.fr/event/202/session/1/contribution/16
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SUMMARY:Local monomialization of analytic maps
DTSTART;VALUE=DATE-TIME:20150622T093000Z
DTEND;VALUE=DATE-TIME:20150622T102000Z
DTSTAMP;VALUE=DATE-TIME:20170919T114421Z
UID:indico-contribution-202-8@cern.ch
DESCRIPTION:Speakers: Mr. CUTKOSKY\, Steven Dale (University of Missouri)\
nWe prove that germs of analytic maps of complex analytic varieties can
be made monomial by sequences of local blow ups of nonsingular analytic su
bvarieties in the domain and target along an arbitrary étoile. An étoile
and the voûte étoilée is a generalization by Hironaka of valuations an
d the Zariski Riemann manifold to analytic spaces.\n\nhttps://indico.math.
cnrs.fr/event/202/session/0/contribution/8
LOCATION:Centre Paul-Langevin AUSSOIS La Parrachée
URL:https://indico.math.cnrs.fr/event/202/session/0/contribution/8
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