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BEGIN:VEVENT
SUMMARY:Aftab Patel ((University of Western Ontario)
DTSTART:20200908T130000Z
DTEND:20200908T140000Z
DTSTAMP:20260404T111443Z
UID:seminadiodesingularidades/1
DESCRIPTION:Title: Equisingular Algebraic Approximation of Real and
Complex Analytic Germs\nby Aftab Patel ((University of Western Ontario
) as part of Seminario de Singularidades UFC\n\n\nAbstract\nIn this talk w
e consider the problem of the approximation of a real or complex analytic
set germ by germs of Nash or even algebraic sets which are equisingular wi
th respect to the Hilbert-Samuel function. We show that a Cohen-Macaulay a
nalytic singularity can be arbitrarily closely approximated by germs of Na
sh sets which are also Cohen-Macaulay and share the same Hilbert-Samuel fu
nction. Also\, we obtain a result that states that every analytic singular
ity is topologically equivalent to a Nash singularity with the same Hilber
t-Samuel function. A key ingredient in our results is a generalization of
Buchberger's criterion to standard bases of power series due to T. Becker
in 1990. This talk is based on joint work with Janusz Adamus at the Univer
sity of Western Ontario\, Canada.\n
LOCATION:https://stable.researchseminars.org/talk/seminadiodesingularidade
s/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Kowalczyk (Jagiellonian University)
DTSTART:20200915T130000Z
DTEND:20200915T140000Z
DTSTAMP:20260404T111443Z
UID:seminadiodesingularidades/2
DESCRIPTION:Title: Real algebraic versions of Cartan's Theorems A an
d B\nby Tomasz Kowalczyk (Jagiellonian University) as part of Seminari
o de Singularidades UFC\n\n\nAbstract\nIt is known that Cartan's Theorem A
does not hold in the real algebraic case\, however I will show that it ho
lds after a sequence of blowing ups along smooth centers. i.e. for any coh
erent sheaf on a real algebraic affine variety there exists a multi-blowup
such that the pullback sheaf is generated by global sections. Also\, an e
xample will be given which shows that this Theorem cannot be generalized t
o quasi-coherent sheaves.There are similar problems with Cartan's Theorem
B\, usually Čech cohomology of a coherent sheaf are infinitely dimensiona
l. I will construct blown-up Čech cohomology\, and show that for some she
aves these cohomology vanish. Finally\, I will use this theory to show uni
versal solvability of a real algebraic first Cousin problem\, after blowin
g up.\n
LOCATION:https://stable.researchseminars.org/talk/seminadiodesingularidade
s/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Pokrovskiy (University College London)
DTSTART:20200922T130000Z
DTEND:20200922T140000Z
DTSTAMP:20260404T111443Z
UID:seminadiodesingularidades/3
DESCRIPTION:Title: Rota's Basis Conjecture holds asymptotically\
nby Alexey Pokrovskiy (University College London) as part of Seminario de
Singularidades UFC\n\n\nAbstract\nRota's Basis Conjecture is a well known
problem\, that states that for any collection of n bases in a rank n matro
id\, it is possible to decompose all the elements into n disjoint rainbow
bases. Here an asymptotic version of this is will be discussed - that it i
s possible to find n − o(n) disjoint rainbow independent sets of size n
− o(n).\n
LOCATION:https://stable.researchseminars.org/talk/seminadiodesingularidade
s/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Philippe Monnier (Université d'Angers)
DTSTART:20200929T140000Z
DTEND:20200929T150000Z
DTSTAMP:20260404T111443Z
UID:seminadiodesingularidades/4
DESCRIPTION:Title: Some normalizations of real algebraic varieties\nby Jean-Philippe Monnier (Université d'Angers) as part of Seminario d
e Singularidades UFC\n\n\nAbstract\nI will introduce the central spectrum
of a commutative ring and explain what is a rational continuous function a
nd a regulous function on the central locus of a real algebraic affine var
iety. After that I will show that we can normalize in different ways real
algebraic varieties by replacing the field of rational functions by the ri
ng of regular functions on the real closed points\, the ring of regulous f
unctions on the central locus and the ring of rational continuous function
s on the central locus. I will provide examples of these normalizations.\n
Most of the results of the talk were obtained with G. Fichou and R. Quarez
.\n\nPlease note the irregular time. We start one hour later than usual at
11:00 (GMT-3).\n
LOCATION:https://stable.researchseminars.org/talk/seminadiodesingularidade
s/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nhan Nguyen (Basque Center for Applied Mathematics)
DTSTART:20201013T130000Z
DTEND:20201013T140000Z
DTSTAMP:20260404T111443Z
UID:seminadiodesingularidades/5
DESCRIPTION:Title: Regular projection in O-minimal structures\nb
y Nhan Nguyen (Basque Center for Applied Mathematics) as part of Seminario
de Singularidades UFC\n\n\nAbstract\nIn this talk\, we will give a proof
for Mostowski's regular projection theorem in o-minimal structures\, which
is a positive answer to the question of Parusinski about a definable vers
ion of the theorem.\n
LOCATION:https://stable.researchseminars.org/talk/seminadiodesingularidade
s/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alicia Dickenstein (Universidad de Buenos Aires and CONICET)
DTSTART:20201103T130000Z
DTEND:20201103T140000Z
DTSTAMP:20260404T111443Z
UID:seminadiodesingularidades/7
DESCRIPTION:Title: Iterated sparse discriminants and singular inters
ections of hypersurfaces\nby Alicia Dickenstein (Universidad de Buenos
Aires and CONICET) as part of Seminario de Singularidades UFC\n\n\nAbstra
ct\nIt is well known that two generic quadric surfaces intersect in a nons
ingular quartic space curve\, but when the intersection is not transverse
this intersection curve may degenerate to a finite number of different pos
sible types of singular curves. In the nice paper by Farouki et al. (1989
)\, the authors formulate a way of computing the condition for a degenerat
e intersection in this case\, which refines in the real case and with an a
lgorithmic point of view a classical treatise by Bromwich (1906). Indepen
dently\, Schläfli (1953) studied the degenerate intersection of two hyper
surfaces described by multilinear equations.\n\nIn joint work with S. di R
occo and R. Morrison\, we present a general framework of iterated sparse
discriminants to characterize the singular intersection of hypersurfaces w
ith a given monomial support A\, which generalizes both previous situation
s. We study the connection of iterated discriminants with the notion of m
ixed discriminant and the singularities of the sparse discriminant associa
ted to A.\n
LOCATION:https://stable.researchseminars.org/talk/seminadiodesingularidade
s/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jawad Snoussi (Universidad Nacional Autónoma de México)
DTSTART:20201027T140000Z
DTEND:20201027T150000Z
DTSTAMP:20260404T111443Z
UID:seminadiodesingularidades/8
DESCRIPTION:Title: On the C_5 cone of complex curves and equisingula
rity\nby Jawad Snoussi (Universidad Nacional Autónoma de México) as
part of Seminario de Singularidades UFC\n\n\nAbstract\nH. Whitney introduc
ed several cones\, candidates to a possible generalization of tangent spac
e at singular points. Many of these cones have an important use in the loc
al study of a singularity. In particular the cones C_3\, C_4 and C_5\, are
extensively used. The two first ones are quite well understood.\nIn this
talk we present a description and a procedure to build the C_5 cone for a
complex curve. The tools we use for that purpose happen to be interesting
in the Lipschitz behavior of a complex curve.\n\nNote the irregular time.
We start one hour later at 11:00 (Fortaleza time\, GMT-3).\n
LOCATION:https://stable.researchseminars.org/talk/seminadiodesingularidade
s/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Alberich-Carramiñana (Universitat Politècnica de Catalu
nya)
DTSTART:20201117T130000Z
DTEND:20201117T140000Z
DTSTAMP:20260404T111443Z
UID:seminadiodesingularidades/10
DESCRIPTION:Title: From local to global properties through plane Cr
emona maps\nby Maria Alberich-Carramiñana (Universitat Politècnic
a de Catalunya) as part of Seminario de Singularidades UFC\n\n\nAbstract\n
Birational transformations\, also known as Cremona maps\, are capable to t
ransform a local feature into a global one and viceversa. We will revise s
ome of these phenomena concerning plane algebraic curves and planar polyno
mial differential systems.\n
LOCATION:https://stable.researchseminars.org/talk/seminadiodesingularidade
s/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcelo Escudeiro Hernandes (Universidade Estadual de Maringá)
DTSTART:20201110T130000Z
DTEND:20201110T140000Z
DTSTAMP:20260404T111443Z
UID:seminadiodesingularidades/11
DESCRIPTION:Title: On the Tjurina number of analytic plane branches
\nby Marcelo Escudeiro Hernandes (Universidade Estadual de Maringá) a
s part of Seminario de Singularidades UFC\n\n\nAbstract\nIn this talk we w
ill address relationships between some analytical invariants of irreducibl
e plane curves and their semi-roots. More specifically\, we will explore t
he Tjurina number of a curve and the set of Kähler differential values of
the local ring associated with the curve.\n
LOCATION:https://stable.researchseminars.org/talk/seminadiodesingularidade
s/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Octave Curmi (Alfréd Rényi Institute of Mathematics)
DTSTART:20201119T130000Z
DTEND:20201119T140000Z
DTSTAMP:20260404T111443Z
UID:seminadiodesingularidades/12
DESCRIPTION:Title: A proof of A. Gabrielov's rank theorem\nby O
ctave Curmi (Alfréd Rényi Institute of Mathematics) as part of Seminario
de Singularidades UFC\n\n\nAbstract\nThis talk is about Gabrielov's rank
Theorem\, a fundamental result in local complex and real-analytic geometry
\, proved in the 1960's. Contrasting with the algebraic case\, it is not i
n general true that the analytic rank of an analytic map (that is\, the di
mension of the analytic-Zariski closure of its image) is equal to the gene
ric rank of the map (that is\, the generic dimension of its image). This p
henomenon is involved in several pathological examples in local real-analy
tic geometry. Gabrielov's rank Theorem provides a formal condition for the
equality to hold.\nDespite its importance\, the original proof is conside
red very difficult. There is no alternative proof in the literature\, besi
des a work from Tougeron\, which is itself considered very difficult. I wi
ll present a new work in collaboration with André Belotto da Silva and Gu
illaume Rond\, where we provide a complete proof of Gabrielov's rank Theor
em\, for which we develop formal-geometric techniques\, inspired by ideas
from Gabrielov and Tougeron\, which clarify the proof. \nI will start with
some fundamental examples of the phenomenon at hand\, and expose the main
ingredients of the strategy of this difficult proof.\n\nNote that this me
eting takes exceptionally place on Thursday.\n
LOCATION:https://stable.researchseminars.org/talk/seminadiodesingularidade
s/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guillaume Rond (Université Aix-Marseille)
DTSTART:20201201T140000Z
DTEND:20201201T150000Z
DTSTAMP:20260404T111443Z
UID:seminadiodesingularidades/13
DESCRIPTION:Title: Algebraic Laurent series\nby Guillaume Rond
(Université Aix-Marseille) as part of Seminario de Singularidades UFC\n\n
\nAbstract\nI will review several results about the algebraic closure of t
he field of power series in several indeterminates. This field can be equi
pped with a non-archimedean absolute value\, and considering its completio
n allows us to work in a bigger field where we can use Newton's method to
find roots of polynomials. Therefore one problem is to determine what are
the elements of this completion that are algebraic over the field of power
series. I will present analogies with the algebraic closure of the field
of rational numbers.\n\nNotice that we start one hour later than usual!\n
LOCATION:https://stable.researchseminars.org/talk/seminadiodesingularidade
s/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Aparecida Soares Ruas (ICMC Universidade de São Paulo)
DTSTART:20201208T130000Z
DTEND:20201208T140000Z
DTSTAMP:20260404T111443Z
UID:seminadiodesingularidades/14
DESCRIPTION:Title: Invariants of essentially isolated determinantal
singularities (EIDS) and equisingularity\nby Maria Aparecida Soares R
uas (ICMC Universidade de São Paulo) as part of Seminario de Singularidad
es UFC\n\n\nAbstract\nWe introduce invariants that control the Whitney equ
isingularity of families of EIDS.\nAs an application of the results\, we g
ive a characterization of generic hyperplanes using\nthe invariants.\n\nTH
IS TALK IS POSTPONED TO A DIFFERENT DATE\, TO BE ANNOUNCED\n
LOCATION:https://stable.researchseminars.org/talk/seminadiodesingularidade
s/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Grandjean (UFC)
DTSTART:20201215T130000Z
DTEND:20201215T140000Z
DTSTAMP:20260404T111443Z
UID:seminadiodesingularidades/15
DESCRIPTION:Title: Do regular bifurcation values exist?\nby Vin
cent Grandjean (UFC) as part of Seminario de Singularidades UFC\n\n\nAbstr
act\nI will partially report on two works in progress one with N. Dutertre
the other one with M. Michalska\, dealing with bifurcation values at infi
nity of tame mappings. This will be the opportunity to review a few defini
tions and results about this topic\, generalize and clarify some of them\,
as well as pointing out modestly some open questions (old and new).\n
LOCATION:https://stable.researchseminars.org/talk/seminadiodesingularidade
s/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Zaidenberg (Institut Fourier de Mathematiques\, Grenoble)
DTSTART:20201222T130000Z
DTEND:20201222T140000Z
DTSTAMP:20260404T111443Z
UID:seminadiodesingularidades/16
DESCRIPTION:Title: Tits-type alternative for nonlinear automorphism
groups\nby Mikhail Zaidenberg (Institut Fourier de Mathematiques\, Gr
enoble) as part of Seminario de Singularidades UFC\n\n\nAbstract\nThe clas
sical Tits alternative asserts that any linear group over a field of zero
characteristic is either virtually solvable\, or contains a nonabelian fre
e sub-group. We survey on recent extensions of the Tits alternative to aut
omorphism groups of algebraic varieties. In the case of affine varieties\,
these automorphism groups are often infinite-dimensional\, hence highly n
onlinear. Sometimes\, they acts highly transitively on the variety\, that
is\, m-transitively for any natural number m. According to Borel\, no alge
braic group acts 4-transitively on an algebraic variety. We show the relat
ions between the alternatives of Tits type and multiple transitivity.\n
LOCATION:https://stable.researchseminars.org/talk/seminadiodesingularidade
s/16/
END:VEVENT
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