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SUMMARY:Boris Shapiro (Stockholm University)
DTSTART:20220210T123000Z
DTEND:20220210T132000Z
DTSTAMP:20260416T025129Z
UID:WSTGRT/1
DESCRIPTION:Title: R
eturn of the plane evolute\nby Boris Shapiro (Stockholm University) as
part of Workshop on Singularity Theory\, Geometry and Related Topics\n\n\
nAbstract\nBelow we consider the evolutes of plane real-algebraic curves a
nd discuss some of their complex and real-algebraic properties. In particu
lar\, for a given degree d ≥ 2\, we provide lower bounds for the followi
ng four numerical invariants: 1) the maximal number of times a real line c
an intersect the evolute of a real-algebraic curve of degree d\; 2) the ma
ximal number of real cusps which can occur on the evolute of a real-algebr
aic curve of degree d\; 3) the maximal number of (cru)nodes which can occu
r on the dual curve to the evolute of a real-algebraic curve of degree d\;
4) the maximal number of (cru)nodes which can occur on the evolute of a r
eal-algebraic curve of degree d.\n
LOCATION:https://researchseminars.org/talk/WSTGRT/1/
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SUMMARY:Umberto Hryniewicz (RWTH Aachen)
DTSTART:20220210T133000Z
DTEND:20220210T142000Z
DTSTAMP:20260416T025129Z
UID:WSTGRT/2
DESCRIPTION:Title: R
esults on abundance of global surfaces of section for Reeb flows\nby U
mberto Hryniewicz (RWTH Aachen) as part of Workshop on Singularity Theory\
, Geometry and Related Topics\n\n\nAbstract\nOne might ask if global surfa
ces of section (GSS) for Reeb flows in dimension 3 are abundant in two dif
ferent senses. One might ask if GSS are abundant for a given Reeb flow\, o
r if Reeb flows carrying some GSS are abundant in the set of all Reeb flow
s. In this talk\, answers to these two questions in specific contexts will
be presented. First\, I would like to discuss a result\, obtained in coll
aboration with Florio\, stating that there are explicit sets of Reeb flows
on which are right-handed in the sense of Ghys\; in particular\, for such
a flow all finite (non-empty) collections of periodic orbits span a GSS.
Then\, I would like to discuss genericity results\, obtained in collaborat
ion with Colin\, Dehornoy and Rechtman\, for Reeb flows carrying a GSS\; a
s a particular case of such results\, we prove that a $C^\\infty$-generic
Reeb flow on an arbitrary closed 3-manifold carries a (rational) GSS.\n
LOCATION:https://researchseminars.org/talk/WSTGRT/2/
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BEGIN:VEVENT
SUMMARY:Ana Menezes (Princeton University)
DTSTART:20220210T150000Z
DTEND:20220210T155000Z
DTSTAMP:20260416T025129Z
UID:WSTGRT/3
DESCRIPTION:Title: A
two-piece property for free boundary minimal surfaces in the ball\nby
Ana Menezes (Princeton University) as part of Workshop on Singularity The
ory\, Geometry and Related Topics\n\n\nAbstract\nIn this talk we will prov
e that every plane passing through the origin divides an embedded compact
free boundary minimal surface of the euclidean 3-ball in exactly two conne
cted surfaces. This result gives evidence to a conjecture by Fraser and Li
. This is a joint work with Vanderson Lima from UFRGS\, Brazil.\n
LOCATION:https://researchseminars.org/talk/WSTGRT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Aparecida Soares Ruas (ICMC-USP)
DTSTART:20220211T123000Z
DTEND:20220211T132000Z
DTSTAMP:20260416T025129Z
UID:WSTGRT/4
DESCRIPTION:Title: L
ipschitz geometry in the space of matrices\nby Maria Aparecida Soares
Ruas (ICMC-USP) as part of Workshop on Singularity Theory\, Geometry and R
elated Topics\n\n\nAbstract\nLipschitz geometry of singular sets is an int
ensively developing subject which started in 1969 with the work of Pham an
d Teissier on the Lipschitz classification of germs of plane complex algeb
raic curves. The purpose of the lecture is to discuss the fundamentals of
this geometry in the space of matrices and show how it relates to recent r
esults of singularity theory.\n
LOCATION:https://researchseminars.org/talk/WSTGRT/4/
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BEGIN:VEVENT
SUMMARY:Gonçalo Oliveira (UFF)
DTSTART:20220211T133000Z
DTEND:20220211T142000Z
DTSTAMP:20260416T025129Z
UID:WSTGRT/5
DESCRIPTION:Title: S
pecial Lagrangians and Lagrangian mean curvature flow\nby Gonçalo Oli
veira (UFF) as part of Workshop on Singularity Theory\, Geometry and Relat
ed Topics\n\n\nAbstract\n(joint work with Jason Lotay) Richard Thomas and
Shing-Tung-Yau proposed two conjectures on the existence of special Lagran
gian submanifolds and on the use of Lagrangian mean curvature flow to find
them. In this talk\, I will report on joint work with Jason Lotay to prov
e these on certain symmetric hyperKahler 4-manifolds. If time permits I ma
y also comment on our work in progress to tackle more refined conjectures
of Dominic Joyce regarding the existence of Bridgeland stability condition
s on Fukaya categories and their interplay with Lagrangian mean curvature
flow.\n
LOCATION:https://researchseminars.org/talk/WSTGRT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Agrachev (SISSA)
DTSTART:20220211T150000Z
DTEND:20220211T155000Z
DTSTAMP:20260416T025129Z
UID:WSTGRT/6
DESCRIPTION:Title: A
symptotic homology of the paths spaces: two cases study\nby Andrei Agr
achev (SISSA) as part of Workshop on Singularity Theory\, Geometry and Rel
ated Topics\n\n\nAbstract\nGiven a nonholonomic vector distribution on a s
mooth manifold M\, it is well-known that embedding of the horizontal loop
space into the whole loop space is a homotopy equivalence. We know however
that horizontal loop spaces have deep singularities and extremely rich lo
cal and global structure even if M is contractible. In principle\, one can
recover hidden structural complexity of the horizontal loop spaces by cal
culating homology of some natural filtrations of the space. I am going to
show two examples of such calculations.\n
LOCATION:https://researchseminars.org/talk/WSTGRT/6/
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