BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Russell Lodge (Indiana State University)
DTSTART:20211206T200000Z
DTEND:20211206T213000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/1
DESCRIPTION:Title: Gasket Julia sets and their symmetries\nby Russell Lodg
e (Indiana State University) as part of Complex Dynamics Week\n\n\nAbstrac
t\nSullivan’s celebrated $\\textit{no-wandering domains}$ theorem for ra
tional maps highlights a close connection or “dictionary” between holo
morphic dynamics and Kleinian groups. The purpose of this talk is to highl
ight a new approach to the Sullivan dictionary\, where for simplicity we f
ocus on limit sets that generalize the Apollonian gasket. To each connecte
d simple planar graph in the Riemann sphere\, there is an associated circl
e packing by a theorem of Koebe-Andreev-Thurston. We give a dynamically na
tural way to associate both a Kleinian group and an anti-rational map to e
ach such packing so that the limit and Julia sets are naturally identified
. This identification enables the computation of the topological symmetry
and quasisymmetry groups of the Julia set\, and has led to new insights o
n the boundedness of deformation spaces and mate-ability.\n\nJoint work wi
th Y. Luo\, M. Lyubich\, S. Merenkov\, S. Mukherjee\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liz Vivas (The Ohio State University)
DTSTART:20211207T150000Z
DTEND:20211207T163000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/2
DESCRIPTION:Title: Stable manifolds of biholomorphisms of $\\mathbb{C}^n$ asym
ptotic to formal curves\nby Liz Vivas (The Ohio State University) as p
art of Complex Dynamics Week\n\n\nAbstract\nGiven a biholomorphism F with
a fixed point from $\\mathbb{C}^n$ to itself that admits a formal invarian
t curve \, we give conditions that guarantee that there exists either a pe
riodic curve\, or a finite family of stable manifolds asymptotic to the fo
rmal curve. This generalizes the result on two dimensions proven by Lopez-
Hernanz\, Raissy\, Ribon and Sanz-Sanchez. \n\nThis is joint work with Lop
ez-Hernanz\, Ribon and Sanz-Sanchez.\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aracelli Bonifant (University of Rhode Island)
DTSTART:20211207T220000Z
DTEND:20211207T233000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/3
DESCRIPTION:Title: Dynamics of cubic polynomial maps\nby Aracelli Bonifant
(University of Rhode Island) as part of Complex Dynamics Week\n\n\nAbstra
ct\nFor each $p>0$ there is a family ${\\mathcal S}_p$ of complex cubic ma
ps with a marked critical orbit of period $p$. For each $q>0$ I will descr
ibe a dynamically defined tessellation of ${\\mathcal S}_p$. Each face of
this tessellations isassociated with one particular behavior for periodic
orbits of\nperiod $q$. \n\nJoint work with John Milnor.\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hongming Nie (Stony Brook)
DTSTART:20211208T130000Z
DTEND:20211208T143000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/4
DESCRIPTION:Title: Boundedness of hyperbolic components for Newton maps\nb
y Hongming Nie (Stony Brook) as part of Complex Dynamics Week\n\n\nAbstrac
t\nA rational map of degree at least 2 is hyperbolic if each of its critic
al points is attracted to an attracting cycle. The hyperbolic maps form an
open subset in the space of rational maps and descends to an open subset
in the corresponding moduli space of rational maps. Each component of this
open subset is a hyperbolic component. In complex dynamics\, an interesti
ng question is to determine which types of hyperbolic components are bound
ed. In this talk\, we study this problem in a well-known slice called Newt
on family. We prove that\, in the moduli space of quartic Newton maps\, a
hyperbolic component is bounded if and only if all its root immediate basi
ns have degree 2. Furthermore\, for each unbounded hyperbolic component\,
we show that its boundary at infinity in the GIT-compactification is eithe
r a closed disk or a singleton. The proof is based on a convergence theore
m of internal rays we establish for degenerate Newton sequences. This is a
joint work with Yan Gao.\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jasmin Raissy (Université de Bordeaux)
DTSTART:20211208T150000Z
DTEND:20211208T163000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/5
DESCRIPTION:Title: A geometric approach to parabolic curves\nby Jasmin Rai
ssy (Université de Bordeaux) as part of Complex Dynamics Week\n\n\nAbstra
ct\nThe local dynamics of a one-dimensional holomorphic germ tangent to th
e identity is described by the classical Leau-Fatou flower Theorem\, showi
ng how a pointed neighbourhood of the fixed point can be obtained as union
of a finite number of forward or backward invariant open sets\, the so-ca
lled petals of the Fatou flower\, where the dynamics is conjugated to a tr
anslation in a half-plane.In this talk I will present what is known about
generalizations of the Leau-Fatou flower Theorem to holomorphic germs tang
ent to the identity in several complex variables\, where petals are replac
ed by parabolic curves. In particular\, I will present a geometric proof o
f the fundamental results obtained by Écalle and Hakim on the existence o
f parabolic curves. This approach allows to give asymptotic expansions for
the parametrization of parabolic curves for tangent to the identity holom
orphic endomorphisms in a given neighbourhood of the fixed point.\n\nJoint
work in progress with X. Buff.\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulio Tiozzo (University of Toronto)
DTSTART:20211207T200000Z
DTEND:20211207T213000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/6
DESCRIPTION:Title: Core entropy along the Mandelbrot set and Thurston’s “M
aster teapot”\nby Giulio Tiozzo (University of Toronto) as part of C
omplex Dynamics Week\n\n\nAbstract\nThe notion of core entropy was introdu
ced by W. Thurston by taking the entropy \nof the restriction of a complex
quadratic polynomial to its Hubbard tree. \nThis function varies wildly a
s the parameter varies\, reflecting the topological complexity \nof the Ma
ndelbrot set. \n\nMoreover\, Thurston also defined the $\\textit{master te
apot}$\, a fractal set obtained by considering\nfor each postcritically fi
nite real quadratic polynomial the Galois conjugates of the entropy. \n\nI
n the talk\, we will discuss generalizations of this fractal from real to
complex polynomials. \nIn particular\, we will define a $\\textit{master t
eapot}$ for each vein the Mandelbrot set\, discuss continuity properties \
nof the core entropy\, and use it to prove geometric properties of the mas
ter teapot.\n\nJoint with Kathryn Lindsey and Chenxi Wu.\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Milnor (Stony Brook)
DTSTART:20211210T200000Z
DTEND:20211210T213000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/7
DESCRIPTION:Title: Real Quadratic Rational Maps\nby John Milnor (Stony Bro
ok) as part of Complex Dynamics Week\n\n\nAbstract\nA study of real quadra
tic rational maps with real critical\npoints up to an orientation preservi
ng fractional linear change of variable.\nThe moduli space consisting of a
ll conjugacy classes of such maps is\ncanonically diffeomorphic to $S^1\\t
imes I$\n\nSome regions of this moduli space correspond to dynamical behav
ior which is easy to describe\, and others are more difficult. The descrip
tion of the most difficult region will be based on the work of Khashayar F
ilom and Kevin Pilgrim. The talk will also briefly describe effective impl
ementation of the Thurston pullback algorithm\, and its behavior (or mis-b
ehavior).\n\nJoint work with Araceli Bonifant and Scott Sutherland.\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luna Lomonaco (IMPA)
DTSTART:20211210T180000Z
DTEND:20211210T193000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/8
DESCRIPTION:Title: Mating quadratic maps with the modular group\nby Luna L
omonaco (IMPA) as part of Complex Dynamics Week\n\n\nAbstract\nHolomorphic
correspondences are polynomial relations $P(z\,w)=0$\, which can be regar
ded as multi-valued self-maps of the Riemann sphere\, this is implicit map
s\nsending $z$ to $w$. The iteration of such a multi-valued map generates
a dynamical system on the Riemann sphere: dynamical system which generalis
es rational maps and finitely generated Kleinian groups. We consider a sp
ecific $1 -$(complex) parameter family of $(2:2)$ correspondences $F_a$ (i
ntroduced by S. Bullett and C. Penrose in 1994)\, which we describe dynami
cally. In particular\, we show that for every parameter in a subset of the
parameter plane called $\\textit{the connectedness locus}$ and denoted by
$M_{\\Gamma}$\, this family behaves as rational maps on a subset of the R
iemann sphere and as the modular group on the complement: in other words\,
these correspondences are mating between the modular group and rational m
aps (in the family $Per_1(1)$). Moreover\, we develop for this family of c
orrespondences a complete dynamical theory which parallels the Douady-Hubb
ard theory of quadratic polynomials\, and we show that $M_{\\Gamma}$ is ho
meomorphic to the parabolic Mandelbrot set $M_1$. This is joint work with
S. Bullett (QMUL).\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Kiwi (Universidad Católica de Chile)
DTSTART:20211209T210000Z
DTEND:20211209T223000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/9
DESCRIPTION:Title: Irreducibility of periodic curves of cubic polynomials\
nby Jan Kiwi (Universidad Católica de Chile) as part of Complex Dynamics
Week\n\n\nAbstract\nIn the moduli space of one variable complex cubic poly
nomials with a marked critical point\, given any $p \\ge 1$\, we prove tha
t the locus formed by polynomials with the marked critical point periodic
of period $p$ is an irreducible curve. Our methods rely on techniques use
d to study one-complex-dimensional parameter spaces.\n\nThis is joint work
with Matthieu Arfeux.\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rudy Rosas (Pontificia Universidad Católica del Perú)
DTSTART:20211209T190000Z
DTEND:20211209T203000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/10
DESCRIPTION:Title: Conjuntos minimales cerca de singularidades de campos de v
ectores holomorfos en dimensión dos\nby Rudy Rosas (Pontificia Univer
sidad Católica del Perú) as part of Complex Dynamics Week\n\n\nAbstract\
nConjuntos minimales cerca de singularidades de campos de vectores holomor
fos en dimensión dos. \nResumen: Como consecuencia inmediata del Teorema
de Poincaré-Bendixson\, sabemos que las singularidades y las órbitas per
iódicas son los únicos conjuntos minimales de un campo de vectores en el
plano bidimensional real. Aunque este resultado no tiene ningún paralelo
en dimensiones mayores\, en esta charla discutiremos una versión local p
ara el caso de campos holomorfos cerca de un punto singular en el plano co
mplejo bidimensional.\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pascale Roesch (Université Toulouse III)
DTSTART:20211206T160000Z
DTEND:20211206T173000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/11
DESCRIPTION:Title: Some examples of descriptions of parameter spaces\nby
Pascale Roesch (Université Toulouse III) as part of Complex Dynamics Week
\n\n\nAbstract\nWe will explain\, with some examples\, several ways to dec
ribe one parameter slices of parameter spaces of rational maps.\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthieu Arfeux (Pontificia Universidad Católica de Valparaiso)
DTSTART:20211208T210000Z
DTEND:20211208T223000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/12
DESCRIPTION:Title: Jumping between trees\nby Matthieu Arfeux (Pontificia
Universidad Católica de Valparaiso) as part of Complex Dynamics Week\n\n\
nAbstract\nEn esta charla presentaré una relación entre los árboles de
Hubbard y los árboles de DeMarco-McMullen ($\\textit{escaping trees}$). D
icha relación tiene lugar en el borde del lugar de conexidad en cierto co
njunto de los polinomios de grado tres con un punto crítico de un periodo
dado. Escribimos con Jan Kiwi una demostración de la conexidad de este c
onjunto de polinomios tal como conjeturado por John Milnor unos 30 años a
trás. Les contaré como el trabajo sobres la relación entre esos árbole
s llevó unos años después a la demostración de la conjetura. Ver: http
s://arxiv.org/abs/1503.02710\, https://arxiv.org/abs/2012.14945\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Suárez (Pontificia Universidad Católica del Perú)
DTSTART:20211210T150000Z
DTEND:20211210T163000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/13
DESCRIPTION:Title: Dynamics of a Blaschke Product\nby Pedro Suárez (Pont
ificia Universidad Católica del Perú) as part of Complex Dynamics Week\n
\n\nAbstract\nThe finite Blaschke products are rational functions on the R
iemann sphere that preserve the unit circle. Generally useful in studying
the dynamics of polynomials\; however\, with a dynamic richness of its own
.\n\nThe purpose of this talk is to explore some dynamical aspects of a Bl
aschke product family depending on a complex parameter\, with a single cri
tical point (cubic type) on the circle\, critical value (the parameter)\,
and two fixed super-atractors at zero and infinity. The variation of the c
ritical value determines in the dynamical plane\, the connectivity of the
Julia sets and in the parameter plane\, the existence of escape components
\, that is\, parameters for which the critical point escapes by iteration
to zero or infinity. Furthermore\, we define the non-escape locus (Blaschk
ebrot) for the Blaschke family\, where numerical experiments suggest the p
resence of baby cubibrots.\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linda Keen (CUNY)
DTSTART:20211209T150000Z
DTEND:20211209T163000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/14
DESCRIPTION:Title: Transcendental functions with two asymptotic values\nb
y Linda Keen (CUNY) as part of Complex Dynamics Week\n\n\nAbstract\nThe wo
rk described in this lecture is part of a general program in complex dynam
ics to understand parameter spaces of transcendental maps.\n\nIn all compl
ex dynamical systems\, the singular values control the stable periodic beh
avior. The singular values of rational functions are their critical values
. Transcendental maps have a new kind of singularity\, an “asymptotic va
lue”: for example\, 0\,$\\infity$ for $e^z$ and $\\pm i$ for $\\tan z$.
These functions belong to the relatively simple family $\\mathcal{F}_2$ of
transcendental maps with exactly two asymptotic values and no critical va
lues. This family\, up to affine conjugation\, depends on two complex para
meters.\n\nIn this lecture\, we will begin by reviewing the structures of
the parameter spaces of the exponential and tangent families which have be
en well studied. We will then describe recent work on two other slices of
the full family $\\mathcal{F}_2$. We will see how phenomena we observe for
the tangent and the exponential families recur and combine in new ways.Th
ese results incorporate various\njoint projects with Tao Chen\, Nuria Fage
lla and Yunping Jiang.\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfredo Poirier (Pontificia Universidad Católica del Perú)
DTSTART:20211206T140000Z
DTEND:20211206T153000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/15
DESCRIPTION:Title: The basics of iteration: Day 1\nby Alfredo Poirier (Po
ntificia Universidad Católica del Perú) as part of Complex Dynamics Week
\n\n\nAbstract\nThis will be a crash course in the theory of iteration of
rational maps. It is oriented to undergraduates and starting graduate stud
ents attending our seminar.\n\nFirst day: The basics.\n\nSquaring as a pro
totype of iteration. The superattractive role of infinity for polynomials.
A closer look at Newton's method. Normal families and Montel's theorem.\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfredo Poirier (Pontificia Universidad Católica del Perú)
DTSTART:20211207T130000Z
DTEND:20211207T143000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/16
DESCRIPTION:Title: The basics of iteration: Day 2\nby Alfredo Poirier (Po
ntificia Universidad Católica del Perú) as part of Complex Dynamics Week
\n\n\nAbstract\nThis will be a crash course in the theory of iteration of
rational maps. It is oriented to undergraduates and starting graduate stud
ents attending our seminar.\n\nSecond day: The Julia set and the Fatou set
.\n\nAttractive and superatractive periodic orbits. The structure of the J
ulia set. Other type of non-caotic behaviour.\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfredo Poirier (Pontificia Universidad Católica del Perú)
DTSTART:20211208T190000Z
DTEND:20211208T203000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/17
DESCRIPTION:Title: The basics of iteration: Day 3\nby Alfredo Poirier (Po
ntificia Universidad Católica del Perú) as part of Complex Dynamics Week
\n\n\nAbstract\nThis will be a crash course in the theory of iteration of
rational maps. It is oriented to undergraduates and starting graduate stud
ents attending our seminar.\n\nThird day: The role of the critical points.
\n\nThe global structure of the Fatou set. Relation between the critical o
rbits and the conexity of the Julia set. The introduction of parameters in
the picture.\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Castillo (Pontificia Universidad Católica del Perú)
DTSTART:20211209T123000Z
DTEND:20211209T143000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/18
DESCRIPTION:Title: Further topics in basic complex dynamics: Day 1\nby Al
berto Castillo (Pontificia Universidad Católica del Perú) as part of Com
plex Dynamics Week\n\n\nAbstract\nThis minicourse is a continuation of pro
fessor Poirier's exposition of basic complex dynamics.\nWe focus on famili
es of rational maps (more preciselly\, polynomial families) and pass from
the\ndynamical to the parameter plane\, dealing with the interplay between
them.\nOur selected topics revolves around the (perhaps) main conjecture
of complex dynamics:\nthe density of hyperbolic components for families of
rational maps.\nWe present well known topics such as renormalization\, in
variant line fields\,\nthe Mañe-Sad-Sullivan paper\, Yoccoz puzzles\, etc
.\nAll these topics are presented in the context of two polynomial familie
s\,\none of them being that of quadratic polynomials\,\nwhose connectednes
s locus is the Mandelbrot set.\nThe other one is a bicritical uniparametri
c family\, object of study of the expositor's thesis.\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Castillo (Pontificia Universidad Católica del Perú)
DTSTART:20211210T123000Z
DTEND:20211210T143000Z
DTSTAMP:20260404T110643Z
UID:ComplexDynamics/19
DESCRIPTION:Title: Further topics in basic complex dynamics: Day 2\nby Al
berto Castillo (Pontificia Universidad Católica del Perú) as part of Com
plex Dynamics Week\n\n\nAbstract\nThis minicourse is a continuation of pro
fessor Poirier's exposition of basic complex dynamics.\nWe focus on famili
es of rational maps (more preciselly\, polynomial families) and pass from
the\ndynamical to the parameter plane\, dealing with the interplay between
them.\nOur selected topics revolves around the (perhaps) main conjecture
of complex dynamics:\nthe density of hyperbolic components for families of
rational maps.\nWe present well known topics such as renormalization\, in
variant line fields\,\nthe Mañe-Sad-Sullivan paper\, Yoccoz puzzles\, etc
.\nAll these topics are presented in the context of two polynomial familie
s\,\none of them being that of quadratic polynomials\,\nwhose connectednes
s locus is the Mandelbrot set.\nThe other one is a bicritical uniparametri
c family\, object of study of the expositor's thesis.\n
LOCATION:https://stable.researchseminars.org/talk/ComplexDynamics/19/
END:VEVENT
END:VCALENDAR