BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Russell Lodge (Indiana State University)
DTSTART:20211206T200000Z
DTEND:20211206T213000Z
DTSTAMP:20260422T225703Z
UID:ComplexDynamics/1
DESCRIPTION:Title: Gasket Julia sets and their symmetries\nby Russell Lodge (Indi
ana State University) as part of Complex Dynamics Week\n\n\nAbstract\nSull
ivan’s celebrated $\\textit{no-wandering domains}$ theorem for rational
maps highlights a close connection or “dictionary” between holomorphic
dynamics and Kleinian groups. The purpose of this talk is to highlight a
new approach to the Sullivan dictionary\, where for simplicity we focus on
limit sets that generalize the Apollonian gasket. To each connected simpl
e planar graph in the Riemann sphere\, there is an associated circle packi
ng by a theorem of Koebe-Andreev-Thurston. We give a dynamically natural w
ay to associate both a Kleinian group and an anti-rational map to each suc
h packing so that the limit and Julia sets are naturally identified. This
identification enables the computation of the topological symmetry and qu
asisymmetry groups of the Julia set\, and has led to new insights on the b
oundedness of deformation spaces and mate-ability.\n\nJoint work with Y. L
uo\, M. Lyubich\, S. Merenkov\, S. Mukherjee\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liz Vivas (The Ohio State University)
DTSTART:20211207T150000Z
DTEND:20211207T163000Z
DTSTAMP:20260422T225703Z
UID:ComplexDynamics/2
DESCRIPTION:Title: Stable manifolds of biholomorphisms of $\\mathbb{C}^n$ asymptotic
to formal curves\nby Liz Vivas (The Ohio State University) as part 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 invariant curve
\, we give conditions that guarantee that there exists either a periodic
curve\, or a finite family of stable manifolds asymptotic to the formal cu
rve. This generalizes the result on two dimensions proven by Lopez-Hernanz
\, Raissy\, Ribon and Sanz-Sanchez. \n\nThis is joint work with Lopez-Hern
anz\, Ribon and Sanz-Sanchez.\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aracelli Bonifant (University of Rhode Island)
DTSTART:20211207T220000Z
DTEND:20211207T233000Z
DTSTAMP:20260422T225703Z
UID:ComplexDynamics/3
DESCRIPTION:Title: Dynamics of cubic polynomial maps\nby Aracelli Bonifant (Unive
rsity of Rhode Island) as part of Complex Dynamics Week\n\n\nAbstract\nFor
each $p>0$ there is a family ${\\mathcal S}_p$ of complex cubic maps with
a marked critical orbit of period $p$. For each $q>0$ I will describe a d
ynamically defined tessellation of ${\\mathcal S}_p$. Each face of this te
ssellations isassociated with one particular behavior for periodic orbits
of\nperiod $q$. \n\nJoint work with John Milnor.\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hongming Nie (Stony Brook)
DTSTART:20211208T130000Z
DTEND:20211208T143000Z
DTSTAMP:20260422T225703Z
UID:ComplexDynamics/4
DESCRIPTION:Title: Boundedness of hyperbolic components for Newton maps\nby Hongm
ing Nie (Stony Brook) as part of Complex Dynamics Week\n\n\nAbstract\nA ra
tional map of degree at least 2 is hyperbolic if each of its critical poin
ts is attracted to an attracting cycle. The hyperbolic maps form an open s
ubset 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 s
ubset is a hyperbolic component. In complex dynamics\, an interesting ques
tion is to determine which types of hyperbolic components are bounded. In
this talk\, we study this problem in a well-known slice called Newton fami
ly. We prove that\, in the moduli space of quartic Newton maps\, a hyperbo
lic component is bounded if and only if all its root immediate basins have
degree 2. Furthermore\, for each unbounded hyperbolic component\, we show
that its boundary at infinity in the GIT-compactification is either a clo
sed disk or a singleton. The proof is based on a convergence theorem of in
ternal rays we establish for degenerate Newton sequences. This is a joint
work with Yan Gao.\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jasmin Raissy (Université de Bordeaux)
DTSTART:20211208T150000Z
DTEND:20211208T163000Z
DTSTAMP:20260422T225703Z
UID:ComplexDynamics/5
DESCRIPTION:Title: A geometric approach to parabolic curves\nby Jasmin Raissy (Un
iversité de Bordeaux) as part of Complex Dynamics Week\n\n\nAbstract\nThe
local dynamics of a one-dimensional holomorphic germ tangent to the ident
ity is described by the classical Leau-Fatou flower Theorem\, showing how
a pointed neighbourhood of the fixed point can be obtained as union of a f
inite number of forward or backward invariant open sets\, the so-called pe
tals of the Fatou flower\, where the dynamics is conjugated to a translati
on in a half-plane.In this talk I will present what is known about general
izations of the Leau-Fatou flower Theorem to holomorphic germs tangent to
the identity in several complex variables\, where petals are replaced by p
arabolic curves. In particular\, I will present a geometric proof of the f
undamental results obtained by Écalle and Hakim on the existence of parab
olic curves. This approach allows to give asymptotic expansions for the pa
rametrization of parabolic curves for tangent to the identity holomorphic
endomorphisms in a given neighbourhood of the fixed point.\n\nJoint work i
n progress with X. Buff.\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulio Tiozzo (University of Toronto)
DTSTART:20211207T200000Z
DTEND:20211207T213000Z
DTSTAMP:20260422T225703Z
UID:ComplexDynamics/6
DESCRIPTION:Title: Core entropy along the Mandelbrot set and Thurston’s “Master t
eapot”\nby Giulio Tiozzo (University of Toronto) as part of Complex
Dynamics Week\n\n\nAbstract\nThe notion of core entropy was introduced by
W. Thurston by taking the entropy \nof the restriction of a complex quadra
tic polynomial to its Hubbard tree. \nThis function varies wildly as the p
arameter varies\, reflecting the topological complexity \nof the Mandelbro
t set. \n\nMoreover\, Thurston also defined the $\\textit{master teapot}$\
, a fractal set obtained by considering\nfor each postcritically finite re
al quadratic polynomial the Galois conjugates of the entropy. \n\nIn the t
alk\, we will discuss generalizations of this fractal from real to complex
polynomials. \nIn particular\, we will define a $\\textit{master teapot}$
for each vein the Mandelbrot set\, discuss continuity properties \nof the
core entropy\, and use it to prove geometric properties of the master tea
pot.\n\nJoint with Kathryn Lindsey and Chenxi Wu.\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Milnor (Stony Brook)
DTSTART:20211210T200000Z
DTEND:20211210T213000Z
DTSTAMP:20260422T225703Z
UID:ComplexDynamics/7
DESCRIPTION:Title: Real Quadratic Rational Maps\nby John Milnor (Stony Brook) as
part of Complex Dynamics Week\n\n\nAbstract\nA study of real quadratic rat
ional maps with real critical\npoints up to an orientation preserving frac
tional linear change of variable.\nThe moduli space consisting of all conj
ugacy classes of such maps is\ncanonically diffeomorphic to $S^1\\times I$
\n\nSome regions of this moduli space correspond to dynamical behavior whi
ch is easy to describe\, and others are more difficult. The description of
the most difficult region will be based on the work of Khashayar Filom an
d Kevin Pilgrim. The talk will also briefly describe effective implementat
ion of the Thurston pullback algorithm\, and its behavior (or mis-behavior
).\n\nJoint work with Araceli Bonifant and Scott Sutherland.\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luna Lomonaco (IMPA)
DTSTART:20211210T180000Z
DTEND:20211210T193000Z
DTSTAMP:20260422T225703Z
UID:ComplexDynamics/8
DESCRIPTION:Title: Mating quadratic maps with the modular group\nby Luna Lomonaco
(IMPA) as part of Complex Dynamics Week\n\n\nAbstract\nHolomorphic corres
pondences are polynomial relations $P(z\,w)=0$\, which can be regarded as
multi-valued self-maps of the Riemann sphere\, this is implicit maps\nsend
ing $z$ to $w$. The iteration of such a multi-valued map generates a dynam
ical system on the Riemann sphere: dynamical system which generalises rati
onal maps and finitely generated Kleinian groups. We consider a specific
$1 -$(complex) parameter family of $(2:2)$ correspondences $F_a$ (introduc
ed by S. Bullett and C. Penrose in 1994)\, which we describe dynamically.
In particular\, we show that for every parameter in a subset of the parame
ter plane called $\\textit{the connectedness locus}$ and denoted by $M_{\\
Gamma}$\, this family behaves as rational maps on a subset of the Riemann
sphere and as the modular group on the complement: in other words\, these
correspondences are mating between the modular group and rational maps (in
the family $Per_1(1)$). Moreover\, we develop for this family of correspo
ndences a complete dynamical theory which parallels the Douady-Hubbard the
ory of quadratic polynomials\, and we show that $M_{\\Gamma}$ is homeomorp
hic to the parabolic Mandelbrot set $M_1$. This is joint work with S. Bull
ett (QMUL).\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Kiwi (Universidad Católica de Chile)
DTSTART:20211209T210000Z
DTEND:20211209T223000Z
DTSTAMP:20260422T225703Z
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 polynomials
with a marked critical point\, given any $p \\ge 1$\, we prove that the l
ocus formed by polynomials with the marked critical point periodic of peri
od $p$ is an irreducible curve. Our methods rely on techniques used to st
udy one-complex-dimensional parameter spaces.\n\nThis is joint work with M
atthieu Arfeux.\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rudy Rosas (Pontificia Universidad Católica del Perú)
DTSTART:20211209T190000Z
DTEND:20211209T203000Z
DTSTAMP:20260422T225703Z
UID:ComplexDynamics/10
DESCRIPTION:Title: Conjuntos minimales cerca de singularidades de campos de vectores
holomorfos en dimensión dos\nby Rudy Rosas (Pontificia Universidad C
atólica del Perú) as part of Complex Dynamics Week\n\n\nAbstract\nConjun
tos minimales cerca de singularidades de campos de vectores holomorfos en
dimensión dos. \nResumen: Como consecuencia inmediata del Teorema de Poin
caré-Bendixson\, sabemos que las singularidades y las órbitas periódica
s son los únicos conjuntos minimales de un campo de vectores en el plano
bidimensional real. Aunque este resultado no tiene ningún paralelo en dim
ensiones mayores\, en esta charla discutiremos una versión local para el
caso de campos holomorfos cerca de un punto singular en el plano complejo
bidimensional.\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pascale Roesch (Université Toulouse III)
DTSTART:20211206T160000Z
DTEND:20211206T173000Z
DTSTAMP:20260422T225703Z
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\nA
bstract\nWe will explain\, with some examples\, several ways to decribe on
e parameter slices of parameter spaces of rational maps.\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthieu Arfeux (Pontificia Universidad Católica de Valparaiso)
DTSTART:20211208T210000Z
DTEND:20211208T223000Z
DTSTAMP:20260422T225703Z
UID:ComplexDynamics/12
DESCRIPTION:Title: Jumping between trees\nby Matthieu Arfeux (Pontificia Univers
idad Católica de Valparaiso) as part of Complex Dynamics Week\n\n\nAbstra
ct\nEn esta charla presentaré una relación entre los árboles de Hubbard
y los árboles de DeMarco-McMullen ($\\textit{escaping trees}$). Dicha re
lación tiene lugar en el borde del lugar de conexidad en cierto conjunto
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 conjunto
de polinomios tal como conjeturado por John Milnor unos 30 años atrás.
Les contaré como el trabajo sobres la relación entre esos árboles llev
ó unos años después a la demostración de la conjetura. Ver: https://ar
xiv.org/abs/1503.02710\, https://arxiv.org/abs/2012.14945\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Suárez (Pontificia Universidad Católica del Perú)
DTSTART:20211210T150000Z
DTEND:20211210T163000Z
DTSTAMP:20260422T225703Z
UID:ComplexDynamics/13
DESCRIPTION:Title: Dynamics of a Blaschke Product\nby Pedro Suárez (Pontificia
Universidad Católica del Perú) as part of Complex Dynamics Week\n\n\nAbs
tract\nThe finite Blaschke products are rational functions on the Riemann
sphere that preserve the unit circle. Generally useful in studying the dyn
amics of polynomials\; however\, with a dynamic richness of its own.\n\nTh
e purpose of this talk is to explore some dynamical aspects of a Blaschke
product family depending on a complex parameter\, with a single critical p
oint (cubic type) on the circle\, critical value (the parameter)\, and two
fixed super-atractors at zero and infinity. The variation of the critical
value determines in the dynamical plane\, the connectivity of the Julia s
ets 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 (Blaschkebrot)
for the Blaschke family\, where numerical experiments suggest the presence
of baby cubibrots.\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linda Keen (CUNY)
DTSTART:20211209T150000Z
DTEND:20211209T163000Z
DTSTAMP:20260422T225703Z
UID:ComplexDynamics/14
DESCRIPTION:Title: Transcendental functions with two asymptotic values\nby Linda
Keen (CUNY) as part of Complex Dynamics Week\n\n\nAbstract\nThe work desc
ribed in this lecture is part of a general program in complex dynamics to
understand parameter spaces of transcendental maps.\n\nIn all complex dyna
mical systems\, the singular values control the stable periodic behavior.
The singular values of rational functions are their critical values. Trans
cendental maps have a new kind of singularity\, an “asymptotic value”:
for example\, 0\,$\\infity$ for $e^z$ and $\\pm i$ for $\\tan z$. These f
unctions belong to the relatively simple family $\\mathcal{F}_2$ of transc
endental maps with exactly two asymptotic values and no critical values. T
his family\, up to affine conjugation\, depends on two complex parameters.
\n\nIn this lecture\, we will begin by reviewing the structures of the par
ameter spaces of the exponential and tangent families which have been well
studied. We will then describe recent work on two other slices of the ful
l family $\\mathcal{F}_2$. We will see how phenomena we observe for the ta
ngent and the exponential families recur and combine in new ways.These res
ults incorporate various\njoint projects with Tao Chen\, Nuria Fagella and
Yunping Jiang.\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfredo Poirier (Pontificia Universidad Católica del Perú)
DTSTART:20211206T140000Z
DTEND:20211206T153000Z
DTSTAMP:20260422T225703Z
UID:ComplexDynamics/15
DESCRIPTION:Title: The basics of iteration: Day 1\nby Alfredo Poirier (Pontifici
a Universidad Católica del Perú) as part of Complex Dynamics Week\n\n\nA
bstract\nThis will be a crash course in the theory of iteration of rationa
l maps. It is oriented to undergraduates and starting graduate students at
tending our seminar.\n\nFirst day: The basics.\n\nSquaring as a prototype
of iteration. The superattractive role of infinity for polynomials. A clos
er look at Newton's method. Normal families and Montel's theorem.\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfredo Poirier (Pontificia Universidad Católica del Perú)
DTSTART:20211207T130000Z
DTEND:20211207T143000Z
DTSTAMP:20260422T225703Z
UID:ComplexDynamics/16
DESCRIPTION:Title: The basics of iteration: Day 2\nby Alfredo Poirier (Pontifici
a Universidad Católica del Perú) as part of Complex Dynamics Week\n\n\nA
bstract\nThis will be a crash course in the theory of iteration of rationa
l maps. It is oriented to undergraduates and starting graduate students at
tending our seminar.\n\nSecond day: The Julia set and the Fatou set.\n\nAt
tractive and superatractive periodic orbits. The structure of the Julia se
t. Other type of non-caotic behaviour.\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfredo Poirier (Pontificia Universidad Católica del Perú)
DTSTART:20211208T190000Z
DTEND:20211208T203000Z
DTSTAMP:20260422T225703Z
UID:ComplexDynamics/17
DESCRIPTION:Title: The basics of iteration: Day 3\nby Alfredo Poirier (Pontifici
a Universidad Católica del Perú) as part of Complex Dynamics Week\n\n\nA
bstract\nThis will be a crash course in the theory of iteration of rationa
l maps. It is oriented to undergraduates and starting graduate students at
tending our seminar.\n\nThird day: The role of the critical points.\n\nThe
global structure of the Fatou set. Relation between the critical orbits a
nd the conexity of the Julia set. The introduction of parameters in the pi
cture.\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Castillo (Pontificia Universidad Católica del Perú)
DTSTART:20211209T123000Z
DTEND:20211209T143000Z
DTSTAMP:20260422T225703Z
UID:ComplexDynamics/18
DESCRIPTION:Title: Further topics in basic complex dynamics: Day 1\nby Alberto C
astillo (Pontificia Universidad Católica del Perú) as part of Complex Dy
namics Week\n\n\nAbstract\nThis minicourse is a continuation of professor
Poirier's exposition of basic complex dynamics.\nWe focus on families of r
ational maps (more preciselly\, polynomial families) and pass from the\ndy
namical to the parameter plane\, dealing with the interplay between them.\
nOur selected topics revolves around the (perhaps) main conjecture of comp
lex dynamics:\nthe density of hyperbolic components for families of ration
al maps.\nWe present well known topics such as renormalization\, invariant
line fields\,\nthe Mañe-Sad-Sullivan paper\, Yoccoz puzzles\, etc.\nAll
these topics are presented in the context of two polynomial families\,\non
e of them being that of quadratic polynomials\,\nwhose connectedness locus
is the Mandelbrot set.\nThe other one is a bicritical uniparametric famil
y\, object of study of the expositor's thesis.\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Castillo (Pontificia Universidad Católica del Perú)
DTSTART:20211210T123000Z
DTEND:20211210T143000Z
DTSTAMP:20260422T225703Z
UID:ComplexDynamics/19
DESCRIPTION:Title: Further topics in basic complex dynamics: Day 2\nby Alberto C
astillo (Pontificia Universidad Católica del Perú) as part of Complex Dy
namics Week\n\n\nAbstract\nThis minicourse is a continuation of professor
Poirier's exposition of basic complex dynamics.\nWe focus on families of r
ational maps (more preciselly\, polynomial families) and pass from the\ndy
namical to the parameter plane\, dealing with the interplay between them.\
nOur selected topics revolves around the (perhaps) main conjecture of comp
lex dynamics:\nthe density of hyperbolic components for families of ration
al maps.\nWe present well known topics such as renormalization\, invariant
line fields\,\nthe Mañe-Sad-Sullivan paper\, Yoccoz puzzles\, etc.\nAll
these topics are presented in the context of two polynomial families\,\non
e of them being that of quadratic polynomials\,\nwhose connectedness locus
is the Mandelbrot set.\nThe other one is a bicritical uniparametric famil
y\, object of study of the expositor's thesis.\n
LOCATION:https://researchseminars.org/talk/ComplexDynamics/19/
END:VEVENT
END:VCALENDAR