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BEGIN:VEVENT
SUMMARY:Myrto Manolaki (University College Dublin)
DTSTART:20200512T130000Z
DTEND:20200512T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/1
DESCRIPTION:Title: Mergelyan-type theorems in several complex variables\nby Myrto Ma
nolaki (University College Dublin) as part of CAvid: Complex Analysis vide
o seminar\n\nLecture held in N/A.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walter Bergweiler (Christian-Albrechts Universität Kiel)
DTSTART:20200519T130000Z
DTEND:20200519T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/2
DESCRIPTION:Title: Entire solutions of linear q-difference equations\nby Walter Berg
weiler (Christian-Albrechts Universität Kiel) as part of CAvid: Complex A
nalysis video seminar\n\nLecture held in N/A.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katsuya Ishizaki (Open University of Japan)
DTSTART:20200526T130000Z
DTEND:20200526T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/3
DESCRIPTION:Title: Meromorphic solutions of Fermat type equations\nby Katsuya Ishiza
ki (Open University of Japan) as part of CAvid: Complex Analysis video sem
inar\n\nLecture held in N/A.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aimo Hinkkanen (University of Illinois)
DTSTART:20200602T130000Z
DTEND:20200602T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/4
DESCRIPTION:Title: A determinant problem for a third order ODE\nby Aimo Hinkkanen (U
niversity of Illinois) as part of CAvid: Complex Analysis video seminar\n\
nLecture held in N/A.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuefei Wang (Chinese Academy of Sciences\, Beijing)
DTSTART:20200609T130000Z
DTEND:20200609T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/5
DESCRIPTION:Title: On the dynamics of entire functions with symmetry\nby Yuefei Wang
(Chinese Academy of Sciences\, Beijing) as part of CAvid: Complex Analysi
s video seminar\n\nLecture held in N/A.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandre Eremenko (Purdue University)
DTSTART:20200616T130000Z
DTEND:20200616T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/6
DESCRIPTION:Title: Moduli spaces for Lamé functions\nby Alexandre Eremenko (Purdue
University) as part of CAvid: Complex Analysis video seminar\n\nLecture he
ld in N/A.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Luca (University College London)
DTSTART:20200623T130000Z
DTEND:20200623T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/7
DESCRIPTION:Title: Mixed boundary value problems for slow viscous flows: new transform m
ethods and applications\nby Elena Luca (University College London) as
part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nA
bstract\nMotivated by microfluidics applications where it is required to m
anipulate viscous fluids at small scales\, we present new transform method
s for solving mixed boundary value problems for biharmonic fields arising
therein. The new methods provide a unified general approach to finding qua
si-analytical solutions to a variety of technologically important problems
of slow viscous flows and lead to fast and accurate schemes for evaluatio
n of the solutions. In this talk\, we focus on problems in simply and mult
iply connected domains\, with boundaries consisting of straight-line or ci
rcular edges.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zinelâabidine Latreuch (University of Mostaganem\, Algeria)
DTSTART:20200630T130000Z
DTEND:20200630T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/8
DESCRIPTION:Title: On meromorphic solutions of non-linear differential equations of Tumu
ra-Clunie type\nby Zinelâabidine Latreuch (University of Mostaganem\,
Algeria) as part of CAvid: Complex Analysis video seminar\n\nLecture held
in N/A.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigor Barsegian (National Academy of Sciences of Armenia)
DTSTART:20200707T130000Z
DTEND:20200707T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/9
DESCRIPTION:Title: A new property of arbitrary complex polynomials\nby Grigor Barseg
ian (National Academy of Sciences of Armenia) as part of CAvid: Complex An
alysis video seminar\n\nLecture held in N/A.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jun Wang (Fudan University\, China)
DTSTART:20200714T130000Z
DTEND:20200714T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/10
DESCRIPTION:Title: Julia limiting directions of meromorphic functions\nby Jun Wang
(Fudan University\, China) as part of CAvid: Complex Analysis video semina
r\n\nLecture held in N/A.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phil Rippon (Open University\, UK)
DTSTART:20200908T130000Z
DTEND:20200908T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/11
DESCRIPTION:Title: Constructing entire functions of small order - motivated by complex
dynamics\nby Phil Rippon (Open University\, UK) as part of CAvid: Comp
lex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nIn 1989\,
Eremenko conjectured that for any transcendental entire function the escap
ing set $I(f) = \\{z:f^n(z)\\to\\infty \\text{ as } n\\to\\infty\\}$ has n
o bounded components -- despite much work this conjecture is still open.\n
\nFor real entire functions $f$ of finite order with only real zeros\, we
have shown that Eremenko's conjecture holds if there exists $r>0$ such tha
t the iterated minimum modulus $m^n(r)\\to\\infty$ as $n\\to\\infty$. Here
$m(r)=\\min_{|z|=r}|f(z)|$.\n\nWe discuss examples of families of entire
functions of small order for which this iterated minimum modulus condition
holds\, and construct examples of functions of small order for which it d
oes not hold\, including examples based on a new development of a method d
ue to Kjellberg.\n\n(Joint work with Dan Nicks and Gwyneth Stallard.)\n\nP
lease e-mail Rod Halburd (r.halburd@ucl.ac.uk) for the Zoom link. Please
let him know if you would like to receive weekly announcements about CAvid
(the Complex Analysis video seminar series).\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuen-Wai Ng (Hong Kong University)
DTSTART:20200915T130000Z
DTEND:20200915T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/12
DESCRIPTION:Title: The squeezing function on doubly-connected domains via the Loewner d
ifferential equation\nby Tuen-Wai Ng (Hong Kong University) as part of
CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract
\nInspired by the work of Liu\, Sun and Yau (2004) on holomorphic homogene
ous regular (HHR) domains and Yeung (2009)’s work on domains with unifor
m squeezing property (another name for HHR domains)\, Deng\, Guan and Zhan
g (2012) introduced a new biholomorphic invariant\, namely\, the squeezing
function for bounded domains in the n-dimensional complex Euclidean space
. Since then it has been one of the most active area in several complex va
riables in recent years.\n\nOn the other hand\, until now\, there is only
one explicit example of non-constant squeezing functions\, namely the sque
ezing function of the punctured ball. In this talk\, we will establish an
explicit formula for the squeezing functions of annuli and hence (up to bi
holomorphisms) for any doubly connected planar domain. The main tools used
to prove this result are the Schottky-Klein prime function (following th
e work of Crowdy) and a version of the Loewner differential equation on an
nuli due to Komatu. We will also show that these results can be used to ob
tain lower bounds on the squeezing function for certain product domains in
the n-dimensional complex Euclidean space.\n\nThis is a joint work with C
hiu Chak Tang and Jonathan Tsai.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukas Geyer (Montana State University)
DTSTART:20200922T130000Z
DTEND:20200922T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/13
DESCRIPTION:Title: Gravitational lensing and critically fixed anti-rational maps\nb
y Lukas Geyer (Montana State University) as part of CAvid: Complex Analysi
s video seminar\n\nLecture held in N/A.\n\nAbstract\nStudying the dynamics
of anti-rational maps\, i.e.\, complex conjugates of rational maps\, is a
subject closely related to holomorphic dynamics\, with intriguing connect
ions to problems in gravitational lensing. In particular\, the lens equati
on for a single-plane gravitational lens made up of N point masses is know
n to be a fixed point equation for an anti-rational map of degree N. These
fixed points are apparent images of a single (point) light source\, and i
t is known from work of Rhie (2003) and Khavinson and Neumann (2006) that
for N>1 there can be at most 5N-5 such images\, and that this bound is sha
rp.\n\nOriginally motivated by the goal of classifying maximal lensing con
figurations\, i.e.\, configurations for which the bound 5N-5 is attained\,
we recently succeeded in giving a complete classification of anti-rationa
l maps for which all critical points are fixed\, through simple topologica
l models associated with certain planar graphs. We will explain this class
ification\, the main ideas in the proof\, and how this yields a partial cl
assification and new examples of maximal lensing configurations. Finally\,
we will discuss some open problems and questions.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norbert Steinmetz (Technische Universität Dortmund)
DTSTART:20200929T130000Z
DTEND:20200929T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/14
DESCRIPTION:Title: Laplace contour integrals and linear differential equations\nby
Norbert Steinmetz (Technische Universität Dortmund) as part of CAvid: Com
plex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nAny linea
r differential equation with coefficients of degree one\n$$w^{(n)}+\\sum_{
j=0}^{n-1}(a_j+b_jz)w^{(j)}=0$$\nhas solutions that may be represented as\
nLaplace contour integrals\n$$f(z)=\\frac1{2\\pi i}\\int_C\\phi(t)e^{-zt}\
\\,dt.$$\nWe will discuss the main properties of\nthese solutions and dete
rmine their order of growth\, asymptotics\, Phragm\\'en-Lindel\\"of indica
tor\, distribution of zeros\,\nNevanlinna functions $T(r\,f)$ and $N(r\,1/
f)$\, and the existence of sub-normal and polynomial solutions.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Nowak (Maria Curie-Skłodowska University\, Poland)
DTSTART:20201006T130000Z
DTEND:20201006T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/15
DESCRIPTION:Title: On kernels of Toeplitz operators\nby Maria Nowak (Maria Curie-Sk
łodowska University\, Poland) as part of CAvid: Complex Analysis video se
minar\n\nLecture held in N/A.\n\nAbstract\nLet $H^2$ denote the standard H
ardy space on the unit disk $\\mathbb\nD$ and let $\\mathbb T=\\partial \\
mathbb D$. Every $f(z)=\\sum_{n=0}^{\\infty}a_nz^n\\in H^2$ has a nontange
ntial limit $f(e^{i\\theta})$ a.e. on $\\mathbb {T}=\\partial\\mathbb {D}$
and this boundary function $f(e^{i\\theta})$ is in $L^2(\\mathbb {T})$.\
nFurthermore\, if $\\{c_n\\}$ are Fourier coefficients of $f(e^{i\\theta})
$ then $c_n=a_n$ for $n\\geq 0$ and $c_n=0$ for $n<0$.\n Actually\, the sp
ace $H^2$ can be identified with a closed subspace of\n$L^2(\\mathbb {T})
$ whose Fourier coefficients with negative indices vanish.\n\n\nFor $\\va
rphi\\in\nL^{\\infty}(\\mathbb T)$ the Toeplitz operator $T_{\\varphi}$ on
$H^2$ is given by\n$T_{\\varphi}f=P_{+}(\\varphi f)$\, where $P_{+}$ is t
he orthogonal\nprojection of $L^2(\\mathbb T)$ onto $H^2$. It is a conseq
uence of Hitt's Theorem that\n$\\ker T_{\\varphi}= fK_I$\, where $K_I= H^
2\\ominus IH^2$\nis the model space corresponding to the inner function $I
$ such that\n$I(0)=0$ and $f$ is an outer function of unit $H^2$ norm that
\nacts as an isometric multiplier from $K_I$ onto $f K_{I}$.\nHowever\,
not all spaces $fK_{I}$\, where $f$ and $K_I$ are as above\, can be ke
rnels of Toeplitz operators.\nThe sufficient and necessary condition for t
he space $fK_I$ to be the kernel of a Toeplitz operator was given by E. Ha
yashi (1990).\nIn 1994 D. Sarason gave another proof of this condition bas
ed on de Branges-Rovnyak spaces theory.\nIf $M= fK_I$ is a kernel of a To
eplitz operator\, then also we have $M=\\ker T_{\\frac{\\overline{If}}{f}}
$\nIn the talk we consider the case when $fK_I\\varsubsetneq \\ker T_{\\fr
ac{\\overline{If}}{f}}$ and try to describe\nthe space $\\ker T_{\\frac{\\
bar I\\bar f}{f}}\\ominus fK_I$. We use Sarason's approach and the stru
cture of de Branges-Rovnyak spaces generated by nonextreme functions.\n\
nThe talk is based on joint work with P. Sobolewski\, A.\nSo{\\l}tysiak an
d M. Wo{\\l}oszkiewicz-Cyll.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shamil Makhmutov (Sultan Qaboos University\, Oman)
DTSTART:20201013T130000Z
DTEND:20201013T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/16
DESCRIPTION:Title: Growth estimates for meromorphic solutions of higher order algebraic
differential equations\nby Shamil Makhmutov (Sultan Qaboos University
\, Oman) as part of CAvid: Complex Analysis video seminar\n\nLecture held
in N/A.\n\nAbstract\nPointwise growth estimates for the spherical derivati
ve of solutions of the first order algebraic differential equations are ob
tained. \nA generalization of this result to higher order equations is als
o given. \nWe discuss the related question of when for a given class X of
meromorphic functions in the unit disc\, \ndefined by means of the spheric
al derivative and integer $n$\, $n>1$\, condition $f^n \\in X$ implies $f
\\in X$. \nAn affirmative answer to this is given in the case of UBC and s
ome other classes. \nHowever\, there are classes when the answer is negat
ive.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Min Ru (University of Houston)
DTSTART:20201020T130000Z
DTEND:20201020T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/17
DESCRIPTION:Title: Recent developments in Nevanlinna theory and Diophantine approximati
on\nby Min Ru (University of Houston) as part of CAvid: Complex Analys
is video seminar\n\nLecture held in N/A.\n\nAbstract\nIn this talk\, I'll
survey the recent results in Nevanlinna theory and Diophantine approximat
ion. I'll focus on the extension of H. Cartan's Second Main Theorem in Nev
anlinna theory.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catherine Bénéteau (University of South Florida)
DTSTART:20201027T130000Z
DTEND:20201027T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/18
DESCRIPTION:Title: A survey of optimal polynomial approximants and connections to digit
al filters\nby Catherine Bénéteau (University of South Florida) as p
art of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAb
stract\nIn this talk\, I will discuss the notion of optimal polynomial app
roximants\, which are polynomials that approximate\, in some sense\, inver
ses of functions in certain Hilbert spaces of analytic functions. In the l
ast 10 years\, a number of papers have appeared examining the zeros of the
se polynomials\, rates of convergence\, efficient algorithms for their com
putation\, and connections to orthogonal polynomials and reproducing kerne
ls\, among other topics. On the other hand\, in the 70s\, researchers in e
ngineering and applied mathematics introduced least squares inverses in th
e context of digital filters in signal processing. It turns out that in th
e Hardy space $H^2$ the optimal polynomial approximants and the least squa
res inverses are identical. In this talk\, I will survey results related t
o the zeros of optimal polynomial approximants and implications for the de
sign of ideal digital filters. This talk is based on a preprint of a surve
y paper that is joint with Ray Centner.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dierk Schleicher (Aix–Marseille Université)
DTSTART:20201103T140000Z
DTEND:20201103T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/19
DESCRIPTION:Title: Finding polynomial roots using complex analysis\, dynamical systems\
, computer algebra\nby Dierk Schleicher (Aix–Marseille Université)
as part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n
\nAbstract\nOne of the classical problems in all areas of mathematics is t
o find roots of complex polynomials. It is well known that this can be don
e only by methods of approximation. We discuss three classical methods: th
e Newton\, Weierstrass\, and Ehrlich-Aberth methods\; these are complex an
alytic maps that\, under iteration\, are supposed to converge to one root\
, resp. all roots of the polynomial. Locally\, these methods converge fast
\, but the global dynamical properties are hard to describe.\n\nWe introdu
ce these complex analytic dynamical systems and describe recent progress t
owards their global dynamical properties. In particular\, the Newton and W
eierstrass methods are not globally convergent: for open sets of polynomia
ls there are open sets of initial points that fail to converge to roots. M
oreover\, for Weierstrass and Ehrlich-Aberth\, there are orbits that are a
lways defined and converge\, but not to roots. For Newton\, there is meanw
hile a rich theory about its global dynamics\, but there are many open que
stions for all these methods.\n\nMuch of this is joint work with members o
f my ERC team\, in particular my PhD student Bernhard Reinke\, as well as
with colleagues.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Trefethen (University of Oxford)
DTSTART:20201110T140000Z
DTEND:20201110T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/20
DESCRIPTION:Title: Approximation on complex domains and Riemann surfaces\nby Nick T
refethen (University of Oxford) as part of CAvid: Complex Analysis video s
eminar\n\nLecture held in N/A.\n\nAbstract\nLet f be a function analytic o
n a closed Jordan region E apart\nfrom a finite number of branch point sin
gularities on the boundary.\nWe show how f can be approximated by rational
functions on E with\nroot-exponential convergence\, i.e.\, errors $O(\\ex
p(-C \\sqrt n))$ with\n$C>0$. Such approximations lead to "lightning solv
ers" for Laplace\nproblems in planar domains. Then we move to "reciprocal
-log" or\n"log-lightning" approximations involving terms of the form\n$c/(
\\log(z-z_k) - s_k)$. Now one gets exponential-minus-log convergence\,\ni
.e.\, $O(\\exp(-C n/\\log n))$. Moreover\, the reciprocal-log functions\n
can be analytically continued around the branch points to provide\napproxi
mation on further Riemann sheets. This work (with Yuji\nNakatsukasa) is v
ery new\, and there are many open questions.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Núria Fagella (University of Barcelona)
DTSTART:20201117T140000Z
DTEND:20201117T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/21
DESCRIPTION:Title: Wandering in complex dynamics\nby Núria Fagella (University of
Barcelona) as part of CAvid: Complex Analysis video seminar\n\nLecture hel
d in N/A.\n\nAbstract\nIn a holomorphic dynamical system a wandering domai
n is a component of the stable (or normal) set whose iterates never meet.
This type of components only exist in the presence of essential singularit
ies and are the most unknown among all the possible kinds. In this talk I
will explain what is and is not known about wandering domains and some of
the most recent progress\, which relates wandering dynamics to sequences o
f holomorphic functions on the unit disk (non-autonomous dynamics).\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gautam Bharali (Indian Institute of Science\, Bangalore)
DTSTART:20201124T140000Z
DTEND:20201124T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/22
DESCRIPTION:Title: The Wolff-Denjoy theorem beyond the unit disc\nby Gautam Bharali
(Indian Institute of Science\, Bangalore) as part of CAvid: Complex Analy
sis video seminar\n\nLecture held in N/A.\n\nAbstract\nThe Wolff-Denjoy th
eorem has been the motivation for a host of results that resemble the clas
sical theorem for holomorphic self-maps of the unit disc. In this talk\, w
e shall look at yet another result in this class. This result applies to a
rather general class of bounded domains in one and higher dimensions\, wh
ich may have rough boundaries and aren't necessarily contractible. While o
ur techniques are motivated by the properties of holomorphic maps in sever
al complex variables\, the theory of such maps turns out to be incidental
to these techniques. In fact\, in this talk\, we shall spend some time exa
mining certain analogies between the Poincaré distance and the Hilbert di
stance on convex domains. This is relevant as there exists a Wolff--Denjoy
-type theorem\, by Beardon\, in the latter setting. It is these analogies
that give rise to the fundamental concept that underlies our result(s): na
mely\, a weak notion of negative curvature for spaces equipped with the Ko
bayashi distance (of which the Poincaré distance is a special case). No k
nowledge of several complex variables will be assumed in this talk: indeed
\, most of the discussion will focus on basic complex analysis and on the
properties of metric spaces and contractive maps. A large part of this tal
k will be based on joint work with Andrew Zimmer and Anwoy Maitra.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Gauthier (Université de Montréal)
DTSTART:20201201T140000Z
DTEND:20201201T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/23
DESCRIPTION:Title: Asymptotic first boundary value problem for holomorphic functions o
f several complex variables\nby Paul Gauthier (Université de Montréa
l) as part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A
.\n\nAbstract\n(Jointly with M. Shirazi)\n\nLet $M$ be a complex manifold
endowed with a distance $d$ and let $U\\subset M$ be an arbitrary Stein do
main. Let $\\mu$ be a regular Borel measure on $U\,$ such that non-empty o
pen sets of $U$ have positive $\\mu$ measure and $\\nu$ a regular Borel me
asure on $\\partial U.$ Let $\\psi$ be a \nBorel measurable function on $\
\partial U\,$ \nwhose restriction to some closed subset $S\\subset\\parti
al U$ is continuous. \nThen\, \nthere exists a holomorphic function $f$
on $U\,$ such that\, for $\\nu$-almost every $p\\in \\partial U$\, \nand
for every $p\\in S\,$ $f(x)\\to \\psi(p)$\, as $x\\to p$ outside a set of
$\\mu$-density zero at $p$ \nrelative to $U.$\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kerstin Jordaan (University of South Africa)
DTSTART:20201208T140000Z
DTEND:20201208T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/24
DESCRIPTION:Title: A characterisation of Askey-Wilson polynomials and the indeterminate
moment problem associated with a limiting case\nby Kerstin Jordaan (U
niversity of South Africa) as part of CAvid: Complex Analysis video semina
r\n\nLecture held in N/A.\n\nAbstract\n(Joint work with M. Kenfack Nangho)
\n\nIn this talk I will complete and prove a conjecture concerning a chara
cterising relation for Askey-Wilson orthogonal polynomials and study a lim
iting case of Askey-Wilson polynomials when one of the parameters goes to
infinity. Solutions to the associated indeterminate moment problem are fo
und and an orthogonality relation is established.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhijit Banerjee (University of Kalyani\, India)
DTSTART:20201215T140000Z
DTEND:20201215T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/25
DESCRIPTION:Title: A survey on different uniqueness and strong uniqueness polynomials a
nd their generating unique range sets\nby Abhijit Banerjee (University
of Kalyani\, India) as part of CAvid: Complex Analysis video seminar\n\nL
ecture held in N/A.\n\nAbstract\nThe notion of unique range sets was intro
duced by Gross-Yang [Proc. Japan Acad.\, 58 (1982)\, 17-20]. Since the inc
eption of the definition\, it became an interesting topic for the research
ers to study. In course of time\, the research had been shifted to-wards t
he characterizations of the polynomial backbone of concerned sets. As a re
sult\, the uniqueness and strong uniqueness polynomial appeared in the lit
erature and made a lusting impression. \n\nIn 2000\, H. Fujimoto [H. Fujim
oto\, On uniqueness of meromorphic functions sharing finite sets\, Amer. J
. Math.\, 122 (2000)\, 1175-1203.] first discovered a special property of
a polynomial\, called it as “property (H)” which played a vital role i
n the research of uniqueness and strong uniqueness polynomial.\n\nWithin t
he realm of Nevanlinna theory\, we wish to elaborately characterize the ex
isting uniqueness as well as strong uniqueness polynomials\, the relation
between them and their contribution in forming the unique range sets under
relaxed sharing hypothesis. We also wish to discuss the scope for future
research and intend to present our humble contribution in this aspect.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mónica Moreno Rocha (Centro de Investigación en Matemáticas\, M
exico)
DTSTART:20210119T140000Z
DTEND:20210119T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/26
DESCRIPTION:Title: Herman rings of elliptic functions\nby Mónica Moreno Rocha (Cen
tro de Investigación en Matemáticas\, Mexico) as part of CAvid: Complex
Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nConsider the f
amily of iterates of a rational or transcendental meromorphic function $f$
. A component of normality that is invariant under some $n$-iterate of $f$
is called a Herman ring if over such a component\, $f^n$ is conformally c
onjugate to an irrational rotation acting on an annulus of finite conforma
l modulus. In that case\, the positive iterates of the Herman ring form a
cycle. Showing the existence of cycles of Herman rings for meromorphic fun
ctions is not an easy task\, and when they exist\, it is natural to ask on
eself if an upper bound for the number of cycles is achievable.\n\nIn the
late 1980s Shishikura introduced the theory of quasiconformal surgery to c
onstruct examples of rational maps with cycles of Herman rings while also
showing that a rational map of degree d has at most d-2 cycles (thus\, rat
ional maps of degree 2 cannot have Herman rings). In the case of elliptic
functions\, Hawkins & Koss showed in 2004 that the Weierstrass P function\
, defined over any given lattice\, cannot have cycles of Herman rings. Thi
s result motivated the question of the existence of Herman rings for ellip
tic functions in terms of their order. In this talk\, I will present recen
t results obtained through the implementation of Shishikura’s surgery te
chniques to the elliptic case. First\, we’ll see that Herman rings can b
e realizable by elliptic functions of order at least 3\, and in particular
\, order 2 elliptic functions cannot have cycles of Herman rings. Then\, I
will present an upper bound for the number of invariant Herman rings in t
erms of the order of the elliptic function and show how to refine that bou
nd using the multiplicity of poles.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Dyakonov (ICREA & Universitat de Barcelona\, Spain)
DTSTART:20210202T140000Z
DTEND:20210202T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/28
DESCRIPTION:Title: Lacunary polynomials in $L^1$: geometry of the unit sphere\nby K
onstantin Dyakonov (ICREA & Universitat de Barcelona\, Spain) as part of C
Avid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\n
Let $\\Lambda$ be a finite set of nonnegative integers\, and let $\\mathca
l P(\\Lambda)$ be the linear hull of the monomials $z^k$ with $k\\in\\Lamb
da$\, viewed as a subspace of $L^1$ on the unit circle. We characterize th
e extreme and exposed points of the unit ball in $\\mathcal P(\\Lambda)$.\
n
LOCATION:https://stable.researchseminars.org/talk/CAvid/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linda Keen (CUNY\, USA)
DTSTART:20210209T140000Z
DTEND:20210209T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/29
DESCRIPTION:Title: Parameter spaces of families of transcendental functions\nby Lin
da Keen (CUNY\, USA) as part of CAvid: Complex Analysis video seminar\n\nL
ecture held in N/A.\n\nAbstract\nThis lecture is based on joint work with
Tao Chen\, Nuria Fagella and Yunping Jiang. It is part of a more general p
rogram to understand parameter spaces of transcendental maps.\n\nIf we per
turb a rational function by a topological conjugacy we obtain a rational f
unction\, so the dynamics depend on the coefficients\, which therefore for
m a natural parameter space. It is not true that there is a natural way of
parameterizing general families of transcendental functions so that a per
turbation of the function remains in the family. This makes it difficult t
o describe how the dynamics varies across these families. We will look at
two examples of reasonably general families of transcendental meromorphic
functions where one can overcome these difficulties. What this means is th
at we will be able to describe the properties of the components defined by
the bifurcation locus. We will see at the end how these examples fit into
the larger program.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Demina (National Research University Higher School of Econom
ics\, Russia)
DTSTART:20210216T140000Z
DTEND:20210216T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/30
DESCRIPTION:Title: Algebraic invariants\, integrability\, and meromorphic solutions
\nby Maria Demina (National Research University Higher School of Economics
\, Russia) as part of CAvid: Complex Analysis video seminar\n\nLecture hel
d in N/A.\n\nAbstract\nConsider an autonomous algebraic ordinary different
ial equation of order higher than one. The aim of the talk is to address t
he following questions.\n\n1. Does there exist an autonomous algebraic fir
st-order ordinary differential equation compatible with the original equat
ion?\n\n2. If yes\, how to find all such equations?\n \n\nBivariate polyno
mials producing autonomous algebraic first-order ordinary differential equ
ations compatible with the equation under consideration are called algebra
ic invariants. The main difficulty in deriving irreducible algebraic invar
iants lies in the fact that the degrees of related bivariate polynomials a
re not known in advance.\n\nAlgebraic invariants are important from theore
tical and practical point of views. In the two-dimensional case algebraic
invariants are key objects in establishing Darboux and Liouvillian integra
bility of the original ordinary differential equation. In addition\, algeb
raic invariants can be used to perform the classification of W-meromorphic
solutions of ordinary differential equations. We shall pay some attention
to these applications.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Risto Korhonen (University of Eastern Finland)
DTSTART:20210323T130000Z
DTEND:20210323T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/31
DESCRIPTION:Title: Delay differential equations and Nevanlinna theory\nby Risto Kor
honen (University of Eastern Finland) as part of CAvid: Complex Analysis v
ideo seminar\n\nLecture held in N/A.\n\nAbstract\nThe idea that the existe
nce of sufficiently many finite-order meromorphic solutions could be used
to single out difference Painlevé equations was introduced by Ablowitz\,
Halburd and Herbst. In this talk necessary conditions are obtained for cer
tain types of delay differential equations to admit a transcendental merom
orphic solution of hyper-order less than one. The equations obtained inclu
de delay Painlevé equations and equations solvable by elliptic functions.
We conclude with recent results on the existence of transcendental meromo
rphic solutions of first-order difference equations\, without growth condi
tions.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Chyzhykov (University of Warmia and Mazury\, Poland)
DTSTART:20210223T140000Z
DTEND:20210223T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/32
DESCRIPTION:Title: Irregular solutions of complex linear differential equations in the
unit disc\nby Igor Chyzhykov (University of Warmia and Mazury\, Poland
) as part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.
\n\nAbstract\nIt is shown that the order and the lower order of growth are
equal for all non-trivial solutions of $f^{(k)}+A f=0$ if and only if the
coefficient $A$ is analytic in the unit disc and $\\log^+ M(r\,A)/\\log(1
-r)$ tends to a~finite limit as $r\\to 1^-$.\nA~family of examples is con
structed\, where the order of solutions remain the same while the lower or
der may vary on a~certain interval depending on the irregular growth of th
e coefficient.\nThese coefficients emerge as the logarithm of their modulu
s approximates smooth radial subharmonic functions of prescribed irregular
growth on a~sufficiently large subset of the unit disc.\nA~result describ
ing the phenomenon behind these examples is also established. En route to
\nresults of general nature\, a~new sharp logarithmic derivative estimate
involving the lower order of growth is discovered.\nIn addition to these e
stimates\,\narguments used are based\, in particular\, on the Wiman-Valiro
n theory adapted for the lower order.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paweł Wójcicki (Warsaw University of Technology\, Poland)
DTSTART:20210302T140000Z
DTEND:20210302T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/33
DESCRIPTION:Title: On an Invariant distance induced by the Szego kernel and its applica
tions\nby Paweł Wójcicki (Warsaw University of Technology\, Poland)
as part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n
\nAbstract\nThe aim of my talk is to recall the notion of the so called Sz
ego kernel and provide some new biholomorphic invariant by means of it. I
n fact\, it is defined on a similar way as the co called Skwarczyński dis
tance by means of the Bergman kernel. The relationship between completen
ess in both cases will be examined. It turns out that the new biholomorph
ic invariant gives rise to some other new invariant\, by means of which we
can estimate the so called Bergman metric by means of the so called Szego
metric.\n\nThis is a joint work with Professor Steven Krantz (WUST\, MO\,
USA)\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chengfa Wu (Shenzhen University\, China)
DTSTART:20210316T130000Z
DTEND:20210316T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/34
DESCRIPTION:Title: Elliptic functions and their applications in complex differential eq
uations\nby Chengfa Wu (Shenzhen University\, China) as part of CAvid:
Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nThis
talk focuses on the applications of elliptic functions in complex differen
tial equations. First\, we discuss classifications of meromorphic solution
s of certain autonomous complex differential equations. In particular\, we
will focus on the Loewy factorizable algebraic ODEs. Then we move to the
study of the autonomous Schwarzian differential equations (SDEs). Ishizaki
showed that there are six canonical types of autonomous SDEs that have tr
anscendental meromorphic solutions. We will construct all transcendental m
eromorphic solutions of five canonical types explicitly. In particular\, t
he solutions of four types are shown to be elliptic functions. Also\, all
transcendental meromorphic solutions that possess a Picard exceptional val
ue are characterized for the remaining canonical type. This talk is based
on joint works with Ng and Liao respectively.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sushil Gorai (Indian Institute of Science Education and Research K
olkata)
DTSTART:20210330T130000Z
DTEND:20210330T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/35
DESCRIPTION:Title: Polynomial convexity and real surfaces with singularity\nby Sush
il Gorai (Indian Institute of Science Education and Research Kolkata) as p
art of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAb
stract\nIn this talk I will first discuss briefly about polynomial convexi
ty and its application in polynomial approximations. Then\, I will discuss
the questions of polynomial convexity and approximation on compact subset
s of a couple of classes of real surfaces in $\\mathbb{C}^2$ with singular
ity\, namely\, the union of three totally real subspaces and surfaces with
isolated CR-singularity.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Caterina Stoppato (Università di Firenze\, Italy)
DTSTART:20210309T140000Z
DTEND:20210309T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/36
DESCRIPTION:Title: Regularity in one hypercomplex variable\nby Caterina Stoppato (U
niversità di Firenze\, Italy) as part of CAvid: Complex Analysis video se
minar\n\nLecture held in N/A.\n\nAbstract\nSince the 1930s\, several funct
ion theories have been introduced over the algebra of quaternions and othe
r alternative algebras. The aim of such constructions is to recover in hig
her dimensions the refined tools available in the theory of holomorphic fu
nctions of one complex variable. The peculiar properties of the higher-dim
ensional algebras considered are reflected in the different theories intro
duced.\n\nA relatively recent breakthrough was the introduction of the cla
ss of slice regular functions of one quaternionic variable by Gentili and
Struppa in 2006. This study\, generalized to alternative $*$-algebras by G
hiloni and Perotti in 2011\, has rapidly developed into a full-fledged the
ory.\n\nThe talk will overview the general problem of function theory in o
ne hypercomplex variable\, the main features of the theory of slice regula
r functions and its applications to open problems from other areas of math
ematics.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yueyang Zhang (University of Science and Technology Beijing)
DTSTART:20210420T130000Z
DTEND:20210420T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/37
DESCRIPTION:Title: On entire function $e^{p(z)}\\int_0^{z}\\beta(t)e^{-p(t)}dt$ with ap
plications to Tumura--Clunie equations and complex dynamics\nby Yueyan
g Zhang (University of Science and Technology Beijing) as part of CAvid: C
omplex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nLet $p(
z)$ be a non-constant polynomial and $\\beta(z)$ be a small entire functio
n of $e^{p(z)}$ in the sense of Nevanlinna. By using the classical Phragm\
\'{e}n--Lindel\\"{o}f theorem\, we analyze the growth behavior of the enti
re function $H(z):=e^{p(z)}\\int_0^{z}\\beta(t)e^{-p(t)}dt$ on the complex
plane $\\mathbb{C}$. We then apply these results to Tumura--Clunie type d
ifferential equation $f(z)^n+P(z\,f)=b_1(z)e^{p_1(z)}+b_2(z)e^{p_2(z)}$\,
where $b_1(z)$ and $b_2(z)$ are non-zero polynomials\, $p_1(z)$ and $p_2(z
)$ are two polynomials of the same degree~$k\\geq 1$ and $P(z\,f)$ is a di
fferential polynomial in $f$ of degree $\\leq n-1$ with meromorphic functi
ons of order less than~$k$ as coefficients\, and precisely characterize en
tire solutions of this equation. This gives an answer to a problem in the
literature and allows to find all zero-free solutions of the second-order
differential equation $f''-(b_1e^{p_1}+b_2e^{p_2}+b_3)f=0$\, where $b_3$ i
s a polynomial. We also use the Phragm\\'{e}n--Lindel\\"{o}f theorem to pr
ove a theorem on certain first-order non-homogeneous linear differential e
quation related to complex dynamics.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara de Fabritiis (Università Politecnica delle Marche\, Italy)
DTSTART:20210427T130000Z
DTEND:20210427T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/38
DESCRIPTION:Title: *-products\, *-exponential\, *-logarithm: some peculiarities of slic
e regular functions on the quaternions\nby Chiara de Fabritiis (Univer
sità Politecnica delle Marche\, Italy) as part of CAvid: Complex Analysis
video seminar\n\nLecture held in N/A.\n\nAbstract\nSlice regular function
s on quaternions were introduced in 2006 by Gentili and Struppa in order t
o generalize the notion of holomorphic functions on complex numbers (for a
n effective introduction you can refer to C. Stoppato's seminar (https://
mediacentral.ucl.ac.uk/Play/59248/). The theory had a quick development in
several directions by many authors\, in this talk I will focus on three u
nexpected behaviours of these functions. The first aspect we deal with is
the *-product\, which is the analogous of pointwise product for holomorphi
c functions\; in particular we give an interpretation of this operation vi
a two operators which resemble the scalar product and the vector product o
n R^3. The second point we investigate is a suitable extension of the noti
on of exponential of a slice regular function\, namely the *-exponential e
xp_*(f) (originally introduced by Colombo\, Sabadini and Struppa)\; we wil
l describe some of its features\, especially with regard to the non-commut
ativity of the *-product and to its connections with *-sine and *-cosine.
Lastly\, we study the possible existence and uniqueness of a *-logarithm o
f a never vanishing slice regular function\, both on slice and on product
domains of the quaternions. We give some existence and non-existence resul
ts for *-logarithm of never-vanishing slice regular functions (according t
o the splitting in real and vectorial part) and an accurate description of
the possible uniqueness of the *-logarithm.\nThis is a joint work with Am
edeo Altavilla (Università di Bari).\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Roth (University of Würzburg)
DTSTART:20210504T130000Z
DTEND:20210504T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/39
DESCRIPTION:Title: A new Schwarz-Pick Lemma at the boundary and rigidity of holomorphic
maps\nby Oliver Roth (University of Würzburg) as part of CAvid: Comp
lex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nWe establi
sh several invariant boundary versions of the (infinitesimal) Schwarz-Pick
lemma for conformal pseudometrics on the unit disk and for holomorphic se
lfmaps of strongly convex domains in CN in the spirit of the boundary Schw
arz lemma of Burns-Krantz. Firstly\, we focus on the case of the unit disk
and prove a general boundary rigidity theorem for conformal pseudometrics
with variable curvature. In its simplest cases this result already includ
es new types of boundary versions of the lemmas of Schwarz-Pick\, Ahlfors-
Schwarz and Nehari-Schwarz. The proof is based on a new Harnack-type inequ
ality as well as a boundary Hopf lemma for conformal pseudometrics which e
xtend earlier interior rigidity results of Golusin\, Heins\, Beardon\, Min
da and others. Secondly\, we prove similar rigidity theorems for sequences
of conformal pseudometrics\, which even in the interior case appear to be
new. For instance\, a first sequential version of the strong form of Ahlf
ors' lemma is obtained. As an auxiliary tool we establish a Hurwitz-type r
esult about preservation of zeros of sequences of conformal pseudometrics.
Thirdly\, we apply the one-dimensional sequential boundary rigidity resul
ts together with a variety of techniques from several complex variables to
prove a boundary version of the Schwarz-Pick lemma for holomorphic maps o
f strongly convex domains in $\\C^N$ for $N>1$.\n\n(This is joint work wit
h Filippo Bracci and Daniela Kraus)\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margaret Stawiska-Friedland\\ (American Mathematical Society/Mathe
matical Reviews\, USA)
DTSTART:20210511T130000Z
DTEND:20210511T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/40
DESCRIPTION:Title: A potential-theoretic characterization of polynomials in holomorphic
dynamics in one variable}\nby Margaret Stawiska-Friedland\\ (America
n Mathematical Society/Mathematical Reviews\, USA) as part of CAvid: Compl
ex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nIn 1960s Ha
ns Brolin initiated systematic application of potential-theoretic methods
in the dynamics of holomorphic maps. Among other things\, he proved the no
w-famous equidistribution theorem: for a complex polynomial $f$ of degree
greater than $1$ the preimages\, under successive iterates of $f$\, of a D
irac measure at an arbitrary point of the complex plane (except at most tw
o so-called exceptional points) converge weakly to the equilibrium measure
(with pole at infinity) for the Julia set $J_f$ of $f$. To a general rati
onal map $f$ of degree $d \\geq 2$ on the Riemann sphere $\\mathbb{CP}^1$
one can associate another measure $\\mu$\, called the balanced measure. It
is supported on the Julia set for $f$ and satisfies $f*\\mu=d \\cdot \\m
u$. Since it also can be obtained as the limit of preimages of quite gene
ral probabilistic measures on $\\mathbb{CP}^1$ (thanks to the results of M
. Lyubich and independently Freire-Lopes-R. Ma\\~ne from 1980s)\, a questi
on arises whether it always equals the equilibrium measure for $J_f$ (when
the latter notion makes sense). Several mathematicians noticed that equa
lity of these two measures (under suitable assumptions on $f$) implies tha
t $f$ is a polynomial. However\, all ``proofs'' of this implication from
before 1990s contained gaps. The proof by S. Lalley from 1992 was fully
successful\, but it was based on the theory of Brownian motions. In this
talk\, I will present a general version of this implication with a proo
f using mainly classical and weighted potential theory: Let $f: \\mathbb{
CP}^1 \\to \\mathbb{CP}^1$ be a rational function of degree $d \\geq 2$ wh
ose Julia set does not contain the point $\\infty$. The following are equi
valent: (i) $f \\circ f$ is a polynomial\; (ii) the balanced measure for $
f$ and the equilibrium measure for the Julia set $J_f$ with pole at infi
nity are equal. This is joint work with Y\\^usuke Okuyama from Kyoto Inst
itute of Technology.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Khavinson (University of South Florida)
DTSTART:20210518T130000Z
DTEND:20210518T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/41
DESCRIPTION:Title: Algebra and PDE : Some Less Traveled Paths Connecting Them\nby
Dmitry Khavinson (University of South Florida) as part of CAvid: Complex A
nalysis video seminar\n\nLecture held in N/A.\n\nAbstract\nHere are sample
s of questions I plan to discuss.\n\n- Let $F(u\,v)$ be a rational functio
n of two variables that has no linear factors and a meromorphic function $
u(x\,y)$ solves the PDE $F(\\nabla u)=0$ near the origin\, say. Then $u$ i
s a linear function\, i.e.\, $u=ax+by+c$. Why? Is it true in three variab
les?\n\n- Does there exist a harmonic polynomial in $\\mathbb{R}^n$ divisi
ble by a non-negative polynomial?\n\n- Let $P(D)[u^k]=0$\, where $P(D)$ is
a partial differential operator with constant\, polynomial \, or even ent
ire coefficients and k runs over an arithmetic progression of positive int
egers\, e. g.\, $k=2n+3$\, $n=1\,2\,\\ldots$. Then the Hessian\, Hess $u$
\, vanishes identically\, so the mapping grad $u:\\\, \\mathbb{C}^n\\mapst
o\\mathbb{C^n}$ is degenerate\, i.e.\, the range is an algebraic variety.
Is it true? \n\n- When we are solving the Dirichlet problem in a domain wi
th an algebraic boundary\, and the Dirichlet data is a polynomial\, a rati
onal or an algebraic function\, is the solution algebraic as well?\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Chuaqui Farrú (Pontificia Universidad Católica de Chile)
DTSTART:20210601T130000Z
DTEND:20210601T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/42
DESCRIPTION:Title: Ahlfors’ Schwarzians for curves\nby Martin Chuaqui Farrú (Pon
tificia Universidad Católica de Chile) as part of CAvid: Complex Analysis
video seminar\n\nLecture held in N/A.\n\nAbstract\nWe discuss Ahlfors' Sc
hwarzian derivatives for curves in euclidean space introduced some three d
ecades ago. The definitions consider separate generalizations of the real
and imaginary part of the classical operator in the complex plane that hav
e important invariance properties with respect to the Möbius group in euc
lidean n-space. We will describe some of the applications of the real Sch
warzian to the study of simple curves in n-space\, to knots in 3-space\, a
s well as to the injectivity of the conformal parametrization of minimal s
urfaces in 3-space. The role of the imaginary Schwarzian will be presented
in euclidean 3-space\, highlighting its connection with the osculating sp
here\, a new transformation law under the Möbius group\, and theorems on
the existence and uniqueness of parametrized curves with prescribed real a
nd imaginary Schwarzians.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasiliki Evdoridou (Open University\, UK)
DTSTART:20210608T130000Z
DTEND:20210608T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/43
DESCRIPTION:Title: Wandering on the boundary\nby Vasiliki Evdoridou (Open Universit
y\, UK) as part of CAvid: Complex Analysis video seminar\n\nLecture held i
n N/A.\n\nAbstract\nIn the theory of iteration of transcendental entire fu
nctions\, wandering domains\, i.e. connected components of the Fatou set t
hat are not eventually periodic\, have been extensively studied in recent
years. For example\, a nine-way classification of the internal dynamics in
simply connected wandering domains has been given. In this talk we focus
on the dynamical behaviour on the boundaries of simply connected wandering
domains. In particular\, we consider the possibility that most boundary o
rbits converge together in a certain sense\, and give sufficient condition
s for such a convergence to hold. Our results are motivated by and extend
classical results on the boundary dynamics of inner functions.\n\nThis is
work in progress joint with A.M. Benini\, N. Fagella\, P. Rippon and G. St
allard.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Galina Filipuk (University of Warsaw)
DTSTART:20210615T130000Z
DTEND:20210615T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/44
DESCRIPTION:Title: Aspects of nonlinear differential equations\nby Galina Filipuk (
University of Warsaw) as part of CAvid: Complex Analysis video seminar\n\n
Lecture held in N/A.\n\nAbstract\nNonlinear differential equations may hav
e complicated singularities in the\ncomplex plane. Painleve equations are
nonlinear second order differential\nequations solutions of which have no
movable critical points. They have a\nlot of nice properties.\n\nIn this t
alk I shall mainly review connection between solutions of the \nPainlev\\
'e equations and recurrence coefficients of semi-classical\northogonal p
olynomials.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jujie Wu (Sun Yat-Sen University)
DTSTART:20210622T130000Z
DTEND:20210622T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/45
DESCRIPTION:Title: Weighted L^2 polynomial approximation in C\nby Jujie Wu (Sun Yat
-Sen University) as part of CAvid: Complex Analysis video seminar\n\nLectu
re held in N/A.\n\nAbstract\nWe study the density of polynomials in $H^2(\
\Omega\, \\varphi)$\, the space of square integrable holomorphic functions
in a bounded domain $\\Omega$ in $\\C$\, where $\\varphi$ is a subharmoni
c function. In particular\, we prove that the density holds in Caratheodo
ry domains for any subharmonic function $\\varphi$ in a neighborhood of th
e closure of $\\Omega$. In non-Caratheodory domains\, we prove that the de
nsity depends on the weight function\, giving examples. We also give a wei
ghted $L^2$ version of Weierstrass theorem and give the example. Some $L^2
$ approximation in higher dimension also will be state here\, which part a
re in progress now.\n\nThis is joint with Severine Biard and John Erik For
naess.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walter Van Assche (KU Leuven)
DTSTART:20210706T130000Z
DTEND:20210706T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/46
DESCRIPTION:Title: Hermite-Padé approximation to two function with branch points\n
by Walter Van Assche (KU Leuven) as part of CAvid: Complex Analysis video
seminar\n\nLecture held in N/A.\n\nAbstract\nHermite-Padé approximation t
o two functions is rational approximation to both functions with a common
denominator and close contact at one point (we will use infinity). The com
mon denominator is a polynomial with orthogonality conditions for two meas
ures. If the two functions have branch points in the complex plane\, then
the asymptotic behaviour of the zeros (the poles of the Hermite-Padé appr
oximants) is determined by algebraic functions satisfying a cubic relation
.\nWe will sketch how to get the full asymptotics of the common denominato
r using the Riemann-Hilbert problem for matrix valued functions for some p
articular choices of branch points\, which appear in applications in numbe
r theory.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Bishop (Stony Brook University\, USA)
DTSTART:20210914T130000Z
DTEND:20210914T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/47
DESCRIPTION:Title: Fast conformal mapping via computational and hyperbolic geometry
\nby Chris Bishop (Stony Brook University\, USA) as part of CAvid: Complex
Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nThe conformal
map from the unit disk to the interior of a polygon P is given by the Sch
warz-Christoffel formula\, but this is stated in terms of parameters that
are hard to compute from P. After some background and motivation\, I expla
in how the medial axis of a domain\, a concept from computational geometry
\, can be used to give a fast approximation to these parameters\, with bou
nds on the accuracy that are independent of P. The precise statement invol
ves quasiconformal mappings\, and proving these bounds uses a result about
hyperbolic convex sets originating in Thurston's work on 3-manifolds. If
time permits\, I will mention some applications to optimal meshing and t
riangulation of planar polygons.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirill Lazebnik (University of Toronto\, Canada)
DTSTART:20210921T130000Z
DTEND:20210921T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/48
DESCRIPTION:Title: Transcendental Julia Sets of Minimal Hausdorff Dimension\nby Kir
ill Lazebnik (University of Toronto\, Canada) as part of CAvid: Complex An
alysis video seminar\n\nLecture held in N/A.\n\nAbstract\nWe discuss an ap
proach to the construction of entire functions with Julia sets having mini
mal Hausdorff dimension. This talk will not assume a background in complex
dynamics. This talk is based on joint work with Jack Burkart.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilin Wang (MIT\, USA)
DTSTART:20210928T130000Z
DTEND:20210928T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/49
DESCRIPTION:Title: Loewner-Kufarev energy and foliations by Weil-Petersson quasicircles
\nby Yilin Wang (MIT\, USA) as part of CAvid: Complex Analysis video s
eminar\n\nLecture held in N/A.\n\nAbstract\nWe use Loewner-Kufarev equatio
n to describe evolutions of univalent functions and introduce an energy on
the driving measure\, called Loewner-Kufarev energy. We show that when th
is energy is finite\, the boundaries of the evolving image domains are Wei
l-Petersson quasicircles which form a foliation of the Riemann sphere. Wei
l-Petersson quasicircles are studied in Teichmuller theory\, geometric fun
ction theory\, and string theory by both mathematicians and physicists. Mo
re than 20 equivalent definitions of this class of Jordan curves are disco
vered so far. In particular\, it is characterized as the class of curves h
aving finite Loewner energy which was also introduced recently. Furthermor
e\, we show that the Loewner-Kufarev energy is dual to the Loewner energy
and exhibits remarkable symmetries. Both energies and their duality result
are inspired by ideas from the probabilistic theory of Schramm-Loewner ev
olutions. This is a joint work with Fredrik Viklund (KTH).\n\nReferences:
\n\nThe Loewner-Kufarev energy and foliations by Weil-Petersson quasicircl
es\nFredrik Viklund\, Yilin Wang (2020)\nhttps://arxiv.org/abs/2012.05771\
n
LOCATION:https://stable.researchseminars.org/talk/CAvid/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Istvan Prause (University of Eastern Finland)
DTSTART:20211005T130000Z
DTEND:20211005T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/50
DESCRIPTION:Title: Probabilistic limit shapes and harmonic functions\nby Istvan Pra
use (University of Eastern Finland) as part of CAvid: Complex Analysis vid
eo seminar\n\nLecture held in N/A.\n\nAbstract\nLimit shapes are surfaces
in $\\mathbb{R^3}$ which arise in the scaling limit of discrete random sur
faces associated to various probability models such as domino tilings\, ra
ndom Young tableaux or the 5-vertex model. The limit surface is a minimise
r of a gradient variational problem with a surface tension which encodes t
he local entropy of the model. I'll show that in an intrinsic complex vari
able these limit shapes can all be parametrised by harmonic functions acro
ss a variety of models. Some new features beyond determinantal settings wi
ll be discussed. The talk is based on joint works with Rick Kenyon.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jörg Winkelmann (Ruhr-Universität Bochum\, Germany)
DTSTART:20211012T130000Z
DTEND:20211012T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/51
DESCRIPTION:Title: On the existence of dense entire holomorphic curves in rationally co
nnected manifolds\nby Jörg Winkelmann (Ruhr-Universität Bochum\, Ger
many) as part of CAvid: Complex Analysis video seminar\n\nLecture held in
N/A.\n\nAbstract\nJoint work with Frederic Campana. We prove that for ever
y rationally connected\nprojective manifold X there exists a holomorphic m
ap from the complex line to X with\ndense image and deduce some related re
sults.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhi-Tao Wen (Shantou University\, China)
DTSTART:20211019T130000Z
DTEND:20211019T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/52
DESCRIPTION:Title: Difference radical in terms of shifting zero and applications to the
Stothers-Mason theorem\nby Zhi-Tao Wen (Shantou University\, China) a
s part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\
nAbstract\nIn this talk\, we show the shifting zeros with its heights and
an analogue to difference radical. We focus on the Stothers-Mason theorem
by using falling factorials. As applications\, we discuss the difference v
ersion of the Fermat type functional equations. Some examples are given. I
t is a joint work with Katsuya Ishizaki.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zeinab Mansour (Cairo University\, Egypt)
DTSTART:20211026T130000Z
DTEND:20211026T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/53
DESCRIPTION:Title: Lidstone expansions of entire functions\nby Zeinab Mansour (Cair
o University\, Egypt) as part of CAvid: Complex Analysis video seminar\n\n
Lecture held in N/A.\n\nAbstract\nLidstone expansions express an entire fu
nction $f(z)$ in terms of the values of the derivatives of even orders at
$0\,1$. The polynomials in the expansion are called Lidstone polynomials.
They are Bernoulli polynomials\; many authors introduced necessary and (or
) sufficient conditions for the absolute convergence of the series in the
expansion. The classical exponential function plays an essential role in
deriving the Lidstone series. In the $q$ theory\, we have three $q$-differ
ence operators\, the Jackson $q$-difference operator\, the symmetric $q$-d
ifference operator\, and the Askey-Wilson $q$-difference operator. Each op
erator is associated with a $q$-analog of the exponential function. In thi
s talk\, we introduce $q$-extensions to the Lidstone expansion associated
with these operators. New three $q$-analogs of Bernoulli polynomials with
nice properties are coming out. \n\nJoint work with Professor Mourad Ismai
l\, University of Central Florida\, USA.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leticia Pardo-Simón (University of Manchester\, UK)
DTSTART:20211102T130000Z
DTEND:20211102T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/54
DESCRIPTION:Title: The maximum modulus set of an entire function\nby Leticia Pardo-
Simón (University of Manchester\, UK) as part of CAvid: Complex Analysis
video seminar\n\nLecture held in N/A.\n\nAbstract\nThe set of points where
an entire function achieves its maximum modulus is known as the maximum m
odulus set\, and usually consists of a collection of disjoint analytic cur
ves. In this talk\, we discuss recent progress on the description of the f
eatures that this set might exhibit. Namely\, on the existence of disconti
nuities\, singleton components\, and on its structure near the origin. Thi
s is based on joint work with D. Sixsmith and V. Evdoridou.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Mityushev (Cracow Technological University\, Poland)
DTSTART:20211109T140000Z
DTEND:20211109T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/55
DESCRIPTION:Title: Riemann-Hilbert problem for a multiply connected domain and its appl
ications to the effective properties of 2D random composites\nby Vladi
mir Mityushev (Cracow Technological University\, Poland) as part of CAvid:
Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nIn th
is talk we answer the following question. "Why did James Bond prefer shake
n\, not stirred martini with ice?" The posed question is resolved by reduc
tion to the scalar Riemann-Hilbert problem Re (a f) = g for a multiply con
nected domain and its complete solution. Relations to the ℝ-linear probl
em and the effective properties of 2D random composites are discussed.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter A. Clarkson (University of Kent\, UK)
DTSTART:20211116T140000Z
DTEND:20211116T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/56
DESCRIPTION:Title: Special polynomials associated with the Painlevá equations\nby
Peter A. Clarkson (University of Kent\, UK) as part of CAvid: Complex Anal
ysis video seminar\n\nLecture held in N/A.\n\nAbstract\nThe six Painlevé
equations\, whose solutions are called the Painlevé transcendents\, were
derived by Painlevé and his colleagues in the late 19th and early 20th ce
nturies in a classification of second order ordinary differential equation
s whose solutions have no movable critical points. In the 18th and 19th ce
nturies\, the classical special functions such as Bessel\, Airy\, Legendre
and hypergeometric functions\, were recognized and developed in response
to the problems of the day in electromagnetism\, acoustics\, hydrodynamics
\, elasticity and many other areas. \n\nAround the middle of the 20th cent
ury\, as science and engineering continued to expand in new directions\, a
new class of functions\, the Painlevé functions\, started to appear in a
pplications. The list of problems now known to be described by the Painlev
é equations is large\, varied and expanding rapidly. The list includes\,
at one end\, the scattering of neutrons off heavy nuclei\, and at the othe
r\, the distribution of the zeros of the Riemann-zeta function on the crit
ical line Re(z) =1/2. Amongst many others\, there is random matrix theory\
, the asymptotic theory of orthogonal polynomials\, self-similar solutions
of integrable equations\, combinatorial problems such as the longest incr
easing subsequence problem\, tiling problems\, multivariate statistics in
the important asymptotic regime where the number of variables and the numb
er of samples are comparable and large\, and also random growth problems.\
n\nThe Painlevé equations possess a plethora of interesting properties in
cluding a Hamiltonian structure and associated isomonodromy problems\, whi
ch express the Painlevé equations as the compatibility condition of two l
inear systems. Solutions of the Painlevé equations have some interesting
asymptotics which are useful in applications. They possess hierarchies of
rational solutions and one-parameter families of solutions expressible in
terms of the classical special functions\, for special values of the param
eters. Further the Painlevé equations admit symmetries under affine Weyl
groups which are related to the associated Bäcklund transformations. \n\n
In this talk I shall discuss special polynomials associated with rational
solutions of Painlevé equations. Although the general solutions of the si
x Painlevé equations are transcendental\, all except the first Painlevé
equation possess rational solutions for certain values of the parameters.
These solutions are expressed in terms of special polynomials. The roots o
f these special polynomials are highly symmetric in the complex plane and
speculated to be of interest to number theorists. The polynomials arise in
applications such as random matrix theory\, vortex dynamics\, in the desc
ription of rogue wave patterns\, in supersymmetric quantum mechanics\, as
coefficients of recurrence relations for semi-classical orthogonal polynom
ials and are examples of exceptional orthogonal polynomials.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thierry Meyrath (University of Luxembourg\, Luxembourg)
DTSTART:20211123T140000Z
DTEND:20211123T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/57
DESCRIPTION:Title: On covering properties of non-normal families of meromorphic functio
ns\nby Thierry Meyrath (University of Luxembourg\, Luxembourg) as part
of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstr
act\nWe study the behaviour of families of meromorphic functions in the ne
ighbourhood of points of non-normality and prove certain covering properti
es that complement Montel's Theorem. Moreover\, we obtain characterization
s of non-normality in terms of such properties. This talk is based on join
t work with Jürgen Müller.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olubunmi A. Fadipe-Joseph (University of Ilorin\, Nigeria)
DTSTART:20211130T140000Z
DTEND:20211130T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/58
DESCRIPTION:Title: The sigmoid function in geometric function theory\nby Olubunmi A
. Fadipe-Joseph (University of Ilorin\, Nigeria) as part of CAvid: Complex
Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nGeometric Fun
ction Theory (GFT) is a branch of complex analysis which studies geometric
properties of analytic functions. Moreover\, in spite of the famous coeff
icient problems\, Bieberbach conjecture that was solved by Louis de Brange
s in 1984 suggested various approaches and directions for study in geometr
ic function theory. Therefore\, one of the major interests in GFT is find
ing the coefficient bounds of univalent and multivalent functions. The bou
nds determine the growth\, distortion properties among others of the analy
tic functions. Special functions are of great interest in mathematics\, ma
thematical\nphysics\, engineering and other fields of science. They are ri
ch in terms of practical applications in solving a wide range of\nproblems
. Recently\, we investigate special functions in geometric function theory
. In particular\, the connection between sigmoid function and geometric fu
nction theory was established.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loredana Lanzani (Syracuse University\, USA)
DTSTART:20211207T140000Z
DTEND:20211207T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/59
DESCRIPTION:Title: The Cauchy-Szegö projection and its commutator for domains in $\\ma
thbb C^n$ with minimal smoothness\nby Loredana Lanzani (Syracuse Unive
rsity\, USA) as part of CAvid: Complex Analysis video seminar\n\nLecture h
eld in N/A.\n\nAbstract\nLet $D\\subset\\C^n$ be a bounded\, strongly pseu
doconvex domain whose boundary $bD$ satisfies the minimal regularity condi
tion of class $C^2$. A 2017 result of Lanzani and Stein states that \nthe
Cauchy-Szegö projection $S_\\omega$ defined with respect to any Leray Le
vi-like measure $\\omega$ is bounded in $L^p(bD\, \\omega)$ for any $1 < p
< \\infty$.\n(For this class of domains\, induced Lebesgue measure is Le
ray Levi-like.)\n Here we show that $S_\\omega$\n is in fact bounded in
$L^p(bD\, \\Omega_p)$ for any $1 < p< \\infty$ and for any $\\Omega_p$ in
the optimal\n class\n of $A_p$ measures\, that is $\\Omega_p = \\psi_p\
\sigma$ where $\\sigma$ is induced Lebesgue measure and $\\psi_p$ is any M
uckenhoupt $A_p$-weight.\n As an application\, we\n characterize bounded
ness and compactness in $L^p(bD\, \\Omega_p)$ for any $1 < p < \\infty$ a
nd for any $A_p$ measure $\\Omega_p$\, of the commutator $[b\, S_p]$ for a
ny Leray Levi-like measure $\\omega$. \n We next introduce the notion of
holomorphic Hardy spaces for $A_p$ measures\,\n $1 < p < \\infty$\, \n
and \n we characterize\n boundedness and compactness in $L^2(bD\, \\Omeg
a_2)$ of the commutator \n $\\displaystyle{[b\,S_{\\Omega_2}]}$ of the Cau
chy-Szegö projection defined with respect to any \n $A_2$ measure $\\Omeg
a_2$.\n Earlier closely related results \n rely upon an asymptotic expans
ion\, and subsequent pointwise estimates\, of the Cauchy-Szegö kernel\, b
ut these are unavailable in the settings of minimal regularity {of $bD$} a
nd/or $A_p$ measures\; it turns out that the real harmonic analysis method
of extrapolation is an appropriate replacement for the missing tools.\n\n
\nThis is joint work with Xuan Thinh Duong (Macquarie University)\, Ji L
i (Macquarie University) and Brett Wick (Washington University in St. Loui
s).\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adri Olde Daalhuis (University of Edinburgh\, UK)
DTSTART:20211214T140000Z
DTEND:20211214T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/60
DESCRIPTION:Title: Asymptotics and complex analysis\nby Adri Olde Daalhuis (Univers
ity of Edinburgh\, UK) as part of CAvid: Complex Analysis video seminar\n\
nLecture held in N/A.\n\nAbstract\nI will discuss the tools from complex a
nalysis that are needed in the study of (uniform) asymptotic expansions\no
f special functions. For many of these divergent expansions it is possible
to construct very efficient\nintegral representations for the coefficient
s and remainders\, and these are needed in implementations\nand sharp erro
r-bounds. I might also discuss exponential asymptotics of the perturbed fi
rst Painlevé equation.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Miller (University of Michigan)
DTSTART:20220111T140000Z
DTEND:20220111T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/61
DESCRIPTION:Title: Rational solutions of the Painlevé-IV equation with large parameter
s\nby Peter Miller (University of Michigan) as part of CAvid: Complex
Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nThe Painlevé-
IV equation has two families of rational solutions\, which can be represen
ted in terms of special polynomials called generalized Hermite polynomials
and generalized Okamoto polynomials\, respectively. The generalized Herm
ite polynomials have a convenient representation in terms of Hankel determ
inants for a suitable weight and hence can be identified with norming cons
tants for certain pseudo-orthogonal polynomials. This connection provides
a path to the analysis of the generalized Hermite rationals when the para
meters are large\; however it is not known whether the generalized Okamoto
polynomials have a similar representation. In this talk\, we explain how
the isomonodromic approach places both families of rational solutions in
terms of special cases of the Riemann-Hilbert inverse monodromy problem fo
r Painlevé-IV. This allows techniques from steepest descent theory to be
used to analyze both families of rational solutions within a common analy
tical framework. This is joint work with Robert Buckingham.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Miriam Benini (Università di Parma)
DTSTART:20220118T140000Z
DTEND:20220118T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/62
DESCRIPTION:Title: Bifurcations arise when there is a drastic change in the solutions o
f some equation depending on a parameter\, as the parameter\nby Anna M
iriam Benini (Università di Parma) as part of CAvid: Complex Analysis vid
eo seminar\n\nLecture held in N/A.\n\nAbstract\nBifurcations arise when th
ere is a drastic change in the solutions of some equation depending on a p
arameter\, as the parameter varies.\nIn this talk we study bifurcations in
holomorphic families of meromorphic maps with finitely many singular val
ues. The equation(s) that we will study are the equations defining periodi
c points of period n. Such equations are crucial in complex dynamics becau
se the Julia set (the set on which the dynamics is chaotic) is the closure
of repelling periodic points. The celebrated results by Mane-Sad-Sullivan
for families of rational maps (and independently by Lyubich\, and by Levi
n for polynomials) show that in a set of parameters where no bifurcation
s of periodic points occur\, the Julia set stays almost the same and so do
es the dynamics\; precisely speaking\, all maps are topologically conjuga
te in such set. Moreover\, they establish a precise correlation between
bifurcations of periodic points and a change of behaviour in the orbits of
singular values.\nThe key new feature that appears for families of mero
morphic maps is that periodic points can disappear at infinity at specifi
c parameters\, creating a new type of bifurcations. Our work connects this
new type of bifurcations with change of behaviour in singular orbits\, to
establish Mane-Sad-Sullivan's Theorem for meromorphic maps.\nThis is jo
int work with Matthieu Astorg and Nùria Fagella.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alastair Fletcher (Northern Illinois University)
DTSTART:20220201T140000Z
DTEND:20220201T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/63
DESCRIPTION:Title: Cantor sets and Julia sets\nby Alastair Fletcher (Northern Illin
ois University) as part of CAvid: Complex Analysis video seminar\n\nLectur
e held in N/A.\n\nAbstract\nOne does not have to study much complex dynami
cs before coming across examples of Julia sets which are Cantor sets. It i
s then a natural question to ask which Cantor sets can be Julia sets? The
rigidity of holomorphic maps precludes certain natural examples\, and so w
e will ask this question in the context of uniformly quasiregular mappings
with a focus on dimensions two and three. This talk is based on joint wor
k with Dan Stoertz and Vyron Vellis.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joan Lind (University of Tennessee)
DTSTART:20220208T140000Z
DTEND:20220208T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/64
DESCRIPTION:Title: The Loewner equation with complex-valued driving functions\nby J
oan Lind (University of Tennessee) as part of CAvid: Complex Analysis vide
o seminar\n\nLecture held in N/A.\n\nAbstract\nThe chordal Loewner equatio
n provides a correspondence between real-valued functions\, called driving
functions\, and certain growing 2-dimensional sets\, called hulls. In th
is talk\, we will consider the generalization to complex-valued driving fu
nctions\, which was first studied by Huy Tran. We will discuss some key d
ifferences between the hulls in the complex-valued setting and those in th
e real-valued setting\, including the question of the phase transition fro
m simple-curve hulls. This is joint work with Jeffrey Utley.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathy Driver (University of Cape Town)
DTSTART:20220215T140000Z
DTEND:20220215T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/65
DESCRIPTION:Title: Interlacing of zeros of Laguerre polynomials\nby Kathy Driver (U
niversity of Cape Town) as part of CAvid: Complex Analysis video seminar\n
\nLecture held in N/A.\n\nAbstract\nThe sequence of Laguerre polynomials $
\\{L_{n}^{(\\alpha)}(x)\\} _{n=0}^\\infty$ is orthogonal on $(0\, \\infty)
$ with respect to the weight function $e^{-x} x^{\\alpha}\,\\alpha > -1$ a
nd the real distinct positive zeros of $L_{n-1}^{(\\alpha)}(x)$ and $L_{n}
^{(\\alpha)}(x)$ are interlacing for $\\alpha >-1\, n \\geq 2.$ D-Muldoo
n (2015-2019) proved that for $\\alpha >-1\,$ the zeros of $L_{n-1}^{(\\a
lpha+t)}(x)$ and $L_{n}^{(\\alpha)}(x)$ are interlacing for $0 \\leq t \\
leq 2\; $ the zeros of the equal degree Laguerre polynomials $L_{n}^{(\\a
lpha)}(x)$ and $L_{n}^{(\\alpha+t)}(x)$ interlace for $0 < t \\leq 2$\,
and the interval $0 \\leq t \\leq 2$ is sharp for interlacing to hold for
every $n \\in \\mathbb{N}$. Further\, the zeros of $L_{n-k}^{(\\alpha+t)}(
x)$ and $L_{n}^{(\\alpha)}(x)$ are interlacing (in the Stieltjes sense) f
or $0 \\leq t \\leq 2k$\, $1 < k < n$ and the interval $0 \\leq t \\leq 2k
$ is sharp. \nAt OPSFA 2019\, Alan Sokal: What happens to interlacing of r
oots if you increase parameter and increase degree of one polynomial relat
ive to the other? Simplest case: Are the zeros of $L_{n}^{(\\alpha)}(x)$
and $L_{n+1}^{(\\alpha+1)}(x)$ interlacing for $\\alpha > -1$ and each $n
\\in \\mathbb{N}$? We discuss this and related cases.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Si Duc Quang (Hanoi National University of Education)
DTSTART:20220222T140000Z
DTEND:20220222T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/66
DESCRIPTION:Title: Second main theorems for meromorphic mappings into projective variet
ies and arbitrary families of hypersurfaces\nby Si Duc Quang (Hanoi Na
tional University of Education) as part of CAvid: Complex Analysis video s
eminar\n\nLecture held in N/A.\n\nAbstract\nIn this talk\, we will give a
short introduction to Nevanlinna theory for meromorphic mappings into proj
ective varieties. Our main aim is to present a second main theorem for mer
omorphic mappings with arbitrary families of hypersurfaces in projective v
arieties. This result is a generalization of the second main theorem for t
he mappings with families of hypersurfaces in subgeneral position.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Nicks (University of Nottingham)
DTSTART:20220308T140000Z
DTEND:20220308T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/67
DESCRIPTION:Title: Iterating the minimum modulus\nby Dan Nicks (University of Notti
ngham) as part of CAvid: Complex Analysis video seminar\n\nLecture held in
N/A.\n\nAbstract\nFor an entire function $f$ there may or may not exist a
n $r > 0$ such that the iterated minimum modulus $m^n(r)$ tends to infinit
y. Here $m(r) = m(r\,f) = \\min\\{ |f(z)| : |z|=r \\}$. Focussing mainly o
n the class of real transcendental entire functions of finite order with o
nly real zeroes\, we discuss some results about the existence of an $r > 0
$ such that $m^n(r) \\to \\infty$. This is motivated by the result that\,
for functions in this class\, the existence of such an r implies connected
ness of the escaping set $\\{ z : f^n(z) \\to \\infty \\}$.\n\nThis is joi
nt work with Phil Rippon and Gwyneth Stallard.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lasse Rempe (University of Liverpool)
DTSTART:20220315T140000Z
DTEND:20220315T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/68
DESCRIPTION:Title: A counterexample to Eremenko's Conjecture\nby Lasse Rempe (Unive
rsity of Liverpool) as part of CAvid: Complex Analysis video seminar\n\nLe
cture held in N/A.\n\nAbstract\nI shall speak within my lecture\n\nabout a
n interesting conjecture\n\nof Eremenko from a fine \n\npaper of 1989.\n\n
>>>\n\nHe asked if each escaping point\n\ncan to infinity be joined\n\nusi
ng a connected shape\n\nall points of which themselves escape.\n\n>>>\n\nA
lthough quite simple it appears\,\n\nthis question has for many years\n\nc
aused me and others some despair\,\n\nsleepless nights and greying hair.\n
\n>>>\n\nThrough our intense investigation\n\nof transcendental iteration\
,\n\nmuch progress was indeed obtained\,\n\nbut the conjecture\, it remain
ed - \n\n>>>\n\ntill now! By work with Waterman\n\nand Martí-Pete\, now I
can\n\ndescribe to you\, within my lecture\,\n\na counterexample to Ereme
nko's Conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duc Quang Si (Hanoi National University of Education)
DTSTART:20220322T130000Z
DTEND:20220322T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/69
DESCRIPTION:by Duc Quang Si (Hanoi National University of Education) as pa
rt of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\nAbstr
act: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rajitha Ranasinghe (University of Peradeniya\, Sri Lanka)
DTSTART:20220329T130000Z
DTEND:20220329T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/70
DESCRIPTION:by Rajitha Ranasinghe (University of Peradeniya\, Sri Lanka) a
s part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\nA
bstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adi Glücksam (Northwestern University)
DTSTART:20220405T130000Z
DTEND:20220405T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/71
DESCRIPTION:Title: The Combinatorial Method for Stopping Time Arguments\nby Adi Gl
ücksam (Northwestern University) as part of CAvid: Complex Analysis video
seminar\n\nLecture held in N/A.\n\nAbstract\nIn this talk I will present
a refinement of the combinatorial technique used by Jones and Makarov in '
95. This method can be used for stopping time arguments in different setti
ngs. I will describe the method\, and present two applications that were a
lready known\, and one new application. Moreover\, I will give an example
showing this method is optimel. Lastly\, I will discuss future directions
and open problems.\n\nThe talk is based on work in progress.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Marti-Pete (University of Liverpool)
DTSTART:20220426T130000Z
DTEND:20220426T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/72
DESCRIPTION:Title: Wandering domains in transcendental dynamics: topology and dynamics<
/a>\nby David Marti-Pete (University of Liverpool) as part of CAvid: Compl
ex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nFor a trans
cendental entire or meromorphic function\, the Fatou set is the largest op
en set on which its iterates are defined and form a normal family. A wande
ring domain is a connected component of the Fatou set which is not eventua
lly periodic. The first example of a transcendental entire function with a
wandering domain was constructed by Baker in the 1970s. \n\nWandering dom
ains\, which do not exist for rational maps\, play an important role in tr
anscendental dynamics and in the last decade there has been a resurgence i
n their interest. For example\, Bishop proved that the Julia sets of trans
cendental entire functions can have Hausdorff dimension 1 by constructing
a function with wandering domains. \n\nWandering domains are very diverse
in terms of both their topology (simply connected or multiply connected) a
nd their dynamics (escaping\, oscillating or\, perhaps\, even have bounded
orbit). Recently\, Boc Thaler proved the surprising result that every bou
nded regular domain such that its closure has a connected complement is th
e wandering domain of some transcendental entire function. Inspired by thi
s result\, together with Rempe and Waterman\, we were able to obtain wande
ring domains that form Lakes of Wada. \n\nIn this talk\, I will describe t
he main topological and dynamical properties of wandering domains (and the
ir boundaries) and give an overview of the current open questions.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Girela (Universidad de Málaga)
DTSTART:20220503T130000Z
DTEND:20220503T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/73
DESCRIPTION:Title: On BMOA and the Bloch space\, normal functions\, and pointwise multi
pliers\nby Daniel Girela (Universidad de Málaga) as part of CAvid: Co
mplex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nLet $\\m
athbb D$ be the unit disc in $\\mathbb C$ and let ${\\rm Hol} (\\mathbb D)
$ denote the space of all holomorphic functions in $\\mathbb D$. In this t
alk we shall be concerned with a number of subspaces of ${\\rm Hol}(\\math
bb D)$\, especially with the space $H^\\infty $ of all bounded analytic fu
nctions in $\\mathbb D$\, the space $BMOA$ which consists of those $f\\in
H^1$ whose boundary values have bounded mean oscillation on $\\partial \\m
athbb D$\, and the Bloch space $\\mathcal B$ which consists of those $f\\i
n{\\rm Hol} (\\mathbb D)$ for which $$\\sup_{z\\in \\mathbb D}(1-\\vert z\
\vert ^2)\\vert f^\\prime (z)\\vert <\\infty .$$ It is well known that $H^
\\infty \\subset BMOA\\subset \\mathcal B$\, and that these inclusions are
strict. \\par A function $f$\, analytic in $\\mathbb D$\, is a normal fun
ction (in the sense of Lehto-Virtanen) if $$\\sup_{z\\in \\mathbb D}(1-\\v
ert z\\vert ^2)\\frac{\\vert f^\\prime (z)\\vert }{1+\\vert f(z)\\vert ^2}
<\\infty .$$ We shall let $\\mathcal N$ denote the class of all normal ana
lytic functions in $\\mathbb D$. We have that $\\mathcal B\\subset \\mathc
al N$ and the inclusion is strict. In fact\, the class $\\mathcal N$ is mu
ch bigger that the Bloch space. \\par Clearly\, $H^\\infty $ is an algebra
\, that is\, the product of two $H^\\infty $-functions lies in $H^\\infty
$. However\, if $f\\in H^\\infty $ and $g$ is a $BMOA$ function or a Bloch
function\, then the product $g\\cdot f$ may not be a normal function: the
re exist pairs of functions $(f\, g)$ with $f\\in H^\\infty $ and $g\\in \
\mathcal B$ such that the product $f\\cdot g$ is not a normal function (or
at least it is not a Bloch function). In this talk we shall present disti
nct examples of such pairs of functions starting with the first ones which
were given in the 1960's and finishing with other which have been recentl
y obtained. We shall reformulate these results in the language of pointwis
e multipliers.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irina Markina (University of Bergen)
DTSTART:20220510T130000Z
DTEND:20220510T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/74
DESCRIPTION:by Irina Markina (University of Bergen) as part of CAvid: Comp
lex Analysis video seminar\n\nLecture held in N/A.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Baddoo (MIT)
DTSTART:20220517T130000Z
DTEND:20220517T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/75
DESCRIPTION:Title: Understanding interacting aerofoils with complex analysis\nby Pe
ter Baddoo (MIT) as part of CAvid: Complex Analysis video seminar\n\nLectu
re held in N/A.\n\nAbstract\nWhen two or more aerofoils move together\, th
eir interactions can significantly affect the characteristics of the surro
unding fluid. We develop a rigorous mathematical theory for these interact
ions using conformal maps\, multiply connected function theory\, and modif
ied Schwarz problems. Via the transcendental Schottky–Klein prime functi
on\, our theory is valid for any connectivity (any number of aerofoils). A
ccordingly\, our approach is very general and permits many aerofoil motion
s (pitching\, heaving\, undulatory) and configurations (tandem\, in-line\,
ground effect). We focus on the (doubly connected) case where there are t
wo interacting swimmers and find that our theory yields excellent agreemen
t with experimental data. We also develop an asymptotic solution that capt
ures the salient features of the prime function solution.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Barnard (Texas Tech University)
DTSTART:20220524T130000Z
DTEND:20220524T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/76
DESCRIPTION:Title: On sharp bounds for ratios of k-balanced hypergeometric functions\nby Roger Barnard (Texas Tech University) as part of CAvid: Complex Anal
ysis video seminar\n\nLecture held in N/A.\n\nAbstract\n(Joint work with K
endall C. Richards\, Southwestern University and Elyssa N. Sliheet\, South
western Methodist University)\n\nIn this talk we begin with a brief histor
y of how the authors’ research\, originally in Geometric Function Theory
\, developed into applications of Special Function Theory to a variety of
fields\, giving examples. Then we discuss one of our latest results in Spe
cial Function Theory i.e. determining the sharp bounds for ratios of k-bal
anced hypergeometric functions.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clare Dunning (University of Canterbury at Kent)
DTSTART:20220531T130000Z
DTEND:20220531T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/77
DESCRIPTION:Title: Polynomials and partitions\nby Clare Dunning (University of Cant
erbury at Kent) as part of CAvid: Complex Analysis video seminar\n\nLectur
e held in N/A.\n\nAbstract\nWronskians of orthogonal polynomials appear in
a range of applications including in random matrix theory\, vortex dynami
cs and supersymmetric quantum mechanics. They are also associated with the
rational solution of Painlevé equations. We discuss how the partitions t
hat label the set of orthogonal polynomials in a particular Wronskian play
a role beyond simple notation. Curiously\, various aspects of the Wronksi
an polynomials can be expressed in terms of partition data.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Heather Wilber (University of Texas at Austin)
DTSTART:20220607T130000Z
DTEND:20220607T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/78
DESCRIPTION:Title: Low rank numerical methods via rational function approximation\n
by Heather Wilber (University of Texas at Austin) as part of CAvid: Comple
x Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nIn this talk
\, we apply classical ideas in approximation theory to design low rank num
erical methods for a range of applications in scientific computing\, inclu
ding the solving of certain linear systems\, matrix equations\, and partia
l differential equations. The primary workhorse in our approach and analys
is is the alternating direction implicit (ADI) method\, and we explore how
this special splitting algorithm is linked to a wealth of concepts from a
pplied mathematics\, including Laplace’s equation and conformal maps for
doubly-connected regions\, matrix and operator function evaluation\, digi
tal filter design\, and the low rank properties of matrices with special d
isplacement structures.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elias Wegert (Technische Universität Bergakademie Freiberg)
DTSTART:20220614T130000Z
DTEND:20220614T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/79
DESCRIPTION:Title: Numerical range\, Blaschke products and Poncelet polygons\nby El
ias Wegert (Technische Universität Bergakademie Freiberg) as part of CAvi
d: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\n(Jo
int work with Ilya Spitkovsky\, New York University Abu Dhabi)\n\nIn 2016\
, Gau\, Wang and Wu conjectured that a partial isometry\nA acting on a $n$
-dimensional complex Hilbert space cannot have \na circular numerical rang
e with a non-zero center.\nIn this talk we present a proof for operators w
ith rank $A=n-1$ \nand any n. It is based on the unitary similarity of A t
o a compressed\nshift operator generated by a finite Blaschke product $B(z
)$.\nWe then use the description of the numerical range by Poncelet\npolyg
ons associated with $zB(z)$\, a special representation of \nBlaschke produ
cts related to boundary interpolation\, and an \nexplicit formula for the
barycenters of the vertices of Poncelet \npolygons involving elliptic func
tions.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jane Hawkins (University of North Carolina)
DTSTART:20220621T130000Z
DTEND:20220621T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/80
DESCRIPTION:Title: Doubly periodic Julia and Fatou sets for iterated meromorphic functi
ons: dynamics on unbounded components\nby Jane Hawkins (University of
North Carolina) as part of CAvid: Complex Analysis video seminar\n\nLectu
re held in N/A.\n\nAbstract\nElliptic functions give rise under iteration
to Julia and Fatou sets that are invariant under the action of translation
by elements of the period lattice. However doubly periodic Julia and Fato
u sets can arise for non-elliptic meromorphic functions as well. Unbounde
d Fatou components in both settings exhibit dynamics different from those
of rational maps and are called toral bands since they can be viewed on a
torus (a fundamental region in the plane with identifications). We discus
s how the dynamics depend on the function and the lattice\, both its shape
and its size\, and what parameter choices produce unbounded components. W
e will also touch on the stability and connectivity of these components.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fiana Jacobzon (Braude College of Engineering\, Karmiel\, Israel)
DTSTART:20220628T130000Z
DTEND:20220628T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/82
DESCRIPTION:Title: An "inverse Fekete-Szegö problem" and filtration of generators\
nby Fiana Jacobzon (Braude College of Engineering\, Karmiel\, Israel) as p
art of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAb
stract\nIn this talk we introduce and discuss a question that can be inter
preted as an "inverse Fekete-Szegö problem". It turns out that this prob
lem links to the so-called filtration of infinitesimal generators. Several
filtration classes have recently been studied\, including their applicati
ons to semigroups of holomorphic mappings in the unit disk.\nTo address th
e circle of questions that arise in this context we introduce new filtrati
on classes using the non-linear differential operator\n\\[\\alpha\\cdot \\
frac{f(z)}{z}+\\beta\\cdot \\frac{zf'(z)}{f(z)}+(1-\\alpha-\\beta)\\cdot \
\left[1+\\frac{zf''(z)}{f'(z)}\\right]\,\\]\nand establish certain propert
ies of these classes. \nSharp upper bounds of the modulus of the Fekete--S
zegö functional over some filtration classes are found. \nWe also present
open problems for further study.\n\n\nJoint work with Mark Elin (Braude C
ollege of Engineering\, Karmiel\, Israel) and \nNikola Tuneski (Ss. Cyril
and Methodius University\, Skopje\, Republic of North Macedonia)\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Waterman (Stony Brook University)
DTSTART:20220920T130000Z
DTEND:20220920T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/83
DESCRIPTION:Title: Maverick points on the boundary of wandering domains\nby James W
aterman (Stony Brook University) as part of CAvid: Complex Analysis video
seminar\n\nLecture held in N/A.\n\nAbstract\nWandering domains\, or wander
ing Fatou components\, are a central object of study in the iteration of t
ranscendental entire functions. We will introduce several basic properties
of wandering domains. Moreover\, focusing on behavior on the boundary of
these domains\, we will discuss the existence of boundary points of a wand
ering domain with accumulation behavior distinct from that of the wanderin
g domain itself. We call such points maverick points. This is joint work w
ith David Martí-Pete and Lasse Rempe.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darren Crowdy (Imperial College London)
DTSTART:20221011T130000Z
DTEND:20221011T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/84
DESCRIPTION:Title: Water waves with vorticity and the Schwarz function\nby Darren C
rowdy (Imperial College London) as part of CAvid: Complex Analysis video s
eminar\n\nLecture held in N/A.\n\nAbstract\nThe theory of water waves is c
enturies old\, but it remains a vibrant area of research. Most theoretical
work on water waves takes the flow to be irrotational\, but there has bee
n growing interest\, especially recently\, in the effect of vorticity on t
he structure of the waves. The assumption of irrotationality has the theor
etical advantage that complex analysis techniques can be used to analyze t
he problem in the two-dimensional setting. This talk will present a novel
theoretical formulation of the problem of steadily-travelling water waves
in the presence of vorticity (where the assumption of irrotationality is d
ropped) but in the absence of gravity or capillarity. The approach is base
d on the notion of a Schwarz function of a curve. It unifies our understan
ding of several recent results in the water wave literature and provides a
wealth of new exact mathematical solutions to this challenging free bound
ary problem.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maurice Kenfack Nangho (University of Dschang\, Cameroon)
DTSTART:20221018T130000Z
DTEND:20221018T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/85
DESCRIPTION:Title: A characterization of Askey-Wilson polynomials: proof of a conjectur
e by Mourad Ismail\nby Maurice Kenfack Nangho (University of Dschang\,
Cameroon) as part of CAvid: Complex Analysis video seminar\n\nLecture hel
d in N/A.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamara Grava (University of Bristol and SISSA)
DTSTART:20220927T130000Z
DTEND:20220927T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/86
DESCRIPTION:Title: The Stieltjes-Fekete problem and degenerate orthogonal polynomials\nby Tamara Grava (University of Bristol and SISSA) as part of CAvid: Co
mplex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nA result
of Stieltjes famously relates the zeroes of the classical orthogonal poly
nomials with the configurations of points on the line that minimize a suit
able logarithmic energy\, or equivalently the solutions\nof a suitable wei
ghted Fekete problem. The optimal configuration satisfies an algebraic set
of equations with the logarithmic derivative of the weight function as ``
external field": we call this set of algebraic\nequations the Stieltjes-Fe
kete problem. In this work we consider the\nStieltjes-Fekete problem with
an arbitrary rational external field. We\nshow that its solutions are in o
ne-to-one correspondence with the zeroes of certain non-hermitean orthogon
al polynomials that satisfy an excess of orthogonality conditions and are
thus termed ``degenerate". This generalizes the above mentioned result of
Stieltjes.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang Chen (University of Macau)
DTSTART:20221025T130000Z
DTEND:20221025T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/87
DESCRIPTION:Title: Laguerre Unitary Ensembles with Multiple Discontinuities\, PDE\, and
the Coupled Painlevé V System\nby Yang Chen (University of Macau) as
part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\n
Abstract\nWe study the Hankl generated by the Laguerre weight with jump\nd
iscontinuities at $t_k$\, $k=1\,2\,\\ldots\,m$. By employing the ladder op
erator approach \nwe establish (multi-time) Riccati equations\, to show th
at $\\sigma_n(t_1\, ...\,t_m)$\,\nthe log derivative of the $n\\times n$ H
ankel determinant\, satisfies a generalization of the $\\sigma$ of a Painl
ev\\'e V equation. Through investigating the Riemann-Hibert problem (or Ho
mogenous Hilbert Problem ) for the orthogonal polynomials\ngenerated by t
he LUEMD and via Lax pair\, we express $\\sigma_n$ in terms of \nsolutions
of a coupled Painlev\\'e V system. We also build relations between the au
xiliary quantities introduced in the above two methods\, which provide\nco
nnections between the Riccati equations and the Lax Pair. \n\nIn addition\
, when each $t_k$ tends to the hard edge of the spectrum and $n$ goes to i
nfinity\, the scaled $\\sigma_n$ is shown to satisfy a generalized Painlev
\\'e III system.\n\nYang Chen (University of Macau\, Macau)\, Shulin Lyu (
Qilu University of Technology\, Shandong Academy of Science)\, Shuai-Xia X
u (Institut Franco-Chinois de l'Energie Nculearie\, Sun Yat-sen Universit
y\, Guangzhou\, China\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jasmin Raissy (Université de Bordeaux)
DTSTART:20221122T140000Z
DTEND:20221122T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/88
DESCRIPTION:by Jasmin Raissy (Université de Bordeaux) as part of CAvid: C
omplex Analysis video seminar\n\nLecture held in N/A.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianhua Zheng (Tsinghua University)
DTSTART:20221101T140000Z
DTEND:20221101T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/89
DESCRIPTION:Title: Classification of Baker domains of meromorphic functions\nby Jia
nhua Zheng (Tsinghua University) as part of CAvid: Complex Analysis video
seminar\n\nLecture held in N/A.\n\nAbstract\nFirst we introduce the defini
tion of Baker domain of a meromorphic\n function\, an absorbing domain of
a Baker domain and a classification of Baker domains with\nconnectivity of
its absorbing domain. Secondly we introduce a more carful classification
of Baker domains according to characteristic of the M\\"obius transformati
on which the function sem-conjugates on the Baker domain in question. Thir
dly\, we say criteria of Baker domain types. The talk mainly comes from a
unpublished paper I finished one year ago.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Argyris Christodoulou (Aristotle University of Thessaloniki)
DTSTART:20221115T140000Z
DTEND:20221115T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/90
DESCRIPTION:Title: Generalising the Denjoy-Wolff theorem\nby Argyris Christodoulou
(Aristotle University of Thessaloniki) as part of CAvid: Complex Analysis
video seminar\n\nLecture held in N/A.\n\nAbstract\nThe starting point for
this talk is the classical Denjoy-Wolff theorem\, which completely describ
es the behaviour of the iterates of a holomorphic self-map of the unit dis
c. Since its inception there have been many attempts at generalising this
result to include compositions of more than one map\, but as of yet there
is no definitive result of this type. We approach this subject by asking t
he following question: Is the result of the Denjoy-Wolff theorem stable wh
en we perturb the iterated function? In particular\, we study the dynamica
l behaviour of compositions arising from a sequence of self-maps of a Riem
ann surface\, when the sequence itself converges to a holomorphic map. Bas
ed on joint work with Marco Abate and Ian Short.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marta Kosek (Jagiellonian University\, Poland)
DTSTART:20230110T140000Z
DTEND:20230110T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/91
DESCRIPTION:Title: On some limits in the theory of Julia sets\nby Marta Kosek (Jagi
ellonian University\, Poland) as part of CAvid: Complex Analysis video sem
inar\n\nLecture held in N/A.\n\nAbstract\nWe will speak about polynomial J
ulia sets in the complex plane\, even\nthough most subjects can be investi
gated also in higher dimensions. We\nconsider some approximation problems.
One of them is approximation of some\nregular sets by polynomial Julia se
ts. It can be seen that a good tool for\nthis approximation is Klimek’s
metric defined with use of Green's\nfunctions of complex sets\, which is m
ore appropriate than the classical\nHausdorff metric. Another problem conc
erns creating computer pictures of\nsome composite Julia sets. Finally\, w
e deal with some sequences defined\nwith use of (compositions of) Chebyshe
v polynomials and obtain their uniform limit.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohamed Nasser (Wichita State University\, USA)
DTSTART:20230117T140000Z
DTEND:20230117T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/92
DESCRIPTION:Title: A boundary integral method for the Riemann–Hilbert problem on mult
iply connected domains\nby Mohamed Nasser (Wichita State University\,
USA) as part of CAvid: Complex Analysis video seminar\n\nLecture held in N
/A.\n\nAbstract\nLet $G$ be a multiply connected domain in the extended co
mplex plane and let $A$ be a complex function on the boundary $\\partial G
$ with $A\\ne0$. \nFor a given real function $\\gamma$ on $\\partial G$\,
the Riemann--Hilbert (RH) boundary value problem requires determining a fu
nction $f$ analytic in $G$ (vanishing at infinity for unbounded $G$)\, con
tinuous in the closure $\\overline{G}$\, and satisfying the boundary condi
tion Re$[Af]=\\gamma$ on $\\partial G.$\n\nA boundary integral method for
solving the above RH problem will be presented in this talk. The method is
based on an integral equation known as {the boundary integral equation wi
th the generalized Neumann kernel}. Applications of the method will be als
o presented.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Vishnyakova (V. N. Karazin Kharkiv National University\, Ukra
ine and Holon Institute of Technology\, Israel and Holon Institute of
Technology\, Israel)
DTSTART:20230124T140000Z
DTEND:20230124T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/93
DESCRIPTION:Title: Necessary and sufficient conditions for entire functions to belong t
o the Laguerre-Polya class\nby Anna Vishnyakova (V. N. Karazin Kharkiv
National University\, Ukraine and Holon Institute of Technology\, Israel
and Holon Institute of Technology\, Israel) as part of CAvid: Complex
Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nThe famous La
guerre-Polya class consists of\nentire functions which are uniform on the\
ncompacts limits of real polynomials having all\nreal zeros. The Laguerre-
Polya class is of interest\nto many areas of mathematics such as complex a
nalysis\,\nstatistical physics\, combinatorics\, asymptotic analysis\,\nth
e theory of mock modular forms and others. We present\nnew necessary and n
ew sufficient conditions for an entire\nfunction to belong to the Laguerre
-Polya class in terms\nof Taylor coefficients of the function. The partial
theta-function\n$g_a(z) =\\sum_{k=0}^{\\infty} \\frac {z^k}{a^{k^2}}\, a>
1\,$\nplays an important role in our investigations. It is known\nthat the
re exists a constant $ q_\\infty\\approx 3{.}23363666\,$\nsuch that the pa
rtial theta-function belongs to the Laguerre-Polya\nclass if and only if $
a^2 \\geq q_\\infty.$ The following statement\nis an example of our resul
ts. Let $f(z)=\\sum_{k=0}^\\infty a_k z^k $\nbe an entire function with po
sitive coefficients. Suppose that the\nsequence $\\frac{a_n^2}{a_{n-1} a_{
n+1}}$ is decreasing in $n$\,\nand the limit of this sequence is greater t
han or equal to\n$\\ q_\\infty.$ Then the function $f$ belongs to the\nLag
uerre-Polya class.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Short (Open University\, UK)
DTSTART:20230207T140000Z
DTEND:20230207T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/94
DESCRIPTION:Title: Iterated function systems in holomorphic dynamics\nby Ian Short
(Open University\, UK) as part of CAvid: Complex Analysis video seminar\n\
nLecture held in N/A.\n\nAbstract\nMotivated by classical results in conti
nued fraction theory\, we explore iterated function systems of holomorphic
self-maps of the disc and other Riemann surfaces. The primary tools in th
is endeavour are the hyperbolic metric and Pick's theorem that holomorphic
maps are contractions of the hyperbolic metric. We will review selected r
esults from this field over the last few decades and finish with work in p
reparation advancing these results by use of the hyperbolic derivative.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonatan Lenells (KTH\, Sweden)
DTSTART:20230131T140000Z
DTEND:20230131T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/95
DESCRIPTION:by Jonatan Lenells (KTH\, Sweden) as part of CAvid: Complex An
alysis video seminar\n\nLecture held in N/A.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adolfo Guillot (National Autonomous University of Mexico)
DTSTART:20230214T140000Z
DTEND:20230214T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/96
DESCRIPTION:Title: Meromorphic vector fields on algebraic surfaces having univalent sol
utions\nby Adolfo Guillot (National Autonomous University of Mexico) a
s part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\
nAbstract\nWe consider algebraic\, first-order\, autonomous ordinary\ndiff
erential equations in two complex variables (meromorphic vector\nfields on
compact algebraic surfaces\, for instance\, those coming from\nrational v
ector fields on affine surfaces)\, and discuss the very\nstrong constraint
s imposed by the existence of one transcendental\nunivalent solution: eith
er there is some variable that integrates\nindependently (the vector field
preserves a fibration on the surface)\,\nor the surface is an abelian one
and the vector field is linear.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Martinez-Finkelshtein (Baylor University\, USA and Universi
ty of Almería\, Spain)
DTSTART:20230221T140000Z
DTEND:20230221T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/97
DESCRIPTION:by Andrei Martinez-Finkelshtein (Baylor University\, USA and U
niversity of Almería\, Spain) as part of CAvid: Complex Analysis video se
minar\n\nLecture held in N/A.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ragnar Sigurdsson (University of Iceland)
DTSTART:20230321T130000Z
DTEND:20230321T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/98
DESCRIPTION:by Ragnar Sigurdsson (University of Iceland) as part of CAvid:
Complex Analysis video seminar\n\nLecture held in N/A.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Sokal (University College London)
DTSTART:20230228T140000Z
DTEND:20230228T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/99
DESCRIPTION:Title: Motion of zeros of polynomial solutions of the one-dimensional heat
equation: A first-order Calogero-Moser system\nby Alan Sokal (Universi
ty College London) as part of CAvid: Complex Analysis video seminar\n\nLec
ture held in N/A.\n\nAbstract\nI study the motion of zeros of polynomial s
olutions $\\phi(x\, t)=\\prod_{i=1}^n[x-x_{i}(t)]$\nof the one-dimensional
heat equation \n$\\displaystyle\\frac{\\partial \\phi}{\\partial t}=\\kap
pa\\frac{\\partial^2\\phi}{\\partial x^2}$\; they satisfy the first-order\
nCalogero–Moser system \n\\[\n\\frac{{\\rm d}x_i}{{\\rm d}t}=\\sum_{j\\n
e i}\\frac{-2\\kappa}{x_i-x_j}.\n\\]\nI am interested in the behavior at c
omplex time $t$ (usually with real initial conditions). My goals are to\n\
n(a) Determine the complex times t at which collisions can or cannot occur
\; and\n\n(b) Control the location of $x_1(t)\,\\ldots\, x_n(t)$ in the co
mplex plane. I have no nontrivial theorems\, but many interesting conjectu
res.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sayani Bera (Indian Association for the Cultivation of Science\, K
olkata)
DTSTART:20230307T140000Z
DTEND:20230307T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/100
DESCRIPTION:Title: Attracting basins of non-autonomous families\nby Sayani Bera (I
ndian Association for the Cultivation of Science\, Kolkata) as part of CAv
id: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nTh
e goal of this talk is to explore the basins of non-autonomous or iterativ
e families of automorphisms of $\\mathbb{C}^m$ \, m ≥ 2\, admitting a co
mmon attracting fixed point\, and their connection to the classical ‘sta
ble manifold theorem’.\nFurther\, we affirmatively answer a conjecture (
formulated by Fornæss and Stensønes in 2004) on non-autonomous basins\,
by generalising appropriate techniques from the (iterative) dynamics of H
énon/regular maps in $\\mathbb{C}^m$\,m ≥ 2. This\, also confirms a str
onger version of the stable manifold theorem\, originally raised as a ques
tion by Bedford in 2000.\nThis is a joint work with K. Verma.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michel Zinsmeister (Université d'Orléans\, France)
DTSTART:20230314T130000Z
DTEND:20230314T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/101
DESCRIPTION:Title: Coullet-Tresser Cascade of Bifurcations in the logistic Family and
Hausdorff Dimension of real quadratic Julia Sets\nby Michel Zinsmeiste
r (Université d'Orléans\, France) as part of CAvid: Complex Analysis vid
eo seminar\n\nLecture held in N/A.\n\nAbstract\nIn a paper with L. Jackszt
as (Adv Math 2020) we have proven that if $c_0$ is a parabolic parameter (
i.e. with a parabolic cycle) in $(c_{Feig}\,1/4)$ ($c_{Feig}$ being the li
mit point of the cascade of bifurcations) then the function $d(c)=$ Hausdo
rff dimension of the Julia set $J_c$ of $z^2+c$ has an infinite derivative
at $c_0$ if $d(c_0)\\leq 4/3$\, while it is $C^1$ across $c_0$ if $d(c_0)
>4/3$.\n\nRecently A. Dudko\, I. Gorobovickis and W. Tucker have proven th
at $d(c)>4/3$ on $[-1.53\,-1.23]$ (arXiv:2204.07880). The combination of t
hese two results implies that $d$ is $C^1$ on $(c_{Feig}\,-3/4)$ while $d'
(-3/4)=-\\infty$ (a former result of L. Jacksztas).\\\\\nAfter some descri
ption (including a history) of the Coullet-Tresser Feigenbaum phenomenon\,
I will outline the proof of J-Z theorem and briefly describe D-G-T's resu
lt. \n\n(Joint work with L. Jacksztas)\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thu Hien Nguyen (Leipzig University\, Germany & V. N. Karazin Khar
kiv University\, Ukraine)
DTSTART:20230425T130000Z
DTEND:20230425T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/102
DESCRIPTION:Title: Some results on entire functions from the Laguerre-Pólya class: pr
oof ideas and techniques\nby Thu Hien Nguyen (Leipzig University\, Ger
many & V. N. Karazin Kharkiv University\, Ukraine) as part of CAvid: Compl
ex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nThe Laguerr
e-P\\'olya class is a class of entire functions that are locally the unifo
rm limit of a sequence of real polynomials that have only real zeros. We
present some simple necessary and sufficient conditions for entire functio
ns to belong to the Laguerre–Pólya class in terms of their Taylor coeff
icients. For an entire function $f(z) = \\sum_{k=0}^{\\infty} a_k z^k$\,
we define the second quotients of Taylor coefficients as $q_n(f) := \\frac
{a_{n-1}^2}{a_{n-2} a_{n}}$\, $n\\geq 2$\, and find conditions on $q_n(f
)$ for $f$ to belong to the Laguerre--P\\'olya class\, or to have only re
al zeros. In this talk\, we will focus on the entire functions with incre
asing second quotients of Taylor coefficients\, and discuss proof ideas an
d techniques we used. \n \n This is joint work with Anna Vishnyakova.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Solynin (Texas Tech University\, USA)
DTSTART:20230502T130000Z
DTEND:20230502T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/103
DESCRIPTION:Title: Quadratic differentials in complex analysis and beyond\nby Alex
ander Solynin (Texas Tech University\, USA) as part of CAvid: Complex Anal
ysis video seminar\n\nLecture held in N/A.\n\nAbstract\nI will discuss the
role of quadratic differentials in the extremal\nproblems in Complex Anal
ysis and beyond. We start with main\ndefinitions\, then discuss \nJenkins'
theory of extremal partitioning\, and then I will\nmention main results o
f the differentiation theory for the\nJenkins' weighted sum of moduli sugg
ested by this speaker in\n1985-2000.\n\nTurning to applications\, I show f
irst how quadratic differentials\ncan be used to study fingerprints of (co
mplex) polynomial\nlemniscates. The main result here includes\, as special
cases\,\nEbenfelt-Khavinson-Shapiro characterization of fingerprints of\n
polynomial lemniscates as well as Younsi characterization of\nrational lem
niscates. Then I will show that every real algebraic\ncurve can be treated
as a trajectory of a quadratic differential\ndefined on a certain Riemann
surface.\n\n\nAfter that\, we will discuss how quadratic differentials on
\n$\\overline{\\mathbf{C}}$ with the minimal possible number of poles\n(th
at is $4$) can be used to solve the problem on the canonical\nembeddings o
f pairs of arcs\, studied recently by M. Bonk and\nA. Eremenko\, and in se
veral other extremal problems on ring\ndomains.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Navneet Lal Sharma (Gati Shakti Vishwavidyalaya\, India)
DTSTART:20230516T130000Z
DTEND:20230516T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/104
DESCRIPTION:by Navneet Lal Sharma (Gati Shakti Vishwavidyalaya\, India) as
part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\nAb
stract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cinzia Bisi (Ferrara University\, Italy)
DTSTART:20230530T130000Z
DTEND:20230530T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/105
DESCRIPTION:Title: Invariants and automorphisms of slice regular functions\nby Cin
zia Bisi (Ferrara University\, Italy) as part of CAvid: Complex Analysis v
ideo seminar\n\nLecture held in N/A.\n\nAbstract\nLet $A$ be one of the fo
llowing Clifford Algebras : C\, H = R2 and R3. For the algebra A\, the aut
omorphism group Aut(A) and its invariants are well known. The talk will de
scribe the invariants of the automorphism group of the algebra of slice re
gular functions over $A$ = H = R2 and over $A$ = R3. This is a joint proje
ct with J. Winklelmann.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Kostov (Université d'Azur\, CNRS\, LJAD)
DTSTART:20230509T130000Z
DTEND:20230509T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/106
DESCRIPTION:Title: Analytic properties of the partial theta function\nby Vladimir
Kostov (Université d'Azur\, CNRS\, LJAD) as part of CAvid: Complex Analys
is video seminar\n\nLecture held in N/A.\n\nAbstract\nWe consider the part
ial theta function $\\theta (q\,x):=\\sum\n_{j=0}^{\\infty}q^{j(j+1)/2}x^j
$\, where $x$ is a variable and $q$ a\nparameter\n($|q|<1$). We deal with
the two possible situations\, when $q$ is real or\ncomplex. In the talk we
focus on the\nanalytic properties of $\\theta$\, such as asymptotic expan
sions for its\nzeros\, its spectrum (i.e. the set of values of the paramet
er $q$\nfor which $\\theta (q\,.)$ has multiple zeros)\, behaviour of its
zeros\,\nespecially of its complex conjugate pairs\, when\nthe parameter $
q$ varies\, separation in modulus of the zeros etc.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Navneet Lal Sharma (Gati Shakti Vishwavidyalaya)
DTSTART:20230523T130000Z
DTEND:20230523T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/107
DESCRIPTION:Title: Estimates logarithmic coefficients for certain classes of univalent
functions\nby Navneet Lal Sharma (Gati Shakti Vishwavidyalaya) as par
t of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbst
ract\nLet $\\mathcal{S}$ be the family of analytic and univalent functions
$f$ in the unit disk $\\mathbb{D}$\nwith the normalization $f(0)=f'(0)-1=
0$.\nThe logarithmic coefficients $\\gamma_n$ of $f\\in \\mathcal{S}$ are
defined by the formula\n$$\\log\\left(\\frac{f(z)}{z}\\right)\\\,=\\\,2\\s
um_{n=1}^{\\infty}\\gamma_n(f)z^n.\n$$\nIn this talk\, we will discuss bou
nds for the logarithmic coefficients for certain geometric subfamilies of
univalent functions as starlike\, convex\, close-to-convex and Janowski st
arlike functions. Also\, we consider the families $\\mathcal{F}(c)$ and \n
$\\mathcal{G}(\\delta)$ of functions $f\\in \\mathcal{S}$ defined by\n$$
{\\rm Re} \\left ( 1+\\frac{zf''(z)}{f'(z)}\\right )>1-\\frac{c}{2}\\\, \
\mbox{ and } \\\,\n{\\rm Re} \\left ( 1+\\frac{zf''(z)}{f'(z)}\\right )<1
+\\frac{\\delta}{2}\,\\quad z\\in \\mathbb{D} $$\nfor some $c\\in(0\,3]$ a
nd $\\delta\\in (0\,1]$\, respectively. We obtain the sharp upper bound fo
r $|\\gamma_n|$ when $n=1\,2\,3$ and $f$ belongs to the classes \n$\\mathc
al{F}(c)$ and $\\mathcal{G}(\\delta)$\, respectively. We conclude with the
following two conjectures:\n\n* If $f\\in\\mathcal{F}(-1/2)$\, then $ \\
displaystyle |\\gamma_n|\\le \\frac{1}{n}\\left(1-\\frac{1}{2^{n+1}}\\righ
t)$\n for $n\\ge 4$\, and\n$$ \\sum_{n=1}^{\\infty}|\\gamma_{n}|^{2} \\le
q \\frac{\\pi^2}{6}+\\frac{1}{4} ~{\\rm Li\\\,}_{2}\\left(\\frac{1}{4}\\ri
ght)\n -{\\rm Li\\\,}_{2}\\left(\\frac{1}{2}\\right)\, $$\nwhere ${\\rm
Li}_2(x)$ denotes the dilogarithm function. \n\n* If $f\\in \\mathcal{G}(\
\delta)$\, then $ \\displaystyle |\\gamma_n|\\\,\\leq \\\,\\frac{\\delta}
{2n(n+1)}$ for $n\\ge 4$.\n\n\nThis talk is based on the following artic
le.\n\nS. Ponnusamy\, N. L. Sharma and K.-J. Wirths\,\nLogarithmic coeffic
ients problems in families related to starlike and convex functions\, . Au
st. Math. Soc.\, 109(2) (2019)\, 230--249.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Fasondini (University of Leicester)
DTSTART:20231017T130000Z
DTEND:20231017T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/108
DESCRIPTION:Title: Complex-plane singularity dynamics for blow up in a nonlinear heat
equation: analysis and computation\nby Marco Fasondini (University of
Leicester) as part of CAvid: Complex Analysis video seminar\n\nLecture hel
d in N/A.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toby Driscoll (University of Delaware)
DTSTART:20231024T130000Z
DTEND:20231024T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/109
DESCRIPTION:Title: AAA for rational interpolation on continuua\nby Toby Driscoll (
University of Delaware) as part of CAvid: Complex Analysis video seminar\n
\nLecture held in N/A.\n\nAbstract\nThe AAA algorithm of Nakatsukasa\, Sè
te\, and Trefethen has rapidly risen to prominence as a fast and powerful
way to approximate functions in the complex plane. As originally presented
\, AAA incrementally constructs an approximation based on a fixed initial
discretization\, which is not ideal in cases where a good initial distribu
tion of nodes may be difficult to discern. By also incrementally adding no
des from the domain based on the latest residual\, the algorithm can be ad
apted to work well automatically even when singularities are very close to
or even on the approximation interval. This capability has been released
as a Julia software package\, and another package is in development to use
these approximations for computing conformal maps to simply- and doubly-c
onnected domains.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luna Lomonaco (Institute of Pure and Applied Mathematics)
DTSTART:20231031T130000Z
DTEND:20231031T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/110
DESCRIPTION:Title: Mating quadratic maps with the modular group\nby Luna Lomonaco
(Institute of Pure and Applied Mathematics) as part of CAvid: Complex Anal
ysis video seminar\n\nLecture held in N/A.\n\nAbstract\nHolomorphic corres
pondences are multi-valued maps defined by polynomial relations $P(z\,w)=0
$. We consider a specific 1-(complex)parameter family of (2:2) corresponde
nces (every point has 2 images and 2 preimages)\nwhich encodes both the dy
namics of a quadratic rational map and the dynamics of the modular group.
We show that the connectedness locus for this family is homeomorphic to th
e parabolic Mandelbrot set\, itself homeomorphic to the Mandelbrot set. Jo
int work with S. Bullett.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Buckingham (University of Cincinnati)
DTSTART:20231107T140000Z
DTEND:20231107T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/111
DESCRIPTION:Title: Asymptotics of Rational Painlevé V Functions\nby Robert Buckin
gham (University of Cincinnati) as part of CAvid: Complex Analysis video s
eminar\n\nLecture held in N/A.\n\nAbstract\nThe Painlevé functions are a
family of ordinary differential equations with myriad applications to math
ematical physics and probability. The rational solutions of these equatio
ns have drawn attention for the remarkable geometric structure of their ze
ros and poles. We study the family of rational solutions of the Painlevé
-V equation built from Umemura polynomials. We derive a new Riemann-Hilbe
rt representation and use it to obtain the boundary of the pole region and
the large-degree behavior in the pole-free region. This is joint work wi
th Matthew Satter of the University of Cincinnati.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liz Vivas (Ohio State University)
DTSTART:20231114T140000Z
DTEND:20231114T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/112
DESCRIPTION:Title: Dimension results on generalized Bergman spaces\nby Liz Vivas (
Ohio State University) as part of CAvid: Complex Analysis video seminar\n\
nLecture held in N/A.\n\nAbstract\nWiegerinck proved that the Bergman spac
e over any domain in the complex plane is either trivial or infinite dimen
sional. In this talk I will discuss various generalizations and open quest
ions related to this theorem. I will survey the case of the complex plane
being replaced by C^n as well as a domain in a compact Riemann Surface.\n\
nThe talked is based in joint work with A-K. Gallagher and P. Gupta.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guang-Yuan Zhang (Tsinghua University)
DTSTART:20231128T140000Z
DTEND:20231128T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/114
DESCRIPTION:Title: The precise form of Ahlfors' Second Fundamental Theorem of covering
surfaces\nby Guang-Yuan Zhang (Tsinghua University) as part of CAvid:
Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nA sim
ply connected covering surface $\\Sigma =\\left( f\,\\overline{\\Delta }%\
n\\right) $ over the unit Riemann sphere $S$ is an orientation-preserving\
,\ncontinuous\, open and finite-to-one mapping (OPCOFOM) $f$ from the clos
ed\nunit disk $\\overline{\\Delta }$ into the sphere $S$. Here open means
that $f$\ncan be extended continuous and open to a neighborhood of $\\over
line{\\Delta }.\n$ We denote by $\\mathbf{F}$ all simply connected surface
s.\n\nLet $E_{q}=\\left\\{ a_{1}\,a_{2}\,\\dots \,a_{q}\\right\\} $ be a s
et on the unit\nRiemann sphere consisting of $q$ distinct points with $q>2
.$ \nAhlfors' second\nfundamental theorem (SFT) states that there exists a
positive number $h$\ndepending only on $E_{q}\,$ such that for any surfac
e $\\Sigma =\\left( f\,%\n\\overline{\\Delta }\\right) \\in \\mathbf{F}\,$
\n\\[\n\\left( q-2\\right) A\\left( \\Sigma \\right) <4\\pi \\overline{n}\
\left( \\Sigma\n\\right) +hL\\left( \\partial \\Sigma \\right) \,\n\\]\nwh
ere $\\Delta $ is the unit disk\, $A\\left( \\Sigma \\right) $ is the sphe
rical\narea of $\\Sigma $\, $L\\left( \\partial \\Sigma \\right) $ is the
spherical\nlength of the boundary curve $\\partial \\Sigma =\\left( f\,\\p
artial \\Delta\n\\right) \,$ and $\\overline{n}\\left( \\Sigma \\right) =\
\#f^{-1}(E_{q})\\cap\n\\Delta .$\n\nIf we define $R\\left( \\Sigma \\right
) =R\\left( \\Sigma \,E_{q}\\right) $ to be\nthe error term in Ahlfors' SF
T\, say\,\n\\[\nR\\left( \\Sigma \\right) =\\left( q-2\\right) A\\left( \\
Sigma \\right) -4\\pi\n\\overline{n}\\left( \\Sigma \\right) \,\n\\]\nthen
Ahlfors' SFT reads\n\\[\nH_{0}=\\sup_{\\Sigma \\in \\mathbf{F}}\\left\\{
\\frac{R(\\Sigma )}{L(\\partial\n\\Delta )}:\\Sigma =\\left( f\,\\overline
{\\Delta }\\right) \\right\\} <+\\infty .\n\\]\nWe call $H_{0}=H_{0}(E_{q}
)$ Ahlfors' constant for simply connected\nsurfaces.\n\nIn this talk\, I w
ill introduce my recent work which identify the precise\nbound $H_{0}=H_{0
}(E_{q}).$\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Faouzi Thabet (University of Gabès)
DTSTART:20231212T140000Z
DTEND:20231212T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/116
DESCRIPTION:Title: Trajectories of Particular Quadratic Differentials on the Riemann S
phere\nby Faouzi Thabet (University of Gabès) as part of CAvid: Compl
ex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nIn this lec
ture\, we give some basics of the theory of Quadratic\nDifferentials on th
e Riemann Sphere. In the first part\, the focus will be on\nthe investigat
ion of the existence of finite critical trajectories\, and the\ndescriptio
n of the critical graph of some quadratic differentials related to\nsoluti
ons as Cauchy transform of a signed measure of an algebraic quadratic\nequ
ation as the form : $p\\left( z\\right) \\mathcal{C}^{2}\\left( z\\right)\
n+q\\left( z\\right) \\mathcal{C}\\left( z\\right) +r=0\,$ for some polyno
mials $p\,$\n$q$ and $r.$ As an example\, we study the large-degree analys
is of the\nbehaviour of the generalized Laguerre polynomials $L_{n}^{(\\al
pha )}$ when\nthe parameters are complex and depend on the degree $n$ line
arly.\n\nIn the second part\, we describe the critical graph of a polynomi
al quadratic\ndifferential related to the Schr\\"{o}dinger equation with c
ubic potential.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva A. Gallardo Gutiérrez (ICMAT)
DTSTART:20231219T140000Z
DTEND:20231219T150000Z
DTSTAMP:20260404T111008Z
UID:CAvid/117
DESCRIPTION:by Eva A. Gallardo Gutiérrez (ICMAT) as part of CAvid: Comple
x Analysis video seminar\n\nLecture held in N/A.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Kecker (University of Portsmouth)
DTSTART:20240423T130000Z
DTEND:20240423T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/118
DESCRIPTION:Title: Geometric approach for quasi-Painlevé Hamiltonian systems\nby
Thomas Kecker (University of Portsmouth) as part of CAvid: Complex Analysi
s video seminar\n\nLecture held in N/A.\n\nAbstract\nWe present some new H
amiltonian systems of quasi-Painlevé type and their Okamoto's spaces of i
nitial conditions. The geometric approach was introduced originally for th
e identification problem of Painlevé equations\, comparing the irreducibl
e components of the inaccessible divisors introduced in the blow-ups to ob
tain the space of initial conditions. Using this method\, we find bi-ratio
nal coordinate changes between some of the systems we introduce\, giving r
ise to a global symplectic structure for these systems. This scheme thus a
llows us to identify (quasi-)Painlevé Hamiltonian systems up to bi-ration
al symplectic maps\, performed here for systems with solutions having mova
ble singularities that are either square-root type algebraic poles or ordi
nary poles.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John King (University of Nottingham)
DTSTART:20240430T130000Z
DTEND:20240430T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/119
DESCRIPTION:Title: Complex-plane analysis of a quasilinear parabolic PDE\nby John
King (University of Nottingham) as part of CAvid: Complex Analysis video s
eminar\n\nLecture held in N/A.\n\nAbstract\nI'll apply a combination of fo
rmal asymptotic methods and applied complex analysis (notably the dynamics
of complex singularities) to give some insight into the qualitative and q
uantitative behaviour of some non-integrable PDEs. This raises some unreso
lved (to me) issues of more general relevance about the complex-plane beha
viour of nonlinear ODEs\, about which I shall ask.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alta Jooste (University of Pretoria)
DTSTART:20240514T130000Z
DTEND:20240514T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/120
DESCRIPTION:Title: Recurrence equations involving orthogonal polynomials with related
weight functions\nby Alta Jooste (University of Pretoria) as part of C
Avid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\n
Every sequence of real polynomials $\\{p_n\\}_{n=0}^\\infty=0$\, orthogona
l with respect to a positive weight function w(x) on the interval $(a\,b)$
\, satisfies a three-term recurrence equation. We discuss the role played
by the polynomials associated to $p_n$\, especially as coefficient polynom
ials in the three-term recurrence equation involving polynomials $p_n$\, $
p_{n-1}$ and $p_{n-m}$\, $m\\in\\{2\,3\,...\,n-1\\}$. Furthermore\, we sh
ow how Christoffel's formula is used to obtain mixed three-term recurrence
equations involving the polynomials $p_n$\, $p_{n-1}$ and\n$g_{n-m\,k}$\,
$m \\in \\{2\,3\,...\,n-1\\}$\,\nwhere the sequence $\\{g_{n\,k}\\}_{n=0}
^\\infty$\, $k \\in {\\mathbb{N}}_0$\, is orthogonal with respect to $c_k(
x)w(x) > 0$ on (a\,b) and $c_k$ is a polynomial of degree $k$ in $x$. We d
iscuss the conditions on $k$\, necessary and sufficient for these equation
s to be in such a form\, that they can be applied in the study of the loca
tion of the zeros of the appropriate polynomials.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Ryan (University of Arkansas)
DTSTART:20240507T130000Z
DTEND:20240507T140000Z
DTSTAMP:20260404T111008Z
UID:CAvid/121
DESCRIPTION:Title: From Dirac type operators to Bosonic Laplacians\nby John Ryan (
University of Arkansas) as part of CAvid: Complex Analysis video seminar\n
\nLecture held in N/A.\n\nAbstract\nLurking behind most familiar second or
der partial differential operators there is a first order differential ope
rator. The familiar second order operators include the Laplace operator\,
the \n$p$-Laplacian\, the conformal Laplacian on the sphere and the Maxwel
l operator. \n\nAll of these operators are conformally invariant. \n\nWe s
hall introduce these operators and associated integral operators together
with some of their basic properties. \n\nThis is joint work with Chao Ding
\, Phouc Tai Nguyen and the late Raymond Walter.\n
LOCATION:https://stable.researchseminars.org/talk/CAvid/121/
END:VEVENT
END:VCALENDAR