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BEGIN:VEVENT
SUMMARY:Myrto Manolaki (University College Dublin)
DTSTART:20200512T130000Z
DTEND:20200512T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/1/">Me
 rgelyan-type theorems in several complex variables</a>\nby Myrto Manolaki 
 (University College Dublin) as part of CAvid: Complex Analysis video semin
 ar\n\nLecture held in N/A.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CAvid/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walter Bergweiler (Christian-Albrechts Universität Kiel)
DTSTART:20200519T130000Z
DTEND:20200519T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/2/">En
 tire solutions of linear q-difference equations</a>\nby Walter Bergweiler 
 (Christian-Albrechts Universität Kiel) as part of CAvid: Complex Analysis
  video seminar\n\nLecture held in N/A.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CAvid/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katsuya Ishizaki (Open University of Japan)
DTSTART:20200526T130000Z
DTEND:20200526T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/3/">Me
 romorphic solutions of Fermat type equations</a>\nby Katsuya Ishizaki (Ope
 n University of Japan) as part of CAvid: Complex Analysis video seminar\n\
 nLecture held in N/A.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CAvid/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aimo Hinkkanen (University of Illinois)
DTSTART:20200602T130000Z
DTEND:20200602T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/4/">A 
 determinant problem for a third order ODE</a>\nby Aimo Hinkkanen (Universi
 ty of Illinois) as part of CAvid: Complex Analysis video seminar\n\nLectur
 e held in N/A.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CAvid/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuefei Wang (Chinese Academy of Sciences\, Beijing)
DTSTART:20200609T130000Z
DTEND:20200609T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/5/">On
  the dynamics of entire functions with symmetry</a>\nby Yuefei Wang (Chine
 se Academy of Sciences\, Beijing) as part of CAvid: Complex Analysis video
  seminar\n\nLecture held in N/A.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CAvid/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandre Eremenko (Purdue University)
DTSTART:20200616T130000Z
DTEND:20200616T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/6/">Mo
 duli spaces for Lamé functions</a>\nby Alexandre Eremenko (Purdue Univers
 ity) as part of CAvid: Complex Analysis video seminar\n\nLecture held in N
 /A.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CAvid/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Luca (University College London)
DTSTART:20200623T130000Z
DTEND:20200623T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/7/">Mi
 xed boundary value problems for slow viscous flows: new transform methods 
 and applications</a>\nby Elena Luca (University College London) as part of
  CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract
 \nMotivated by microfluidics applications where it is required to manipula
 te viscous fluids at small scales\, we present new transform methods for s
 olving mixed boundary value problems for biharmonic fields arising therein
 . The new methods provide a unified general approach to finding quasi-anal
 ytical solutions to a variety of technologically important problems of slo
 w viscous flows and lead to fast and accurate schemes for evaluation of th
 e solutions. In this talk\, we focus on problems in simply and multiply co
 nnected domains\, with boundaries consisting of straight-line or circular 
 edges.\n
LOCATION:https://researchseminars.org/talk/CAvid/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zinelâabidine Latreuch (University of Mostaganem\, Algeria)
DTSTART:20200630T130000Z
DTEND:20200630T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/8/">On
  meromorphic solutions of non-linear differential equations of Tumura-Clun
 ie type</a>\nby Zinelâabidine Latreuch (University of Mostaganem\, Algeri
 a) as part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A
 .\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CAvid/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigor Barsegian (National Academy of Sciences of Armenia)
DTSTART:20200707T130000Z
DTEND:20200707T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/9/">A 
 new property of arbitrary complex polynomials</a>\nby Grigor Barsegian (Na
 tional Academy of Sciences of Armenia) as part of CAvid: Complex Analysis 
 video seminar\n\nLecture held in N/A.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CAvid/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jun Wang (Fudan University\, China)
DTSTART:20200714T130000Z
DTEND:20200714T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/10/">J
 ulia limiting directions of meromorphic functions</a>\nby Jun Wang (Fudan 
 University\, China) as part of CAvid: Complex Analysis video seminar\n\nLe
 cture held in N/A.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CAvid/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phil Rippon (Open University\, UK)
DTSTART:20200908T130000Z
DTEND:20200908T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/11/">C
 onstructing entire functions of small order - motivated by complex dynamic
 s</a>\nby Phil Rippon (Open University\, UK) as part of CAvid: Complex Ana
 lysis video seminar\n\nLecture held in N/A.\n\nAbstract\nIn 1989\, Eremenk
 o conjectured that for any transcendental entire function the escaping set
  $I(f) = \\{z:f^n(z)\\to\\infty \\text{ as } n\\to\\infty\\}$ has no bound
 ed components -- despite much work this conjecture is still open.\n\nFor r
 eal entire functions $f$ of finite order with only real zeros\, we have sh
 own that Eremenko's conjecture holds if there exists $r>0$ such that the i
 terated 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 functio
 ns of small order for which this iterated minimum modulus condition holds\
 , and construct examples of functions of small order for which it does not
  hold\, including examples based on a new development of a method due to K
 jellberg.\n\n(Joint work with Dan Nicks and Gwyneth Stallard.)\n\nPlease 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 C
 omplex Analysis video seminar series).\n
LOCATION:https://researchseminars.org/talk/CAvid/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuen-Wai Ng (Hong Kong University)
DTSTART:20200915T130000Z
DTEND:20200915T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/12/">T
 he squeezing function on doubly-connected domains via the Loewner differen
 tial equation</a>\nby Tuen-Wai Ng (Hong Kong University) as part of CAvid:
  Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nInspi
 red by the work of Liu\, Sun and Yau (2004) on holomorphic homogeneous reg
 ular (HHR) domains and Yeung (2009)’s work on domains with uniform squee
 zing property (another name for HHR domains)\, Deng\, Guan and Zhang (2012
 ) introduced a new biholomorphic invariant\, namely\, the squeezing functi
 on for bounded domains in the n-dimensional complex Euclidean space. Since
  then it has been one of the most active area in several complex variables
  in recent years.\n\nOn the other hand\, until now\, there is only one exp
 licit example of non-constant squeezing functions\, namely the squeezing f
 unction of the punctured ball. In this talk\, we will establish an explici
 t formula for the squeezing functions of annuli and hence (up to biholomor
 phisms) for any doubly connected planar domain. The main tools used to pro
 ve this result are the Schottky-Klein prime function  (following the work 
 of Crowdy) and a version of the Loewner differential equation on annuli du
 e to Komatu. We will also show that these results can be used to obtain lo
 wer bounds on the squeezing function for certain product domains in the n-
 dimensional complex Euclidean space.\n\nThis is a joint work with Chiu Cha
 k Tang and Jonathan Tsai.\n
LOCATION:https://researchseminars.org/talk/CAvid/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukas Geyer (Montana State University)
DTSTART:20200922T130000Z
DTEND:20200922T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/13/">G
 ravitational lensing and critically fixed anti-rational maps</a>\nby Lukas
  Geyer (Montana State University) as part of CAvid: Complex Analysis video
  seminar\n\nLecture held in N/A.\n\nAbstract\nStudying the dynamics of ant
 i-rational maps\, i.e.\, complex conjugates of rational maps\, is a subjec
 t closely related to holomorphic dynamics\, with intriguing connections to
  problems in gravitational lensing. In particular\, the lens equation for 
 a single-plane gravitational lens made up of N point masses is known 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 it is kn
 own 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 sharp.\n\n
 Originally motivated by the goal of classifying maximal lensing configurat
 ions\, i.e.\, configurations for which the bound 5N-5 is attained\, we rec
 ently succeeded in giving a complete classification of anti-rational maps 
 for which all critical points are fixed\, through simple topological model
 s associated with certain planar graphs. We will explain this classificati
 on\, the main ideas in the proof\, and how this yields a partial classific
 ation and new examples of maximal lensing configurations. Finally\, we wil
 l discuss some open problems and questions.\n
LOCATION:https://researchseminars.org/talk/CAvid/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norbert Steinmetz (Technische Universität Dortmund)
DTSTART:20200929T130000Z
DTEND:20200929T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/14/">L
 aplace contour integrals and linear differential equations</a>\nby Norbert
  Steinmetz (Technische Universität Dortmund) as part of CAvid: Complex An
 alysis video seminar\n\nLecture held in N/A.\n\nAbstract\nAny linear diffe
 rential 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\nLaplac
 e 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 determine t
 heir order of growth\, asymptotics\, Phragm\\'en-Lindel\\"of indicator\, d
 istribution of zeros\,\nNevanlinna functions $T(r\,f)$ and $N(r\,1/f)$\, a
 nd the existence of sub-normal and polynomial solutions.\n
LOCATION:https://researchseminars.org/talk/CAvid/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Nowak (Maria Curie-Skłodowska University\, Poland)
DTSTART:20201006T130000Z
DTEND:20201006T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/15/">O
 n kernels of Toeplitz operators</a>\nby Maria Nowak (Maria Curie-Skłodows
 ka University\, Poland) as part of CAvid: Complex Analysis video seminar\n
 \nLecture held in N/A.\n\nAbstract\nLet $H^2$ denote the standard Hardy sp
 ace 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 nontangential l
 imit $f(e^{i\\theta})$ a.e. on $\\mathbb {T}=\\partial\\mathbb {D}$ and th
 is boundary function  $f(e^{i\\theta})$ is in $L^2(\\mathbb {T})$.\nFurthe
 rmore\, 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 space $H^
 2$  can be identified with a closed subspace of\n$L^2(\\mathbb {T})$  whos
 e Fourier coefficients with negative indices vanish.\n\n\nFor $\\varphi\\i
 n\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 the orth
 ogonal\nprojection of $L^2(\\mathbb T)$ onto $H^2$.  It is a consequence o
 f Hitt's Theorem  that\n$\\ker T_{\\varphi}= fK_I$\, where $K_I= H^2\\omin
 us 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  kernels o
 f Toeplitz operators.\nThe sufficient and necessary condition for the spac
 e $fK_I$ to be the kernel of a Toeplitz operator was given by E. Hayashi (
 1990).\nIn 1994 D. Sarason gave another proof of this condition based on d
 e Branges-Rovnyak  spaces theory.\nIf $M= fK_I$ is a kernel of a Toeplitz 
 operator\, then also we have $M=\\ker T_{\\frac{\\overline{If}}{f}}$\nIn t
 he talk we consider the case when $fK_I\\varsubsetneq \\ker T_{\\frac{\\ov
 erline{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 structure  
 of de Branges-Rovnyak  spaces generated by nonextreme functions.\n\nThe ta
 lk is based on joint work with P. Sobolewski\, A.\nSo{\\l}tysiak and M. Wo
 {\\l}oszkiewicz-Cyll.\n
LOCATION:https://researchseminars.org/talk/CAvid/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shamil Makhmutov (Sultan Qaboos University\, Oman)
DTSTART:20201013T130000Z
DTEND:20201013T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/16/">G
 rowth estimates for meromorphic solutions of higher order algebraic differ
 ential equations</a>\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 derivative of s
 olutions of the first order algebraic differential equations are obtained.
  \nA generalization of this result to higher order equations is also given
 . \nWe discuss the related question of when for a given class X of meromor
 phic functions in the unit disc\, \ndefined by means of the spherical deri
 vative 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 some oth
 er classes.  \nHowever\, there are classes when the answer is negative.\n
LOCATION:https://researchseminars.org/talk/CAvid/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Min Ru (University of Houston)
DTSTART:20201020T130000Z
DTEND:20201020T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/17/">R
 ecent developments in Nevanlinna theory and Diophantine approximation</a>\
 nby Min Ru (University of Houston) as part of CAvid: Complex Analysis vide
 o seminar\n\nLecture held in N/A.\n\nAbstract\nIn this talk\, I'll survey 
 the recent results in  Nevanlinna theory and Diophantine approximation. I'
 ll focus on the extension of H. Cartan's Second Main Theorem in Nevanlinna
  theory.\n
LOCATION:https://researchseminars.org/talk/CAvid/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catherine Bénéteau (University of South Florida)
DTSTART:20201027T130000Z
DTEND:20201027T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/18/">A
  survey of optimal polynomial approximants and connections to digital filt
 ers</a>\nby Catherine Bénéteau (University of South Florida) as part of 
 CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\
 nIn this talk\, I will discuss the notion of optimal polynomial approximan
 ts\, which are polynomials that approximate\, in some sense\, inverses of 
 functions in certain Hilbert spaces of analytic functions. In the last 10 
 years\, a number of papers have appeared examining the zeros of these poly
 nomials\, rates of convergence\, efficient algorithms for their computatio
 n\, and connections to orthogonal polynomials and reproducing kernels\, am
 ong other topics. On the other hand\, in the 70s\, researchers in engineer
 ing and applied mathematics introduced least squares inverses in the conte
 xt of digital filters in signal processing. It turns out that in the Hardy
  space $H^2$ the optimal polynomial approximants and the least squares inv
 erses are identical. In this talk\, I will survey results related to the z
 eros of optimal polynomial approximants and implications for the design of
  ideal digital filters. This talk is based on a preprint of a survey paper
  that is joint with Ray Centner.\n
LOCATION:https://researchseminars.org/talk/CAvid/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dierk Schleicher (Aix–Marseille Université)
DTSTART:20201103T140000Z
DTEND:20201103T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/19/">F
 inding polynomial roots using complex analysis\, dynamical systems\, compu
 ter algebra</a>\nby Dierk Schleicher (Aix–Marseille Université) as part
  of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstr
 act\nOne of the classical problems in all areas of mathematics is to find 
 roots of complex polynomials. It is well known that this can be done only 
 by methods of approximation. We discuss three classical methods: the Newto
 n\, Weierstrass\, and Ehrlich-Aberth methods\; these are complex analytic 
 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 introduce thes
 e complex analytic dynamical systems and describe recent progress towards 
 their global dynamical properties. In particular\, the Newton and Weierstr
 ass methods are not globally convergent: for open sets of polynomials ther
 e are open sets of initial points that fail to converge to roots. Moreover
 \, for Weierstrass and Ehrlich-Aberth\, there are orbits that are always d
 efined and converge\, but not to roots. For Newton\, there is meanwhile a 
 rich theory about its global dynamics\, but there are many open questions 
 for all these methods.\n\nMuch of this is joint work with members of my ER
 C team\, in particular my PhD student Bernhard Reinke\, as well as with co
 lleagues.\n
LOCATION:https://researchseminars.org/talk/CAvid/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Trefethen (University of Oxford)
DTSTART:20201110T140000Z
DTEND:20201110T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/20/">A
 pproximation on complex domains and Riemann surfaces</a>\nby Nick Trefethe
 n (University of Oxford) as part of CAvid: Complex Analysis video seminar\
 n\nLecture held in N/A.\n\nAbstract\nLet f be a function analytic on a clo
 sed Jordan region E apart\nfrom a finite number of branch point singularit
 ies on the boundary.\nWe show how f can be approximated by rational functi
 ons on E with\nroot-exponential convergence\, i.e.\, errors $O(\\exp(-C \\
 sqrt n))$ with\n$C>0$.  Such approximations lead to "lightning solvers" fo
 r Laplace\nproblems in planar domains.  Then we move to "reciprocal-log" o
 r\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\ncan be 
 analytically continued around the branch points to provide\napproximation 
 on further Riemann sheets.  This work (with Yuji\nNakatsukasa) is very new
 \, and there are many open questions.\n
LOCATION:https://researchseminars.org/talk/CAvid/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Núria Fagella (University of Barcelona)
DTSTART:20201117T140000Z
DTEND:20201117T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/21/">W
 andering in complex dynamics</a>\nby Núria Fagella (University of Barcelo
 na) as part of CAvid: Complex Analysis video seminar\n\nLecture held in N/
 A.\n\nAbstract\nIn a holomorphic dynamical system a wandering domain is a 
 component of the stable (or normal) set whose iterates never meet. This ty
 pe of components only exist in the presence of essential singularities and
  are the most unknown among all the possible kinds. In this talk I will ex
 plain what is and is not known about wandering domains and some of the mos
 t recent progress\, which relates wandering dynamics to sequences of holom
 orphic functions on the unit disk (non-autonomous dynamics).\n
LOCATION:https://researchseminars.org/talk/CAvid/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gautam Bharali (Indian Institute of Science\, Bangalore)
DTSTART:20201124T140000Z
DTEND:20201124T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/22/">T
 he Wolff-Denjoy theorem beyond the unit disc</a>\nby Gautam Bharali (India
 n Institute of Science\, Bangalore) as part of CAvid: Complex Analysis vid
 eo seminar\n\nLecture held in N/A.\n\nAbstract\nThe Wolff-Denjoy theorem h
 as been the motivation for a host of results that resemble the classical t
 heorem for holomorphic self-maps of the unit disc. In this talk\, we 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\, which may
  have rough boundaries and aren't necessarily contractible. While our tech
 niques are motivated by the properties of holomorphic maps in several comp
 lex variables\, the theory of such maps turns out to be incidental to thes
 e techniques. In fact\, in this talk\, we shall spend some time examining 
 certain analogies between the Poincaré distance and the Hilbert distance 
 on convex domains. This is relevant as there exists a Wolff--Denjoy-type t
 heorem\, by Beardon\, in the latter setting. It is these analogies that gi
 ve rise to the fundamental concept that underlies our result(s): namely\, 
 a weak notion of negative curvature for spaces equipped with the Kobayashi
  distance (of which the Poincaré distance is a special case). No knowledg
 e of several complex variables will be assumed in this talk: indeed\, most
  of the discussion will focus on basic complex analysis and on the propert
 ies of metric spaces and contractive maps. A large part of this talk will 
 be based on joint work with Andrew Zimmer and Anwoy Maitra.\n
LOCATION:https://researchseminars.org/talk/CAvid/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Gauthier (Université de Montréal)
DTSTART:20201201T140000Z
DTEND:20201201T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/23/">A
 symptotic first boundary value problem for holomorphic functions  of sever
 al complex variables</a>\nby Paul Gauthier (Université de Montréal) as p
 art of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAb
 stract\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 domain. L
 et $\\mu$ be a regular Borel measure on $U\,$ such that non-empty open set
 s of $U$ have positive $\\mu$ measure and $\\nu$ a regular Borel measure o
 n $\\partial U.$ Let $\\psi$ be a \nBorel measurable function on $\\partia
 l U\,$  \nwhose restriction to some closed subset $S\\subset\\partial U$ i
 s continuous.  \nThen\,   \nthere exists a holomorphic function $f$ on $U\
 ,$  such that\, for $\\nu$-almost every $p\\in \\partial U$\, \nand for ev
 ery $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://researchseminars.org/talk/CAvid/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kerstin Jordaan (University of South Africa)
DTSTART:20201208T140000Z
DTEND:20201208T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/24/">A
  characterisation of Askey-Wilson polynomials and the indeterminate moment
  problem associated with a limiting case</a>\nby Kerstin Jordaan (Universi
 ty of South Africa) as part of CAvid: Complex Analysis video seminar\n\nLe
 cture 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 characterisi
 ng relation for Askey-Wilson orthogonal polynomials and study a limiting c
 ase of Askey-Wilson polynomials when one of the parameters goes to infinit
 y. Solutions to the associated indeterminate moment problem  are found and
  an orthogonality relation is established.\n
LOCATION:https://researchseminars.org/talk/CAvid/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhijit Banerjee (University of Kalyani\, India)
DTSTART:20201215T140000Z
DTEND:20201215T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/25/">A
  survey on different uniqueness and strong uniqueness polynomials and thei
 r generating unique range sets</a>\nby Abhijit Banerjee (University of Kal
 yani\, India) as part of CAvid: Complex Analysis video seminar\n\nLecture 
 held in N/A.\n\nAbstract\nThe notion of unique range sets was introduced b
 y Gross-Yang [Proc. Japan Acad.\, 58 (1982)\, 17-20]. Since the inception 
 of the definition\, it became an interesting topic for the researchers to 
 study. In course of time\, the research had been shifted to-wards the char
 acterizations of the polynomial backbone of concerned sets. As a result\, 
 the uniqueness and strong uniqueness polynomial appeared in the literature
  and made a lusting impression. \n\nIn 2000\, H. Fujimoto [H. Fujimoto\, O
 n uniqueness of meromorphic functions sharing finite sets\, Amer. J. Math.
 \, 122 (2000)\, 1175-1203.] first discovered a special property of a polyn
 omial\, called it as “property (H)” which played a vital role in the r
 esearch of uniqueness and strong uniqueness polynomial.\n\nWithin the real
 m of Nevanlinna theory\, we wish to elaborately characterize the existing 
 uniqueness as well as strong uniqueness polynomials\, the relation between
  them and their contribution in forming the unique range sets under relaxe
 d sharing hypothesis. We also wish to discuss the scope for future researc
 h and intend to present our humble contribution in this aspect.\n
LOCATION:https://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:20260422T165132Z
UID:CAvid/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/26/">H
 erman rings of elliptic functions</a>\nby Mónica Moreno Rocha (Centro de 
 Investigación en Matemáticas\, Mexico) as part of CAvid: Complex Analysi
 s video seminar\n\nLecture held in N/A.\n\nAbstract\nConsider the family o
 f iterates of a rational or transcendental meromorphic function $f$. A com
 ponent of normality that is invariant under some $n$-iterate of $f$ is cal
 led a Herman ring if over such a component\, $f^n$ is conformally conjugat
 e to an irrational rotation acting on an annulus of finite conformal modul
 us. In that case\, the positive iterates of the Herman ring form a cycle. 
 Showing the existence of cycles of Herman rings for meromorphic functions 
 is not an easy task\, and when they exist\, it is natural to ask oneself i
 f an upper bound for the number of cycles is achievable.\n\nIn the late 19
 80s Shishikura introduced the theory of quasiconformal surgery to construc
 t 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\, rational m
 aps of degree 2 cannot have Herman rings). In the case of elliptic functio
 ns\, Hawkins & Koss showed in 2004 that the Weierstrass P function\, defin
 ed over any given lattice\, cannot have cycles of Herman rings. This resul
 t motivated the question of the existence of Herman rings for elliptic fun
 ctions in terms of their order. In this talk\, I will present recent resul
 ts obtained through the implementation of Shishikura’s surgery technique
 s to the elliptic case. First\, we’ll see that Herman rings can be reali
 zable by elliptic functions of order at least 3\, and in particular\, orde
 r 2 elliptic functions cannot have cycles of Herman rings. Then\, I will p
 resent an upper bound for the number of invariant Herman rings in terms of
  the order of the elliptic function and show how to refine that bound usin
 g the multiplicity of poles.\n
LOCATION:https://researchseminars.org/talk/CAvid/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Dyakonov (ICREA & Universitat de Barcelona\, Spain)
DTSTART:20210202T140000Z
DTEND:20210202T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/28/">L
 acunary polynomials in $L^1$: geometry of the unit sphere</a>\nby Konstant
 in Dyakonov (ICREA & Universitat de Barcelona\, Spain) as part of CAvid: C
 omplex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nLet $\\
 Lambda$ be a finite set of nonnegative integers\, and let $\\mathcal P(\\L
 ambda)$ be the linear hull of the monomials $z^k$ with $k\\in\\Lambda$\, v
 iewed as a subspace of $L^1$ on the unit circle. We characterize the extre
 me and exposed points of the unit ball in $\\mathcal P(\\Lambda)$.\n
LOCATION:https://researchseminars.org/talk/CAvid/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linda Keen (CUNY\, USA)
DTSTART:20210209T140000Z
DTEND:20210209T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/29/">P
 arameter spaces of families of transcendental functions</a>\nby Linda Keen
  (CUNY\, USA) as part of CAvid: Complex Analysis video seminar\n\nLecture 
 held in N/A.\n\nAbstract\nThis lecture is based on joint work with Tao Che
 n\, Nuria Fagella and Yunping Jiang. It is part of a more general program 
 to understand parameter spaces of transcendental maps.\n\nIf we perturb a 
 rational function by a topological conjugacy we obtain a rational function
 \, so the dynamics depend on the coefficients\, which therefore form a nat
 ural parameter space. It is not true that there is a natural way of parame
 terizing general families of transcendental functions so that a perturbati
 on of the function remains in the family. This makes it difficult to descr
 ibe how the dynamics varies across these families. We will look at two exa
 mples of reasonably general families of transcendental meromorphic functio
 ns where one can overcome these difficulties. What this means is that we w
 ill be able to describe the properties of the components defined by the bi
 furcation locus. We will see at the end how these examples fit into the la
 rger program.\n
LOCATION:https://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:20260422T165132Z
UID:CAvid/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/30/">A
 lgebraic invariants\, integrability\, and meromorphic solutions</a>\nby Ma
 ria Demina (National Research University Higher School of Economics\, Russ
 ia) as part of CAvid: Complex Analysis video seminar\n\nLecture held in N/
 A.\n\nAbstract\nConsider an autonomous algebraic ordinary differential equ
 ation of order higher than one. The aim of the talk is to address the foll
 owing questions.\n\n1. Does there exist an autonomous algebraic first-orde
 r ordinary differential equation compatible with the original equation?\n\
 n2. If yes\, how to find all such equations?\n \n\nBivariate polynomials p
 roducing autonomous algebraic first-order ordinary differential equations 
 compatible with the equation under consideration are called algebraic inva
 riants. The main difficulty in deriving irreducible algebraic invariants l
 ies in the fact that the degrees of related bivariate polynomials are not 
 known in advance.\n\nAlgebraic invariants are important from theoretical a
 nd practical point of views. In the two-dimensional case algebraic invaria
 nts are key objects in establishing Darboux and Liouvillian integrability 
 of the original ordinary differential equation. In addition\, algebraic in
 variants can be used to perform the classification of W-meromorphic soluti
 ons of ordinary differential equations. We shall pay some attention to the
 se applications.\n
LOCATION:https://researchseminars.org/talk/CAvid/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Risto Korhonen (University of Eastern Finland)
DTSTART:20210323T130000Z
DTEND:20210323T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/31/">D
 elay differential equations and Nevanlinna theory</a>\nby Risto Korhonen (
 University of Eastern Finland) as part of CAvid: Complex Analysis video se
 minar\n\nLecture held in N/A.\n\nAbstract\nThe idea that the existence of 
 sufficiently many finite-order meromorphic solutions could be used to sing
 le out difference Painlevé equations was introduced by Ablowitz\, Halburd
  and Herbst. In this talk necessary conditions are obtained for certain ty
 pes of delay differential equations to admit a transcendental meromorphic 
 solution of hyper-order less than one. The equations obtained include dela
 y Painlevé equations and equations solvable by elliptic functions. We con
 clude with recent results on the existence of transcendental meromorphic s
 olutions of first-order difference equations\, without growth conditions.\
 n
LOCATION:https://researchseminars.org/talk/CAvid/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Chyzhykov (University of Warmia and Mazury\, Poland)
DTSTART:20210223T140000Z
DTEND:20210223T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/32/">I
 rregular solutions of complex linear differential equations in the unit di
 sc</a>\nby Igor Chyzhykov (University of Warmia and Mazury\, Poland) as pa
 rt of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbs
 tract\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 coeffi
 cient $A$ is analytic in the unit disc and $\\log^+ M(r\,A)/\\log(1-r)$ te
 nds to a~finite limit as $r\\to 1^-$.\nA~family of  examples is constructe
 d\, where the order of solutions remain the same while the lower order may
  vary on a~certain interval depending on the irregular growth of the coeff
 icient.\nThese coefficients emerge as the logarithm of their modulus appro
 ximates smooth radial subharmonic functions of prescribed irregular growth
  on a~sufficiently large subset of the unit disc.\nA~result describing the
  phenomenon behind these  examples is also established. En route to\nresul
 ts of general nature\, a~new sharp logarithmic derivative estimate involvi
 ng the lower order of growth is discovered.\nIn addition to these estimate
 s\,\narguments used are based\, in particular\, on the Wiman-Valiron theor
 y adapted for the lower order.\n
LOCATION:https://researchseminars.org/talk/CAvid/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paweł Wójcicki (Warsaw University of Technology\, Poland)
DTSTART:20210302T140000Z
DTEND:20210302T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/33
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/33/">O
 n an Invariant distance induced by the Szego kernel and its applications</
 a>\nby Paweł Wójcicki (Warsaw University of Technology\, Poland) as part
  of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstr
 act\nThe aim of my talk is to recall the notion of the so called Szego ker
 nel and provide some new biholomorphic invariant by means of it.  In fact\
 , it is defined on a similar way as the co called Skwarczyński distance b
 y means of the Bergman kernel.  The relationship  between completeness in 
 both cases will be examined.  It turns out that the new biholomorphic inva
 riant gives rise to some other new invariant\, by means of which we can es
 timate 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://researchseminars.org/talk/CAvid/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chengfa Wu (Shenzhen University\, China)
DTSTART:20210316T130000Z
DTEND:20210316T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/34/">E
 lliptic functions and their applications in complex differential equations
 </a>\nby Chengfa Wu (Shenzhen University\, China) as part of CAvid: Comple
 x Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nThis talk fo
 cuses on the applications of elliptic functions in complex differential eq
 uations. First\, we discuss classifications of meromorphic solutions of ce
 rtain autonomous complex differential equations. In particular\, we will f
 ocus on the Loewy factorizable algebraic ODEs. Then we move to the study o
 f the autonomous Schwarzian differential equations (SDEs). Ishizaki showed
  that there are six canonical types of autonomous SDEs that have transcend
 ental meromorphic solutions. We will construct all transcendental meromorp
 hic solutions of five canonical types explicitly. In particular\, the solu
 tions of four types are shown to be elliptic functions. Also\, all transce
 ndental meromorphic solutions that possess a Picard exceptional value are 
 characterized for the remaining canonical type. This talk is based on join
 t works with Ng and Liao respectively.\n
LOCATION:https://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:20260422T165132Z
UID:CAvid/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/35/">P
 olynomial convexity and real surfaces with singularity</a>\nby Sushil Gora
 i (Indian Institute of Science Education and Research Kolkata) as part of 
 CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\
 nIn this talk I will first discuss briefly about polynomial convexity and 
 its application in polynomial approximations. Then\, I will discuss the qu
 estions of polynomial convexity and approximation on compact subsets of a 
 couple of classes of real surfaces in $\\mathbb{C}^2$ with singularity\, n
 amely\, the union of three totally real subspaces and surfaces with isolat
 ed CR-singularity.\n
LOCATION:https://researchseminars.org/talk/CAvid/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Caterina Stoppato (Università di Firenze\, Italy)
DTSTART:20210309T140000Z
DTEND:20210309T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/36
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/36/">R
 egularity in one hypercomplex variable</a>\nby Caterina Stoppato (Universi
 tà di Firenze\, Italy) as part of CAvid: Complex Analysis video seminar\n
 \nLecture held in N/A.\n\nAbstract\nSince the 1930s\, several function the
 ories have been introduced over the algebra of quaternions and other alter
 native algebras. The aim of such constructions is to recover in higher dim
 ensions the refined tools available in the theory of holomorphic functions
  of one complex variable. The peculiar properties of the higher-dimensiona
 l algebras considered are reflected in the different theories introduced.\
 n\nA relatively recent breakthrough was the introduction of the class of s
 lice regular functions of one quaternionic variable by Gentili and Struppa
  in 2006. This study\, generalized to alternative $*$-algebras by Ghiloni 
 and Perotti in 2011\, has rapidly developed into a full-fledged theory.\n\
 nThe talk will overview the general problem of function theory in one hype
 rcomplex variable\, the main features of the theory of slice regular funct
 ions and its applications to open problems from other areas of mathematics
 .\n
LOCATION:https://researchseminars.org/talk/CAvid/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yueyang Zhang (University of Science and Technology Beijing)
DTSTART:20210420T130000Z
DTEND:20210420T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/37/">O
 n entire function $e^{p(z)}\\int_0^{z}\\beta(t)e^{-p(t)}dt$ with applicati
 ons to Tumura--Clunie equations and complex dynamics</a>\nby Yueyang Zhang
  (University of Science and Technology Beijing) as part of CAvid: Complex 
 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 function 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 entire func
 tion $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 differen
 tial 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 different
 ial polynomial in $f$ of degree $\\leq n-1$ with meromorphic functions of 
 order less than~$k$ as coefficients\, and precisely characterize entire so
 lutions of this equation. This gives an answer to a problem in the literat
 ure and allows to find all zero-free solutions of the second-order differe
 ntial equation $f''-(b_1e^{p_1}+b_2e^{p_2}+b_3)f=0$\, where $b_3$ is a pol
 ynomial. We also use the Phragm\\'{e}n--Lindel\\"{o}f theorem to prove a t
 heorem on certain first-order non-homogeneous linear differential equation
  related to complex dynamics.\n
LOCATION:https://researchseminars.org/talk/CAvid/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara de Fabritiis (Università Politecnica delle Marche\, Italy)
DTSTART:20210427T130000Z
DTEND:20210427T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/38
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/38/">*
 -products\, *-exponential\, *-logarithm: some peculiarities of slice regul
 ar functions on the quaternions</a>\nby Chiara de Fabritiis (Università P
 olitecnica delle Marche\, Italy) as part of CAvid: Complex Analysis video 
 seminar\n\nLecture held in N/A.\n\nAbstract\nSlice regular functions on qu
 aternions were introduced in 2006 by Gentili and Struppa in order to gener
 alize the notion of holomorphic functions on complex numbers (for an effec
 tive introduction you can refer to C. Stoppato's seminar  (https://mediace
 ntral.ucl.ac.uk/Play/59248/). The theory had a quick development in severa
 l directions by many authors\, in this talk I will focus on three unexpect
 ed behaviours of these functions. The first aspect we deal with is the *-p
 roduct\, which is the analogous of pointwise product for holomorphic funct
 ions\; in particular we give an interpretation of this operation via two o
 perators which resemble the scalar product and the vector product on R^3. 
 The second point we investigate is a suitable extension of the notion of e
 xponential of a slice regular function\, namely the *-exponential exp_*(f)
  (originally introduced by Colombo\, Sabadini and Struppa)\; we will descr
 ibe some of its features\, especially with regard to the non-commutativity
  of the *-product and to its connections with *-sine and *-cosine. Lastly\
 , we study the possible existence and uniqueness of a *-logarithm of a nev
 er vanishing slice regular function\, both on slice and on product domains
  of the quaternions. We give some existence and non-existence results for 
 *-logarithm of never-vanishing slice regular functions (according to the s
 plitting in real and vectorial part) and an accurate description of the po
 ssible uniqueness of the *-logarithm.\nThis is a joint work with Amedeo Al
 tavilla (Università di Bari).\n
LOCATION:https://researchseminars.org/talk/CAvid/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Roth (University of Würzburg)
DTSTART:20210504T130000Z
DTEND:20210504T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/39/">A
  new Schwarz-Pick Lemma at the boundary and rigidity of holomorphic maps</
 a>\nby Oliver Roth (University of Würzburg) as part of CAvid: Complex Ana
 lysis video seminar\n\nLecture held in N/A.\n\nAbstract\nWe establish seve
 ral invariant boundary versions of the (infinitesimal) Schwarz-Pick lemma 
 for conformal pseudometrics on the unit disk and for holomorphic selfmaps 
 of strongly convex domains in CN in the spirit of the boundary Schwarz lem
 ma of Burns-Krantz. Firstly\, we focus on the case of the unit disk and pr
 ove a general boundary rigidity theorem for conformal pseudometrics with v
 ariable curvature. In its simplest cases this result already includes 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 inequality a
 s well as a boundary Hopf lemma for conformal pseudometrics which extend e
 arlier interior rigidity results of Golusin\, Heins\, Beardon\, Minda and 
 others. Secondly\, we prove similar rigidity theorems for sequences of con
 formal pseudometrics\, which even in the interior case appear to be new. F
 or instance\, a first sequential version of the strong form of Ahlfors' le
 mma is obtained. As an auxiliary tool we establish a Hurwitz-type result a
 bout preservation of zeros of sequences of conformal pseudometrics. Thirdl
 y\, we apply the one-dimensional sequential boundary rigidity results toge
 ther with a variety of techniques from several complex variables to prove 
 a boundary version of the Schwarz-Pick lemma for holomorphic maps of stron
 gly convex domains in $\\C^N$ for $N>1$.\n\n(This is joint work with Filip
 po Bracci and Daniela Kraus)\n
LOCATION:https://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:20260422T165132Z
UID:CAvid/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/40/">A
  potential-theoretic characterization of polynomials in holomorphic dynami
 cs in one  variable}</a>\nby Margaret Stawiska-Friedland\\ (American Mathe
 matical Society/Mathematical Reviews\, USA) as part of CAvid: Complex Anal
 ysis video seminar\n\nLecture held in N/A.\n\nAbstract\nIn 1960s Hans Brol
 in initiated systematic application of potential-theoretic methods in the 
 dynamics of holomorphic maps. Among other things\, he proved the now-famou
 s equidistribution theorem: for a complex polynomial $f$ of degree greater
  than $1$ the preimages\, under successive iterates of $f$\, of a Dirac me
 asure at an arbitrary point of the complex plane (except at most two so-ca
 lled exceptional points) converge weakly to the equilibrium measure (with 
 pole at infinity) for the Julia set $J_f$ of $f$. To a general rational ma
 p $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 sup
 ported on the Julia set for $f$ and satisfies  $f*\\mu=d \\cdot \\mu$. Sin
 ce it also can be obtained as the limit of  preimages of quite general pro
 babilistic measures on $\\mathbb{CP}^1$ (thanks to the results of M. Lyubi
 ch and independently Freire-Lopes-R. Ma\\~ne from 1980s)\, a question aris
 es whether it always equals the equilibrium measure for $J_f$ (when the la
 tter notion makes sense). Several mathematicians noticed  that equality of
  these two measures (under suitable assumptions on $f$) implies that $f$ i
 s a polynomial. However\, all  ``proofs''  of this implication from  befor
 e 1990s contained gaps. The proof  by S. Lalley from 1992 was fully succes
 sful\, but it was based on the theory of Brownian motions. In this talk\, 
 I will present a  general version  of this implication  with a proof 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$ whose Jul
 ia set does not contain the point $\\infty$. The following are equivalent:
  (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 infinity ar
 e equal. This  is joint work with Y\\^usuke Okuyama from Kyoto Institute o
 f Technology.\n
LOCATION:https://researchseminars.org/talk/CAvid/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Khavinson (University of South Florida)
DTSTART:20210518T130000Z
DTEND:20210518T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/41
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/41/">A
 lgebra and PDE :  Some Less Traveled Paths Connecting Them</a>\nby Dmitry 
 Khavinson (University of South Florida) as part of CAvid: Complex Analysis
  video seminar\n\nLecture held in N/A.\n\nAbstract\nHere are samples of qu
 estions I plan to discuss.\n\n- Let $F(u\,v)$ be a rational function of tw
 o 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$ is a lin
 ear function\, i.e.\, $u=ax+by+c$. Why?  Is it true in three variables?\n\
 n- Does there exist a harmonic polynomial in $\\mathbb{R}^n$ divisible by 
 a non-negative polynomial?\n\n- Let $P(D)[u^k]=0$\, where $P(D)$ is a part
 ial differential operator with constant\, polynomial \, or even entire coe
 fficients and k runs over an arithmetic progression of positive integers\,
  e. g.\, $k=2n+3$\, $n=1\,2\,\\ldots$.  Then the Hessian\, Hess $u$\, vani
 shes identically\, so the mapping grad $u:\\\, \\mathbb{C}^n\\mapsto\\math
 bb{C^n}$ is degenerate\, i.e.\, the range is an algebraic variety. Is it t
 rue? \n\n- When we are solving the Dirichlet problem in a domain with an a
 lgebraic boundary\, and the Dirichlet data is a polynomial\, a rational or
  an algebraic function\, is the solution algebraic as well?\n
LOCATION:https://researchseminars.org/talk/CAvid/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Chuaqui Farrú (Pontificia Universidad Católica de Chile)
DTSTART:20210601T130000Z
DTEND:20210601T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/42/">A
 hlfors’ Schwarzians for curves</a>\nby Martin Chuaqui Farrú (Pontificia
  Universidad Católica de Chile) as part of CAvid: Complex Analysis video 
 seminar\n\nLecture held in N/A.\n\nAbstract\nWe discuss Ahlfors' Schwarzia
 n derivatives for curves in euclidean space introduced some three decades 
 ago. The definitions consider separate generalizations of the real and ima
 ginary part of the classical operator in the complex plane that have impor
 tant invariance properties with respect to the Möbius group in euclidean 
 n-space.  We will describe some of the applications of the real Schwarzian
  to the study of simple curves in n-space\, to knots in 3-space\, as well 
 as to the injectivity of the conformal parametrization of minimal surfaces
  in 3-space. The role of the imaginary Schwarzian will be presented in euc
 lidean 3-space\, highlighting its connection with the osculating sphere\, 
 a new transformation law under the Möbius group\, and theorems on the exi
 stence and uniqueness of parametrized curves with prescribed real and imag
 inary Schwarzians.\n
LOCATION:https://researchseminars.org/talk/CAvid/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasiliki Evdoridou (Open University\, UK)
DTSTART:20210608T130000Z
DTEND:20210608T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/43/">W
 andering on the boundary</a>\nby Vasiliki Evdoridou (Open University\, UK)
  as part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\
 n\nAbstract\nIn the theory of iteration of transcendental entire functions
 \, wandering domains\, i.e. connected components of the Fatou set that 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 domain
 s. In particular\, we consider the possibility that most boundary orbits c
 onverge together in a certain sense\, and give sufficient conditions for s
 uch a convergence to hold. Our results are motivated by and extend classic
 al 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. Stallard.
 \n
LOCATION:https://researchseminars.org/talk/CAvid/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Galina Filipuk (University of Warsaw)
DTSTART:20210615T130000Z
DTEND:20210615T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/44
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/44/">A
 spects of nonlinear differential equations</a>\nby Galina Filipuk (Univers
 ity of Warsaw) as part of CAvid: Complex Analysis video seminar\n\nLecture
  held in N/A.\n\nAbstract\nNonlinear differential equations may have compl
 icated singularities in the\ncomplex plane. Painleve equations are nonline
 ar second order differential\nequations solutions of which have no movable
  critical points. They have a\nlot of nice properties.\n\nIn this talk I s
 hall mainly review connection between solutions of the  \nPainlev\\'e equa
 tions and   recurrence coefficients of semi-classical\northogonal polynomi
 als.\n
LOCATION:https://researchseminars.org/talk/CAvid/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jujie Wu (Sun Yat-Sen University)
DTSTART:20210622T130000Z
DTEND:20210622T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/45
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/45/">W
 eighted L^2 polynomial approximation in C</a>\nby Jujie Wu (Sun Yat-Sen Un
 iversity) as part of CAvid: Complex Analysis video seminar\n\nLecture 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 b
 ounded domain $\\Omega$ in $\\C$\, where $\\varphi$ is a subharmonic funct
 ion.  In particular\, we prove that the density holds in Caratheodory doma
 ins for any subharmonic function $\\varphi$ in a neighborhood of the closu
 re of $\\Omega$. In non-Caratheodory domains\, we prove that the density d
 epends on the weight function\, giving examples. We also give a weighted $
 L^2$ version of Weierstrass theorem and give the example. Some $L^2$ appro
 ximation in higher dimension also will be state here\, which part are in p
 rogress now.\n\nThis is joint with Severine Biard and John Erik Fornaess.\
 n
LOCATION:https://researchseminars.org/talk/CAvid/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walter Van Assche (KU Leuven)
DTSTART:20210706T130000Z
DTEND:20210706T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/46/">H
 ermite-Padé approximation to two function with branch points</a>\nby Walt
 er Van Assche (KU Leuven) as part of CAvid: Complex Analysis video seminar
 \n\nLecture held in N/A.\n\nAbstract\nHermite-Padé approximation to two f
 unctions is rational approximation to both functions with a common denomin
 ator and close contact at one point (we will use infinity). The common den
 ominator is a polynomial with orthogonality conditions for two measures. I
 f the two functions have branch points in the complex plane\, then the asy
 mptotic behaviour of the zeros (the poles of the Hermite-Padé approximant
 s) is determined by algebraic functions satisfying a cubic relation.\nWe w
 ill sketch how to get the full asymptotics of the common denominator using
  the Riemann-Hilbert problem for matrix valued functions for some particul
 ar choices of branch points\, which appear in applications in number theor
 y.\n
LOCATION:https://researchseminars.org/talk/CAvid/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Bishop (Stony Brook University\, USA)
DTSTART:20210914T130000Z
DTEND:20210914T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/47
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/47/">F
 ast conformal mapping via computational and hyperbolic geometry</a>\nby Ch
 ris Bishop (Stony Brook University\, USA) as part of CAvid: Complex Analys
 is video seminar\n\nLecture held in N/A.\n\nAbstract\nThe conformal map fr
 om the unit disk to the interior of a polygon P is given by the Schwarz-Ch
 ristoffel formula\, but this is stated in terms of parameters that are har
 d to compute from P. After some background and motivation\, I explain how 
 the medial axis of a domain\, a concept from computational geometry\, can 
 be used to give a fast approximation to these parameters\, with bounds on 
 the accuracy that are independent of P. The precise statement involves qua
 siconformal mappings\, and proving these bounds uses a result about hyperb
 olic convex sets originating in Thurston's work on 3-manifolds.  If time p
 ermits\,  I will mention some applications to optimal meshing and triangul
 ation of planar polygons.\n
LOCATION:https://researchseminars.org/talk/CAvid/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirill Lazebnik (University of Toronto\, Canada)
DTSTART:20210921T130000Z
DTEND:20210921T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/48/">T
 ranscendental Julia Sets of Minimal Hausdorff Dimension</a>\nby Kirill Laz
 ebnik (University of Toronto\, Canada) as part of CAvid: Complex Analysis 
 video seminar\n\nLecture held in N/A.\n\nAbstract\nWe discuss an approach 
 to the construction of entire functions with Julia sets having minimal Hau
 sdorff dimension. This talk will not assume a background in complex dynami
 cs. This talk is based on joint work with Jack Burkart.\n
LOCATION:https://researchseminars.org/talk/CAvid/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilin Wang (MIT\, USA)
DTSTART:20210928T130000Z
DTEND:20210928T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/49/">L
 oewner-Kufarev energy and foliations by Weil-Petersson quasicircles</a>\nb
 y Yilin Wang (MIT\, USA) as part of CAvid: Complex Analysis video seminar\
 n\nLecture held in N/A.\n\nAbstract\nWe use Loewner-Kufarev equation to de
 scribe evolutions of univalent functions and introduce an energy on the dr
 iving measure\, called Loewner-Kufarev energy. We show that when this ener
 gy is finite\, the boundaries of the evolving image domains are Weil-Peter
 sson quasicircles which form a foliation of the Riemann sphere. Weil-Peter
 sson quasicircles are studied in Teichmuller theory\, geometric function t
 heory\, and string theory by both mathematicians and physicists. More than
  20 equivalent definitions of this class of Jordan curves are discovered s
 o far. In particular\, it is characterized as the class of curves having f
 inite Loewner energy which was also introduced recently. Furthermore\, we 
 show that the Loewner-Kufarev energy is dual to the Loewner energy and exh
 ibits remarkable symmetries. Both energies and their duality result are in
 spired by ideas from the probabilistic theory of Schramm-Loewner evolution
 s. This is a joint work with Fredrik Viklund (KTH).\n\nReferences: \n\nThe
  Loewner-Kufarev energy and foliations by Weil-Petersson quasicircles\nFre
 drik Viklund\, Yilin Wang (2020)\nhttps://arxiv.org/abs/2012.05771\n
LOCATION:https://researchseminars.org/talk/CAvid/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Istvan Prause (University of Eastern Finland)
DTSTART:20211005T130000Z
DTEND:20211005T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/50
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/50/">P
 robabilistic limit shapes and harmonic functions</a>\nby Istvan Prause (Un
 iversity of Eastern Finland) as part of CAvid: Complex Analysis video semi
 nar\n\nLecture held in N/A.\n\nAbstract\nLimit shapes are surfaces in $\\m
 athbb{R^3}$ which arise in the scaling limit of discrete random surfaces a
 ssociated to various probability models such as domino tilings\, random Yo
 ung tableaux or the 5-vertex model. The limit surface is a minimiser of a 
 gradient variational problem with a surface tension which encodes the loca
 l entropy of the model. I'll show that in an intrinsic complex variable th
 ese limit shapes can all be parametrised by harmonic functions across a va
 riety of models. Some new features beyond determinantal settings will be d
 iscussed. The talk is based on joint works with Rick Kenyon.\n
LOCATION:https://researchseminars.org/talk/CAvid/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jörg Winkelmann (Ruhr-Universität Bochum\, Germany)
DTSTART:20211012T130000Z
DTEND:20211012T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/51
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/51/">O
 n the existence of dense entire holomorphic curves in rationally connected
  manifolds</a>\nby Jörg Winkelmann (Ruhr-Universität Bochum\, Germany) a
 s part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\
 nAbstract\nJoint work with Frederic Campana. We prove that for every ratio
 nally connected\nprojective manifold X there exists a holomorphic map from
  the complex line to X with\ndense image and deduce some related results.\
 n
LOCATION:https://researchseminars.org/talk/CAvid/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhi-Tao Wen (Shantou University\, China)
DTSTART:20211019T130000Z
DTEND:20211019T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/52
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/52/">D
 ifference radical in terms of shifting zero and applications to the Stothe
 rs-Mason theorem</a>\nby Zhi-Tao Wen (Shantou University\, China) as part 
 of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstra
 ct\nIn this talk\, we show the shifting zeros with its heights and an anal
 ogue to difference radical. We focus on the Stothers-Mason theorem by usin
 g falling factorials. As applications\, we discuss the difference version 
 of the Fermat type functional equations. Some examples are given. It is a 
 joint work with Katsuya Ishizaki.\n
LOCATION:https://researchseminars.org/talk/CAvid/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zeinab Mansour (Cairo University\, Egypt)
DTSTART:20211026T130000Z
DTEND:20211026T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/53/">L
 idstone expansions of entire functions</a>\nby Zeinab Mansour (Cairo Unive
 rsity\, Egypt) as part of CAvid: Complex Analysis video seminar\n\nLecture
  held in N/A.\n\nAbstract\nLidstone expansions express an entire function 
 $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 ar
 e Bernoulli polynomials\; many authors introduced necessary and (or) suffi
 cient conditions for the absolute convergence of the series in the expansi
 on.  The classical exponential function plays an essential role in derivin
 g the Lidstone series. In the $q$ theory\, we have three $q$-difference op
 erators\, the Jackson $q$-difference operator\, the symmetric $q$-differen
 ce operator\, and the Askey-Wilson $q$-difference operator. Each operator 
 is associated with a $q$-analog of the exponential function. In this talk\
 , we introduce $q$-extensions to the Lidstone expansion associated with th
 ese operators. New three $q$-analogs of Bernoulli polynomials with nice pr
 operties are coming out. \n\nJoint work with Professor Mourad Ismail\, Uni
 versity of Central Florida\, USA.\n
LOCATION:https://researchseminars.org/talk/CAvid/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leticia Pardo-Simón (University of Manchester\, UK)
DTSTART:20211102T130000Z
DTEND:20211102T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/54
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/54/">T
 he maximum modulus set of an entire function</a>\nby Leticia Pardo-Simón 
 (University of Manchester\, UK) as part of CAvid: Complex Analysis video s
 eminar\n\nLecture held in N/A.\n\nAbstract\nThe set of points where an ent
 ire function achieves its maximum modulus is known as the maximum modulus 
 set\, and usually consists of a collection of disjoint analytic curves. In
  this talk\, we discuss recent progress on the description of the features
  that this set might exhibit. Namely\, on the existence of discontinuities
 \, singleton components\, and on its structure near the origin. This is ba
 sed on joint work with D. Sixsmith and V. Evdoridou.\n
LOCATION:https://researchseminars.org/talk/CAvid/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Mityushev (Cracow Technological University\, Poland)
DTSTART:20211109T140000Z
DTEND:20211109T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/55
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/55/">R
 iemann-Hilbert problem for a multiply connected domain and its application
 s to the effective properties of 2D random composites</a>\nby Vladimir Mit
 yushev (Cracow Technological University\, Poland) as part of CAvid: Comple
 x Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nIn this talk
  we answer the following question. "Why did James Bond prefer shaken\, not
  stirred martini with ice?" The posed question is resolved by reduction to
  the scalar Riemann-Hilbert problem Re (a f) = g for a multiply connected 
 domain and its complete solution. Relations to the ℝ-linear problem and 
 the effective properties of 2D random composites are discussed.\n
LOCATION:https://researchseminars.org/talk/CAvid/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter A. Clarkson (University of Kent\, UK)
DTSTART:20211116T140000Z
DTEND:20211116T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/56
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/56/">S
 pecial polynomials associated with the Painlevá equations</a>\nby Peter A
 . Clarkson (University of Kent\, UK) as part of CAvid: Complex Analysis vi
 deo seminar\n\nLecture held in N/A.\n\nAbstract\nThe six Painlevé equatio
 ns\, whose solutions are called the Painlevé transcendents\, were derived
  by Painlevé and his colleagues in the late 19th and early 20th centuries
  in a classification of second order ordinary differential equations whose
  solutions have no movable critical points. In the 18th and 19th centuries
 \, the classical special functions such as Bessel\, Airy\, Legendre and hy
 pergeometric functions\, were recognized and developed in response to the 
 problems of the day in electromagnetism\, acoustics\, hydrodynamics\, elas
 ticity and many other areas. \n\nAround the middle of the 20th century\, a
 s science and engineering continued to expand in new directions\, a new cl
 ass of functions\, the Painlevé functions\, started to appear in applicat
 ions. The list of problems now known to be described by the Painlevé equa
 tions is large\, varied and expanding rapidly. The list includes\, at one 
 end\, the scattering of neutrons off heavy nuclei\, and at the other\, the
  distribution of the zeros of the Riemann-zeta function on the critical li
 ne Re(z) =1/2. Amongst many others\, there is random matrix theory\, the a
 symptotic theory of orthogonal polynomials\, self-similar solutions of int
 egrable equations\, combinatorial problems such as the longest increasing 
 subsequence problem\, tiling problems\, multivariate statistics in the imp
 ortant asymptotic regime where the number of variables and the number of s
 amples are comparable and large\, and also random growth problems.\n\nThe 
 Painlevé equations possess a plethora of interesting properties including
  a Hamiltonian structure and associated isomonodromy problems\, which expr
 ess the Painlevé equations as the compatibility condition of two linear s
 ystems. Solutions of the Painlevé equations have some interesting asympto
 tics which are useful in applications. They possess hierarchies of rationa
 l solutions and one-parameter families of solutions expressible in terms o
 f the classical special functions\, for special values of the parameters. 
 Further the Painlevé equations admit symmetries under affine Weyl groups 
 which are related to the associated Bäcklund transformations. \n\nIn this
  talk I shall discuss special polynomials associated with rational solutio
 ns of Painlevé equations. Although the general solutions of the six Painl
 evé equations are transcendental\, all except the first Painlevé equatio
 n possess rational solutions for certain values of the parameters. These s
 olutions are expressed in terms of special polynomials. The roots of these
  special polynomials are highly symmetric in the complex plane and specula
 ted to be of interest to number theorists. The polynomials arise in applic
 ations such as random matrix theory\, vortex dynamics\, in the description
  of rogue wave patterns\, in supersymmetric quantum mechanics\, as coeffic
 ients of recurrence relations for semi-classical orthogonal polynomials an
 d are examples of exceptional orthogonal polynomials.\n
LOCATION:https://researchseminars.org/talk/CAvid/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thierry Meyrath (University of Luxembourg\, Luxembourg)
DTSTART:20211123T140000Z
DTEND:20211123T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/57/">O
 n covering properties of non-normal families of meromorphic functions</a>\
 nby Thierry Meyrath (University of Luxembourg\, Luxembourg) as part of CAv
 id: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nWe
  study the behaviour of families of meromorphic functions in the neighbour
 hood of points of non-normality and prove certain covering properties that
  complement Montel's Theorem. Moreover\, we obtain characterizations of no
 n-normality in terms of such properties. This talk is based on joint work 
 with Jürgen Müller.\n
LOCATION:https://researchseminars.org/talk/CAvid/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olubunmi A. Fadipe-Joseph (University of Ilorin\, Nigeria)
DTSTART:20211130T140000Z
DTEND:20211130T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/58
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/58/">T
 he sigmoid function in geometric function theory</a>\nby Olubunmi A. Fadip
 e-Joseph (University of Ilorin\, Nigeria) as part of CAvid: Complex Analys
 is video seminar\n\nLecture held in N/A.\n\nAbstract\nGeometric Function T
 heory (GFT) is a branch of complex analysis which studies geometric proper
 ties of analytic functions. Moreover\, in spite of the famous coefficient 
 problems\, Bieberbach conjecture that was solved by Louis de Branges in 19
 84 suggested various approaches and directions for study in geometric func
 tion theory.  Therefore\, one of the major interests in GFT is finding the
  coefficient bounds of univalent and multivalent functions. The bounds det
 ermine the growth\, distortion properties among others of the analytic fun
 ctions. Special functions are of great interest in mathematics\, mathemati
 cal\nphysics\, engineering and other fields of science. They are rich in t
 erms of practical applications in solving a wide range of\nproblems. Recen
 tly\, we investigate special functions in geometric function theory. In pa
 rticular\, the connection between sigmoid function and geometric function 
 theory was established.\n
LOCATION:https://researchseminars.org/talk/CAvid/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loredana Lanzani (Syracuse University\, USA)
DTSTART:20211207T140000Z
DTEND:20211207T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/59
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/59/">T
 he Cauchy-Szegö projection and its commutator for domains in $\\mathbb C^
 n$ with minimal smoothness</a>\nby Loredana Lanzani (Syracuse University\,
  USA) as part of CAvid: Complex Analysis video seminar\n\nLecture held in 
 N/A.\n\nAbstract\nLet $D\\subset\\C^n$ be a bounded\, strongly pseudoconve
 x domain whose boundary $bD$ satisfies the minimal regularity condition 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 Levi-like
  measure $\\omega$ is bounded in $L^p(bD\, \\omega)$ for any $1 < p < \\in
 fty$.\n(For this class of domains\, induced Lebesgue measure  is Leray Lev
 i-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 opt
 imal\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 Muckenho
 upt $A_p$-weight.\n   As an application\, we\n characterize boundedness an
 d compactness  in $L^p(bD\, \\Omega_p)$ for any $1 < p < \\infty$ and for 
 any $A_p$ measure $\\Omega_p$\, of the commutator $[b\, S_p]$ for any Lera
 y Levi-like measure $\\omega$. \n  We next introduce the notion of holomor
 phic Hardy spaces for $A_p$ measures\,\n   $1 < p < \\infty$\,  \n  and \n
  we characterize\n boundedness and compactness  in $L^2(bD\, \\Omega_2)$ o
 f the commutator \n $\\displaystyle{[b\,S_{\\Omega_2}]}$ of the Cauchy-Sze
 gö projection defined with respect to any \n $A_2$ measure $\\Omega_2$.\n
  Earlier closely related results \n  rely upon an asymptotic expansion\, a
 nd subsequent pointwise estimates\, of the Cauchy-Szegö kernel\, but thes
 e are unavailable in the settings of minimal regularity {of $bD$} and/or $
 A_p$ measures\; it turns out that the real harmonic analysis method of ext
 rapolation is an appropriate replacement for the missing tools.\n\n  \nThi
 s is joint work with Xuan Thinh Duong (Macquarie University)\, Ji Li (Macq
 uarie University) and Brett Wick (Washington University in St. Louis).\n
LOCATION:https://researchseminars.org/talk/CAvid/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adri Olde Daalhuis (University of Edinburgh\, UK)
DTSTART:20211214T140000Z
DTEND:20211214T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/60
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/60/">A
 symptotics and complex analysis</a>\nby Adri Olde Daalhuis (University of 
 Edinburgh\, UK) as part of CAvid: Complex Analysis video seminar\n\nLectur
 e held in N/A.\n\nAbstract\nI will discuss the tools from complex analysis
  that are needed in the study of (uniform) asymptotic expansions\nof speci
 al functions. For many of these divergent expansions it is possible to con
 struct very efficient\nintegral representations for the coefficients and r
 emainders\, and these are needed in implementations\nand sharp error-bound
 s. I might also discuss exponential asymptotics of the perturbed first Pai
 nlevé equation.\n
LOCATION:https://researchseminars.org/talk/CAvid/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Miller (University of Michigan)
DTSTART:20220111T140000Z
DTEND:20220111T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/61
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/61/">R
 ational solutions of the Painlevé-IV equation with large parameters</a>\n
 by Peter Miller (University of Michigan) as part of CAvid: Complex Analysi
 s video seminar\n\nLecture held in N/A.\n\nAbstract\nThe Painlevé-IV equa
 tion has two families of rational solutions\, which can be represented in 
 terms of special polynomials called generalized Hermite polynomials and ge
 neralized Okamoto polynomials\, respectively.  The generalized Hermite pol
 ynomials have a convenient representation in terms of Hankel determinants 
 for a suitable weight and hence can be identified with norming constants f
 or certain pseudo-orthogonal polynomials.  This connection provides a path
  to the analysis of the generalized Hermite rationals when the parameters 
 are large\; however it is not known whether the generalized Okamoto polyno
 mials have a similar representation.  In this talk\, we explain how the is
 omonodromic approach places both families of rational solutions in terms o
 f special cases of the Riemann-Hilbert inverse monodromy problem for Painl
 evé-IV.  This allows techniques from steepest descent theory to be used t
 o analyze both families of rational solutions within a common analytical f
 ramework.  This is joint work with Robert Buckingham.\n
LOCATION:https://researchseminars.org/talk/CAvid/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Miriam Benini (Università di Parma)
DTSTART:20220118T140000Z
DTEND:20220118T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/62
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/62/">B
 ifurcations arise when there is a drastic change in the solutions of some 
 equation depending on a parameter\, as the parameter</a>\nby Anna Miriam B
 enini (Università di Parma) as part of CAvid: Complex Analysis video semi
 nar\n\nLecture held in N/A.\n\nAbstract\nBifurcations arise when there is 
 a drastic change in the solutions of some equation depending on a paramete
 r\, as the parameter varies.\nIn this talk we study bifurcations in holomo
 rphic families  of meromorphic maps with finitely many singular values. Th
 e equation(s) that we will study are the equations defining periodic point
 s of period n. Such equations are crucial in complex dynamics because the 
 Julia set (the set on which the dynamics is chaotic) is the closure of rep
 elling periodic points. The celebrated results by Mane-Sad-Sullivan for fa
 milies of rational maps (and independently by Lyubich\, and by Levin for p
 olynomials) show that   in a set of parameters where no bifurcations of pe
 riodic points occur\, the Julia set stays almost the same and so does the 
 dynamics\; precisely speaking\,  all maps are topologically conjugate in s
 uch set.  Moreover\, they establish a  precise correlation between bifurca
 tions of periodic points and a change of behaviour in the orbits of singul
 ar values.\nThe key new feature that appears for   families of meromorphic
  maps is that periodic points  can disappear at infinity at specific param
 eters\, creating a new type of bifurcations. Our work connects this new ty
 pe of bifurcations with change of behaviour in singular orbits\, to establ
 ish  Mane-Sad-Sullivan's Theorem  for meromorphic maps.\nThis is joint wor
 k with Matthieu Astorg and Nùria Fagella.\n
LOCATION:https://researchseminars.org/talk/CAvid/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alastair Fletcher (Northern Illinois University)
DTSTART:20220201T140000Z
DTEND:20220201T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/63
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/63/">C
 antor sets and Julia sets</a>\nby Alastair Fletcher (Northern Illinois Uni
 versity) as part of CAvid: Complex Analysis video seminar\n\nLecture held 
 in N/A.\n\nAbstract\nOne does not have to study much complex dynamics befo
 re coming across examples of Julia sets which are Cantor sets. It is then 
 a natural question to ask which Cantor sets can be Julia sets? The rigidit
 y of holomorphic maps precludes certain natural examples\, and so we 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 work with 
 Dan Stoertz and Vyron Vellis.\n
LOCATION:https://researchseminars.org/talk/CAvid/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joan Lind (University of Tennessee)
DTSTART:20220208T140000Z
DTEND:20220208T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/64
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/64/">T
 he Loewner equation with complex-valued driving functions</a>\nby Joan Lin
 d (University of Tennessee) as part of CAvid: Complex Analysis video semin
 ar\n\nLecture held in N/A.\n\nAbstract\nThe chordal Loewner equation provi
 des a correspondence between real-valued functions\, called driving functi
 ons\, and certain growing 2-dimensional sets\, called hulls.  In this talk
 \, we will consider the generalization to complex-valued driving functions
 \, which was first studied by Huy Tran.  We will discuss some key differen
 ces between the hulls in the complex-valued setting and those in the real-
 valued setting\, including the question of the phase transition from simpl
 e-curve hulls.  This is joint work with Jeffrey Utley.\n
LOCATION:https://researchseminars.org/talk/CAvid/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathy Driver (University of Cape Town)
DTSTART:20220215T140000Z
DTEND:20220215T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/65
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/65/">I
 nterlacing of zeros of Laguerre polynomials</a>\nby Kathy Driver (Universi
 ty of Cape Town) as part of CAvid: Complex Analysis video seminar\n\nLectu
 re 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$ and the 
 real distinct positive zeros of $L_{n-1}^{(\\alpha)}(x)$ and $L_{n}^{(\\al
 pha)}(x)$ are interlacing for $\\alpha >-1\,  n \\geq 2.$  D-Muldoon (2015
 -2019) proved that for $\\alpha >-1\,$  the zeros of $L_{n-1}^{(\\alpha+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}^{(\\alpha)}(
 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) for $0 \
 \leq t \\leq 2k$\, $1 < k < n$ and the interval $0 \\leq t \\leq 2k$ is sh
 arp. \nAt OPSFA 2019\, Alan Sokal: What happens to interlacing of roots if
  you increase parameter and increase degree of one polynomial relative 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://researchseminars.org/talk/CAvid/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Si Duc Quang (Hanoi National University of Education)
DTSTART:20220222T140000Z
DTEND:20220222T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/66
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/66/">S
 econd main theorems for meromorphic mappings into projective varieties and
  arbitrary families of hypersurfaces</a>\nby Si Duc Quang (Hanoi National 
 University of Education) as part of CAvid: Complex Analysis video seminar\
 n\nLecture held in N/A.\n\nAbstract\nIn this talk\, we will give a short i
 ntroduction to Nevanlinna theory for meromorphic mappings into projective 
 varieties. Our main aim is to present a second main theorem for meromorphi
 c mappings with arbitrary families of hypersurfaces in projective varietie
 s. This result is a generalization of the second main theorem for the mapp
 ings with families of hypersurfaces in subgeneral position.\n
LOCATION:https://researchseminars.org/talk/CAvid/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Nicks (University of Nottingham)
DTSTART:20220308T140000Z
DTEND:20220308T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/67
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/67/">I
 terating the minimum modulus</a>\nby Dan Nicks (University of Nottingham) 
 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 an $r > 
 0$ such that the iterated minimum modulus $m^n(r)$ tends to infinity. Here
  $m(r) = m(r\,f) = \\min\\{ |f(z)| : |z|=r \\}$. Focussing mainly on the c
 lass of real transcendental entire functions of finite order with only rea
 l 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 fun
 ctions in this class\, the existence of such an r implies connectedness of
  the escaping set $\\{ z : f^n(z) \\to \\infty \\}$.\n\nThis is joint work
  with Phil Rippon and Gwyneth Stallard.\n
LOCATION:https://researchseminars.org/talk/CAvid/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lasse Rempe (University of Liverpool)
DTSTART:20220315T140000Z
DTEND:20220315T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/68
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/68/">A
  counterexample to Eremenko's Conjecture</a>\nby Lasse Rempe (University o
 f Liverpool) as part of CAvid: Complex Analysis video seminar\n\nLecture h
 eld in N/A.\n\nAbstract\nI shall speak within my lecture\n\nabout an inter
 esting conjecture\n\nof Eremenko from a fine \n\npaper of 1989.\n\n>>>\n\n
 He asked if each escaping point\n\ncan to infinity be joined\n\nusing a co
 nnected shape\n\nall points of which themselves escape.\n\n>>>\n\nAlthough
  quite simple it appears\,\n\nthis question has for many years\n\ncaused m
 e and others some despair\,\n\nsleepless nights and greying hair.\n\n>>>\n
 \nThrough our intense investigation\n\nof transcendental iteration\,\n\nmu
 ch progress was indeed obtained\,\n\nbut the conjecture\, it remained - \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 Eremenko's C
 onjecture.\n
LOCATION:https://researchseminars.org/talk/CAvid/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duc Quang Si (Hanoi National University of Education)
DTSTART:20220322T130000Z
DTEND:20220322T140000Z
DTSTAMP:20260422T165132Z
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://researchseminars.org/talk/CAvid/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rajitha Ranasinghe (University of Peradeniya\, Sri Lanka)
DTSTART:20220329T130000Z
DTEND:20220329T140000Z
DTSTAMP:20260422T165132Z
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://researchseminars.org/talk/CAvid/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adi Glücksam (Northwestern University)
DTSTART:20220405T130000Z
DTEND:20220405T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/71
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/71/">T
 he Combinatorial Method for Stopping Time Arguments</a>\nby Adi Glücksam 
 (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 refine
 ment of the combinatorial technique used by Jones and Makarov in '95. This
  method can be used for stopping time arguments in different settings. I w
 ill describe the method\, and present two applications that were already k
 nown\, 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://researchseminars.org/talk/CAvid/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Marti-Pete (University of Liverpool)
DTSTART:20220426T130000Z
DTEND:20220426T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/72
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/72/">W
 andering domains in transcendental dynamics: topology and dynamics</a>\nby
  David Marti-Pete (University of Liverpool) as part of CAvid: Complex Anal
 ysis video seminar\n\nLecture held in N/A.\n\nAbstract\nFor a transcendent
 al entire or meromorphic function\, the Fatou set is the largest open set 
 on which its iterates are defined and form a normal family. A wandering do
 main is a connected component of the Fatou set which is not eventually per
 iodic. The first example of a transcendental entire function with a wander
 ing domain was constructed by Baker in the 1970s. \n\nWandering domains\, 
 which do not exist for rational maps\, play an important role in transcend
 ental dynamics and in the last decade there has been a resurgence in their
  interest. For example\, Bishop proved that the Julia sets of transcendent
 al entire functions can have Hausdorff dimension 1 by constructing a funct
 ion with wandering domains. \n\nWandering domains are very diverse in term
 s of both their topology (simply connected or multiply connected) and thei
 r dynamics (escaping\, oscillating or\, perhaps\, even have bounded orbit)
 . Recently\, Boc Thaler proved the surprising result that every bounded re
 gular domain such that its closure has a connected complement is the wande
 ring domain of some transcendental entire function. Inspired by this resul
 t\, together with Rempe and Waterman\, we were able to obtain wandering do
 mains that form Lakes of Wada. \n\nIn this talk\, I will describe the main
  topological and dynamical properties of wandering domains (and their boun
 daries) and give an overview of the current open questions.\n
LOCATION:https://researchseminars.org/talk/CAvid/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Girela (Universidad de Málaga)
DTSTART:20220503T130000Z
DTEND:20220503T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/73
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/73/">O
 n BMOA and the Bloch space\, normal functions\, and pointwise multipliers<
 /a>\nby Daniel Girela (Universidad de Málaga) as part of CAvid: Complex A
 nalysis video seminar\n\nLecture held in N/A.\n\nAbstract\nLet $\\mathbb D
 $ be the unit disc in $\\mathbb C$ and let ${\\rm Hol} (\\mathbb D)$ denot
 e the space of all holomorphic functions in $\\mathbb D$. In this talk we 
 shall be concerned with a number of subspaces of ${\\rm Hol}(\\mathbb D)$\
 , especially with the space $H^\\infty $ of all bounded analytic functions
  in $\\mathbb D$\, the space $BMOA$ which consists of those $f\\in H^1$ wh
 ose boundary values have bounded mean oscillation on $\\partial \\mathbb D
 $\, and the Bloch space $\\mathcal B$ which consists of those $f\\in{\\rm 
 Hol} (\\mathbb D)$ for which $$\\sup_{z\\in \\mathbb D}(1-\\vert z\\vert ^
 2)\\vert f^\\prime (z)\\vert <\\infty .$$ It is well known that $H^\\infty
  \\subset BMOA\\subset \\mathcal B$\, and that these inclusions are strict
 . \\par A function $f$\, analytic in $\\mathbb D$\, is a normal function (
 in the sense of Lehto-Virtanen) if $$\\sup_{z\\in \\mathbb D}(1-\\vert z\\
 vert ^2)\\frac{\\vert f^\\prime (z)\\vert }{1+\\vert f(z)\\vert ^2}<\\inft
 y .$$ We shall let $\\mathcal N$ denote the class of all normal analytic f
 unctions in $\\mathbb D$. We have that $\\mathcal B\\subset \\mathcal N$ a
 nd the inclusion is strict. In fact\, the class $\\mathcal N$ is much bigg
 er that the Bloch space. \\par Clearly\, $H^\\infty $ is an algebra\, that
  is\, the product of two $H^\\infty $-functions lies in $H^\\infty $. Howe
 ver\, if $f\\in H^\\infty $ and $g$ is a $BMOA$ function or a Bloch functi
 on\, then the product $g\\cdot f$ may not be a normal function: there exis
 t pairs of functions $(f\, g)$ with $f\\in H^\\infty $ and $g\\in \\mathca
 l B$ such that the product $f\\cdot g$ is not a normal function (or at lea
 st it is not a Bloch function). In this talk we shall present distinct exa
 mples of such pairs of functions starting with the first ones which were g
 iven in the 1960's and finishing with other which have been recently obtai
 ned. We shall reformulate these results in the language of pointwise multi
 pliers.\n
LOCATION:https://researchseminars.org/talk/CAvid/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irina Markina (University of Bergen)
DTSTART:20220510T130000Z
DTEND:20220510T140000Z
DTSTAMP:20260422T165132Z
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://researchseminars.org/talk/CAvid/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Baddoo (MIT)
DTSTART:20220517T130000Z
DTEND:20220517T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/75
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/75/">U
 nderstanding interacting aerofoils with complex analysis</a>\nby Peter Bad
 doo (MIT) as part of CAvid: Complex Analysis video seminar\n\nLecture held
  in N/A.\n\nAbstract\nWhen two or more aerofoils move together\, their int
 eractions can significantly affect the characteristics of the surrounding 
 fluid. We develop a rigorous mathematical theory for these interactions us
 ing conformal maps\, multiply connected function theory\, and modified Sch
 warz problems. Via the transcendental Schottky–Klein prime function\, ou
 r theory is valid for any connectivity (any number of aerofoils). Accordin
 gly\, our approach is very general and permits many aerofoil motions (pitc
 hing\, heaving\, undulatory) and configurations (tandem\, in-line\, ground
  effect). We focus on the (doubly connected) case where there are two inte
 racting swimmers and find that our theory yields excellent agreement with 
 experimental data. We also develop an asymptotic solution that captures th
 e salient features of the prime function solution.\n
LOCATION:https://researchseminars.org/talk/CAvid/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Barnard (Texas Tech University)
DTSTART:20220524T130000Z
DTEND:20220524T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/76
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/76/">O
 n sharp bounds for ratios of k-balanced hypergeometric functions</a>\nby R
 oger Barnard (Texas Tech University) as part of CAvid: Complex Analysis vi
 deo seminar\n\nLecture held in N/A.\n\nAbstract\n(Joint work with Kendall 
 C. Richards\, Southwestern University and Elyssa N. Sliheet\, Southwestern
  Methodist University)\n\nIn this talk we begin with a brief history of ho
 w the authors’ research\, originally in Geometric Function Theory\, deve
 loped into applications of Special Function Theory to a variety of fields\
 , giving examples. Then we discuss one of our latest results in Special Fu
 nction Theory i.e. determining the sharp bounds for ratios of k-balanced h
 ypergeometric functions.\n
LOCATION:https://researchseminars.org/talk/CAvid/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clare Dunning (University of Canterbury at Kent)
DTSTART:20220531T130000Z
DTEND:20220531T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/77
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/77/">P
 olynomials and partitions</a>\nby Clare Dunning (University of Canterbury 
 at Kent) as part of CAvid: Complex Analysis video seminar\n\nLecture held 
 in N/A.\n\nAbstract\nWronskians of orthogonal polynomials appear in a rang
 e of applications including in random matrix theory\, vortex dynamics and 
 supersymmetric quantum mechanics. They are also associated with the ration
 al solution of Painlevé equations. We discuss how the partitions that lab
 el the set of orthogonal polynomials in a particular Wronskian play a role
  beyond simple notation. Curiously\, various aspects of the Wronksian poly
 nomials can be expressed in terms of partition data.\n
LOCATION:https://researchseminars.org/talk/CAvid/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Heather Wilber (University of Texas at Austin)
DTSTART:20220607T130000Z
DTEND:20220607T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/78
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/78/">L
 ow rank numerical methods via rational function approximation</a>\nby Heat
 her Wilber (University of Texas at Austin) as part of CAvid: Complex Analy
 sis video seminar\n\nLecture held in N/A.\n\nAbstract\nIn this talk\, we a
 pply classical ideas in approximation theory to design low rank numerical 
 methods for a range of applications in scientific computing\, including th
 e solving of certain linear systems\, matrix equations\, and partial diffe
 rential equations. The primary workhorse in our approach and analysis is t
 he alternating direction implicit (ADI) method\, and we explore how this s
 pecial splitting algorithm is linked to a wealth of concepts from applied 
 mathematics\, including Laplace’s equation and conformal maps for doubly
 -connected regions\, matrix and operator function evaluation\, digital fil
 ter design\, and the low rank properties of matrices with special displace
 ment structures.\n
LOCATION:https://researchseminars.org/talk/CAvid/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elias Wegert (Technische Universität Bergakademie Freiberg)
DTSTART:20220614T130000Z
DTEND:20220614T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/79
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/79/">N
 umerical range\, Blaschke products and Poncelet polygons</a>\nby Elias Weg
 ert (Technische Universität Bergakademie Freiberg) as part of CAvid: Comp
 lex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\n(Joint wor
 k 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$-dimens
 ional complex Hilbert space cannot have \na circular numerical range with 
 a non-zero center.\nIn this talk we present a proof for operators with ran
 k $A=n-1$ \nand any n. It is based on the unitary similarity of A to a com
 pressed\nshift operator generated by a finite Blaschke product $B(z)$.\nWe
  then use the description of the numerical range by Poncelet\npolygons ass
 ociated with $zB(z)$\, a special representation of \nBlaschke products rel
 ated to boundary interpolation\, and an \nexplicit formula for the barycen
 ters of the vertices of Poncelet \npolygons involving elliptic functions.\
 n
LOCATION:https://researchseminars.org/talk/CAvid/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jane Hawkins (University of North Carolina)
DTSTART:20220621T130000Z
DTEND:20220621T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/80
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/80/">D
 oubly periodic Julia and Fatou sets for iterated meromorphic functions:  d
 ynamics on unbounded components</a>\nby Jane Hawkins (University of North 
 Carolina) as part of CAvid: Complex Analysis video seminar\n\nLecture held
  in N/A.\n\nAbstract\nElliptic functions give rise under iteration to Juli
 a and Fatou sets that are invariant under the action of translation by ele
 ments of the period lattice. However doubly periodic Julia and Fatou sets 
 can arise for non-elliptic meromorphic functions as well.  Unbounded Fatou
  components in both settings exhibit dynamics different from those of rati
 onal maps and are called toral bands since they can be viewed on a torus (
 a fundamental region in the plane with identifications).  We discuss how t
 he dynamics depend on the function and the lattice\, both its shape and it
 s size\, and what parameter choices produce unbounded components. We will 
 also touch on the stability and connectivity of these components.\n
LOCATION:https://researchseminars.org/talk/CAvid/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fiana Jacobzon (Braude College of Engineering\, Karmiel\, Israel)
DTSTART:20220628T130000Z
DTEND:20220628T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/82
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/82/">A
 n "inverse Fekete-Szegö problem" and filtration of generators</a>\nby Fia
 na Jacobzon (Braude College of Engineering\, Karmiel\, Israel) as part of 
 CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\
 nIn this talk we introduce and discuss a question that can be interpreted 
 as an "inverse Fekete-Szegö problem".  It turns out that this problem lin
 ks to the so-called filtration of infinitesimal generators. Several filtra
 tion classes have recently been studied\, including their applications to 
 semigroups of holomorphic mappings in the unit disk.\nTo address the circl
 e of questions that arise in this context we introduce new filtration clas
 ses 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 properties of 
 these classes. \nSharp upper bounds of the modulus of the Fekete--Szegö f
 unctional over some filtration classes are found. \nWe also present open p
 roblems for further study.\n\n\nJoint work with Mark Elin (Braude College 
 of Engineering\, Karmiel\, Israel) and \nNikola Tuneski (Ss. Cyril and Met
 hodius University\, Skopje\, Republic of North Macedonia)\n
LOCATION:https://researchseminars.org/talk/CAvid/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Waterman (Stony Brook University)
DTSTART:20220920T130000Z
DTEND:20220920T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/83
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/83/">M
 averick points on the boundary of wandering domains</a>\nby James Waterman
  (Stony Brook University) as part of CAvid: Complex Analysis video seminar
 \n\nLecture held in N/A.\n\nAbstract\nWandering domains\, or wandering Fat
 ou components\, are a central object of study in the iteration of transcen
 dental entire functions. We will introduce several basic properties of wan
 dering domains. Moreover\, focusing on behavior on the boundary of these d
 omains\, we will discuss the existence of boundary points of a wandering d
 omain with accumulation behavior distinct from that of the wandering domai
 n itself. We call such points maverick points. This is joint work with Dav
 id Martí-Pete and Lasse Rempe.\n
LOCATION:https://researchseminars.org/talk/CAvid/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darren Crowdy (Imperial College London)
DTSTART:20221011T130000Z
DTEND:20221011T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/84
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/84/">W
 ater waves with vorticity and the Schwarz function</a>\nby Darren Crowdy (
 Imperial College London) as part of CAvid: Complex Analysis video seminar\
 n\nLecture held in N/A.\n\nAbstract\nThe theory of water waves is centurie
 s old\, but it remains a vibrant area of research. Most theoretical work o
 n water waves takes the flow to be irrotational\, but there has been growi
 ng interest\, especially recently\, in the effect of vorticity on the stru
 cture of the waves. The assumption of irrotationality has the theoretical 
 advantage that complex analysis techniques can be used to analyze the prob
 lem in the two-dimensional setting. This talk will present a novel theoret
 ical formulation of the problem of steadily-travelling water waves in the 
 presence of vorticity (where the assumption of irrotationality is dropped)
  but in the absence of gravity or capillarity. The approach is based on th
 e notion of a Schwarz function of a curve. It unifies our understanding of
  several recent results in the water wave literature and provides a wealth
  of new exact mathematical solutions to this challenging free boundary pro
 blem.\n
LOCATION:https://researchseminars.org/talk/CAvid/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maurice Kenfack Nangho (University of Dschang\, Cameroon)
DTSTART:20221018T130000Z
DTEND:20221018T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/85
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/85/">A
  characterization of Askey-Wilson polynomials: proof of a conjecture by Mo
 urad Ismail</a>\nby Maurice Kenfack Nangho (University of Dschang\, Camero
 on) as part of CAvid: Complex Analysis video seminar\n\nLecture held in N/
 A.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CAvid/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamara Grava (University of Bristol and SISSA)
DTSTART:20220927T130000Z
DTEND:20220927T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/86
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/86/">T
 he Stieltjes-Fekete problem and degenerate orthogonal polynomials</a>\nby 
 Tamara Grava (University of Bristol and SISSA) as part of CAvid: Complex A
 nalysis video seminar\n\nLecture held in N/A.\n\nAbstract\nA result of Sti
 eltjes famously relates the zeroes of the classical orthogonal polynomials
  with the configurations of points on the line that minimize a suitable lo
 garithmic energy\, or equivalently the solutions\nof a suitable weighted F
 ekete problem. The optimal configuration satisfies an algebraic set of equ
 ations with the logarithmic derivative of the weight function as ``externa
 l field": we call this set of algebraic\nequations the Stieltjes-Fekete pr
 oblem. In this work we consider the\nStieltjes-Fekete problem with an arbi
 trary rational external field. We\nshow that its solutions are in one-to-o
 ne correspondence with the zeroes of certain non-hermitean orthogonal poly
 nomials that satisfy an excess of orthogonality conditions and are thus te
 rmed ``degenerate". This generalizes the above mentioned result of Stieltj
 es.\n
LOCATION:https://researchseminars.org/talk/CAvid/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang Chen (University of Macau)
DTSTART:20221025T130000Z
DTEND:20221025T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/87
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/87/">L
 aguerre Unitary Ensembles with Multiple Discontinuities\, PDE\, and the Co
 upled Painlevé V System</a>\nby Yang Chen (University of Macau) as part o
 f CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstrac
 t\nWe study the Hankl generated by the Laguerre weight with jump\ndisconti
 nuities at $t_k$\, $k=1\,2\,\\ldots\,m$. By employing the ladder operator 
 approach \nwe establish (multi-time) Riccati equations\, to show that $\\s
 igma_n(t_1\, ...\,t_m)$\,\nthe log derivative of the $n\\times n$ Hankel d
 eterminant\, satisfies a generalization of the $\\sigma$ of a Painlev\\'e 
 V equation. Through investigating the Riemann-Hibert problem (or Homogenou
 s Hilbert Problem )  for the orthogonal polynomials\ngenerated by the LUEM
 D and via Lax pair\, we express $\\sigma_n$ in terms of \nsolutions of a c
 oupled Painlev\\'e V system. We also build relations between the auxiliary
  quantities introduced in the above two methods\, which provide\nconnectio
 ns 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 infinity
 \, the scaled $\\sigma_n$ is shown to satisfy a generalized Painlev\\'e II
 I system.\n\nYang Chen (University of Macau\, Macau)\, Shulin Lyu (Qilu Un
 iversity of Technology\, Shandong Academy of Science)\, Shuai-Xia Xu (Inst
 itut Franco-Chinois  de l'Energie Nculearie\, Sun Yat-sen University\, Gua
 ngzhou\, China\n
LOCATION:https://researchseminars.org/talk/CAvid/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jasmin Raissy (Université de Bordeaux)
DTSTART:20221122T140000Z
DTEND:20221122T150000Z
DTSTAMP:20260422T165132Z
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://researchseminars.org/talk/CAvid/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianhua Zheng (Tsinghua University)
DTSTART:20221101T140000Z
DTEND:20221101T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/89
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/89/">C
 lassification of Baker domains of meromorphic functions</a>\nby Jianhua Zh
 eng (Tsinghua University) as part of CAvid: Complex Analysis video seminar
 \n\nLecture held in N/A.\n\nAbstract\nFirst we introduce the definition 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 ab
 sorbing domain. Secondly we introduce a more carful classification of Bake
 r domains according to characteristic of the M\\"obius transformation whic
 h the function sem-conjugates on the Baker domain in question. Thirdly\, w
 e say criteria of Baker domain types. The talk mainly comes from a unpubli
 shed paper I finished one year ago.\n
LOCATION:https://researchseminars.org/talk/CAvid/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Argyris Christodoulou (Aristotle University of Thessaloniki)
DTSTART:20221115T140000Z
DTEND:20221115T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/90
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/90/">G
 eneralising the Denjoy-Wolff theorem</a>\nby Argyris Christodoulou (Aristo
 tle University of Thessaloniki) as part of CAvid: Complex Analysis video s
 eminar\n\nLecture held in N/A.\n\nAbstract\nThe starting point for this ta
 lk is the classical Denjoy-Wolff theorem\, which completely describes the 
 behaviour of the iterates of a holomorphic self-map of the unit disc. Sinc
 e 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 d
 efinitive result of this type. We approach this subject by asking the foll
 owing question: Is the result of the Denjoy-Wolff theorem stable when we p
 erturb the iterated function? In particular\, we study the dynamical behav
 iour of compositions arising from a sequence of self-maps of a Riemann sur
 face\, when the sequence itself converges to a holomorphic map. Based on j
 oint work with Marco Abate and Ian Short.\n
LOCATION:https://researchseminars.org/talk/CAvid/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marta Kosek (Jagiellonian University\, Poland)
DTSTART:20230110T140000Z
DTEND:20230110T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/91
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/91/">O
 n some limits in the theory of Julia sets</a>\nby Marta Kosek (Jagiellonia
 n University\, Poland) as part of CAvid: Complex Analysis video seminar\n\
 nLecture held in N/A.\n\nAbstract\nWe will speak about polynomial Julia se
 ts in the complex plane\, even\nthough most subjects can be investigated a
 lso in higher dimensions. We\nconsider some approximation problems. One of
  them is approximation of some\nregular sets by polynomial Julia sets. 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 more app
 ropriate than the classical\nHausdorff metric. Another problem concerns cr
 eating computer pictures of\nsome composite Julia sets. Finally\, we deal 
 with some sequences defined\nwith use of (compositions of) Chebyshev polyn
 omials and obtain their uniform limit.\n
LOCATION:https://researchseminars.org/talk/CAvid/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohamed Nasser (Wichita State University\, USA)
DTSTART:20230117T140000Z
DTEND:20230117T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/92
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/92/">A
  boundary integral method for the Riemann–Hilbert problem on multiply co
 nnected domains</a>\nby Mohamed Nasser (Wichita State University\, USA) as
  part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\n
 Abstract\nLet $G$ be a multiply connected domain in the extended complex p
 lane 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 Rie
 mann--Hilbert (RH) boundary value problem requires determining a function 
 $f$ analytic in $G$ (vanishing at infinity for unbounded $G$)\, continuous
  in the closure $\\overline{G}$\, and satisfying the boundary condition 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 with the 
 generalized Neumann kernel}. Applications of the method will be also prese
 nted.\n
LOCATION:https://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:20260422T165132Z
UID:CAvid/93
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/93/">N
 ecessary and sufficient conditions for entire functions to belong to the L
 aguerre-Polya class</a>\nby Anna Vishnyakova (V. N. Karazin Kharkiv Nation
 al University\, Ukraine and Holon Institute of Technology\, Israel						an
 d Holon Institute of Technology\, Israel) as part of CAvid: Complex Analys
 is video seminar\n\nLecture held in N/A.\n\nAbstract\nThe famous Laguerre-
 Polya class consists of\nentire functions which are uniform on the\ncompac
 ts limits of real polynomials having all\nreal zeros. The Laguerre-Polya c
 lass is of interest\nto many areas of mathematics such as complex analysis
 \,\nstatistical physics\, combinatorics\, asymptotic analysis\,\nthe theor
 y of mock modular forms and others. We present\nnew necessary and new suff
 icient 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\,$\np
 lays an important role in our investigations. It is known\nthat there exis
 ts a constant $ q_\\infty\\approx 3{.}23363666\,$\nsuch that the partial t
 heta-function belongs to the Laguerre-Polya\nclass if and only if $a^2 \\g
 eq  q_\\infty.$ The following statement\nis an example of our results. Let
  $f(z)=\\sum_{k=0}^\\infty a_k z^k $\nbe an entire function with positive 
 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 than or 
 equal to\n$\\ q_\\infty.$ Then the function $f$ belongs to the\nLaguerre-P
 olya class.\n
LOCATION:https://researchseminars.org/talk/CAvid/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Short (Open University\, UK)
DTSTART:20230207T140000Z
DTEND:20230207T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/94
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/94/">I
 terated function systems in holomorphic dynamics</a>\nby Ian Short (Open U
 niversity\, UK) as part of CAvid: Complex Analysis video seminar\n\nLectur
 e held in N/A.\n\nAbstract\nMotivated by classical results in continued fr
 action theory\, we explore iterated function systems of holomorphic self-m
 aps of the disc and other Riemann surfaces. The primary tools in this ende
 avour are the hyperbolic metric and Pick's theorem that holomorphic maps a
 re contractions of the hyperbolic metric. We will review selected results 
 from this field over the last few decades and finish with work in preparat
 ion advancing these results by use of the hyperbolic derivative.\n
LOCATION:https://researchseminars.org/talk/CAvid/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonatan Lenells (KTH\, Sweden)
DTSTART:20230131T140000Z
DTEND:20230131T150000Z
DTSTAMP:20260422T165132Z
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://researchseminars.org/talk/CAvid/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adolfo Guillot (National Autonomous University of Mexico)
DTSTART:20230214T140000Z
DTEND:20230214T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/96
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/96/">M
 eromorphic vector fields on algebraic surfaces having univalent solutions<
 /a>\nby Adolfo Guillot (National Autonomous University of Mexico) as part 
 of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstra
 ct\nWe consider algebraic\, first-order\, autonomous ordinary\ndifferentia
 l equations in two complex variables (meromorphic vector\nfields on compac
 t algebraic surfaces\, for instance\, those coming from\nrational vector f
 ields on affine surfaces)\, and discuss the very\nstrong constraints impos
 ed by the existence of one transcendental\nunivalent solution: either ther
 e is some variable that integrates\nindependently (the vector field preser
 ves a fibration on the surface)\,\nor the surface is an abelian one and th
 e vector field is linear.\n
LOCATION:https://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:20260422T165132Z
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://researchseminars.org/talk/CAvid/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ragnar Sigurdsson (University of Iceland)
DTSTART:20230321T130000Z
DTEND:20230321T140000Z
DTSTAMP:20260422T165132Z
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://researchseminars.org/talk/CAvid/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Sokal (University College London)
DTSTART:20230228T140000Z
DTEND:20230228T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/99
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/99/">M
 otion of zeros of polynomial solutions of the one-dimensional heat equatio
 n: A first-order Calogero-Moser system</a>\nby Alan Sokal (University Coll
 ege London) as part of CAvid: Complex Analysis video seminar\n\nLecture he
 ld in N/A.\n\nAbstract\nI study the motion of zeros of polynomial solution
 s $\\phi(x\, t)=\\prod_{i=1}^n[x-x_{i}(t)]$\nof the one-dimensional heat e
 quation \n$\\displaystyle\\frac{\\partial \\phi}{\\partial t}=\\kappa\\fra
 c{\\partial^2\\phi}{\\partial x^2}$\; they satisfy the first-order\nCaloge
 ro–Moser system \n\\[\n\\frac{{\\rm d}x_i}{{\\rm d}t}=\\sum_{j\\ne i}\\f
 rac{-2\\kappa}{x_i-x_j}.\n\\]\nI am interested in the behavior at complex 
 time $t$ (usually with real initial conditions). My goals are to\n\n(a) De
 termine 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 complex p
 lane. I have no nontrivial theorems\, but many interesting conjectures.\n
LOCATION:https://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:20260422T165132Z
UID:CAvid/100
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/100/">
 Attracting basins of non-autonomous families</a>\nby Sayani Bera (Indian A
 ssociation for the Cultivation of Science\, Kolkata) as part of CAvid: Com
 plex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nThe goal 
 of this talk is to explore the basins of non-autonomous or iterative famil
 ies of automorphisms of $\\mathbb{C}^m$ \, m ≥ 2\, admitting a common at
 tracting fixed point\, and their connection to the classical ‘stable man
 ifold theorem’.\nFurther\, we affirmatively answer a conjecture (formula
 ted by Fornæss and Stensønes in 2004) on non-autonomous basins\, by gene
 ralising appropriate techniques from the (iterative) dynamics of Hénon/re
 gular maps in $\\mathbb{C}^m$\,m ≥ 2. This\, also confirms a stronger ve
 rsion of the stable manifold theorem\, originally raised as a question by 
 Bedford in 2000.\nThis is a joint work with K. Verma.\n
LOCATION:https://researchseminars.org/talk/CAvid/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michel Zinsmeister (Université d'Orléans\, France)
DTSTART:20230314T130000Z
DTEND:20230314T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/101
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/101/">
 Coullet-Tresser Cascade of Bifurcations in the logistic Family and Hausdor
 ff Dimension of real quadratic Julia Sets</a>\nby Michel Zinsmeister (Univ
 ersité d'Orléans\, France) as part of CAvid: Complex Analysis video semi
 nar\n\nLecture held in N/A.\n\nAbstract\nIn a paper with L. Jacksztas (Adv
  Math 2020) we have proven that if $c_0$ is a parabolic parameter (i.e. wi
 th a parabolic cycle) in $(c_{Feig}\,1/4)$ ($c_{Feig}$ being the limit poi
 nt of the cascade of bifurcations) then the function $d(c)=$ Hausdorff dim
 ension 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 that $d(c
 )>4/3$ on $[-1.53\,-1.23]$ (arXiv:2204.07880). The combination of these tw
 o 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 description (
 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 result. \n\
 n(Joint work with L. Jacksztas)\n
LOCATION:https://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:20260422T165132Z
UID:CAvid/102
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/102/">
 Some results on entire functions from the Laguerre-Pólya class: proof ide
 as and techniques</a>\nby Thu Hien Nguyen (Leipzig University\, Germany & 
 V. N. Karazin Kharkiv University\, Ukraine) as part of CAvid: Complex Anal
 ysis video seminar\n\nLecture held in N/A.\n\nAbstract\nThe Laguerre-P\\'o
 lya class is a class of entire functions that are locally the uniform limi
 t of a sequence of real polynomials that have only real zeros.  We present
  some simple necessary and sufficient conditions for entire functions to b
 elong to the Laguerre–Pólya class in terms of their Taylor coefficients
 .  For an entire function $f(z) = \\sum_{k=0}^{\\infty} a_k z^k$\, we defi
 ne 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 real zero
 s.  In this talk\, we will focus on the entire functions with increasing s
 econd quotients of Taylor coefficients\, and discuss proof ideas and techn
 iques we used. \n \n This is joint work with Anna Vishnyakova.\n
LOCATION:https://researchseminars.org/talk/CAvid/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Solynin (Texas Tech University\, USA)
DTSTART:20230502T130000Z
DTEND:20230502T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/103
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/103/">
 Quadratic differentials in complex analysis and beyond</a>\nby Alexander S
 olynin (Texas Tech University\, USA) as part of CAvid: Complex Analysis vi
 deo seminar\n\nLecture held in N/A.\n\nAbstract\nI will discuss the role o
 f quadratic differentials in the extremal\nproblems in Complex Analysis an
 d beyond. We start with main\ndefinitions\, then discuss \nJenkins' theory
  of extremal partitioning\, and then I will\nmention main results of the d
 ifferentiation theory for the\nJenkins' weighted sum of moduli suggested b
 y this speaker in\n1985-2000.\n\nTurning to applications\, I show first ho
 w quadratic differentials\ncan be used to study fingerprints of (complex) 
 polynomial\nlemniscates. The main result here includes\, as special cases\
 ,\nEbenfelt-Khavinson-Shapiro characterization of fingerprints of\npolynom
 ial lemniscates as well as Younsi characterization of\nrational lemniscate
 s. Then I will show that every real algebraic\ncurve can be treated as a t
 rajectory of a quadratic differential\ndefined on a certain Riemann surfac
 e.\n\n\nAfter that\, we will discuss how quadratic differentials on\n$\\ov
 erline{\\mathbf{C}}$ with the minimal possible number of poles\n(that is $
 4$) can be used to solve the problem on the canonical\nembeddings of pairs
  of arcs\, studied recently by M. Bonk and\nA. Eremenko\, and in several o
 ther extremal problems on ring\ndomains.\n
LOCATION:https://researchseminars.org/talk/CAvid/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Navneet Lal Sharma (Gati Shakti Vishwavidyalaya\, India)
DTSTART:20230516T130000Z
DTEND:20230516T140000Z
DTSTAMP:20260422T165132Z
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://researchseminars.org/talk/CAvid/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cinzia Bisi (Ferrara University\, Italy)
DTSTART:20230530T130000Z
DTEND:20230530T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/105
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/105/">
 Invariants and automorphisms of slice regular functions</a>\nby Cinzia Bis
 i (Ferrara University\, Italy) as part of CAvid: Complex Analysis video se
 minar\n\nLecture held in N/A.\n\nAbstract\nLet $A$ be one of the following
  Clifford Algebras : C\, H = R2 and R3. For the algebra A\, the automorphi
 sm group Aut(A) and its invariants are well known. The talk will describe 
 the invariants of the automorphism group of the algebra of slice regular f
 unctions over $A$ = H = R2 and over $A$ = R3. This is a joint project with
  J. Winklelmann.\n
LOCATION:https://researchseminars.org/talk/CAvid/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Kostov (Université d'Azur\, CNRS\, LJAD)
DTSTART:20230509T130000Z
DTEND:20230509T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/106
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/106/">
 Analytic properties of the partial theta function</a>\nby Vladimir Kostov 
 (Université d'Azur\, CNRS\, LJAD) as part of CAvid: Complex Analysis vide
 o seminar\n\nLecture held in N/A.\n\nAbstract\nWe consider the partial the
 ta function $\\theta (q\,x):=\\sum\n_{j=0}^{\\infty}q^{j(j+1)/2}x^j$\, whe
 re $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 expansions f
 or its\nzeros\, its spectrum (i.e. the set of values of the parameter $q$\
 nfor which $\\theta (q\,.)$ has multiple zeros)\, behaviour of its zeros\,
 \nespecially of its complex conjugate pairs\, when\nthe parameter $q$ vari
 es\, separation in modulus of the zeros etc.\n
LOCATION:https://researchseminars.org/talk/CAvid/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Navneet Lal Sharma (Gati Shakti Vishwavidyalaya)
DTSTART:20230523T130000Z
DTEND:20230523T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/107
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/107/">
 Estimates logarithmic coefficients for certain classes of univalent functi
 ons</a>\nby Navneet Lal Sharma (Gati Shakti Vishwavidyalaya) as part of CA
 vid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nL
 et $\\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$.\nTh
 e logarithmic coefficients $\\gamma_n$ of $f\\in \\mathcal{S}$ are defined
  by the formula\n$$\\log\\left(\\frac{f(z)}{z}\\right)\\\,=\\\,2\\sum_{n=1
 }^{\\infty}\\gamma_n(f)z^n.\n$$\nIn this talk\, we will discuss bounds for
  the logarithmic coefficients for certain geometric subfamilies of univale
 nt functions as starlike\, convex\, close-to-convex and Janowski starlike 
 functions. Also\, we consider the families $\\mathcal{F}(c)$ and \n$\\math
 cal{G}(\\delta)$  of functions $f\\in \\mathcal{S}$ defined by\n$$ {\\rm R
 e}  \\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} $$\nfor some $c\\in(0\,3]$ and $\\d
 elta\\in (0\,1]$\, respectively. We obtain the sharp upper bound for $|\\g
 amma_n|$ when $n=1\,2\,3$ and $f$ belongs to the classes \n$\\mathcal{F}(c
 )$ and $\\mathcal{G}(\\delta)$\, respectively. We conclude with the follow
 ing two conjectures:\n\n* If $f\\in\\mathcal{F}(-1/2)$\, then  $ \\display
 style |\\gamma_n|\\le \\frac{1}{n}\\left(1-\\frac{1}{2^{n+1}}\\right)$\n f
 or $n\\ge 4$\,  and\n$$ \\sum_{n=1}^{\\infty}|\\gamma_{n}|^{2} \\leq \\fra
 c{\\pi^2}{6}+\\frac{1}{4} ~{\\rm Li\\\,}_{2}\\left(\\frac{1}{4}\\right)\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 article.\n\n
 S. Ponnusamy\, N. L. Sharma and K.-J. Wirths\,\nLogarithmic coefficients p
 roblems in families related to starlike and convex functions\, . Aust. Mat
 h. Soc.\, 109(2) (2019)\, 230--249.\n
LOCATION:https://researchseminars.org/talk/CAvid/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Fasondini (University of Leicester)
DTSTART:20231017T130000Z
DTEND:20231017T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/108
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/108/">
 Complex-plane singularity dynamics for blow up in a nonlinear heat equatio
 n: analysis and computation</a>\nby Marco Fasondini (University of Leicest
 er) as part of CAvid: Complex Analysis video seminar\n\nLecture held in N/
 A.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CAvid/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toby Driscoll (University of Delaware)
DTSTART:20231024T130000Z
DTEND:20231024T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/109
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/109/">
 AAA for rational interpolation on continuua</a>\nby Toby Driscoll (Univers
 ity of Delaware) as part of CAvid: Complex Analysis video seminar\n\nLectu
 re held in N/A.\n\nAbstract\nThe AAA algorithm of Nakatsukasa\, Sète\, an
 d 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 discret
 ization\, which is not ideal in cases where a good initial distribution of
  nodes may be difficult to discern. By also incrementally adding nodes fro
 m the domain based on the latest residual\, the algorithm can be adapted t
 o work well automatically even when singularities are very close to or eve
 n on the approximation interval. This capability has been released as a Ju
 lia software package\, and another package is in development to use these 
 approximations for computing conformal maps to simply- and doubly-connecte
 d domains.\n
LOCATION:https://researchseminars.org/talk/CAvid/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luna Lomonaco (Institute of Pure and Applied Mathematics)
DTSTART:20231031T130000Z
DTEND:20231031T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/110
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/110/">
 Mating quadratic maps with the modular group</a>\nby Luna Lomonaco (Instit
 ute of Pure and Applied Mathematics) as part of CAvid: Complex Analysis vi
 deo seminar\n\nLecture held in N/A.\n\nAbstract\nHolomorphic correspondenc
 es are multi-valued maps defined by polynomial relations $P(z\,w)=0$. We c
 onsider a specific 1-(complex)parameter family of (2:2) correspondences (e
 very point has 2 images and 2 preimages)\nwhich encodes both the dynamics 
 of a quadratic rational map and the dynamics of the modular group. We show
  that the connectedness locus for this family is homeomorphic to the parab
 olic Mandelbrot set\, itself homeomorphic to the Mandelbrot set. Joint wor
 k with S. Bullett.\n
LOCATION:https://researchseminars.org/talk/CAvid/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Buckingham (University of Cincinnati)
DTSTART:20231107T140000Z
DTEND:20231107T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/111
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/111/">
 Asymptotics of Rational Painlevé V Functions</a>\nby Robert Buckingham (U
 niversity of Cincinnati) as part of CAvid: Complex Analysis video seminar\
 n\nLecture held in N/A.\n\nAbstract\nThe Painlevé functions are a family 
 of ordinary differential equations with myriad applications to mathematica
 l physics and probability.  The rational solutions of these equations have
  drawn attention for the remarkable geometric structure of their zeros and
  poles.  We study the family of rational solutions of the Painlevé-V equa
 tion built from Umemura polynomials.  We derive a new Riemann-Hilbert repr
 esentation and use it to obtain the boundary of the pole region and the la
 rge-degree behavior in the pole-free region.  This is joint work with Matt
 hew Satter of the University of Cincinnati.\n
LOCATION:https://researchseminars.org/talk/CAvid/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liz Vivas (Ohio State University)
DTSTART:20231114T140000Z
DTEND:20231114T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/112
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/112/">
 Dimension results on generalized Bergman spaces</a>\nby Liz Vivas (Ohio St
 ate University) as part of CAvid: Complex Analysis video seminar\n\nLectur
 e held in N/A.\n\nAbstract\nWiegerinck proved that the Bergman space over 
 any domain in the complex plane is either trivial or infinite dimensional.
  In this talk I will discuss various generalizations and open questions re
 lated to this theorem. I will survey the case of the complex plane being r
 eplaced by C^n as well as a domain in a compact Riemann Surface.\n\nThe ta
 lked is based in joint work with A-K. Gallagher and P. Gupta.\n
LOCATION:https://researchseminars.org/talk/CAvid/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guang-Yuan Zhang (Tsinghua University)
DTSTART:20231128T140000Z
DTEND:20231128T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/114
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/114/">
 The precise form of Ahlfors' Second Fundamental Theorem of covering surfac
 es</a>\nby Guang-Yuan Zhang (Tsinghua University) as part of CAvid: Comple
 x Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nA simply con
 nected covering surface $\\Sigma =\\left( f\,\\overline{\\Delta }%\n\\righ
 t) $ over the unit Riemann sphere $S$ is an orientation-preserving\,\ncont
 inuous\, open and finite-to-one mapping (OPCOFOM) $f$ from the closed\nuni
 t disk $\\overline{\\Delta }$ into the sphere $S$. Here open means that $f
 $\ncan be extended continuous and open to a neighborhood of $\\overline{\\
 Delta }.\n$ We denote by $\\mathbf{F}$ all simply connected surfaces.\n\nL
 et $E_{q}=\\left\\{ a_{1}\,a_{2}\,\\dots \,a_{q}\\right\\} $ be a set on t
 he unit\nRiemann sphere consisting of $q$ distinct points with $q>2.$ \nAh
 lfors' second\nfundamental theorem (SFT) states that there exists a positi
 ve number $h$\ndepending only on $E_{q}\,$ such that for any surface $\\Si
 gma =\\left( f\,%\n\\overline{\\Delta }\\right) \\in \\mathbf{F}\,$\n\\[\n
 \\left( q-2\\right) A\\left( \\Sigma \\right) <4\\pi \\overline{n}\\left( 
 \\Sigma\n\\right) +hL\\left( \\partial \\Sigma \\right) \,\n\\]\nwhere $\\
 Delta $ is the unit disk\, $A\\left( \\Sigma \\right) $ is the spherical\n
 area of $\\Sigma $\, $L\\left( \\partial \\Sigma \\right) $ is the spheric
 al\nlength of the boundary curve $\\partial \\Sigma =\\left( f\,\\partial 
 \\Delta\n\\right) \,$ and $\\overline{n}\\left( \\Sigma \\right) =\\#f^{-1
 }(E_{q})\\cap\n\\Delta .$\n\nIf we define $R\\left( \\Sigma \\right) =R\\l
 eft( \\Sigma \,E_{q}\\right) $ to be\nthe error term in Ahlfors' SFT\, say
 \,\n\\[\nR\\left( \\Sigma \\right) =\\left( q-2\\right) A\\left( \\Sigma \
 \right) -4\\pi\n\\overline{n}\\left( \\Sigma \\right) \,\n\\]\nthen Ahlfor
 s' SFT reads\n\\[\nH_{0}=\\sup_{\\Sigma \\in \\mathbf{F}}\\left\\{ \\frac{
 R(\\Sigma )}{L(\\partial\n\\Delta )}:\\Sigma =\\left( f\,\\overline{\\Delt
 a }\\right) \\right\\} <+\\infty .\n\\]\nWe call $H_{0}=H_{0}(E_{q})$ Ahlf
 ors' constant for simply connected\nsurfaces.\n\nIn this talk\, I will int
 roduce my recent work which identify the precise\nbound $H_{0}=H_{0}(E_{q}
 ).$\n
LOCATION:https://researchseminars.org/talk/CAvid/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Faouzi Thabet (University of Gabès)
DTSTART:20231212T140000Z
DTEND:20231212T150000Z
DTSTAMP:20260422T165132Z
UID:CAvid/116
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/116/">
 Trajectories of Particular Quadratic Differentials on the Riemann Sphere</
 a>\nby Faouzi Thabet (University of Gabès) as part of CAvid: Complex Anal
 ysis video seminar\n\nLecture held in N/A.\n\nAbstract\nIn this lecture\, 
 we give some basics of the theory of Quadratic\nDifferentials on the Riema
 nn Sphere. In the first part\, the focus will be on\nthe investigation of 
 the existence of finite critical trajectories\, and the\ndescription of th
 e critical graph of some quadratic differentials related to\nsolutions as 
 Cauchy transform of a signed measure of an algebraic quadratic\nequation a
 s the form : $p\\left( z\\right) \\mathcal{C}^{2}\\left( z\\right)\n+q\\le
 ft( z\\right) \\mathcal{C}\\left( z\\right) +r=0\,$ for some polynomials $
 p\,$\n$q$ and $r.$ As an example\, we study the large-degree analysis of t
 he\nbehaviour of the generalized Laguerre polynomials $L_{n}^{(\\alpha )}$
  when\nthe parameters are complex and depend on the degree $n$ linearly.\n
 \nIn the second part\, we describe the critical graph of a polynomial quad
 ratic\ndifferential related to the Schr\\"{o}dinger equation with cubic po
 tential.\n
LOCATION:https://researchseminars.org/talk/CAvid/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva A. Gallardo Gutiérrez (ICMAT)
DTSTART:20231219T140000Z
DTEND:20231219T150000Z
DTSTAMP:20260422T165132Z
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://researchseminars.org/talk/CAvid/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Kecker (University of Portsmouth)
DTSTART:20240423T130000Z
DTEND:20240423T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/118
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/118/">
 Geometric approach for quasi-Painlevé Hamiltonian systems</a>\nby Thomas 
 Kecker (University of Portsmouth) as part of CAvid: Complex Analysis video
  seminar\n\nLecture held in N/A.\n\nAbstract\nWe present some new Hamilton
 ian systems of quasi-Painlevé type and their Okamoto's spaces of initial 
 conditions. The geometric approach was introduced originally for the ident
 ification problem of Painlevé equations\, comparing the irreducible compo
 nents of the inaccessible divisors introduced in the blow-ups to obtain th
 e space of initial conditions. Using this method\, we find bi-rational coo
 rdinate changes between some of the systems we introduce\, giving rise to 
 a global symplectic structure for these systems. This scheme thus allows u
 s to identify (quasi-)Painlevé Hamiltonian systems up to bi-rational symp
 lectic maps\, performed here for systems with solutions having movable sin
 gularities that are either square-root type algebraic poles or ordinary po
 les.\n
LOCATION:https://researchseminars.org/talk/CAvid/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John King (University of Nottingham)
DTSTART:20240430T130000Z
DTEND:20240430T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/119
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/119/">
 Complex-plane analysis of a quasilinear parabolic PDE</a>\nby John King (U
 niversity of Nottingham) as part of CAvid: Complex Analysis video seminar\
 n\nLecture held in N/A.\n\nAbstract\nI'll apply a combination of formal as
 ymptotic methods and applied complex analysis (notably the dynamics of com
 plex singularities) to give some insight into the qualitative and quantita
 tive behaviour of some non-integrable PDEs. This raises some unresolved (t
 o me) issues of more general relevance about the complex-plane behaviour o
 f nonlinear ODEs\, about which I shall ask.\n
LOCATION:https://researchseminars.org/talk/CAvid/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alta Jooste (University of Pretoria)
DTSTART:20240514T130000Z
DTEND:20240514T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/120
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/120/">
 Recurrence equations involving orthogonal polynomials with related weight 
 functions</a>\nby Alta Jooste (University of Pretoria) as part of CAvid: C
 omplex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nEvery s
 equence of real polynomials $\\{p_n\\}_{n=0}^\\infty=0$\, orthogonal with 
 respect to a positive weight function w(x) on the interval $(a\,b)$\, sati
 sfies a three-term recurrence equation. We discuss the role played by the 
 polynomials associated to $p_n$\, especially as coefficient polynomials 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 show how 
 Christoffel's formula is used to obtain mixed three-term recurrence equati
 ons involving the polynomials $p_n$\, $p_{n-1}$ and\n$g_{n-m\,k}$\, $m \\i
 n \\{2\,3\,...\,n-1\\}$\,\nwhere the sequence $\\{g_{n\,k}\\}_{n=0}^\\inft
 y$\, $k \\in {\\mathbb{N}}_0$\, 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 discuss 
 the conditions on $k$\, necessary and sufficient for these equations to be
  in such a form\, that they can be applied in the study of the location of
  the zeros of the appropriate polynomials.\n
LOCATION:https://researchseminars.org/talk/CAvid/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Ryan (University of Arkansas)
DTSTART:20240507T130000Z
DTEND:20240507T140000Z
DTSTAMP:20260422T165132Z
UID:CAvid/121
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/121/">
 From Dirac type operators to Bosonic Laplacians</a>\nby John Ryan (Univers
 ity of Arkansas) as part of CAvid: Complex Analysis video seminar\n\nLectu
 re held in N/A.\n\nAbstract\nLurking behind most familiar second order par
 tial differential operators there is a first order differential operator. 
 The familiar second order operators include the Laplace operator\, the \n$
 p$-Laplacian\, the conformal Laplacian on the sphere and the Maxwell opera
 tor. \n\nAll of these operators are conformally invariant. \n\nWe shall in
 troduce these operators and associated integral operators together with so
 me of their basic properties. \n\nThis is joint work with Chao Ding\, Phou
 c Tai Nguyen and the late Raymond Walter.\n
LOCATION:https://researchseminars.org/talk/CAvid/121/
END:VEVENT
END:VCALENDAR