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SUMMARY:Jean-Pierre Demailly (Université Grenoble Alpes/ Institut Fourier
)
DTSTART;VALUE=DATE-TIME:20210507T140000Z
DTEND;VALUE=DATE-TIME:20210507T152000Z
DTSTAMP;VALUE=DATE-TIME:20210612T222540Z
UID:Rutgers_Complex/1
DESCRIPTION:Title: Hermitian-Yang-Mills approach to the conjecture of Griffiths on th
e positivity of ample vector bundles\nby Jean-Pierre Demailly (Univers
ité Grenoble Alpes/ Institut Fourier) as part of Rutgers Seminar on Compl
ex Analysis\, Harmonic Analysis and Complex Geometry\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Rutgers_Complex/1/
END:VEVENT
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SUMMARY:Yum-Tong Siu (Harvard University)
DTSTART;VALUE=DATE-TIME:20210514T143000Z
DTEND;VALUE=DATE-TIME:20210514T153000Z
DTSTAMP;VALUE=DATE-TIME:20210612T222540Z
UID:Rutgers_Complex/2
DESCRIPTION:Title: Global non-deformability\, super rigidity\, and rigidity of vector
bundles and CR manifolds\nby Yum-Tong Siu (Harvard University) as par
t of Rutgers Seminar on Complex Analysis\, Harmonic Analysis and Complex G
eometry\n\n\nAbstract\nAbstract: Flat directions are obstacles and at the
same time also essential tools for a number of fundamental problems in sev
eral complex variables involving rigidity and regularity. Among them are
the following examples.\n\n(i) The global non-deformability of irreducibl
e compact Hermitian symmetric manifolds.\n\n(ii) The strong rigidity and s
uper rigidity problem of holomorphic maps with curvature condition on the
target manifold.\n\n(iii) The regularity question of the complex Neumann p
roblem for weakly pseudoconvex domains.\n\n(iv) Rigidity and strong rigidi
ty problems of holomorphic vector bundles.\n\n(v) Rigidity and strong rigi
dity problems of CR manifolds.\n\nFor global nondeformability and regulari
ty problems for pseudoconvexity domains flat directions are obstacles. Fo
r rigidity of metrics and CR manifolds with the possibility of small pertu
rbations\, flat directions are essential tools. The talk starts with the h
istoric motivations of the problems and does not assume any background mor
e than basic complex analysis. After discussing the general techniques in
volving flat directions\, we will focus on the global non-deformability pr
oblem and some recent methods in this area.\n
LOCATION:https://researchseminars.org/talk/Rutgers_Complex/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loredana Lanzani (Syracuse University)
DTSTART;VALUE=DATE-TIME:20210528T143000Z
DTEND;VALUE=DATE-TIME:20210528T153000Z
DTSTAMP;VALUE=DATE-TIME:20210612T222540Z
UID:Rutgers_Complex/3
DESCRIPTION:Title: The commutator of the Cauchy-Szegö projection for domains in \\C^
n with minimal smoothness\nby Loredana Lanzani (Syracuse University) a
s part of Rutgers Seminar on Complex Analysis\, Harmonic Analysis and Comp
lex Geometry\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Rutgers_Complex/3/
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SUMMARY:Jim Wright (The University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20210604T143000Z
DTEND;VALUE=DATE-TIME:20210604T153000Z
DTSTAMP;VALUE=DATE-TIME:20210612T222540Z
UID:Rutgers_Complex/4
DESCRIPTION:Title: A theory for complex oscillatory integrals\nby Jim Wright (The
University of Edinburgh) as part of Rutgers Seminar on Complex Analysis\,
Harmonic Analysis and Complex Geometry\n\n\nAbstract\nHere we develop a t
heory for oscillatory integrals with complex phases. Basic scale-invariant
bounds for these oscillatory integrals do not hold in the generality that
they do in the real setting. In fact they fail in the category of complex
analytic phases but we develop a perspective and arguments to establish s
cale-invariant bounds for complex polynomial phases.\n
LOCATION:https://researchseminars.org/talk/Rutgers_Complex/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xianghong Gong (University of Wisconsin-Madison)
DTSTART;VALUE=DATE-TIME:20210611T143000Z
DTEND;VALUE=DATE-TIME:20210611T153000Z
DTSTAMP;VALUE=DATE-TIME:20210612T222540Z
UID:Rutgers_Complex/5
DESCRIPTION:Title: On regularity of $\\dbar$ solutions on $a_q$ domains with $C^2$ bo
undary in complex manifolds\nby Xianghong Gong (University of Wisconsi
n-Madison) as part of Rutgers Seminar on Complex Analysis\, Harmonic Analy
sis and Complex Geometry\n\n\nAbstract\nWe study regularity of $\\dbar$ so
lutions on a relatively compact $C^2$ domain $D$ in a complex manifold. Su
ppose that the boundary of the domain has everywhere either $(q+1)$ negati
ve or $(n-q)$ positive Levi eigenvalues. Under a necessary condition on th
e existence of a locally $L^2$ solution on the domain\, we show the existe
nce of the solutions on the closure of the domain that gain $1/2$ derivati
ve when $q=1$ and the given $(0\,q)$ form in the $\\dbar$ equation is in t
he H\\"older-Zygmund space $\\Lambda^r(\\overline D)$ with $r>1$. For $q>1
$\, the same regularity for the solutions is achieved when the boundary is
either sufficiently smooth or of $(n-q)$ positive Levi eigenvalues everyw
here.\n
LOCATION:https://researchseminars.org/talk/Rutgers_Complex/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Malchiodi (The University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20210618T143000Z
DTEND;VALUE=DATE-TIME:20210618T153000Z
DTSTAMP;VALUE=DATE-TIME:20210612T222540Z
UID:Rutgers_Complex/6
DESCRIPTION:Title: On the Sobolev quotient in sub-Riemannian geometry\nby Andrea
Malchiodi (The University of Edinburgh) as part of Rutgers Seminar on Comp
lex Analysis\, Harmonic Analysis and Complex Geometry\n\n\nAbstract\nWe co
nsider three-dimensional CR manifolds\, which are modelled on the Heisenbe
rg group. We introduce a natural concept of “mass” and prove its posit
ivity under the condition that the scalar curvature is positive and in rel
ation to their embeddability properties. We apply this result to the CR Ya
mabe problem\, and we discuss extremality of Sobolev-type quotients\, givi
ng some counterexamples for “Rossi spheres”. This is joint work with J
.H.Cheng and P.Yang.\n
LOCATION:https://researchseminars.org/talk/Rutgers_Complex/6/
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