Scheduled
talks at Analysis Seminar - fall 2009
See the
departmental seminar calendar
for additional information.
This semester the seminar meets at 3 pm on Mondays in Kassar 105
unless
otherwise indicated.
Sep. 09 Organizational
Meeting
Sep. 14 No seminar
Sep. 21 Katharine Ott
(U. Kentucky)
The mixed problem for the
Laplacian in Lipschitz domains
Abstract: Two classical boundary value problems for the Laplacian are
the
Dirichlet and Neumann problems. A third type of boundary value problem
is
the mixed problem, where we specify Dirichlet data on a portion of the
boundary and Neumann data on the remaining portion. In this talk I will
discuss recent progress on the mixed problem in bounded Lipschitz
domains.
This is joint work with Russell Brown.
Sep. 28 Sergei Treil
(Brown U.)
Weak-star convergence in
multiparameter Hardy space H^1
Abstract: I discuss a recent joint work with J. Pipher about a
generalization of a theorem of Journe-Jones to the case of multiparamter
Hardy spaces. The result says that any bounded sequence of H^1 functions
converging a.e. also converges in weak-star topology of H^1 to the same
function. Generalization of this result to the multiparameter situation
is far from trivial: it requires a clever induction in the number of
parameters argument.
Oct. 5 Benoit
Pausader (Brown U.)
The mass-critical
fourth-order Schrodinger equation in high dimensions
Abstract: We study the fourth-order Schrodinger equation
$iu_t+\Delta^2u+s|u|^{8/n}u=0$ in high dimensions $n\ge 5$. We prove
that solutions exists for all time and approach linear solutions in the
defocusing case s=1. In the focusing case s=-1, the behavior is probably
more difficult and we give some results. If time permits we will also
mention a few words about lower dimensions.
Oct. 12 No seminar
(Fall Weekend)
Oct. 14 Sandra Pott (U.
Glasgow)
Special Wednesday Seminar:
12 pm, Kassar 105
The multiplier algebra of
the product BMO space
(joint work with B. Sehba,
Glasgow)
Abstract: The product BMO space of Chang and Fefferman has received much
attention in recent years in the work of Lacey, Muscalu, Petermichl,
Pipher, Tao, Thiele, Treil, Wick, and others. In this talk, we identify
its multplier algebra. The central tools are endpoint estimates
for
paraproducts and the connection between the dyadic and
continuous
version of product BMO, as recently found by Pipher, Ward, and Treil.
Oct. 19 Ron Blei (U.
Conn.)
The Grothendieck inequality
revisited (yet again)
Abstract: In a context of classical functional analysis, the
venerable
Grothendieck inequality is tied to an old recurring theme: how to
represent a given function in terms of simpler functions. Modulo
some
basic graduate courses in analysis, the talk will be elementary, and
(meant to be) accessible to graduate students.
Oct. 26 Alexander
Borichev (U. Marseilles)
Special Monday Seminar: 12
pm, Kassar 105
Weighted completeness of
exponents
Abstract: Given a finite positive measure on the real line we would like
to know how many exponential functions (say with exponents from -a to a)
do we need to be able to approximate every function square summable with
respect to this measure. More precisely, we discuss what perturbations
of the measure preserve the critical value of a.
Oct. 26 Lesley Ward (U.
South Australia)
Harmonic measure
distribution functions for sequences of planar domains
Abstract: The harmonic measure distribution function h(r) of a planar
domain D specifies the harmonic measure of the part of the boundary of D
that lies within distance r of a fixed basepoint in D. It thus relates
the geometry of the domain to the behavior of Brownian motion in the
domain. We establish sufficient conditions under which these functions
h_n for a sequence of domains D_n converge pointwise to the function h
for a limiting domain D, at all points of continuity of h. We
establish
this convergence for a model example. This is joint work with M.
Snipes.
Nov. 2 Marie
Snipes (Kenyon College)
Flat forms in Banach spaces
Abstract: The flat forms of Whitney have been useful in solving many
problems in geometric analysis and elsewhere. A classical theorem
of
Wolfe states that the space of flat forms is in fact the dual to the
space
of flat chains in Euclidean space. Recent work by Adams
generalizes
flat chains to Banach spaces. We will define a flat differential
form
in a Banach space and discuss the generalization of Wolfe's theorem to
this setting.
Nov. 9 George
Daskalopoulos (Brown U.)
Analytic aspects of
geometric rigidity
Abstract: I will discuss questions of existence and regularity of
harmonic
maps between singular spaces and how these techniques can be applied to
problems of geometric superrigidity.
Nov. 30 Xiaomin Ma
(Brown U.)
Special Monday Seminar: 4
pm, Kassar 105
Joint Analysis/Number Theory
Serminar
Discrepancy of point
distributions