Talk_id  Date  Speaker  Title 
14372

Monday 8/20 11:00 AM

Soumyashant Nayak, University of Pennsylvania

Analyticity in Operator Algebras
 Soumyashant Nayak, University of Pennsylvania
 Analyticity in Operator Algebras
 08/20/2018
 11:00 AM  12:00 PM
 C517 Wells Hall
The title of this talk is borrowed from a seminal paper by Arveson discussing noncommutative analogues of the Hardy space H^∞(T) via the socalled subdiagonal algebras. Subdiagonal algebras are a family of nonselfadjoint operator algebras which give a common perspective to the study of some triangular operator algebras (for example, the algebra of block upper triangular matrices in M_n(C)), Dirichlet function algebras, etc. The first part of the talk will be about a noncommutative version of innerouter factorization in finite maximal subdiagonal algebras. We will then discuss a proof of a version of Jensen's inequality in this setting which relates to some classical results by Szegö.

15401

Wednesday 9/12 4:00 PM

Alex Waldron, MSU

YangMills flow in dimension four
 Alex Waldron, MSU
 YangMills flow in dimension four
 09/12/2018
 4:00 PM  4:50 PM
 C517 Wells Hall
Among the classical geometric evolution equations, YM flow is the least nonlinear and best behaved. Nevertheless, curvature concentration is a subtle problem when the base manifold has dimension four. I'll discuss my proof that finitetime singularities do not occur, and briefly describe the infinitetime picture.
This talk will be more analytic and contains <50% overlap with my talk last Thursday.

14348

Wednesday 9/19 4:10 PM

Richard Kollar, Comenius University, Bratislava, Slovakia

Krein signature  three unexpected lessons
 Richard Kollar, Comenius University, Bratislava, Slovakia
 Krein signature  three unexpected lessons
 09/19/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
Krein signature is an algebraic quantity characterizing purely imaginary eigenvalues of linearized Hamiltonian systems. Instabilities growing from a stable state in these systems are caused by HamiltonianHopf bifurcations, i.e. events when two purely imaginary eigenvalues collide and split off the imaginary axis. The necessary condition for such an event is that the colliding eigenvalues must have mixed signature. In the talk we present three elegant results related to Krein signature  graphical Krein signature and its use to simplify proofs, a connection to stability in general extended systems, and ability to characterize the nature of the eigenvalue collisions directly from the reduced dispersion relation.

15389

Wednesday 10/3 4:10 PM

N. K. Nikolski, University of Bordeaux

V.Ya.Kozlov's completeness problem
 N. K. Nikolski, University of Bordeaux
 V.Ya.Kozlov's completeness problem
 10/03/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
In 19481950, V.Ya.Kozlov (19142007) stated a series of
interesting geometric properties of dilated systems D(f)= {f(kx): k=
1,2,...} in the spaces L^p(0,1). Since that, no proofs were published.
In particular, for a RademacherHaarWalsh type generator f=
2periodic odd extension of the indicator function of (0,a), 0<a<1,
the system D(f) was claimed to be complete/incomplete for many
particular values of a. We prove all Kozlov's statements and several
new, as well as discuss other geometric properties of D(f).

15390

Wednesday 10/10 4:10 PM

N. K. Nikolski, University of Bordeaux

Dilated systems and multivariable analysis
 N. K. Nikolski, University of Bordeaux
 Dilated systems and multivariable analysis
 10/10/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
Geometric L^2(0,1) properties of dilated function systems D(f)= {f(kx): k= 1,2,...} are discussed, as completeness, Riesz basis property, etc. (Completeness of D(f) for f(x)= 1/x[1/x] is equivalent to the Riemann Hypothesis). The Bohr's lift techniques permit to explain (all) known results and show some new, as well as to discuss open problems.

15391

Wednesday 10/17 4:10 PM

Irina Holmes, MSU and Texas A&M

Bellman and Bollobas Functions
 Irina Holmes, MSU and Texas A&M
 Bellman and Bollobas Functions
 10/17/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
No abstract available.

15406

Wednesday 10/24 4:10 PM

A. N. Karapetyants, Southern Federal University, Rostov on Don, Russia

On Bergman type spaces of functions of nonstandard growth and some related questions.
 A. N. Karapetyants, Southern Federal University, Rostov on Don, Russia
 On Bergman type spaces of functions of nonstandard growth and some related questions.
 10/24/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
We study various Banach spaces of holomorphic functions on the unit
disc and half plane. As a main question we investigate the boundedness
of the corresponding holomorphic projection. We exploit the idea of
V.P.Zaharyuta, V.I.Yudovich (1962) where the boundedness of the
Bergman projection in Lebesgue spaces was proved using
CalderonZygmund operators. We treat the cases of variable exponent
Lebesgue space, Orlicz space, Grand Lebesgue space and variable
exponent generalized Morrey space. The major idea is to show that the
approach can be applied to a wide range of function spaces. This opens
a door in a sense for introducing and studying new function spaces of
Bergman type in complex analysis. We also study the rate of growth of
functions near the boundary in spaces under consideration and their
approximation by mollifying dilations.

15392

Wednesday 11/14 4:10 PM

Dominique Maldague, UC Berkeley

TBA
 Dominique Maldague, UC Berkeley
 TBA
 11/14/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
No abstract available.
