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# Geometrisen analyysin seminaari, 2012-2013

Ilkka Holopainen
p. 191-51452

Eero Saksman
p. 191-51500

Seminaari kokoontuu perinteiseen aikaan perjantaisin kello 14-16 salissa C124.
Aiheet vaihtelevat puhujista riippuen.

## Syksyn 2012 esitelmiä

Maanantai, 27.8.2012 klo 14-16 C124 (huom. poikkeuksellinen aika!)

Maria Carmen Reguera (Lund)

"On a conjecture of Sarason on the composition of Toeplitz operators"

ABSTRACT: We consider the Bergman space L^2_a(D), the space of analytic
functions in the disk that are L^2 bounded. A conjecture of Sarason discusses
a characterization of the composition of two Toeplitz operators in the Hardy
and Bergman spaces. The case of the Hardy space it is now well understood,
and the conjecture was proven to be false by F. Nazarov. The Bergman
space case, however, is still an open question and is the one we will discuss
in this seminar. As in the case of the Hardy space, there is a connection
between the composition of Toeplitz operators and a two weight inequality
for the Bergman projection. We will further explain this connection and show
necessary and suffcient conditions for the composition of Toeplitz operators
to be bounded.

Perjantai, 7.9.2012 klo 14-16 C124

Alberto Setti

"Stochastic properties of Riemannian manifolds and application to PDEs"

ABSTRACT: The asymptotic behavior of the heat kernel of a Riemannian manifold gives rise to the classical concepts of parabolicity, stochastic completeness (or conservative property) and Feller property (or $C^0$-diffusion property).

Both parabolicity and stochastic completeness have been the subject of a systematic study, which led to discovering sharp geometric conditions for their validity and to a rich array of tools, techniques and equivalent concepts ranging from maximum principles at infinity, function theoretic tests (Khas'minskii
criterion), comparison techniques etc.... We aim at describing a number of steps forward in the development of a similar apparatus for the Feller property, and to present a number of applications of the Feller property to the asymptotic behavior of PDE's on the manifold.

Perjantai, 14.9.2012 klo 14-16 C124

Ei seminaaria.

Perjantai, 21.9.2012 klo 14-16 C124

Ei seminaaria

Perjantai, 28.9.2012 klo 14-16 C124

Tuomo Kuusi

"Linear potentials in nonlinear potential theory"

ABSTRACT: We give an update to some aspects of theory for solutions to nonlinear elliptic or parabolic, possibly degenerate, equations involving p-Laplacean type operators and datum, which, in full generality, can be a measure. The main focus is to describe recent pointwise potential estimates for gradients of solutions.

Perjantai, 5.10.2012 klo 14-16 C124

Mikko Parviainen (Jyväskylä)

"Tug-of-war with selling option, discontinuous gradient constraints,
and the infinity Laplacian"

Perjantai, 12.10.2012 klo 14-16 C124

Jasun Gong

"The Lip-lip condition on doubling metric measure spaces"

Perjantai, 19.10.2012 klo 14-16 C124

Zoltan Buczolich

"Multifractal Hölder spectra of generic functions and measures"

Perjantai, 26.10.2012 klo 14-15 C124

Kenneth Falconer

ABSTRACT: I will discuss the construction of certain families of self-similar fractals which display various symmetries. I will then indicate how methods from group theory may be used to analyse the symmetries and enumerate the fractals in such families with each symmetry group.

The talk should be appropriate to a reasonably broad audience.

Perjantai, 2.11.2012 klo 14-16 C124

Ei seminaaria.

Perjantai, 9.11.2012 klo 14-16 C124

Ei seminaaria.

Perjantai, 16.11.2012 klo 14-16 C124

Alexei Poltoratski

"5. Lecture of the crash course (title TBA)"

Perjantai, 23.11.2012 klo 14-16 C124

Juhana Siljander

"Harnack type estimates for time-fractional heat equation"

Perjantai, 30.11.2012 klo 14-16 C124

Jan Cristina

"Energy minimising quasiconformal frames"

Perjantai, 7.12.2012 klo 14-16 C124

Ei seminaaria.

Perjantai, 14.12.2012 klo 14-16 C124

Pekka Pankka

"Little is big after rescaling for quasiregular essential singularities"

## Kevään 2013 esitelmiä

Perjantai, 11.1.2013 klo 14-16 C124

Naotaka Kajino

"Analysis and geometry of the measurable Riemannian structure
on the Sierpinski gasket (and other fractals)"

Perjantai, 18.1.2013 klo 14-16 C124

Lizaveta Ihnatsyeva

"Tangential behaviour of Poisson integrals of regular functions"

Perjantai, 25.1.2013 klo 14-16 C124

Esa Järvenpää

"Dimensions of random affine code tree fractals"

Perjantai, 1.2.2013 klo 14-16 C124

Dmitry Chelkak

"Extremal length and other conformal invariants in discrete complex analysis"

Perjantai, 8.2.2013 klo 14-16 C124

TBA

Torstai, 14.2.2013 klo 12-14 C124  Funktionaalianalyysin, Geometrisen analyysin, ja Analyysin ja geometrian (Aalto) yhteisseminaari

Luca Capogna

"Regularity for subelliptic PDE through uniform estimates in multi-scale geometries"

ABSTRACT:

This talk will focus on some recent results concerning existence and regularity of certain subelliptic evolution equations through a "multi-scale" Riemannian approximation scheme, in which the "forbidden" directions are penalized by a parameter $\epsilon$. The main technical novelties are Gaussian estimates, doubling and Poincare inequalities which are stable as the parameter $\epsilon \to 0$ and the Riemannian ambient geometry collapses to the sub-Riemannian structure. These results are part of an ongoing program joint with Citti, Manfredini, Rea and Senni Guidotti Magnani.

Perjantai, 15.2.2013 klo 14-16 C124

Ei seminaaria

Perjantai, 22.2.2013 klo 14-16 C124

Raul Serapioni

"Intrinsic Lipschitz graphs in Carnot groups"

Perjantai, 1.3.2013 klo 14-16 C124

Gregory Arone

"Polynomial approximations in topology"

Perjantai, 8.3.2013

Anton Lukyanenko

"Heisenberg Continued Fractions"

Perjantai, 15.3.2013 klo 14-16 C124

Juhani Koivisto

"Generalizing Kazhdan's property (T) and cohomological vanishing for uniformly bounded representations"

Perjantai, 22.3.2013 klo 14-16 C124

"Curvature problems for p-harmonic mappings in the plane"

ABSTRACT:

In this talk we will discuss p-harmonic mappings in planar domains. These are nonlinear counterparts of  harmonic mappings arising naturally in nonlinear elasticity theory and differential geometry.
First we will set up the stage and discuss basic properties of p-harmonic functions and mappings and their relations to quasiregular mappings. Then, we will investigate the curvature of level curves for component functions of a p-harmonic mapping, estimate their lengths and present variant of an isoperimetric inequality for level curves. If time permits we will discuss some open problems.

Perjantai, 29.3.2013 klo 14-16 C124

Ei seminaaria (Pitkäperjantai)

Perjantai, 5.4.2013 klo 14-16 C124

Pekka Pankka

"Rickman's Picard construction in all dimensions II: partitions"

Perjantai, 12.4.2013 klo 14-16 C124

Ei seminaaria

Perjantai, 19.4.2013 klo 14-16 C124

Ei seminaaria

Perjantai, 26.4.2013 klo 14-16 C124

Pekka Pankka

"Rickman's Picard construction in all dimensions III"

Perjantai, 3.5.2013 klo 14-16 C124

Pekka Pankka

"Rickman's Picard construction in all dimensions IV: pillows"

Perjantai, 10.5.2013 klo 14-16 C124

Jan Cristina

"Holonomy bounds for non-smooth connections"

## Syksyn 2013 esitelmiä

Tiistai, 27.8.2013 klo 14-16 C124 (huom. poikkeuksellinen aika!)

Nils Dencker (Lund)

"The solvability and range of differential operators"

Perjantai, 1.11.2013 klo 14-16 C124

Riikka Korte

"TBA"

Perjantai, 8.11.2013 klo 14-16 C124

Tuomo Kuusi

"TBA (part II)"

Tervetuloa!

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