Back to the home page of A.Grigor'yan

Oberseminar Geometric Analysis

SFB 701, project A6

Sommersemester 2010

20.04.10  10:15   U2-135 
                  Wolfhard Hansen (Bielefeld)
                  3G-inequality for planar domains
27.04.10  10:15   U2-135 
                  Markus Biegert (Ulm)
                  Does diffusion determine the manifold?
04.05.10  10:15   U2-135 
                  Xueping Huang  (Bielefeld)
                  Stochastic completeness of graphs
14.05.10  14:15   V4-116 
                  Radoslaw Wojciechowski (University of Lisbon)
                  Spherically symmetric graphs
Abstract: We introduce the class of spherically symmetric graphs of unbounded geometry.  We will then discuss their stochastic completeness and basic spectral properties.  We also show how to use this class to obtain some comparison results.  
18.05.10  10:15   U2-135 
                  Jun Masamune (Pennsylvania State University, USA)
                  Homogenization and its application to probability theory
Abstract: I will show the Mosco convergence of the Dirichlet forms which is defined on a cylinder with highly conductive boundary. The tightness of the associated Wiener measures will be shown, and as a conclusion, we will obtain the weak-convergence of those Wiener measures.
25.05.10  10:15   U2-135 
                  Bartlomiej Dyda (Bielefeld)
                  On inequalities concerning functions of fractional smoothness
01.06.10  10:15   U2-135 
                  Shun-Xiang Ouyang (Bielefeld) 
                  Heat kernel estimates and  functional inequalities on Dirichlet spaces
08.06.10  10:15   U2-135 
                  Alexander Bendikov (University of Wroclaw / Bielefeld) 
                  On a class of random walks on ultra-metric spaces 1
15.06.10  10:15   U2-135 
                  Alexander Bendikov (University of Wroclaw / Bielefeld)
                  On a class of random walks on ultra-metric spaces 2
22.06.10  10:15   U2-135 
                  Jun  Masamune (Pennsylvania State University, USA)
                  The conservation property of non-local Dirichlet forms
Abstract: In this talk, I would like to show the conservation property of a non-local regular Dirichlet form on an Euclidean space with Radon measure under a volume growth condition. Our approach is to develop the integral deviation property and to apply the method by M.P. Gaffney. If the time permits, I would like to talk also on the L^p Liouville property for the same forms. Both results were obtained in joint works with Toshihiro Uemura.
29.06.10  10:15   U2-135 
                  Igor Verbitsky (University of Missouri, USA)
                  Nonlinear equations with natural growth terms
06.07.10  10:15   U2-135 
                  Jiaxin Hu (Tsinghua University, Beijing)
                  Generalized Bessel and Riesz potentials on metric measure spaces
13.07.10  10:15   U2-135 
                  Alexander Loboda (Voronezh, Russia)
                  Homogeneity of embedded  manifolds
Abstract: We discuss the problem of description of real hypersurfaces that are (locally) homogeneous with respect to different structures (holomorphic, affine, projective) of the ambient complex spaces of small dimensions. The history of this problem goes back to 1932 when E. Cartan gave a complete solution of the holomorphic homogeneity problem in the case of 2-dimensional complex spaces. It was not until 1995 when a comprehensive description of affinely homogeneous surfaces of 3-dimensional real space was obtained by Doubrov, Komrakov and Rabinovich. 
We describe a coefficient approach to the problem, that is connected to the use of the canonical equations of the manifolds under consideration and to the description of Lie algebras of vector fields on these surfaces. Recent results of the author  about the homogeneity in 2- and 3-dimensional complex spaces will be presented. 
20.07.10  10:15   U2-135 
                  Satoshi Ishiwata (Tsukuba University, Japan)
                  Heat kernel estimates on non-compact gluings

Wintersemester 2009/2010

09.09.09  10:15   V3-201 
                  Jiaxin Hu (Tsinghua University, Beijing)
                  Comparison inequalities for heat kernels
10.09.09  10:15   V3-201 
                  Alexander Bendikov (University of Wroclaw)
                  Spectral properties of some random walks on locally finite groups
11.09.09  10:15   V3-201 
                  Boguslaw Zegarlinski  (CNRS Toulouse)
                  Ergodicity of Markov semigroups in infinite dimensions
14.09.09  10:15   V3-201 
                  Naotaka  Kajino (Kyoto University, Japan)
                  Short time asymptotics of the heat kernels on the usual and harmonic Sierpinski gaskets
15.09.09  10:15   V3-201 
                  Satoshi  Ishiwata  (Tsukuba University, Japan)
               Smallness of the first Neumann eigenvalues under a bottleneck heat kernel estimate
16.09.09  10:15   V3-201 
                  Wolfhard  Hansen (Bielefeld University)
                  One radius results for supermedian functions on Rd, d ≤2
17.09.09  10:15   V3-201 
                  Ivan  Netuka (University of Prague)
                  An excursion into infinite dimensional convexity
21.09.09  10:15   V3-201 
                  Minoru Murata (Tokyo Institute of Technology)
                  Structure of non-negative solutions to parabolic equations and perturbation theory for elliptic operators
22.09.09  10:15   V3-201 
                  Wolfhard Hansen (Bielefeld University)
                  Harnack inequality and Hölder continuity for harmonic functions
23.09.09  10:15   V3-201 
                  Shun-Xiang Ouyang  (Bielefeld University)
                  Harnack inequalities and applications for Ornstein-Uhlenbeck semigroups with jump
02.10.09  10:15   V3-201 
                  Michiel  van den Berg  (University of Bristol)
                  Minimization of Dirichlet eigenvalues with geometric constraints
27.10.09  10:15   V3-201 
                  Alexander Teplyaev  (University of Connecticut)
                  Uniqueness of Brownian motion on Sierpinski carpets, part I
03.11.09  10:15   V3-201 
                  Alexander Teplyaev  (University of Connecticut)
                  Uniqueness of Brownian motion on Sierpinski carpets, part II
10.11.09  10:15   V3-201 
                  Alexander Teplyaev  (University of Connecticut)
                  Uniqueness of Brownian motion on Sierpinski carpets, part III
22.12.09  10:15   V3-201 
                  Wei Liu  (Bielefeld)
                  Dimension-free Harnack inequality and its applications
12.01.10  10:15   V3-201 
                  Nikolai Nikolov (Sofia) 
                  Estimates of invariant metrics on C-convex domains
19.01.10  10:15   V3-201 
                  Uta Freiberg  (Jena/Siegen)
                  Einstein relation on fractals
02.02.10  10:15   V3-201 
                  Moritz Kaßmann  (Bielefeld)
                  Jump processes, integro-differential operators, and regularity

Sommersemester 2009

30.04.09  12:00 C2-144 
                  Hendrik Vogt (TU Dresden)
                  Kato class and Gaussian bounds for the heat equation on the half space
07.05.09  12:00 C2-144 
                  Satoshi Ishiwata (Tsukuba University, Japan)
                  The gradient heat kernel estimate on gluings
14.05.09  14:00 U2-241 
                  Elmar Teufl (Bielefeld)
                  A determinant identity of Sylvester, an inverse problem concerning effective resistances, and computing the number of spanning trees via electrical network theory
Abstract: Given an electrical network (a finite set of nodes and resistances between pairs of nodes), there is, for every pair of nodes, a number called effective resistance, so that the network with respect to this pair of nodes is equivalent to a single wire equipped with the effective resistance. Given the $\binom{n}{2}$ resistances we can compute the set of $\binom{n}{2}$ effective resistances (e.g. using Schur complements). We are interested in the inverse problem. Given effective resistances, can we recover the original resistances? Kigami showed that there is at most one network solving this inverse problem without giving an explicit solution. We will give an explicit solution using an old determinant identity due to Sylvester and point out a connection to the problem of counting spanning trees.
18.06.09  16:00 C2-144 
                  Wolfhard Hansen (Bielefeld)
                  Harmonic measures for a point may form a square
25.06.09  16:00 C2-144 
                  Igor Verbitsky (Missouri)
                 Quasilinear and Hessian equations and inequalities
02.07.09  16:00 C2-144 
                   Gerasim Kokarev (University of Edinburgh)
               Variational aspects of Laplace eigenvalues on Riemannian surfaces
23.07.09  16:00 C2-144 
                  Eva Touris  (University of Madrid)
                  Gromov hyperbolic equivalence of the hyperbolic and quasihyperbolic metrics in Denjoy domains

Sommersemester 2008

23.06.08  16:00 S2-121 
                  Wolfhard Hansen (Bielefeld)
                  Density of extremal measures in parabolic potential theory
16.06.08  16:00 V3-201 
                  Verfahren W2 Analysis
09.06.08  16:00 V3-201 
                  Verfahren W2 Analysis
02.06.08  16:00 S2-121 
                  Denis Labutin (Bielefeld / UCSB)
                  Partial regularity for the Monge-Ampere equation
26.05.08  16:00 V3-201 
                  Verfahren W2 Analysis
19.05.08  16:00  S2-121
                 Elton P. Hsu  (Northwestern University)
                 Bismut's formula for heat kernels on vector bundles
05.05.08  16:00  S2-121
                 Dan Mangoubi  (MPIM Bonn)
                 Geometry of nodal domains

Wintersemester 2007/8

31.01.08  16:00  V2-216
                 Denis Labutin (Bielefeld / UCSB)
                 Critical regularity for non-linear elliptic equations
24.01.08  16:00  V2-216
                 Moritz Kassmann (Bonn)
                 Critical regularity questions for local and non-local problems
17.01.08  16:00  V2-216
                 Laurent Saloff-Coste (Cornell)
                 Analysis on inner uniform domains 
06.12.07  16:00  V2-216
                 Jun Kigami (Kyoto)
                 Analysis on fractals
29.11.07  16:00  V2-216
                Alexander Grigoryan (Bielefeld)
                 Heat kernels on metric measure spaces
Abstract: The recent development of Analysis on fractal spaces has motivated the study of abstract heat kernels on metric measure spaces. An abstract heat kernel is a function on such a space that by definition satisfies certain standard properties of the classical heat kernels, such as positivity, symmetry, the semi-group property, approximation of identity, and stochastic completeness. Such a heat kernel is associated with a Markov process on the space in question and is, in fact, its transition density. In many cases of interest, heat kernels satisfy two-sided estimates of two types:
(1) Gaussian or, more generally, sub-Gaussian estimate, which is typical for diffusion processes;
(2) estimate with a polynomial tail, which is typical for symmetric stable processes.
One of the main results is that, under certain mild assumptions, these two cases exhaust all possible heat kernel estimates of homogeneous type. 
22.11.07  V2-216
                 Ben Hambly (Oxford)
                 Local limit theorems for random walks on percolation clusters
Abstract: The talk will consider the simple random walk on the supercritical clusters of bond percolation in the d-dimensional integer lattice. It is now well known that there are Gaussian heat kernel estimates and a quenched invariance principle for this process. We establish a parabolic Harnack inequality and show that this leads to a local limit theorem for the convergence of the transition kernel for the random walk to the Gaussian heat kernel. These ideas can be extended to other random walks on sequences of graphs.
                 Christophe Sabot (Lyon)
                 Limit laws for one dimensional random walks in random environments
Abstract: In 1975, Kesten, Kozlov and Spitzer proved a limit theorem for one dimensional random walks in random environments with null speed. They
proved that the RWRE properly renormalised converges to a stable law, but they left open the explicit description of the parameters of this law. In this talk, based on a joint work with N. Enriquez and O. Zindy, I will present a different proof of this limit theorem, based on the analysis of the potential associated with the environment, which leads to a description of the parameters of the law. The case of beta environments appears to be particularly explicit. 
15.11.07  16:00  V2-216
                 Vladimir Kondratiev (Moscow/Bielefeld)
                 Asymptotic behaviour  of solutions of nonlinear diffusion equations
08.11.07  16:00  V2-216
                 Wolfhard Hansen  (Bielefeld)
                 Convexity properties of harmonic measures
25.10.07  16:00  V2-216
                 Alexander Bendikov (Wroclaw/Bielefeld)
                 Long time decay of the return probability for random walks without second moment
18.10.07  16:00  V2-216
                 Christoph Richard (Bielefeld)
                 Random colourings of aperiodic graphs: Ergodic and spectral properties. 
04.10.07  16:00  V3-204
                 Takashi Kumagai (Kyoto)
                 Heat kernel estimates and Harnack inequalities for jump processes
Abstract: I will talk about the relationships between the parabolic Harnack inequality, heat kernel estimates, some geometric conditions, and some analytic conditions for random walks with long range jumps. Unlike the case of diffusion processes, the parabolic Harnack inequality
does not, in general, imply the corresponding heat kernel estimates. This is a joint work with M.T. Barlow, A. Grigor'yan and with M.T. Barlow, R.F. Bass.
02.08.07  V2-216
                 14:00-15:00  Wolf-Jürgen Beyn (Bielefeld)
                 Nonlinear stability of patterns and the method of freezing
                15:30-16:30  Sergey Bobkov (Minnesota)
                 Poincaré-type inequalities for multidimensional convex bodies and log-concave probability distributions

Sommersemester 2007

Di  14:30-17:00    T2-213

17.04.07  Jiaxin Hu (Beijing)
                 Domains of Dirichlet forms and the effective resistance estimates on p.c.f. fractals
08.05.07  Gilles Carron (Nantes)
                 Riesz transform and connected sum
Abstract: We will present recent  results (both positive and negative) on the following question. Assume that M is a complete Riemannian manifold such that the Riesz transform D-1/2 is bounded on Lp for a certain p in ]1,∞[. Is it true that the Riesz transform is bounded on the Lp on the connected sum M#M?  This is partially a joint work with T. Coulhon (Cergy) and A. Hassell (Canberra).
                 14:30-15:30  Michiel Van den Berg (Bristol)
                 Heat flow and Hardy inequality in complete Riemannian manifolds with singular initial conditions
                16:00-17:00  Yuri Kondratiev (Bielefeld)
                 Jump generators related to some spatial Markov processes
19.06.07  June Masamune (Worcester, USA)                 
                  Conservative principle for differential forms
26.06.07   14:00-16:00
                   Guido Elsner (Bielefeld)
                  Geometric and probabilistic estimates of higher-order eigenvalues of finite Markov chains
03.07.07   Alexander Teplyaev (Connecticut, USA)
                 Spectral analysis and Gaussian type heat kernel estimates on the Sierpinski gasket type fractals
10.07.07  Ivan Netuka (Prague)
                 Potential theory of the farthest point distance function 

Wintersemester 2006-7

Mi  15:30-18:00    U5-133

08.11.06  Andras Telcs (Budapest)
                 Heat kernels on graphs, isoperimetric inequalities, and Einstein relation
15.11.06  Wolfhard Hansen (Bielefeld)
                 Convexity of limits of harmonic measures
22.11.06  Laurent Saloff-Coste (Cornell)
                 Heat kernels, Neumann and Dirichlet, in intrinsically uniform domains
Abstract: There are many great work dealing with the Dirichlet problem and the Martin boundary of Euclidean domains, starting with the paper by Hunt and Wheeden (1970) on the Martin Boundary of Lipschitz domains, the papers of Dahlberg (1977), Ancona (1978) and Wu (1978), the work of Jerison and Kenig (1982) and more recent work of Aikawa. These works are concerned with the elliptic theory. Aspects of the parabolic case appears in work  by E. Fabes and M. Safonov and their collaborators including Garofalo, Salsa, and Yuan. Strangely enough, the heat kernel is absent of most (if not all) of these works and only appeared quite recently in work of N. Varopoulos (and also Q.S. Zhang and R. Song). In this talk, I will discuss a recent joint work with my graduate student Pavel Gyrya where we study the heat kernel (with either Neumann or Dirichlet boundary conditions) in a large class of domains that includes the domain above the graph of any Lipschitz function and the exterior of any convex set in Euclidean n-space.
29.11.06  jointly with the probability seminar, room V3-201
                 Anatoly Vershik (St. Petersburg)
                 Classification of the metric spaces with measure and random matrices
Abstract: There is a simple classification of the metric triples (=metric spaces with measure) up to measure preserving isometries  (Gromov-V), which is a particular case of the classification of the measurable functions of several variables. The invariant is a measure on the space of so called distance matrices. There are many open problems related to this subject.
06.12.06  Elmar Teufl (Bielefeld)
                 Simple random walks on nice trees
17.01.07  Alexander Grigoryan (Bielefeld)
                 Function theory on metric measure spaces and application to stochastic processes
                 15:30-16:30 Andras Telcs (Budapest)
                 Potential theory on graphs
                 17:00-18:00 Sergey Piskarev (Moscow)
                 Crank-Nicolson scheme for abstract linear systems
31.01.07  jointly with the probability seminar, room V3-201
                  Gerhard Huisken (Potsdam)
                  Isoperimetric inequalities via curvature flows
Abstract: Geometric evolution equations for hypersurfaces can be used to prove several sharp isoperimetric inequalities. The lecture concentrates on the
analytical aspects of this method
07.02.07  jointly with the probability seminar, room V3-201
                 Theo Sturm (Bonn)
                 Optimal transportation, Ricci curvature and diffusions on the L2-Wasserstein space
Abstract: We introduce and analyze generalized Ricci curvature bounds for metric measure spaces (M;d;m), based on convexity properties of the relative entropy Ent(:jm). For Riemannian manifolds, Curv(M;d;m) ¸ K if and only if Ric(M) ¸ K; for the Wiener space, Curv(M;d;m) = 1. One of the main results is that these lower curvature bounds are stable under (e.g. measured Gromov-Hausdorff) convergence. This solves one of the basic problems in this field, open for many years. Furthermore, we introduce a (more restrictive) curvature-dimension condition CD(K;N) which implies sharp versions of the Brunn-Minkowski inequality, of the Bishop-Gromov volume comparison theorem and of the Bonnet-Myers theorem. Moreover, it allows to construct a canonical Dirichlet form with Gaussian bounds for the corresponding heat kernel. Finally, we indicate how to construct a canonical reversible process on the L2-Wasserstein space of probability measures P(R), regarded as an infinite dimensional Riemannian manifold. This process has an invariant measure P¯ which may be characterized as the 'uniform distribution' on P(R) with weight function 1/Z exp(¡¯ ¢Ent(:jm)) where m denotes a given finite measure on R. One of the key results is the quasi-invariance of this measure P¯ under push forwards ¹ 7! h¤¹ by means of smooth di®eomorphisms h of R.