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Oberseminar Geometric Analysis

SFB 1283, project A3
IRTG 2235, area D

Wintersemester 2019/20

Di    10:15-11:45   V4-112

29.10.19  10:15   V4-112 
               Meng Yang (Bielefeld)
               Metrics and uniform Harnack Inequality on the Strichartz hexacarpet
19.11.19  10:15   V4-112 
               Shilei Kong (Bielefeld)
               Compact quasi-metric spaces as hyperbolic boundaries
26.11.19  10:15   V4-112 
               Satoshi Ishiwata (Yamagata University, Japan)
               Poincare constant on manifolds with ends
Abstract. It is a well-known fact that the Poincare inequality does not hold on a connected sum Rn#Rn for n>2. In this talk, we discuss the estimates of the Poincare constant on manifolds with ends, where the Poincare constant is given by the supremum of variance over the Dirichlet energy form of functions on balls. This talk is based on a joint work with A. Grigor'yan and L. Saloff-Coste.
03.12.19  10:15   V4-112 
                Shilei Kong (Bielefeld)
               Compact quasi-metric spaces as hyperbolic boundaries II
10.12.19  10:15   V4-112 
                Alexander Grigor'yan (Bielefeld)
                Analysis on manifolds and volume growth
17.12.19  10:15   V4-112 
                Melissa Meinert (Bielefeld)
                Linear partial differential equations on compact resistance spaces
07.01.20  10:15   V4-112 
                Michael Hinz (Bielefeld)
                Removable sets and uniqueness of operator extensions on manifolds and metric measure spaces
Abstract. We study removable sets (in the sense of Mazja) and Lp-uniqueness problems on manifolds and metric measure spaces. The Laplacian, considered on suitable spaces of test functions vanishing in a neighborhood of a 'removed' null set, has a unique extension if and only if this set has vanishing second order capacity. If the semigroup is strong Feller and satisfies a specific gradient inequality then two types of capacities are comparable and the critical size of the removed set can be expressed in terms of Hausdorff measures. As an application we show that from the point of view of essential self-adjointness the Laplacian on certain Gromov-Hausdorff limits of non-collapsing spaces 'ignores' the singular part of the limit space. This is joint work with Jun Masamune (Sapporo) and Kohei Suzuki (Pisa).
21.12.19  10:15   V4-112 
                Anna Muranova (Bielefeld)
                On the notion of effective impedance for finite and infinite networks
28.01.20  10:15   V4-112 
                Wolfhard Hansen (Bielefeld)
                Evans' and Choquet's theorem for polar sets
Abstract. By classical results of G.C.Evans and G.Choquet on ''good kernels G in potential theory'', for every polar Fs-set P, there exists finite measure μ on P such that Gμ= on P, and a set P admits a finite measure μ on P such that 
{Gμ=}=P if and only if P is a polar Gd-set. A known application of Evans' theorem yields the solutions of the generalized Dirichlet problem for open sets by the Perron-Wiener-Brelot method using only harmonic  upper and lower functions.

In this talk it is shown that, by elementary ''metric'' considerations and without using any potential theory, such results can be obtained for general kernels 
G satisfying a local triangle property. The particular case, G(x,y)=|xy|a−d on Rd  where  2<a<da<d,  solves an open problem from the book of N.S.Landkoff on ''Foundations of Modern Potential Theory''.

Sommersemester 2019

Di    10:15-11:45   V4-119

16.04.19  10:15   V4-119 
                 Andrey Piatnitski (Narvik)
                 Homogenization of non-symmetric convolution type operators with integrable kernels in periodic media
23.04.19  10:15   V4-119
                 Simon Nowak (Bielefeld)
                 Hs,p regularity theory for a class of nonlocal elliptic equations
30.04.19  10:15   V4-119
                 Rostislav Grigorchuk (Texas A&M University)
                 On spectra of  graphs  and  groups
07.05.19  10:15   V4-119
                 Jun Cao (Bielefeld)
                 Heat kernels and Besov spaces on metric measure spaces
14.05.19 10:15   V4-119
                 Jun Cao (Bielefeld)
                 Heat kernels and Besov spaces on metric measure spaces II
21.05.19 10:15   V4-119
                 Jun Cao (Bielefeld)
                 Construction of wavelets on metric measure spaces
04.06.19 10:15   V4-119
                 Mathav Murugan (University of British Columbia)
                 A bridge between elliptic and parabolic Harnack inequalities 
Abstract. The notion of conformal walk dimension serves as a bridge between elliptic and parabolic Harnack inequalities. The importance of this notion is due to the fact that the finiteness of the conformal walk dimension characterizes the elliptic Harnack inequality. Roughly speaking, the conformal walk dimension is the infimum of all possible values of the walk dimension that can be attained by a time-change of the process and by a quasisymmetric change of the metric. Two natural questions arise 
(a) What are the possible values of the conformal walk dimension? 
(b) When is the infimum attained? 
In this talk, I will explain the answer to (a), and mention partial progress towards (b). 
This talk is based on joint work with Naotaka Kajino.
05.06.19 10:15   V2-121
                 Patricia Alonso-Ruiz (University of Connecticut)
                 Heat kernels on generalized diamond fractals
Abstract. In this talk we introduce (in some sense natural) diffusion processes on a parametric family of fractals called generalized diamond fractals. These spaces arise as scaling limits of diamond hierarchical lattices, which are studied in the physics literature in relation to random polymers, Ising and Potts models among others. In the case of constant parameters, diamond fractals are self-similar sets. This property was exploited in earlier investigations by Hambly and Kumagai to study the properties of the corresponding diffusion process and its associated heat kernel. These questions are of interest in particular because in this setting some usual assumptions like volume doubling are not satisfied. Alternatively, a diamond fractal can also be regarded as an inverse limit of metric measure graphs. Through a procedure proposed by Barlow and Evans, one can construct a canonical diffusion process for more general parameters, also in the absence of self-similarity. It turns out that it is possible to give a rather explicit expression of the associated heat kernel, which is in particular uniformly continuous and admits an analytic continuation.
11.06.19 10:15   V4-119
                 Jiaxin Hu (Tsinghua University)
                 Parabolic mean value inequality and heat kernel upper bounds
18.06.19 10:15   V4-119
                 Timothy Candy (University of Otago)
                 Global existence for the Zakharov system
Abstract.The Zakharov system is a system of coupled Schrödinger-wave equations which was originally derived as a model in plasma physics. We show that in dimensions d>3 for large wave data, and small Schrödinger data, solutions to the Zakharov system exist globally in time and scatter. Moreover, we extend the regularity region for well-posedness to the sharp region. The key step is to prove a Strichartz estimate for the Schrödinger equation with a potentially large free wave potential. In contrast to previous work on the Zakharov system, we avoid the use of normal forms, and instead work with spaces which are carefully adapted to control bilinear interactions between solutions to the Schrödinger and wave equations. Avoiding the use of normal forms allows us to consider data with regularity in the extended full region of local well-posedness. This is joint work with Sebastian Herr and Kenji Nakanishi.
25.06.19 10:15   V4-119
                 Takashi Kumagai (Kyoto)
                 Stability of heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms
Abstract. We consider symmetric Dirichlet forms that consist of strongly local (diffusion) part and non-local (jump) part on a metric measure space. Under general volume doubling condition and some mild assumptions on scaling functions, we establish stability of two-sided heat kernel estimates in terms of Poincare inequalities, jumping kernels and generalized capacity inequalities. We also discuss characterizations of the associated parabolic Harnack inequalities. Our results apply to symmetric diffusions with jumps even when the underlying spaces have walk dimensions larger than 2. This is a joint work with Z.Q. Chen (Seattle) and J. Wang (Fuzhou). 
02.07.19 10:15   V4-119
                 Sergey Bobkov (University of Minnesota) 
                 Moments of scores
Abstract. If a random variable X has an absolutely continuous density f(x), its score is defined to be the random variable 
\rho(X) = f'(X)/f(X), where f'(x) is the derivative of f. We will discuss upper bounds on the moments of the scores, especially in the case when X represents the sum of independent random variables.
09.07.19 10:15   V4-119
                 Wolfhard Hansen (Bielefeld)
                 Equicontinuity of harmonic functions and compactness of potential kernels
Abstract. Within the framework of balayage spaces (the analytical equivalent of nice Hunt processes), we prove  equicontinuity of bounded families of harmonic functions and apply it to obtain criteria for compactness of potential kernels.
11.07.19 10:15   T2-227
                 Anatoly Vershik (Steklov Institute, St. Petersburg)
                 Random walks on groups and the absolute
Abstract. An important problem in the theory of random processes and random fields (Dynkin, Dobrushin etc.) is to describe the probability measures with given co-transition distributions, e.g. to find all Markov processes with the same co-transition distributions as a given Markov process. The set of all such measures is referred to as the Absolute. This problem is solved on certain groups, including commutative groups, nilpotent groups, trees. Connections with the theory of harmonic functions, Poisson-Furstenberg boundaries and others will be explained.
16.07.19 10:15   V4-119
                 Stanislav Molchanov (UNC Charlotte and HSE Moscow)
                 Generalizations of Dickman's Law and their applications
Abstract. The Duckman's function and distribution are well-known in physical and applied probabilistic literature. They are practically unknown among "pure probabilists". My talk will contain the introduction to the subject and several extensions of the theory. The applications include the member theory ( the works of Dickman and de Bruijn), cell-growth models, limit theorems on solvable Lie groups, differential-functional equations etc.
23.07.19 10:15   V4-119
                Alexander Teplyaev (University of Connecticut)
                BV and Besov spaces on fractals with Dirichlet forms
Abstract. We introduce heat semigroup-based Besov classes in the general framework of Dirichlet spaces. General properties of those classes are studied and quantitative regularization estimates for the heat semigroup in this scale of spaces are obtained. As a highlight of the work, we obtain a far reaching $L^p$-analogue, $p \ge 1$, of the Sobolev inequality that was proved for $p=2$ by N. Varopoulos under the assumption of ultracontractivity for the heat semigroup. The case $p=1$ is of special interest because it may yield isoperimetric type inequalities and Bounded Variation (BV) function spaces. This is a joint work with Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen, Luke Rogers, Nageswari Shanmugalingam.

Wintersemester 2018/19

Di    10:15-11:45    V4-116

23.10.18  10:15   V4-116 
               Wolfhard Hansen (Bielefeld)
               Nearly hyperharmonic functions are infima of excessive  functions
30.10.18  10:15   V4-116 
               Wolfhard Hansen (Bielefeld)
               Nearly hyperharmonic functions are infima of excessive  functions II
20.11.18  10:15   V4-116 
               Jun Cao (Zhejiang University of Technology und Bielefeld)
               Heat kernels and Besov spaces associated with second order divergence form elliptic operators
27.11.18  10:15   V4-116 
               Jun Cao (Zhejiang University of Technology und Bielefeld)
               Heat kernels and Besov spaces associated with second order divergence form elliptic operators II
04.12.18  10:15   V4-116 
               Jian Wang (Fujian Normal University, China)
               Heat kernel and Harnack inequalities for random walks among random conductances with stable-like jumps
18.12.18  10:15   V4-116 
               Michael Hinz (Bielefeld)
               Hydrodynamic limits of exclusion processes on the Sierpinski gasket
15.01.19  10:15   V4-116 
               Shilei Kong (Bielefeld)
               On a class of hyperbolic graphs arising from iterations
22.01.19  10:15   V4-116 
               Melissa Meinert (Bielefeld)
               On the viscous Burgers equation on metric graphs and fractals
29.01.19  10:15   V4-116 
               Meng Yang (Bielefeld)
               Resistance Estimates and Heat Kernel Estimates

Sommersemester 2018

Di    10:15-11:45    V4-116

24.04.18  10:15   V4-116 
               Shilei King (Bielefeld)
               Random walks and induced energy forms on compact doubling spaces
08.05.18  10:15   V4-116 
               Philipp Sürig (Bielefeld)
               Regularity results for fully nonlinear equations
15.05.18  10:15   V4-116 
                Shilei King (Bielefeld)
               Random walks and induced energy forms on compact doubling spaces II
22.05.18  10:15   V4-116 
                Shilei King (Bielefeld)
               Random walks and induced energy forms on compact doubling spaces III
29.05.18  10:15   V4-116 
               Meng Yang (Bielefeld)
               Construction of a local Dirichlet form on Sierpinski gasket 
05.06.18  10:15   V4-116 
               Jun Cao (Bielefeld)
               The lifting-transference method for Grushin operators in Hardy spaces
19.06.18  10:15   V4-116 
               Michael Hinz (Bielefeld)
               Canonical diffusions on the pattern spaces of aperiodic Delone sets
26.06.18  10:15   V4-116 
               Wolfhard Hansen (Bielefeld)
               Nearly hyperharmonic functions and Jensen measures  
03.07.18  10:15   V4-116 
               Andrey Piatnitski (Narvik) and Elena Zhizhina (Moscow)
               Pointwise estimates for heat kernels of convolution type operators               
10.07.18  10:15   V4-116 
               Stanislav Molchanov (University of North Carolina, Charlotte, USA)
               Global limit theorems for the moderate tails
17.07.18  10:15   V4-116 
               Stanislav Molchanov (University of North Carolina, Charlotte, USA)
               Survey on the spectral theory of fractals

Sommersemester 2017

SFB 701, projects A6, A10

Di    10:15-11:45    V4-119

2.05.17  10:15   V4-119 
               Jun Cao (Zhejiang University of Technology, China)
               Differential operators, semigroup and Hardy spaces
16.05.17  10:15   V4-119 
               Martin Barlow (University of British Columbia)
               Stability of the elliptic Harnack Inequality
Abstract:  Following the work of Moser, as well as de Giorgi and Nash, Harnack inequalities have proved to be a powerful tool in PDE as well as in the study of the geometry of spaces. In the early 1990s Grigor'yan and Saloff-Coste gave a characterisation of the parabolic Harnack inequality (PHI). This characterisation implies that the PHI is stable under bounded perturbation of weights, as well as rough isometries. In this talk we prove the stability of the EHI. This is joint work with Mathav Murugan (UBC).
23.05.17  10:15   V4-119 
               Marcel Schmidt (Jena)
               Energy forms - Basic theory
30.05.17  10:15   V4-119 
               Marcel Schmidt (Jena)
               Energy forms - Silverstein extensions 
06.06.17  10:15   V4-119 
               Alexander Bendikov (Wroclaw)
               On stable-like Markov generators on ultrametric spaces
13.06.17  10:15   V4-119 
               Sergey Grigorian (University of Texas Rio Grande Valley)
               G2-structures and octonion bundles
20.06.17  10:15   V4-119 
               Karol Szczypkowski (Bielefeld)
               Heat kernels of non-symmetric Levy processes
Abstract: Motivated by the literature we consider several peculiar conditions on the heat kernel and the characteristic exponent of a Levy process in Rd and we show that they are equivalent. Next, we discuss (local) lower bounds for the heat kernel under those conditions. Assuming comparability with an isotropic unimodal Levy process on the level of Levy measures we complement the lower bound and also prove upper bound. The talk is based on a joint work with Tomasz Grzywny.
27.06.17  10:15   V4-119 
               Stanislav Molchanov (University of North Carolina, Charlotte, USA)
               Lost mass problem
04.07.17  10:15   V4-119 
               Andrey Piatnitski (Arctic University of Norway, Narvik, Norway)
               Einstein relation in periodic and random media
11.07.17  10:15   V4-119 
               Jiaxin Hu (Tsinghua University)
               Two-sided estimates of heat kernels of jump type Dirichlet forms
18.07.17  10:15   V4-119 
               Eryan Hu (Bielefeld)
               Heat kernels and Dirichlet forms on ultra-metric spaces 
25.07.17  10:15   V4-119 
                Igor Verbitsky (University of Missouri, USA)
               Pointwise estimates of solutions to nonlinear equations with nonlocal operators

Wintersemester 2016/17

Di    10:15-11:45    V3-204/V3-201

25.10.16  10:15   V3-204 
               Eryan Hu (Bielefeld)
               Two-sided estimates of heat kernels of jump type Dirichlet forms
08.11.16  10:15   V3-204 
               Eryan Hu (Bielefeld)
               Two-sided estimates of heat kernels of jump type Dirichlet forms II
15.11.16  10:15   V3-204 
               Yuhua Sun  (Nankai University)
               On nonnegative solutions of semilinear elliptic inequalities on Riemannian manifolds
06.12.16  10:15   V3-204 
               Wolfhard Hansen (Bielefeld)
               Reduced functions and Jensen measures
13.12.16  10:15   V3-204 
               Michael Hinz (Bielefeld)
               First order calculus for Dirichlet forms and some applications to PDE
20.12.16  10:15   V3-204 
               Pavlo Tkachev  (Bielefeld)
               Acceleration and constant speed of propagation in non-local mono-stable reaction-diffusion equations
10.01.16  10:15   V3-204 
               Delio Mugnolo (Hagen)
               The Airy equation on a quantum graph
17.01.16  10:15   V3-204 
               Moritz Kassmann (Bielefeld)
               On Li-Yau estimates on graphs
24.01.16  10:15   V3-204 
               Elena Zhizhina (Bielefeld)
               Nonlocal operators with bounded kernels and homogenization
31.01.16  10:15   V3-204 
               Olaf Post (Trier)
               Norm resolvent convergence for operators in varying spaces and applications

Sommersemester 2016

Di    10:15-11:45    V3-204/V3-201

19.04.16  10:15   V3-204 
               Boguslaw Zegarlinski (Imperial College London)
               Application of log-Sobolev inequality to reaction-diffusion system
26.04.16  10:15   V3-204 
               Jun Masamune (Tohoku University, Japan)
               Existence of non-constant integrable harmonic functions on Riemannian manifolds
10.05.16  10:15   V3-204 
               Jun Masamune (Tohoku University, Japan)
               Existence of non-constant integrable harmonic functions on Riemannian manifolds II
13.05.16  10:15   V3-201  
               Jun Kigami (Kyoto University, Japan)
               Time change of Brownian motion - Poincaré inequality, protodistance and heat kernel estimates
24.05.16  10:15   V3-204 
               Dimitri Volchenkov (Bielefeld)
               Diffusion metrics and geometrization of finite graphs and relational databases
07.06.16  10:15   V3-204 
               Meng Yang (Bielefeld)
               Jump processes on Sierpinski gasket
14.06.16  10:15   V3-204 
               Meng Yang (Bielefeld)
               Jump processes on Sierpinski gasket II
21.06.16  10:15   V3-201
               Meng Yang (Bielefeld)
               Jump processes on Sierpinski gasket and carpet
28.06.16  10:15   V3-201                
               Jiaxin Hu (Tsinghua University, China)
               The Davies method for heat kernel upper bounds of regular Dirichlet forms on metric spaces
19.07.16  10:15   V3-201 
               Michael Hinz (Bielefeld)
               Some questions related to metric cohomology

Wintersemester 2015/16

Di    10:15-11:45    V4-116 

03.11.15  10:15   V4-116 
               Bartosz Trojan (Wroclaw)
               Random Walks on Grids
Abstract: The aim of the talk is to present the asymptotic of the heat kernel $p(n, x)$ for a finitely supported random walk on $\ZZ^d$, uniform in $n$ and $x$ on a large region.
10.11.15  10:15   V4-116 
               Moritz Kaßmann (Bielefeld)
               On Li-Yau Harnack inequalities on graphs
Abstract: We review the main ideas of the article "Li-Yau inequality on graphs" by Frank Bauer, Paul Horn, Yong Lin, Gabor Lippner, Dan Mangoubi, and Shing-Tung Yau. We present the idea in the simplest context of finite and infinite but flat graphs.
17.11.15  10:15   V4-116 
               Satoshi Ishiwata (Yamagata University)
               Long time behavior of the heat kernel on connected sums of parabolic manifolds
24.11.15  10:15   V4-116 
               Tomasz Grzywny (Wroclaw University of Technology)
               Asymptotics and estimates of slowly varying convolution semigroups
Abstract: We present the asymptotic formulas and estimates for the transition densities of isotropic unimodal convolution semigroups of probability measures on R^d under the assumption that its Levy
exponent varies slowly. The talk is based on the joint project with M. Ryznar and B. Trojan.
01.12.15  10:15   V4-116 
               Wolfhard Hansen (Bielefeld)
               Darning and gluing of Brownian motion on spaces of different dimensions
12.01.16  10:15   V4-116 
               Wolfhard Hansen (Bielefeld)
               Darning and gluing for diffusions
19.01.16  10:15   V4-116 
               Wolfhard Hansen (Bielefeld)
               Darning and gluing for diffusions II
26.01.16  10:15   V4-116 
               Akif Ibragimov (Texas Tech University)
               On nonlinear flow in porous media and applications
02.02.16  10:15   V4-116 
               Akif Ibragimov (Texas Tech University)
               On nonlinear flow in porous media and applications II

Sommersemester 2015

Di    10:15-11:45    V4-116 

14.04.15  10:15   V4-116 
               Christian Rose (Chemnitz)
               Schrödinger operators on manifolds: the role of curvature 
16.04.15  15:00-16:00   U2-147 
               Naotaka Kajino (Kobe University, Japan)
               Heat kernel analysis for Brownian motion of 2-dimensional Liouville quantum gravity
21.04.15  10:15   V4-116 
               Alexander Bendikov (Wroclaw/Bielefeld)  
               Random perturbations of the hierarchical Laplacian 
05.05.15  10:15   V4-116 
               Wolfhard Hansen (Bielefeld)
               A general approach to Harnack inequalities and Hölder continuity for harmonic functions 
19.05.15  10:15   V4-116 
               Olaf Müller (Regensburg)
               Existence of a metric of bounded geometry in every conformal class and implications for the Yamabe flow 
26.05.15  10:15   V4-116 
               Tomasz Grzywny (Wroclaw University of Technology)
               Asymptotics of heat kernels of unimodal convolution semigroups 
Abstract:  In this talk we investigate  behaviour of densities for isotropic unimodal Lévy processes.
The main result is a description of the asymptotics under an assumption that the Lévy-Khinchine
exponent varies regularly of index between 0 and 2. Moreover, we show that for unimodal Lévy processes, the regular variation of  the characteristic exponent  is equivalent to the  asymptotic behaviour for the transition density.
02.06.15  10:15   V4-116 
               Shiping Liu (Durham)
               Cheeger inequalities for magnetic Laplacians 
09.06.15  10:15   V4-116 
               Michael Hinz (Bielefeld)
               Densely defined non-closable curl on topologically one-dimensional fractals 
Abstract:  The talk deals with the exterior derivative operator defined on 1-forms on topologically one dimensional spaces with a strongly local regular Dirichlet form. It is proved that exterior derivative operator taking 1-forms into 2-forms is not closable if the martingale dimension is larger than one. Although  the main results are applicable to general diffusions, some of the most interesting examples  include the  non self-similar Sierpinski carpets recently introduced by Mackay, Tyson and Wildrick. For these carpets we prove that not only the curl operator is not closable, but that its adjoint operator has a trivial domain.
16.06.15  10:15   V4-116 
               Abderrahman Boukricha (University of Tunis - El Manar)
               Cloaking via change of variables in quasilinear elliptic equations
Abstract:  After the pioneer works on cloaking (electromagnetic invisibility) simultaneously publisched by Leonahrdt (Science 312, 2006, 1777-1780) and Pendry, Shurig and Smith (Science 312, 2006, 1780-1782), several papers gave a general definition of cloaking in closely related setting of electric impedance tomography and for the Helmoltz Equation. Among others R.V.Kohn et al (Inverse Problems 2007 and Comm.  Pure and Appl. Math. Vol LX III, 2010) gave the following definition: a region of space is cloaked for a particular class of measurements if its contents and even the existence of the cloak are invisible  using such measurements.  In a joint project with Michael Roeckner we will present a preliminary version for the cloaking related to a quasilinear elliptic differential equation.
30.06.15  10:15   V4-116 
               Igor Verbitsky (University of Missouri, USA)
               Pointwise estimates of solutions to linear and nonlinear elliptic equations on weighted manifolds
07.07.15  10:15   V4-116 
               Alexander Teplyaev (University of Connecticut, USA)
               Spectral problems on finitely ramified fractals
14.07.15  10:15   V4-116 
               Jiaxin Hu (Tsinghua)
               Lower estimates of heat kernels for non-local Dirichlet forms on metric spaces 

Wintersemester 2014/15

Di 10:15-11:45, V4-112 

28.10.14  10:15   V4-112 
               Satoshi Ishiwata (Yamagata University, Japan)
               A central limit theorem for non-symmetric random walk on crystal lattices
04.11.14  10:15   V4-112 
               Matthias Keller (Jena)
               Spectral theory and intrinsic metrics on graphs
11.11.14  10:15   V4-112 
               Shun-Xiang Ouyang (Bielefeld)
               Volume growth and escape rate of diffusion processes
18.11.14  10:15   V4-112 
               Shiping Liu (Durham, UK)
               Eigenvalue ratios on closed Riemannian manifolds with nonnegative Ricci curvature
27.11.14  10:15   V3-201 
               Asma Hassannezhad (MPI Bonn)
               Eigenvalue bounds in Riemannian and sub-Riemannian geometry
13.01.15  10:15   V4-112 
               Michael Hinz (Bielefeld)
               Magnetic fields on resistance spaces
20.01.15  10:15   V4-112 
               Wolfgang Hansen (Bielefeld)
               Hunt's hypothesis (H) and triangle property for the Green function
03.02.15  10:15   V4-112 
               Moritz Kaßmann (Bielefeld)
               Intrinsic scaling for jump processes

Sommersemester 2014

Di 10:15-11:45, V4-116 

08.04.14  10:15   V4-116 
               Thierry Coulhon (Australian National University, Canberra)
               New approaches to Gaussian heat kernel upper and lower bounds
15.04.14  10:15   V4-116 
               Wolfhard Hansen (Bielefeld)
               Potential theory for processes with isotropic unimodal Green function
29.04.14  10:15   V4-116 
               Wolfhard Hansen (Bielefeld)
               Unavoidable collections of balls for processes with isotropic unimodal Green function
06.05.14  10:15   V4-116 
               Wolfhard Hansen (Bielefeld)
               Unavoidable collections of balls for processes with isotropic unimodal Green function II
13.05.14  10:15   V4-116 
               Michael Hinz (Bielefeld)
               Feynman-Kac-Ito formulas for local regular Dirichlet forms
26.05.14  10:15   D2-136 
               Tomasz Grzywny (Wroclaw University of Technology)
               Exit time and survival probability for unimodal Levy processes
Abstract:  The basic object of interest in this talk is the expected exit time from a bounded smooth domain for arbitrary starting point of an isotropic unimodal Levy process. We derive sharp estimates up to the boundary of the set by giving barriers for the ball of arbitrary radius and subharmonic functions in the complement of the ball. Next we discus applications of those  for instance estimates of the survival probability in bounded smooth domains or exteriors sets.
27.05.14  10:15   V4-116 
               David Applebaum (University of Sheffield, UK)
               Probabilistic approach to the Hardy-Littlewood-Sobolev inequality
03.06.14  10:15   V3-201 
               Stanislav Molchanov (University of North Carolina, Charlotte, USA)  
               Spectral theory of Schrödinger operators on fractals. Technique of the cluster expansions. 
10.06.14  10:15   V3-201 
               Nikolai Nadirashvili (Marseille)
               Non-uniqueness in martingale problem and good solutions of elliptic  equations in non-divergence form. 
17.06.14  10:15   V3-201 
               Stanislav Molchanov (University of North Carolina, Charlotte, USA)
               Spectral theory of Schrödinger operators on fractals. Technique of the cluster expansions II.
24.06.14  10:15   V4-116 
               Stanislav Molchanov (University of North Carolina, Charlotte, USA)
               Spectral theory of on exotic graphs.
01.07.14  10:15   V4-116 
               Maria Gordina (University of Connecticut, USA)
               A random walk through sub-Riemannian geometry
Abstract: A sub-Riemannian manifold M is a connected smooth manifold such that the only smooth curves in M which are admissible are those whose tangent vectors at any point are restricted to a particular subset of all possible tangent vectors. Such spaces have several applications in physics and engineering, as well as in the study of hypo-elliptic operators. In this talk, we will construct a family of geometrically natural sub-elliptic Laplacian operators and discuss the trouble with defining one which is canonical. We will also construct a random walk on M which converges weakly to a process whose infinitesimal generator is one of our sub-elliptic Laplacian operators. This is joint work with Tom Laetsch.
08.07.14  10:15   V4-116 
               Igor Verbitsky (University of Missouri, USA)
               Sublinear elliptic equations and new potentials of Wolff type
15.07.14  10:15   V4-116 
               Alexander Teplyaev (University of Connecticut, USA)
               Waves, energy on fractals and related questions
               Daniel Kelleher (Purdue University, USA)
               From self-similar groups to intrinsic metrics on fractals

Wintersemester 2013/14

Di 10:15-11:45, V3-204 

22.10.13  10:15   V3-204 
               Yuhua Sun (Bielefeld)
               On nonexistence of positive solutions of quasilinear elliptic inequalities on Riemannian manifolds
29.10.13  10:15   V3-204 
               Tomasz Grzywny (Wroclaw University of Technology / Bielefeld)
               On isotropic unimodal Levy processes
Abstract:  I will present recently obtained results about isotropic unimodal Levy processes. These include: the Harnack inequality, the boundary Harnack inequality, estimates of the expected exit time (up to the boundary of set), the survival probabilities and Dirichlet heat kernel of a ball, a half-space and  the complement of a ball.
05.11.13  10:15   V3-204 (joint with A5 and A10) 
               Pavlo Tkachov (Bielefeld)
               On a class of nonlocal nonlinear evolution equations
08.11.13  15:15   V3-201
               Liguang Liu (Bielefeld)
               A heat semigroup characterization of Lipschitz-Besov spaces on metric measure spaces
12.11.13  10:15   V3-204 
               Peter Sjögren (University of Gothenburg, Sweden)
               Weak type 1,1 estimates for operators related to the Laplacian with drift
Abstract:  The related heat maximal operator and the first-order Riesz transform will be seen to be of weak type 1,1 for the appropriate measure.
19.11.13  10:15   V3-204  (joint with B8)
                Zihua Guo (Beijing University)
               Fourier restriction estimate and its applications in PDEs
Abstract:  Fourier restriction conjecture is one of the most well-known open problems in harmonic analysis. It is closely related to many other problems. In this talk, I will focus on its role in PDEs. The content of the talk is: (I) Introduction on the Fourier restriction conjecture (II) Weak Fourier restriction estimate (III) Connection to the Strichartz estimates and generalizations (IV) Application to Zakharov system.
20.11.13  14:15   V3-201 
               Jingfen Lan (Bielefeld)
               Graphs minimizing the spectral radius with fixed diameter D (2n-2)/3 and n/3<D<n/2
21.11.13  10:15   V3-201 
               Peter Stollmann (Chemnitz)
               The complex Laplacian and its heat semigroup
26.11.13  10:15   V3-204 
               Elton P. Hsu (Northwestern University, USA)
               Geometric Deviation from Levy's arcsine law
03.12.13  10:15   V3-204 (joint with B8)
               Junfeng Li (Beijing Normal University / Bonn)
               Some results in the well posedness of KP II problems
Abstract:  In this talk, I will present some recent results on the well posedness of KP II problems. In these results, we find that  the Galilean invariant are very important. By decomposing the nonlinear 
part of the problems into some Galilean invariant terms, we could obtain some more interesting bilinear estimates which we thought be very nature in the context of KP.
10.12.13  10:15   V3-204 (joint with B8)
               Sebastian Herr (Bielefeld)
               On endpoint Strichartz estimates for Dirac and Klein-Gordon equations
Abstract: We will review the classical Strichartz estimates for wave and Schroedinger equations and related tools from harmonic analysis. For the Dirac equation and the Klein-Gordon equation we will present new endpoint estimates in dimension three, which have been obtained recently in collaboration with Ioan Bejenaru (UC San Diego).  
17.12.13  10:15   V3-204 (joint with B8)
               Sebastian Herr (Bielefeld)
               On endpoint Strichartz estimates for Dirac and Klein-Gordon equations - Part II
07.01.14  10:15   V3-204  (joint with A8 and A10)
               Moritz Kassmann (Bielefeld)
               Differential Operators of arbitrary order between zero and two
Abstract: We discuss a subclass of (integro-)differential operators of fractional order. These operators are related to semi-groups and stochastic processes in a natural way. In the talk we present definitions, basic results as well as recent developments for linear and nonlinear equations. The main
emphasis is on new intrinsic scaling properties. 
14.01.14  10:15   V3-204 
               Wolfhard Hansen (Bielefeld)
               Volume mean  densities for the heat equation
21.01.14  10:15   V3-204 
               Michael Hinz (Bielefeld)
               Energy dominance and closability for bilinear forms
28.01.14  10:15   V3-204 
               Michael Hinz (Bielefeld)
               Energy dominance and closability for bilinear forms II
04.02.14  10:15   V3-204 
               Liguang Liu (Bielefeld)
               Proof of Strichartz estimate on metric measure spaces