# Oberseminar Geometric Analysis

SFB 1283, project A3
IRTG 2235, area D

# 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.

# 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
and
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