Seminar (2017)

November 7, 2017.

Jian Wang (Fujian Normal University, China):
Heat kernel estimates and Harnack inequalities for symmetric non-local Dirichlet forms and their applications.
( slides)
Place: Room A-404, New Science Building, Tsinghua University.

October 17, 2017.

Alexander Grigoryan(University of Bielefeld, Germany):
On semi-linear elliptic inequalities on Riemannian manifolds.
Place: Room A-404, New Science Building, Tsinghua University.

Seminar (2016)

September 28, 2016.

Alexander Grigoryan(University of Bielefeld, Germany):
Heat kernels of some Schroedinger operators. ( slides)
Place: Room A-304, New Science Building, Tsinghua University.

Seminar (2015)

October 9, 2015.

Alexander Grigoryan(University of Bielefeld, Germany):
Homologies of digraphs and Kuenneth formula. ( slides)
Place: Room A-404, New Science Building, Tsinghua University.

Seminar (2014)

December 3, 2014.

Alexander Grigoryan(University of Bielefeld, Germany):
Homology and homotopy of finite graphs.
Place: Room A-304, New Science Building, Tsinghua University.

Abstract: We introduce the notions of homology and homotopy for digraphs (directed graphs) and present their basic properties. In particular, homology groups are homotopy invariant, and the first homology group is abelization of the fundamental group.

Seminar (2013)

December 5, 2013.

Alexander Grigoryan(University of Bielefeld, Germany):
On nonnegative solutions for semilinear elliptic inequalities on complete Riemannian manifolds.
Place: Room A-304, New Science Building, Tsinghua University.

Abstract: We provide optimal condition in terms of the volume growth of a Riemannian manifold that ensures that any non-negative solution to the inequality $\Delta u + u^{\sigma}\le 0$ on this manifold is identically equal to 0. ( pdf)

June 14, 2013.

Prof. Zhen-Qing Chen (University of Washington, Seattle):
Brownian Motion on Spaces with Varying Dimension.
Place: Room A-404, New Science Building, Tsinghua University.

Abstract: Brownian motion is a building block of modern probability theory.It has important and intrinsic connections to analysis and partial differential equations.In real world, there are many examples of spaces with varying dimensions. For example, image an insect moves randomly in a plane with an infinite pole installed on it.In this talk,I will introduce and discuss Brownian motion on a state space with varying dimension, as well as its infinitesimal generator. I will present sharp two-sided estimates on its transition density function (also called heat kernel).The two-sided estimates is of Guassian type but the parabolic Harnack inequality fails for such process and the measure on the underlying state space does not satisfy volume doubling property.

Seminar (2012)

Dec 4, 2012.

Prof. Dr. Martina Zaehle (University of Jena, Germany):
Approximation of fractals by tubular neighborhoods - geometric and analytic properties.
Place: Room A-304, New Science Building, Tsinghua University.

Nov 29, 2012.

Jiaxin Hu:
Heat kernels and Green functions on metric measure spaces.
Place: Room A-203, New Science Building, Tsinghua University.

Seminar (2011)

Dec 15, 2011.

Jiaxin Hu:
Heat kernel estimates of non-local Dirichlet forms on metric spaces.
Place: Room 2203, New Science Building, Tsinghua University.

Seminar (2010)

Reading Seminar (Every Wednesday 15:30-16:30, 2011 Spring.)

Sep 16, 2010.

Kenneth Falconer(University of St-Andrews,UK):
Symmetry and Enumeration of Fractals.
Place: Room 1304, New Science Building, Tsinghua University.

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. (file ) (movie1 ) (movie2 ) (movie3 ) (movie4 ) (movie5 ) (movie6 )

Seminar (2009)

Dec 18, 2009.

Alexander Grigoryan(University of Bielefeld, Germany):
Random walks and analysis on graphs (III).
Place: The Morningside Center, Chinese Academy of Sciences (CAS).

Dec 14, 2009.

Alexander Grigoryan(University of Bielefeld, Germany):
Random walks and analysis on graphs (II).
Place: The Morningside Center, CAS.

Dec 10, 2009.

Alexander Grigoryan(University of Bielefeld, Germany):
On positive solutions of semi-linear elliptic inequalities on complete Riemannian manifolds.
Place: Room 1304, New Science Building, Tsinghua University.

Abstract: We consider elliptic inequalities of the type $\Delta u+u^{\sigma }\leq 0$ on geodesically complete Riemannian manifolds and provide sharp sufficient conditions in terms of capacities and volumes for the non-existence of positive solutions. This is a joint work with V.A.Kondratiev

Dec 7, 2009.

Alexander Grigoryan(University of Bielefeld, Germany):
Random walks and analysis on graphs (I).
Place: The Morningside Center, CAS.

Nov. 21, 2009.

Jiaxin Hu:
分形世界---一个破碎的梦: 从康托 集和他的忧郁症说起(in memory of Loo-Keng Hua (华罗庚) on the occasion of his 99th birthday).
Place: 郑裕彤讲堂, 清华大学.

Abstract: This talk is divided into two parts. The first part is for the general audience where I will give a brief introduction of fractal geometry, such as the concepts of self-similar set, Hausdorff measure and Hausdorff dimension. The second part is for more restricted audience where I will survey my recent joint work with Alexander Grigoryan (Bielefeld) and Ka-Sing Lau (Hong Kong) on heat kernels on metric measure spaces, including fractal domains.

Seminar (2007)

Place: Room 2203, Math Building