** Email grigor at
math.uni-bielefeld.de**

** Tel **: +49
-(0)521-106-4996

** Address**: Fakultät
für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld,
Germany

** Room**: V4-234

* Married, two children, two
grandchildren*.

This includes partial differential equations of elliptic and parabolic types
on Riemannian manifolds, random walks on graphs, function theory and
diffusion processes on fractal spaces, etc. The
main direction of my research is investigation of the global properties of
solutions to elliptic and parabolic equations in connection with the geometry
"in the large" of the underlying space. Here are some examples of such
properties: heat kernel estimates, Liouville properties, recurrence and
non-explosion of the heat semigroup, estimates of the eigenvalues of the

- "Analysis on manifolds", WS 2016/17
- "Analysis of Elliptic Differential Operators", SS 2016
- "Partial Differential Equations", WS 2015/16
- "Gewöhnliche Differentialgleichungen" SS 2015
- "Analysis 2", WS 2014/15
- "Analysis 1", SS 2014
- "Maß- und Integrationstheorie", WS 2013/14
- "Funktionalanalysis", SS 2013
- "Analysis 1", SS 2012
- "Analysis on graphs", WS 2011/12
- "Gewöhnliche Differentialgleichungen" SS 2011
- "Probability Theory" WS 2010/11
- "Gewöhnliche Differentialgleichungen" SS 2010
- "Analysis on graphs", WS 2009/ 2010
- "Ordinary Differential Equations" SS 2009
- "Ordinary Differential Equations" SS 2008
- "Measure Theory and Probability" WS 2007/08
- "Ordinary Differential Equations" SS 2007
- "Analysis 2", WS 2006/07
- "Analysis 1", SS 2006

- Seminar "Analysis" WS 2016/17
- Proseminar "Analysis" SS 2015
- Seminar "Analysis" WS 2013/14
- Seminar "Analysis und Differentialoperatoren", WS 2011/12
- Proseminar "Funktionen und Folgen", SS 2011
- Seminar "Differentialoperatoren", WS 2010/11
- Seminar "Funktionalanalysis" SS 2010
- Proseminar "Analysis", WS 2009/10
- Seminar "Analysis and Probability on Graphs", WS 2007/08

__Harnack inequality for elliptic PDEs__(CUHK, March 2016)- Homologies of digraphs and Künneth formula (Tsinghua University, October 2015)
- Heat kernels on manifolds with parabolic ends (Renmin University, Beijing, October 2015)
- Heat kernel estimates on Riemannian manifolds (Fudan University, Shanghai, September 2015)
- Heat kernel on manifolds with ends: non-parabolic case (CUHK, April 2015)
- Homotopy and homology of digraphs (CUHK, March 2015)
- Negative eigenvalues of Schrödinger operators (Nantes, February 2015)
- Heat kernel and Harnack inequality on Riemannian manifolds (CUHK, February 2014)
- Estimating the number of negative eigenvalues of Schrödinger operators (CUHK, March 2012)
__Analysis and Geometry on Graphs__, part 1, part 2 (Tsinghua University, February 2012)- Stochastic completeness of Markov processes (CUHK, February-March 2011)
- Heat kernels on metric measure spaces (6th Cornell Probability Summer School, July 2010)

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__This page was last updated on September
10, 2016__