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

** Tel **: +49-(0)521-106-4996,
**Secretary:** +49-(0)521-106-4775

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

** Room**: V4-234

This includes partial differential equations of elliptic and parabolic types
on Riemannian manifolds,

analysis and random walks on graphs, function theory and Markov 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

and Schrödinger operators on various spaces, long time behavior of random walks and diffusions,
etc.

Awards

**"Analysis I", WS 2024/25**- "Analysis on manifolds", SS 2024
- "Elliptic Partial Differential Equations", WS 2023/24
- "Partial Differential Equations", SS 2023
- "Funktionalanalysis", SS 2022
- "Maß- und Integrationstheorie", WS 2021/22
- "Analysis II", SS 2021
- "Analysis I", WS 2020/21
- "Funktionalanalysis", SS 2020
- "Maß-
und Integrationstheorie", WS 2019/20
- "Funktionalanalysis", SS
2019
- "Analysis II", WS 2018/19
- "Analysis I", SS 2018
- "Funktionen", SS 2017
- "Analysis on manifolds", WS 2016/17
- "Analysis of Elliptic Differential Operators", SS 2016
- "Partial Differential Equations", WS 2015/16
- "Gewöhnliche
Differentialgleichungen" SS 2015
- "Analysis II", WS 2014/15
- "Analysis I", SS 2014
- "Maß- und
Integrationstheorie", WS 2013/14
- "Funktionalanalysis", SS
2013
- "Analysis I", 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 II", WS 2006/07
- "Analysis I", SS 2006

- Proseminar "Analysis", SS 2022
- Seminar
"Analysis" WS 2020/21
- Seminar "Analysis" WS
2019/20
- Proseminar "Funktionen und
Folgen", WS 2018/19
- 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

- Analysis on fractal spaces and walk dimension (ICBS, Beijing, July 2024)
- Leibenson’s equation on Riemannian manifolds (in Russian, Volgograd State University, April 2024)
- Analysis on fractal spaces and heat kernels (Tsinghua University, April 2024)
- Lectures on path homology and Hodge Laplacian on digraphs (YMSC, Beijing, February-April 2024)
- Homotopy and homology of digraphs (BIMSA, Beijing, March 2024)
- Tail estimates of heat kernels for jump processes (Zhejiang University of Technology, Hangzhou, March 2024)
- Propagation speed of non-linear parabolic equations on Riemannian manifolds (Nankai University, March 2024)
- Tails of heat kernels of jump processes (CUHK, Hong Kong, December 2023)
- Leibenson’s equation on Riemannian manifolds (Chemnitz, October 2023)
- Path homology and Hodge Laplacian on digraphs (Wuppertal, July 2023)
- Heat kernels on fractals and walk dimension (Angers, June 2023)
- Hodge Laplacian on digraphs (BIMSA, Beijing, June 2023)
- Analysis on fractal spaces and heat kernels (Steklov Math Institute, Moscow, May 2023)
- Heat kernels of diffusion and jump processes on fractals (Weizmann Institute, Tel Aviv, May 2023)
- Finite propagation speed of non-linear parabolic equations on Riemannian manifolds (Hagen, April 2023)
- Off-diagonal esitmates of heat kernels for jump processes (Okinawa, March 2023)
- Propagation speed of non-linear parabolic equations on Riemannian manifolds (CUHK, February 2023)
- Analysis on ultra-metric and fractal spaces. Heat equation approach (Steklov Math Institute, Moscow, January 2023)
- Overview of path homology theory of digraphs II (BIMSA and YMSC, Beijing, 2022-23)
- Leibenson’s equation on Riemannian manifolds (BIMSA, Beijing, September 2022)
- Finite propagation speed for Leibenson’s equation on Riemannian manifolds (Bonn, August 2022)
- Tail estimates of the heat kernel for jump processes (Kansai University, Osaka, August 2022)
- Overview of path homology theory of digraphs I (BIMSA and YMSC, Beijing, February-May 2022)
- Path homology and join of digraphs (HSE, Moscow, March 2022)
- Landis' proof of Harnack inequalities (MSU, Moscow, December 2021)
- Analysis and heat kernels on ultra-metric spaces (Kyoto, September 2021)
- Heat kernels on manifolds and fractals (IRTG, Bielefeld, April 2021)
- Heat kernels on ultra-metric spaces (Steklov Math Institute, Moscow, September 2020)
- Laplace operator on weighted graphs (Nankai University, September 2019)
- Analysis on manifolds and volume growth (Nankai University, September 2019)
- Analysis on fractal spaces and heat kernels (Aveiro, July 2019)
- Analysis of the heat equation on Riemannian manifolds III (CUHK, February-March 2019)
- Random walks on ultra-metric spaces (AMSS CAS, September 2018)
- Heat kernels on manifolds with ends (St.Petersburg, June 2018)
- Heat kernels on Riemannian manifolds II (CUHK, March 2018)
- On positive solutions of semi-linear elliptic inequalities on Riemannian manifolds (Minnecota, February 2018)
- Path homologies of digraphs (YMSC, Tsinghua University, November 2017)
__Heat kernels on Riemannian manifolds__(Nankai University, October 2017)- Heat equation and heat kernel on an arbitrary manifold I (CUHK, February-March 2017)
__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
August 19, 20**24*