Abstract

We discuss the notions of path homology and homotopy of digraphs. The following topic will bepresented.

. Homology groups of digraphs.

. Homotopy of digraph maps and digraphs. lnvariance of homology groups under homotopy.

Fundamental group of a digraph. Invariance of the fundamental group under homotopy.

Relation between the fundamental group and first homology group.

Speaker Intro

Professor Alexander Grigor'yan received his PhD from Lomonosov Moscow University in 1982Since then, he worked at the State University of Volgograd and the lnstitute of Control Sciences inMoscow with receiving his habilitation in 1989. He has been a Humboldt Fellow at BielefeldUniversity in 1992-93 and a Guest Scholar at Harvard University in 1993/94. After working fromlecturer to professor at lmperial College London in 1994-2005, he became a professor at BielefeldUniversity from 2005.

Professor Grigor'yan won a gold medal at International Mathematical Olympiad when he was 17awarded by the Prize of the Moscow Mathematical Society in 1988, and received the WhiteheadPrize of London Mathematical Society in 1997. He was an invited speaker of European Congressof Mathematicians in Barcelona in 2000.

Professor Grigor'yan is one of the top experts in geometric analysis on Riemannian manifoldsmetric spaces and graphs, with making various important contributions on the topics.