The All Union workshop on Algebraic Systems, Sokhumi (Georgia), 1982
Algebra seminar, Moscow St. Univ. (Russia), 1982
The All Union Algebraic Conference, Minsk (Belarus), 1983
The All Union Algebraic Conference Kishinev (Moldova), 1985
Algebra seminar, Leningrad St. Univ. (Russia), 1986
The All Union Algebraic Conference, L'vov (Ukraine), 1987
Agebra seminar, Belarusian St. Univ., Minsk (Belarus), 1988
International Malcev Conference on Algebra and Analysis, Novosibirsk (Russia), 1989
Algebraic geometry seminar (3 talks), University of Chicago (USA), 1991
Workshop on Commutative Algebra, Trieste (Italy), 1992
Conference on Commutative Algebra, Vechta (Germany), 1994
1st Congress of Georgian Mathematicians, Tbilisi (Georgia), 1994
Algebra seminar, University of Bochum, (Germany), 1995
Algebra seminar, University of Essen, (Germany), 1995
Algebra seminar, Humboldt University (Germany), 1995
Algebra seminar, University of Osnabrueck (Germany),  1995
Public Lecture: Fermat Last Theorem (after A. Wiles), Tbilisi St. Univ. (Georgia), 1995
Algebraic geometry seminar (3 talks), University of Chicago (USA), 1995
Colloquium, New Mexico State University (USA), 1995
Colloquium, Nijmegen Universirty (Netherlands), 1996
Colloquium, University of Osnabrueck (Germany), 1996
Algebra seminar, University of Bochum (Germany), 1996
Algebra seminar, University of Essen (Germany), 1996
Colloquium, University of Oldenburg (Germany), 1997
Algebra seminar, Universitiy of Basel (Switzerland), 1997
Conference on Algebraic Groups and Related Topics, Ascona (Switzerland), 1997
Workshop on Syzygies, Catania (Italy), 1997
Conference on Combinatorial Commutative Algebra, Essen (Germany), 1997
School on Algebraic K-Theory and its Application, Trieste (Italy), 1997
Algebra seminar, Genova (Italy), 1997
Algebra seminar, Strasbourg (France), 1997
Joint AMS-MAA Meeting, Section Commutative Algebra & Algebraic Geometry, Baltimore (USA), 1998
Algebra seminar, University of Wisconsin, Madison (USA), 1998
Algebra seminar, Queen's University, Kingston (Canada), 1998
Colloquium, University of Osnabrueck (Germany), 1998
Algebra seminar (2 talks), University of Bucharest (Romania), 1998
D. Buchsbaum Conference, Genova (Italy), 1998
Algebra seminar, University of Genova, Genova (Italy), 1999
Conference on Algebraic Geometry and Commutative Algebra, Messina (Italy), 1999
Colloquium, University of Osnabrueck (Germany), 1999
Oberseminar Algebra, University of Essen (Germany), 1999
Seminar, University of Minnesota, Minneapolis (USA), 1999
Oberseminar (2 lectures) Max-Planck-Insitute, Bonn, (Germany), 2000
Seminar, University of Strasbourg (France), 2000
Colloquium, IRMA, Strasbourg (France), 2000
Colloquium, University of Osnabrueck (Germany), 2000
Conference on Combinatorial Convexity and Algebraic Geometry, MFO, Oberwolfach (Germany), 2001
Conference on Commutative Algebra and Interactions with Algebraic Geometry, Grenoble (France), 2001
Oberseminar, University of Bochum (Germany), 2001
Algebra seminar (3 talks), Univ. Strasbourg, Strasbourg (France), 2001
Algebra seminar, University of Genova (Italy), 2002
1st joint AMS-UMI Meeting, section Hilbert Functions, Homological Methods, and Combinatorial Aspects, Pisa (Italy), 2002
Seminar on Commutative Algebra and Algebraic Geometry, University of California, Berkeley (USA), 2002
Bay Area Discrete Mathematics Day, Davis (USA), 2003
Seminar on Homological Methods in Commutative Algebra (2 talks), MSRI, Berkeley (USA), 2003
AMS Sectional Meeting, Session on Commutative Algebra, San Francisco (USA), 2003
Seminar on commutative algebra and algebraic geometry, UC Berkeley (USA), 2003
Algebra seminar, University of Washington, Seattle (USA), 2003
Seminar on Discrete & Computational Geometry, MSRI, Berkeley (USA), 2003
Seminar on Algebraic Methods, Stanford (USA), 2003
Conference on Commutative Algebra, Oberwolfach (Germany), 2005
Combinatorics seminar, UC Davis (USA), 2005
Seminar on commutative algebra and algebraic geometry, UC Berkeley (USA), 2005
Algebra Colloquium, UC San Diego (USA), 2005
Brunsfest: Conference on Commutative Algebra, University of Osnabrueck (Germany), 2006
Algebra seminar, NEU, Boston (USA), 2006
Seminar on Commutative Algebra, University of Nebraska-Lincoln, Lincoln (USA), 2006
Colloquium, University of Nebraska-Lincoln, Lincoln (USA), 2006
Colloquium, University of Osnabueck, Osnabrueck (Germany), 2007
Seminar on Combinatorial Group Theory, MSRI, Berkeley (USA), 2007
AMS Sectional Meeting, Session on Toric Varieties, New Brunswick (USA), 2007
AMS Sectional Meeting, Session on Algebraic K-theory & Nil-Groups in Algebra and Geometry, Bloomington (USA), 2008
Conference on Commutative Algebra and Interactions with Algebraic Geometry, Luminy (France), 2008
AMS Sectional Meeting, Session on Algebra & Number Theory with Polyhedra, San Francisco (USA), 2009
Conference on Combinatorial Structures in Algebra and Topology, University of Osnabrueck (Germany), 2009