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International Workshop

In the frame of the grant FR-21.4713 of Shota Rustaveli National Science Foundation of Georgia

“Algebraic Geometry and Model Theory

of Groups and Algebras”

Program

Part 1

Exponential Groups

Dates: 01/09/2023–03/09/2023

Place: Akaki Tsereteli State University, Kutaisi, Georgia

Program: 

September 1st

  1. 9 am–9.55 am Alexei Miasnikov “Open problems and recent tendencies in the theory of exponential groups”
  2. 10 am–10.50 am Tengiz Bokelavadze “On bi-interpretability of nilpotent k-groups and nilpotent k-algebras Lie”
  3. 11 am–11.50 am Evelina Daniyarova “Extensions of centralizers in nilpotent groups”
  4. 12 am–14 am Discussion

September 2nd 

  1. 9 am–9.55 am Mikheil Amaglobeli “Tenzor completions in varieties of exponential groups”
  2. 10 am–10.50 am Evelina Daniyarova “Limit exponential groups”
  3. 11 am–11.50 am Alexander Treyer “On a maximal rank of a free two step nilpotent group embeddable into UT_n(Z)”
  4. 12 am–14 am Discussion

September 3rd 

9 am–14 am Discussion on perspectives of the theory of exponential groups

Excursion to Okatse Canyon Natural Monument

Organizing committee:

  1. M. Amaglobeli
  2. T. Bokelavadze
  3. O. Kharlampovich

Part 2

Model Theory of Groups and Algebras

Dates: 04/09/2023–08/09/2023

Place: Shota Rustaveli State University, Batumi, Georgia

Program: 

September 4th

  1. 9 am–9.55 am Evelina Daniyarova “Bi-interpretations”
  2. 10 am–10.50 am Alexei Miasnikov “Theory of interpretations”
  3. 11 am–13 am Discussion

September 5th

  1. 9 am–9.55 am Alexander Treyer “Bi-interpretability of ZwrZ with Z”
  2. 10 am–10.50 am Elena Bunina “Abstract isomorphisms and bi-interpretability of Chevalley groups”
  3. 11 am–13 am Discussion

September 6th

  1. 9 am–9.55 am Alexander Treyer “Definable subgroups of free nilpotent groups”
  2. 10 am–10.50 am Andrey Nikolaev “Non-standard polynomials”
  3. 11 am–13 am Discussion

September 7th

  1. 9 am–9.55 am Olga Kharlampovich “Non-standard free metabelian groups”
  2. 10 am–10.50 am Andrey Nikolaev “Non-standard free groups”
  3. 11 am–13 am Discussion

September 8th

  1. 9 am–9.55 am Eugene Plotkin ”Isotypic groups and rings”
  2. 10 am–10.50 Elena Bunina TBA
  3. 11 am–13 am General discussion

Excursion to the Batumi Botanical Garden

Organizing committee:

  1. M. Amaglobeli
  2. T. Bokelavadze
  3. O. Kharlampovich
  4. A. Miasnikov
  5. E. Plotkin

Part 3

Algebraic and Logical Geometries over Nilpotent Groups and Algebras

Dates: 10/09/2023–14/09/2023

Place: Batumi, Georgia

Program: 

September 10th

  1. 9 am–9.55 am Alexander Treyer “One variable equations over free nilpotent groups” 
  2. 10 am–10.50 am Alexei Mishchenko “Equations in partially commutative 2-nilpotent groups”
  3. 11 am–11.50 am Ivan Buchinskiy “Equations over Heisenberg groups”

September 11th

  1. 9 am–9.55 am Eugene Plotkin “Logical geometries by Boris Plotkin”
  2. 10 am–10.50 am Evelina Daniyarova “Logical geometries and interpretations”

September 12th

  1. 9 am–9.55 am Alexei Miasnikov “Coordinate groups of irreducible algebraic sets over free nilpotent groups”
  2. 10 am–10.50 am Anthony Gaglione and Dennis Spellman “Axioms of the universal theory of Heisenberg group” 

September 13th

  1. 9 am–9.55 am Evelina Daniyarova “Remeslennikov’s approach to universal classes of 2―nilpotent R-groups”
  2. 10 am–10.50 am Alexei Miasnikov “K-theory for completions of nilpotent groups”
  3. 11 am–11.50 am Mikheil Amaglobeli “Exponential nilpotent groups”

September 14th

General discussion

Organizing committee:

  1. M. Amaglobeli
  2. T. Bokelavadze
  3. O. Kharlampovich
  4. E. Plotkin

Participants

Alexei Miasnikov, Stevens Institute of Technology, Hoboken, USA

Tengiz Bokelavadze, Akaki Tsereteli State University, Kutaisi, Georgia

Evelina Daniyarova, Sobolev Institute of Mathematics, Omsk, Russia

Mikheil Amaglobeli, Ivane Javakhishvili Tbilisi State University, Tbilisi, Georgia

Alexander Treyer, Sobolev Institute of Mathematics, Omsk, Russia

Eugene Plotkin, Bar Ilan University, Tel Aviv, Israel

Elena Bunina, Bar Ilan University, Tel Aviv, Israel

Andrey Nikolaev, Stevens Institute of Technology, Hoboken, USA

Olga Kharlampovich, City University of New York, New York, USA

Alexei Mishchenko, Sobolev Institute of Mathematics, Omsk, Russia

Ivan Buchinskiy, Sobolev Institute of Mathematics, Omsk, Russia

Anthony Gaglione, United States Naval Academy, Annapolis, USA

Dennis Spellman, Temple University, Philadelphia, USA