The first conference of this series shortly named "BGL" (Bolyai-Gauss-Lobachevsky) was organised by the Bogolyubov Institute for Theoretical Physics ( Kiev , Ukraine ) and it was held in 1997 in Uzhgorod, a small university town on the border between Ukraine , Romania and Hungary . The next one held in Nyiregyhaza ( Hungary ) in 1999. The 3-d conference dedicated to the bicentenary of Janos Bolyai was held in his native town - Targu-Mures (Marosvasarhely), Romania - in 2002. Nizhny Novgorod (formerly Gorky ) is Lobachevsky's native city. The University of Nizhny Novgorod named after N.I. Lobachevsky is the organizer of the next conference "BGL-4". The Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine , the Hungarian Academy of Sciences as well as the Nizhny Novgorod Mathematical Society will act as co-organisers.

Nizhny Novgorod is a large Russian university city situated at the confluence of two great Russian rivers Volga and Oka , with the international airport and  convenient train connections with Moscow . It has several comfortable hotels with restaurants which can meet the participants needs at the future conference. The Conference will be held at the Nizhny Novgorod Lobachevsky State University (UNN) ( 23 Gagarin Ave. , Nizhny Novgorod , Russia ; tel. (8312)657-776, (8312)657-601; fax: (8312)658592). The university campus will offer  conference rooms and all necessary infrastructure (internet, e-mail connection, computers, printers, copying machines, library, dining rooms, cafeteria, etc) for a smooth running of the conference. The Mathematical Department of the  Nizhny Novgorod Lobachevsky State University is well known amoung the international scientific community for its high-level performance in teaching and research.

The program of the future conference will contain talks on various applications of non-Euclidean geometry in modern physics and mathematics. Among them there will be recent developments in astroparticle physics, namely the evolution of the early universe, the problem of the dark matter and possible geometrical interpretations, symmetries and their breakings in the hot and dense universe, the fate of the late universe (flat, closed or open ?), evolution of stars, supergravity and superstrings, the brane uviverse, possibilities of detecting mini-black holes and higher dimensions in cosmic rays and/or at accelerator (Fermilab) energies, quantum groups and quantum deformations. All these topics are closely related to the non-Euclidean geometry. Mathematical part of the discussion will contain recent applications of non-Euclidean geometry to different topics of modern mathematics - geometry, algebra, dynamical systems and other fields.