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Full Name
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Zangurashvili Dali
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| Address | |
| A. Razmadze Mathematical Institute of the Georgian Academy of Sciences, 1 Aleksidze Street, 0193 Tbilisi, Georgia | |
| Phone | |
| 778675, 893350823 | |
| Fax | |
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E-mail
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| Web Page | |
| Date Of Birth | |
| 1968-01-24 | |
| Education | |
| 1989: Graduated from Tbilisi State University (Faculty of Mechanics and Mathematics). 1989-1992: Post-graduate student of A. Razmadze Mathematical Institute. 1993: Ph.D, Tbilisi State University. | |
| Position | |
| Senior Scientist of A. Razmadze Mathematical Institute | |
| Publications | |
| Main Publications: 1. D. Zangurashvili, On some categorical algebraic properties of functor categories with values in concrete categories, Bull. Georgian Acad. Sci. 135 , N.2, 1989, 17-19. (in Russian). 2. D. Zangurashvili, Some categorical algebraic properies of quasi-varieties of algebras internal to a Grothendieck topos, Bull. Georgian Acad. Sci. 139, N.1, 1990, 25-28. 3. D. Zangurashvili, On some categorical algebraic properties of functor categories, Bull. Georgian Acad. Sci. 141, N.2, 1991, 269-272.(in Georgian). 4. D. Zangurashvili, On some categorical algebraic properties of functor categories, II. Counter-examples. Proc. A. Razmadze Math. Inst. Georgian Acad. Sci. 113, 1995, 155-172. 5. D. Zangurashvili, Factorization systems and adjunctions , Georgian Math. J. 6 (2), 1999, 191-200. 6. D. Zangurashvili, Adjunctions and locally transferable factorization systems, Applied Categorical Structures, 9 (6), 2001, 625-650. 7. D. Zangurashvili, The strong amalgamation property and codescent morphisms, Proc. A. Razmadze Math. Inst. 131 (2003), 150. 8. D. Zangurashvili, The strong amalgamation property and (effective) codescent morphisms, Theory and Applications of Categories, 11, N.20 (2003), 438-449. 9. D. Zangurashvili, Several constructions for factorization systems, Theory and Applications of Categories, 12, 2004, No. 11, 326-354. 10. D. Zangurashvili, Some categorical algebraic properties: counter-examples for functor categories, Appl. Categ. Structures, 13(2), 2005, 113-120. 11. D. Zangurashvili, Effective codescent morphisms, amalgamations and factorization systems (accepted by J. Pure Appl. Algebra). | |
| Conferences,contacts,other scientific and educational activities | |
| Post-doctoral position at the University of Coimbra(1997-1998) Conferences: 1. Talk “Some categorical-algebraic properties of functor categories” at International Conference in Algebra (Novosibirsk, USSR, 1989). 2. Talk “Some categorical-algebraic properties of categories of functors with values in categories without products” at International Meeting in Category Theory (Montreal, Canada, 1991). 3. Talk “Categories of functors with values in metric spaces, finite groups, fields and integral domains” at I Congress of Georgian Mathematicians ( Tbilisi, 1994). 4. Talk “Factorization systems and adjunctions” at II Congress of Georgian Mathematicians (Tbilisi, 1997). 5. Talk “Factorization systems and adjunctions” in workshop “Métodos Categóricos em Topologia” (Coimbra, Portugal, 1997). 6. Talk “The algebra of factorization systems on Heyting algebras” in Encontro Projectos ESCoLa-ACL (Coimbra, Portugal, 1998). 7. Talk “Adjunctions and locally transferable factorization systems” at International Symposium on Applications of Categorical Methods (Antwerp, Belgium, 1998). 8. Small intensive course “Amalgamation properties of functor categories”, Univetsity of Coimbra (Portugal, 1998). 9. Talk “Several generalizations of one theorem” at III Congress of Georgian Mathematicians (Tbilisi, 2001). 10. Talk “The strong amalgamation property and codescent morphisms” at Conference “Modern algebra and its applications” (Tbilisi, 2002). 11. Abstract “One factorization theorem for morphisms of groups with operators”, Int. School and Workshop “Geometric and Group Theory Methods in Physics and Mathematics” (Batumi, 2003). Educational activities: 1. Lecture course in General Mathematics (Greek-Georgian University, 1992-1996), 2. Lecture course in Algebra (Tbilisi Pedagogical University, 1998-2000), 3. Lecture course “Stone theorem for Boolean algebras” (Tbilisi State University, since 1999 ). 4. Lecture course in Linear Algebra, (Tbilisi State University, since 2002 ). | |
| Participation in Grant Projects | |
| 1. INTAS Grant 93-436-EXT (1997-1998). 2. Post-doctoral grant from Centro de Matemática da Universidade de Coimbra/FCT (1997-1998). 3. INTAS Grant 97 31961 (1999-2002). 4. Research Grant of President of Georgia for young scientists (the second degree, 2002-2003). | |
| Languages | |
| Georgian, English, Russian | |
| Scientific interests | |
| Category Theory(Descent Theory, General Category Theory), Universal Algebra, General Topology, Mathematical Modeling | |
| Current scientific activities | |
| I’ve studied the amalgamation, transferability and some other categorical algebraic properties in functor and more general categories. I’ve worked out the methods of constructing factorization systems in abstact categories. Applying them, I’ve constucted a range of new factorization systems in categories of groups with operators, abelian groups, topological spaces over a given space and some others. I’ve obtained several results related to (effective)codescent morphisms in categories with the amalgamation properties. In particular, I’ve proved the effectiveness of all codescent morphisms of groups. | |
| Future work plans | |
| To describe effective codescent morphisms in some particular varieties of universal algebras. | |
| Department | |
| Theoretical Foundations in Mathematics |