Giorgi Khimshiashvili

 

Personal

Born 28.10.1951 in Tbilisi

Married 6.07.1991 to Tamar Lomadze

Education

1968 – graduated with golden medal from secondary school No.42, Tbilisi

1973 – graduated from the Faculty of Mechanics and Mathematics of Moscow State University, Honours Diploma C 572684

Languages

Georgian, Russian, English, Polish (fluent), German, French (conversational)

 

Scientific degrees and titles

 1977 – Candidate Phys. Math. Sci., Diploma MFM 043682, issued by VAK USSR

1992 – Doctor Phys. Math. Sci., Diploma DT 016471, issued by VAK USSR

2000 – Titular Professor, Diploma GA 000179, issued by Tbilisi State University

Distinction

1981 - Medal with prize of the Georgian Academy of Sciences for young scientists

Visiting positions

1983-1985 – Associate Researcher at MSU

1986 – Associate researcher at Steklov Mathematical Institute

1993 – Visiting researcher at Banach Center (3 months)

1994 – Visiting researcher at Heidelberg university (2 months)

1995 – Visiting Professor at Lodz University (9 months)

1996 – Visiting researcher at Freiberg Technical University (2 months)

1997 – Visiting Professor at Lodz University (9 months)

1998 - Visiting researcher at Freiberg Technical University (2 months)

1999 - Visiting researcher at Utrecht University (4 months)

1999-2000 – Visiting researcher at Uppsala University (9 months)

2000 – Visiting Professor at Ohio State University (3 months)

2001 – Visiting Professor at Lodz University (9 months)

2002 - Visiting Professor at Ohio State University (1 month)

2003 – Visiting Professor at Lodz University (6 months)

Other positions

Member of the Scientific Council of A.Razmadze Mathematical Institute

Member of the editorial board of journal “Contemporary mathematics and its applications”

Local coordinator in the framework of INTAS cooperation

Head of a research group in the framework of a grant of the Georgian Academy of Sciences

Teaching experience

1972-1973 – Assistant Professor at MSU

1978-1982 – Associate Professor at TSU

1995, 1997, 2001, 2003 – Visiting Professor at Lodz University

2000 – Visiting Professor at Ohio State University

One- and two-semester courses in calculus, topology, singularity theory, mathematical physics

Ph. D. students

1. M.Shubladze, thesis “Certain classes of non-isolated singularities of analytic functions”, defended in 1990 at TSU.

2. T.Aliashvili, thesis “On the number of real roots of polynomial automorphism”, defended in 1994 at TSU.

3. R.Prszybysz, thesis “On Poisson structures generated by Jacobian”, defended in 2002 at Lodz University.

4. N.Topuridze, thesis “On the roots of quaternionic polynomials” (ready for submission)

5. G.Bibileishvili, thesis “Topological degree of quasihomogeneous mapping” (ready for submission)

Grants

1992-1995 – personal grant of American Mathematical Society

1996-1997 – DFG grant for cooperation with Freiberg Technical University

1997-1998, 1999-2000, 2001-2003 – INTAS grants

1999 – Swedish Institute grant for scientific research in Sweden

2000-2001 – COBASE grant for cooperation between Georgia and USA

1999-present – grants of the Georgian Academy of Sciences

Participation in international conferences

Speaker at international conferences in topology (Tbilisi 1972, Prague 1981, Leningrad 1982, Tiraspol 1983, Eger 1984, Baku 1987)

Speaker at international conferences in singularity theory (Cambridge 2001, Anger 2001, Banach Center 2002, Moscow 2002, St.-Marienthal 2002, Edinburgh 2003)

Speaker at international conferences in complex analysis (Varna 1981, 1983, 1987, Halle 1984, Dubrovnik 1988)

Speaker at international conferences in differential equations (Donetsk 1978, Moscow 1984, Tbilisi 1987, Potsdam 1993, Moscow 2001)

Speaker at international conferences in operator theory (Timisoara 1990, Mexico 1994)

Speaker at international conferences in Clifford analysis (Seiffen 1996, Banach Center 1998)

Speaker at international conferences in algebra (Novosibirsk 1990, Kaiserslautern 2003)

Speaker at international conferences in mathematical physics (Lodz 1997, Tbilisi 1999)

Invited speaker at four Banach Center conferences (1993, 1998, 2001, 2002) and two NATO Advanced Research Workshops (Prague 2000, Liverpool 2001)

Two contributed talks at International Congresses of Mathematicians (Zuerich 1994, Berlin 1998)

Monographs

  1. Signature formulae for topological invariants. A.Razmadze Mathematical Institute Proc. 125(2001), 1-121.
  2. Geometric aspects of Riemann-Hilbert problems. Memoirs on Diff. Eq. Math. Phys. 27(2002), 1-114.

Selected publications list

  1. On the local degree of smooth mapping. Bull. Acad. Sci. Georgian SSR 85, 1977, 309-312.
  2. On the small solutions of analytic Fredholm equations. Vestnik Mosk. Gos. Univ. 2, 1977, 27-31.
  3. Branching of solutions of nonlinear boundary value problems. In: Proc. Conf. “Differential equations and boundary value problems”, Naukova Dumka, Kiev, 1979, 77-78.
  4. On the local degree of smooth mapping. Proc. RMI 64, 1980, 105-124.
  5. Fredholm analytic sets and branching of solutions of nonlinear equations. Trudy Tbiliss. Univ. 218, 1981, 159-182.
  6. Euler characteristic and critical points of smooth functions. Proc. RMI 85, 1982, 123-141.
  7. Development of specialization processes in course of scientific and technical progress. In: “Problems of measuring the influence of scientific-technical progress on industry”, Leningrad, 1983, 89-98. (with R.Satanovsky and E.Sheremetjeva).
  8. On the number of solutions of analytic equations. In: “Complex Analysis and its Applications”, Bulgarian Ac. Sci., Sofia, 1984, 239-245.
  9. The index formula for a holomorphic image of commuting operators. Uspekhi matem. nauk 40, 1985, 157-158.
  10. On the topology of invertible linear singular integral operators. Springer Lecture Notes Math. 1214, 1986, 211-230.
  11. Polysingular operators and topology of invertible singular operators. Zeitschr. Anal. Anw. 5, 1986, 139-145.
  12. The non-commutative functional calculus and Fredholm theory. In: Proc. Symp. “Modern problems of mathematical physics”, Tbilisi, 1987, 404-410.
  13. On the Riemann problem with values in a compact Lie group. Trudy Inst. Prikl. Math. TGU 5, 1988, 186-189.
  14. On the topology of generalized Riemann-Hilbert problem. BGAS 135, 1989, 241-244.
  15. On the Riemann-Hilbert problem for a compact Lie group. Doklady AN SSSR 310, 1990, 1055-1058.
  16. On the generalized Riemann-Hilbert problem with coefficients in a compact Lie group. Pitman. Res. Notes Math. 256, 1991, 86-94.
  17. Lie groups and linear conjugation problems for Riemann surfaces. Contemp. Math. 131, 1992, 164-178.
  18. On Fredholmian aspects of linear transmission problems. Springer Lecture Notes Math. 1520, 1992, 193-216.
  19. Loop groups and Fredholm operators. Pitman Res. Notes Math. 271, 1992, 116-127.
  20. Some topological aspects of elliptic boundary problems. In: Proc. Conf. “Partial Differential Equations”, MPI Bonn, 1993, 30-33.
  21. On the cardinality of semi-algebraic subset. Georgian Math. J. 1, 1994, 311-321.
  22. Remarks on PI-algebras and category-like invariants. Proc. RMI 104, 1995, 95-109.
  23. Elliptic boundary problems for generalized Cauchy-Riemann systems. In: Proc. Symp. “Analytical and Numerical methods in Quaternionic and Clifford analysis” Seiffen, 1996, 77-83.
  24. Stability of analytic discs in Riemann-Hilbert setting. In: Proc. 1st Polish Symp. Nonlin. Anal., Lodz University1997, 77-82.
  25. Nonlinear transmission problems. Memoirs on Diff. Eq. Math. Phys. 12(1997), 223-230. (with E.Wegert and I.Spitkovsky)

26. Homotopy classes of elliptic transmission problems over C*-algebras. Georgian Math. J. 5(1998),

453-468.

27. On totally real non-compact manifolds globally foliated by analytic discs. In: “Partial Diff.

Int. Equations”, Kluwer, Dordrecht, 1999, 107-123. (with E.Wegert and I.Spitkovsky)

28. Elliptic cells in Riemann-Hilbert setting. Bull. Soc. Sci. Lett. Lodz 31, 2000, 107-119.

29. On generalized Sklyanin algebras. Georgian Math. J. 7, 2000, 789-800. (with R.Przybysz)

30. Minimal round functions on low-dimensional manifolds. Bull. Georgian Acad. Sci. 162, 2000,

No. 4, 3-7. (with D.Siersma)

31. On local invariants of totally real surfaces. Georgian Math. J. 8, 2001, 97-109.

32. Hyper-holomorphic cells and Riemann-Hilbert problems. In: “Clifford analysis and its

applications”, NATO Sci. Ser. II Math. Phys. Chem. 25, Kluwer, Dordrecht, 2001, 123-133.

33. Global geometric aspects of Riemann-Hilbert problems. Georgian Math. J. 8(2001), 713-726.

(with B.Bojarski)

34. Counting roots of quaternionic polynomials. BGAS 165, 2002, 465-468.

35. On certain super-integrable Hamiltonian systems. J. Dyn. Contr. Syst. 8, 2002, 217-244. (with

R.Przybysz)

36. Analytic discs and complex points of totally real surfaces. Bull. Soc. Sci. Lett. Lodz 33, 2002,

121-134. (with E.Wegert)

37. On configuration spaces of planar pentagons. Nauchn. Zap. Semin. Sankt. Peterb. Otd. Mat.

Inst. Steklova 292, 2002, 121-128.