Rouben V. Ambartzumian

Rouben V. Ambartzumian
Born	(1941-10-28)October 28, 1941
Nationality	Armenia
Fields	Integral Geometry, Stochastic Geometry,
Education	Mathematician, Academician NAS RA

Rouben V. Ambartzumian (Russian: Рубен В. Амбарцумян) (born 1941) is an Armenian mathematician and Academician of National Academy of Sciences of Republic of Armenia . He became famous for his work in Stochastic Geometry and Integral Geometry where he created a new branch Combinatorial Integral Geometry. The subject of Combinatorial Integral Geometry received vigorous support from mathematicians K. Krickeberg and D. G. Kendalll at the 1976 Sevan Symposium (Armenia) which was sponsored by Royal Society of London and The London Mathematical Society. In the framework of the later theory he solved a number of classical problems in particular the solution to the Buffon Sylvester problem as well as the Hilbert's fourth problem in 1976.^[1] He is a holder of the Rollo Davidson Prize of Cambridge University of 1982.^[2] The interest to Integral Geometry Rouben V. Ambartzumian author of a number of books and multiple research publications in that field inherited from his father (world famous scientist Victor Hambardzumyan) who's contribution to that field was described by Nobel prize winner Allan McLeod Cormack Laureate for Tomography who wrote: "Ambartsumian gave the first numerical inversion of the Radon transform and it gives the lie to the often made statement that computed tomography would have been impossible without computers"^[3]). Victor Hambardzumyan in his book "A Life in Astrophysics"^[4] wrote about the work of Rouben V. Ambartzumian "More recently, it came to my knowledge that the invariance principle or invariant embedding was applied in a purely mathematical field of integral geometry where it gave birth to a novel, combinatorial branch (see R. V. Ambartzumian, «Combinatorial Integral Geometry», John Wiley, 1982).^[5]

Experience

• 1968 – present, Head of department, Institute of Mathematics, National Academy of Sciences of Republic of Armenia
• 1990 – 2010 Chief Editor of the Izvestia NAN RA Matematika (in Russian)
• 1990 – 2010 Translation Editor of Journal of Contemporary Mathematical Analysis, Allerton Press, Inc. New York (the English Translation of Izvestia NAS RA Matematika)
• 2009 -2013 Director of the FREEZWATER project, Yerevan, Armenia

Education, scientific degrees

• 1986 Academician of National Academy of Sciences of Armenia
• 1975 Soviet Doctor of Mathematics and Physics, from Steklov Mathematical Institute, Moscow
• 1968 Soviet Kandidat of Mathematics and Physics , from Steklov Mathematical Institute, Moscow
• 1959–1964 Moscow State University diploma,Mathematician.

Books

• 1982 – R.V. Ambartzumian "Combinatorial Integral Geometry with Applications to Mathematical Stereology’’, John Wiley, Chichester, NY^[6]

The book was positively reviewed in many journals. In particular Ralph Alexander wrote in the Bulletin (New Series) of the American Math Society the following^[7] "Ambartzumian established a base camp in a little explored area of geometry. From here a number of interesting problems can be seen from a new perspective. With luck a boom town could arise. At the very least this work is a significant contribution to the foundations of integral geometry".

• 1989 – R.V. Ambartzumian, D.Stoyan, J.Mecke “Introduction to Stochastic Geometry”, Nauka, Moscow (in Russian)
• 1990 – R.V. Ambartzumian “Factorization Calculus and Geomertic Probability’’, Encyclopedia of Mathematics and Its Applications 33, Cambridge University Press, Cambridge^[8]
• 1989 – R.V. Ambartzumian, J.Mecke, D.Stoyan “Geometrische Wahrscheinlichkeiten und Stochastische Geometrie” Akademie Verlag, Berlin^[9]

Collections of papers, Editor

• “Combinatorial Principles in Stochastic Geometry” (in Russian) NASRA Publishing House, Yerevan 1980

The paper contains a review of the main results of Yerevan research group in planar stochastic geometry, in particular the second order random geometrical processes using the methods of integration of combinatorial decompositions and invariant imbedding.

• “Stochastic Geometry, Geometric Statistics, Stereology” (Proceedings of the Conference held at Oberwolfach, 1983). Teubner - Texte zur Mathematik, Band 65, Leipzig 1983
• “Stochastic and Integral Geometry”, (Proceedings of the Second Sevan Symposium on Integral and Stochastic Geometry), in Acta Applicandae Mathematicae, Vol 9, Nos 1-2 (1987)

Organizer of International Conferences

• 1978 – I Sevan Symposium on Integral Geometry “200 anniversary of Buffon problem”, Sevan, Armenia. Sponsorship from the Royal Society of London
• 1983 – Conference on Stochastic Geometry, Geometic Statistics and Stereology, Oberwolfach (Germany)^[10]
• 1985 – II Sevan Symposium on Integral and Stochastic Geometry, Sevan, Armenia
• 1991- Conference on Stochastic Geometry, Oberwolfach (Germany)
• 2013 Swiss –Armenian Round Table^[11]

Recent research papers

The latest research of Rouben V. Ambartzumian has proved that his solution to Hilbert's fourth problem given in 1976 works for dimension 3 as well. See paper R. V. Ambartzumian, ’Remarks on Combinatorics of Planes in Euclidean Three Dimensions’, SOP Transactions on Applied Mathematics^[12]

• R.V.Ambartzumian "Sevan Methodologies revisited: Random line processes", Journal of Contemporary Mathematical Analysis , Volume 48, 2013, Issue 1, pp. 4–22^[13]
• R.V.Ambartzumian "Parallel X-ray Tomography of Convex Domains as a Search Problem in Two Dimensions", Journal of Contemporary Mathematical Analysis , Volume 48, 2013, Issue 1, pp. 23–34

The Most Famous Research papers

• R.V. Ambartzumian, A note on pseudometrics on the plane. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete,^[14] 37, 145-155 (1976).^[1]

This paper is considered by many as giving an independent solution of Hilbert’s Fourth Problem.^[15]

References

^{[16] [17] [18] [19] [20]}