Rouben V. Ambartzumian

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

Rouben V. Ambartzumian (Armenian: Ռուբեն Վ․ Համբարձումյան;Russian: Рубен В. Амбарцумян) (born 1941) is an Armenian mathematician and Academician of National Academy of Sciences of Republic of Armenia . He worked in Stochastic Geometry and Integral Geometry where he created a new branch, combinatorial integral geometry. The subject of combinatorial integral geometry received support from mathematicians K. Krickeberg and D. G. Kendall 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] Rouben's interest in Integral Geometry was inherited from his father. Nobel prize winner Allan McLeod Cormack Laureate for Tomography 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 Geometric 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, Geometric 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

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]

Research in History

Recently Rouben V. Ambartzumian has made a personal contribution in the commemoration of the 100 Years of the Armenian Genocide by releasing a booklet named "Wilsonain Armenia: stories behind the failed project".

The term “Wilsonian Armenia” refers to the US president who launched the idea of independent Armenian State in Western Armenia, on the territory of former Ottoman Empire. Put forward at the 1919 Paris Peace Conference, the idea magnetized the leaders of victorious Entente nations. At Sevres Conference of 1920 a mirage of Wilsonian Armenia was born (Sevres Treaty), only to be totally dispelled within several months. Was the absence of the USA signature under Sevres Treaty the cause for this outcome? Trying to resolve this paradox, the book scrutinizes certain political forces both within and outside America. The time range covered is from the Goeben-Breslau masquerade of 1914 (i.e. the entrance of German warships into Black Sea) to Lausanne Conference 1922 that buried the Wilsonian idea officially. Essentially, the booklet is a journalist reportage from the pages of publications mainly from the historical epoch in question. Some passages probably contribute to the genre of historical detection.

References

^{[16] [17] [18] [19] [20] [21]}

1. R. V. Ambartzumian, A note on pseudo-metrics on the plane, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 1976, Volume 37, Issue 2, pp 145-155
2. "Prize Winners 1976-2014". cam.ac.uk.
3. Computed Tomography, Some History and Recent Developments, Proc. of Symposia in Applied Mathematics, Vol. 29, p. 35, 1985
4. V. A. Ambartsumian, A Life in Astrophysics : Selected Papers of Viktor Ambartsumian, New York: Allerton Press, 1998, ISBN 0-89864-082-2
5. http://ambartsumian.ru/en/papers/epilogue-ambartsumian’-s-paper/
6. "Combinatorial Integral Geometry With Applications to Mathematical Stereology". abebooks.co.uk. 12 February 1982.
7. Alexander, Ralph. Review: R. V. Ambartzumian, Combinatorial integral geometry with applications to mathematical stereology . Bull. Amer. Math. Soc. (N.S.) 10 (1984), no. 2, 318--321. http://projecteuclid.org/euclid.bams/1183551587
8. "Factorization Calculus and Geometric Probability". Cambridge University Press.
9. bücher.de IT and Production. "Ruben V. Ambartzumjan, Joseph Mecke, Dietrich Stoyan, sowie Werner Nagel ( Hrsg)". buecher.de.
10. "Schedule — MFO". mfo.de.
11. "Snow Storage – Perspective for Armenia?". ecolur.org.
12. R. V. Ambartzumian, Remarks on Combinatorics of Planes in Euclidean Three Dimensions, SOP Transactions on Applied Mathematics, Volume 1, Number 2, pp.29-43, 2014.
13. "Sevan methodologies revisited: Random line processes". springer.com.
14. "Journal of Theoretical Probability". springer.com.
15. J.C. Alvarez Paiva, Hilbert’s Fourth Problem in Two Dimensions Mass Selecta: Teaching and Learning Advanced Undergraduate Mathematics. S. Katok, A. Sossinsky, and S. Tabachnikov (eds.), Amer. Math. Soc., Rhode Island, 2003, 165--183.
16. "Academician R. V. Ambartzumian". springer.com.
17. "Publications of Rouben V. Ambartzumian in J CONTEMP MATH ANAL-ARMEN ACA - Journal of Contemporary Mathematical Analysis-armenian Academy of Sciences". msra.cn.
18. Ambartzumian, R. V. (2007). Chord calculus and stochastic geometry. Journal of Contemporary Mathematical Analysis, 42(1), 3-27
19. Ambartzumian, R. V., Wicksell problem for planar particles of random shape http://www.math.uni-magdeburg.de/stoch2002/abstracts/s6-ambartzumian.pdf
20. "Risultati sintetici  ". sbn.it.
21. Ambartzumian, R. V, Wilsonain Armenia: stories behind the failed project https://www.lap-publishing.com/catalog/details/store/de/book/978-3-659-75300-8/wilsonian-armenia:-stories-behind-the-failed-project?search=wilsonian%20armeina