Context_1 : In topology, the nerve of an open covering is a construction of an abstract simplicial complex from an open covering of a topological space "X" that captures many of the interesting topological properties in an algorithmic or combinatorial way. It was introduced by Pavel Alexandrov. and now has many variants and generalisations, among them the Čech nerve of a cover, which in turn is generalised by hypercoverings. Context_2 : Alexandrovo-Gaysky District (Russian: Алекса́ндрово-Га́йский райо́н ) is an administrative and municipal district (raion), one of the thirty-eight in Saratov Oblast, Russia. It is located in the southeast of the oblast. The area of the district is 2700 km2 . Its administrative center is the rural locality (a "selo") of Alexandrov Gay. Population: 16,855 (2010 Census);  (2002 Census) ;  (1989 Census) The population of Alexandrov Gay accounts for 57.7% of the district's total population. Context_3 : Yuri Vladimirovich Matiyasevich, (Russian: Ю́рий Влади́мирович Матиясе́вич ; born March 2, 1947, in Leningrad) is a Russian mathematician and computer scientist. He is best known for his negative solution of Hilbert's tenth problem (Matiyasevich's theorem), which was presented in his doctoral thesis at LOMI (the Leningrad Department of the Steklov Institute of Mathematics). Context_4 : Pavel Sergeyevich Alexandrov (Russian: Па́вел Серге́евич Алекса́ндров ), sometimes romanized Paul Alexandroff or Aleksandrov (7 May 1896 – 16 November 1982), was a Soviet mathematician. He wrote about three hundred papers, making important contributions to set theory and topology. Context_5 : Géraud Sénizergues (born 1957) is a French computer scientist at the University of Bordeaux. With Yuri Matiyasevich he obtained results about the Post correspondence problem. He won the 2002 Gödel Prize "for proving that equivalence of deterministic pushdown automata is decidable" Context_6 : Alexandrovsky District (Russian: Алекса́ндровский райо́н ) is an administrative and municipal district (raion), one of the sixteen in Vladimir Oblast, Russia. It is located in the west of the oblast. The area of the district is 1834 km2 . Its administrative center is the town of Alexandrov. Population:  (2010 Census) ; 55,207 (2002 Census);  (1989 Census) The population of Alexandrov accounts for 54.0% of the total district's population. Context_7 : Alan Davies (born December 22, 1945) is a British professor of mathematics at the University of Hertfordshire. He obtained a first class honours degree in mathematics (1968) from Southampton University. He followed that with a master's degree, with distinction, in structural engineering (1974) and a doctorate in numerical computation (1989) from Imperial College. He has spent most of his working life as an academic at the University of Hertfordshire (UH), formerly the Hatfield Polytechnic. He had short spells in industry working as a research engineer in the aircraft industry and as a process engineer in the food industry. During his time in Hatfield his major activity has been teaching mathematics to undergraduates and postgraduates in mathematics, science and engineering. He has also been engaged in research in numerical computation. In 1992 he became Head of the Department of Mathematics and was appointed Professor of Mathematics and, in 2004, the Department merged with Physical Sciences and Alan was appointed head of the School of Physics, Astronomy and Mathematics. During his time as HoD he became increasingly involved with outreach activities with both schools and the general public. He retired from his full-time post in 2006 and is currently Professor Emeritus in mathematics and is currently a London Mathematical Society Holgate Lecturer. Context_8 : Pavel Alexandrovich Alexandrov, Aleksandrov Pavel Alexandrovich (Russian: Павел Александрович Александров , 1866, Saint Petersburg - September 24, 1940, Moscow) was a distinguished lawyer and state official of the Russian Empire, councillor of state. He investigated the most sensational crimes of the late 19th and early 20th centuries, which received wide coverage in the mass media. Context_9 : In the mathematical field of topology, the Alexandroff extension is a way to extend a noncompact topological space by adjoining a single point in such a way that the resulting space is compact. It is named for the Russian mathematician Pavel Alexandrov. Context_10 : Pavel Samuilovich Urysohn (Па́вел Самуи́лович Урысо́н ) (February 3, 1898 – August 17, 1924) was a Soviet mathematician of Jewish origin who is best known for his contributions in dimension theory, and for developing Urysohn's Metrization Theorem and Urysohn's Lemma, both of which are fundamental results in topology. His name is also commemorated in the terms Urysohn universal space, Fréchet–Urysohn space, Menger–Urysohn dimension and Urysohn integral equation. He and Pavel Alexandrov formulated the modern definition of compactness in 1923. fact_1 : Pavel Sergeyevich Alexandrov (Russian: Па́вел Серге́евич Алекса́ндров ), sometimes romanized Paul Alexandroff or Aleksandrov (7 May 1896 – 16 November 1982), was a Soviet mathematician. fact_2 : Yuri Vladimirovich Matiyasevich, (Russian: Ю́рий Влади́мирович Матиясе́вич ; born March 2, 1947, in Leningrad) is a Russian mathematician and computer scientist. fact_3 :  He is best known for his negative solution of Hilbert's tenth problem (Matiyasevich's theorem), which was presented in his doctoral thesis at LOMI (the Leningrad Department of the Steklov Institute of Mathematics). Question: Were Pavel Alexandrov and Yuri Matiyasevich both working in the same area of mathematics?
Output: no