During the years of work as vice-rector for scientific work and rector, Volodymyr Kryvtsov made a significant contribution to the development of scientific research at the university, the education and training of pedagogical personnel, the improvement of the educational process, and the improvement of the quality of specialist training. In the difficult time of the 90s, thanks to perseverance, initiative, extraordinary organizational skills, Volodymyr Kryvtsov managed to preserve the scientific potential of the institute and highly qualified scientific personnel, continue scientific research on the most important topics of departments and scientific schools, and educate young scientists. In 1998, KAI was granted the status of the State Aerospace University, in September 2000 – the National Aerospace University. The contingent of students under contract is expanding, including under an industry-specific order, which made it possible to restore and develop the material and technical and educational and laboratory base of the university, to take a strategic course on the implementation of modern information technologies in the training of specialists for the aerospace industry of Ukraine.

A lot of work is being done on the reorganization of the departments and the structure of the faculties in order to increase the efficiency of their activities. New faculties are being organized: humanities, correspondence studies, work with foreign students, new promising specialties are being opened, which are in demand in the modern labor market of Ukraine. Every year, the ranks of teaching and research staff of the university are replenished at the expense of promising graduates who are sent to the departments after graduating from Khai. The effectiveness of postgraduate studies is increasing. As a result, the team of teachers and research staff has become younger in recent years, and there have been more teachers with academic degrees and titles.

In 1998, Kryvtsov headed the Department of Aircraft Production Technology. Under his leadership, the department is implementing a program of comprehensive implementation of modern information technologies for the production of aviation equipment. The talented teacher paid great attention to the education of young scientists-pedagogues. He is the author of monographs and textbooks, which are in great demand in the higher education of Ukraine, was a scientific director and consultant of candidates and doctors of sciences. Organized relations with enterprises of the industry and involved leading enterprises to participate in the educational process of students. So at ANTK named after Antonova, Kyiv and JSC Motor-Sich, Zaporizhzhia successfully operate branches of faculties. Branches and departments for new directions of development of aerospace science and technology are organized at leading enterprises of the aerospace industry.

Under the direct leadership of Kryvtsov, new scientific directions are being created at the Khai, international relations in the field of the scientific and technical community are being expanded, and international projects for the training of masters and doctors of science are being implemented in Mexico and Iran.

Kryvtsov was a member of the Council on Science and Scientific and Technical Policy under the President of Ukraine, headed the aerospace engineering department of the Academy of Engineering Sciences of Ukraine, was a member of the informatics section of the Committee for State Awards of Ukraine in the field of science and technology, a member of the bureau of the North-Eastern Scientific Center of the National Academy of Sciences of Ukraine, academician of the Russian Academy of Cosmonautics named after Tsiolkovsky, head of the specialized Scientific Council for the defense of candidate and doctoral theses, editor-in-chief of the scientific and technical magazine "Aviation and Technical Engineering and Technology", head of the Scientific and Methodological Council of the Ministry of Education and Science of Ukraine in the field of "Aviation and Cosmonautics". He was elected a deputy of the Kharkiv City Council of People's Deputies, and was awarded the "For Labor Award" medal (1980).