Graduate School of Science and Engineering（Science）
理工学専攻（数理科学）
日本語
Update date：2025/01/09
Professor
Shakhmatov Dmitri

Education

  1. Moscow State University1983
  2. モスクワ国立大学1983
  3. Moscow State University1986
  4. モスクワ国立大学,力学・数学学部大学院1986

Degree

  1. Ph. D.

Research Areas

Research Interests

  1. topological group
  2. topology

Research Projects

  1. Japan Society for the Promotion of ScienceGrants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)Topological groups with fixed point on compacta property and potentially dense subsets of groupsGrant-in-Aid for Scientific Research (C)2020/04-2025/03
  2. Japan Society for the Promotion of ScienceGrants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)Structure of compact-like abelian groups and realization of Markov density by a group topologyGrant-in-Aid for Scientific Research (C)2014/04-2018/03Principal investigatorWe confirm 70 years old conjecture of Markov concerning the algebraic structure of connected groups in the class of abelian groups. Answering a question of Comfort and Gould, we completely describe the algebraic structure of abelian topological groups having the small subgroup generating property. We construct a countable free closed non-relexive subgroup in the product of continuum many integers. We introduce a notion of selectively sequentially pseudocompact space and study basic properties of this new subclass of pseudocompact spaces. Answering a question of Tkachenko, we prove that a weakly pseudocompact precompact group is pseudocompact.
  3. Japan Society for the Promotion of ScienceGrants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)Interplay between algebraic and topological closure operators, and existence of compact-like group topologies on abelian groupsGrant-in-Aid for Scientific Research (C)2010/04-2014/03We characterize potentially dense subsets of abelian groups G of size at most the power set of the continuum, and we show that the Markov-Zariski closure of a subset S of such a group G can be realized in some precompact group topology on G. (In particular, potential denseness of a set in G can be witnessed by some precompact group topology of G.) New metrizability criteria for compcat groups are obtained. We also provide various characterizations of Lie groups by means of controlling their zero-dimensional closed subgroups. Multiplier convergence theory of topological groups is developed.
  4. Study of the structure of the Markov-Zariski topology of a group and convergence properties of compact-like topological groups基盤研究(C)Principal investigator
  5. Algebraic structure of compact-like topological groups and convergence properties基盤研究(C)Principal investigator
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Books and Other Publications

  1. Algebraic structure of Pseudocompact groupsAmerican Mathematical SocietyMemoucs of the American Mathemational Society1998
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Papers

  1. Star covering properties and neighborhood assignments2023/03/23Fortunata Aurora Basile, Maddalena Bonanzinga, Fortunato Maesano, Dmitri B. ShakhmatovAtti Accad. Peloritana Pericolanti Cl. Sci. Fis. Mat. Natur101/ 1, A7, 1-14Research paper (scientific journal)10.1478/AAPP.1011A7
  2. On subsets of R^n spanning it via positive integers as multipliers2021/09/01Vitalij A. Chatyrko Dimitri B. ShakhmatovTopology and its Applications301/ 107497, 1-14Research paper (scientific journal)10.1016/j.topol.2020.107497Elsevier BV
  3. Compactness properties defined by open-point games2020/10/01A. Dorantes-Aldama D. ShakhmatovTopology and its Applications284/ 107196, 1-21Research paper (scientific journal)10.1016/j.topol.2020.107196Elsevier BV
  4. Automorphism groups of dense subgroups of R^n2020/04/15Vitalij Chatyrko Dmitri ShakhmatovTopology and its Applications275/ 107000, 1-19Research paper (scientific journal)10.1016/j.topol.2019.107000Elsevier BV
  5. Topological groups all continuous automorphisms of which are open2020/04/15Vitalij A. Chatyrko Dmitri B. ShakhmatovTopology and its Applications275/ 107051, 1-18Research paper (scientific journal)10.1016/j.topol.2019.107051Elsevier BV
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Presentations

  1. Applications of reflection principle in groupsThe 4th International Conference on Topological Algebras and Their Applications2024/04/14Oral presentation(invited, special)
  2. Markov and Zariski topologies in free groups in a given varietyNing-jin-tai Topology Workshop (Dedicated to 60th Anniversary of Professor Wei He)2024/01/13Oral presentation(invited, special)
  3. Zariski and (precompact) Markov topologies in free groups and their subgroupsInternational conference "Algebra, Topology and Their Interactions" (Udine University, Italy)2022/09/12Oral presentation(invited, special)URLURL_2
  4. On Markov's problem for free groupsGeneral Topology Symposium 2021 (Takasaki City University of Economics, Takasaki, Japan)2021/12/07Oral presentation(general)
  5. Unconditionally closed subsets of free (non-commutative) groupsInternational Conference on Topology and its Applications dedicated to the 100th anniversary of the birthday of Yu. M. Smirnov (Moscow State University, Russia)2021/09/21Oral presentation(general)
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Allotted Class

  1. 2024Introduction to Mathematics
  2. 2024TopologyⅠ
  3. 2024Set Theory and TopologyⅡ
  4. 2024Introduction to Geometry
  5. 2024General Topology
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Social Activities

  1. Questions and Answers in General Topology2010/01/01-presentAn international journal devoted primarily to rapid publication of questions and answers that arise from research in general and geometric topology including set-theoretic topology, topological algebras, theory of continua, topological dynamics and related fields. Founded by Jun-iti Nagata in 1983.
  2. Topology Proceedings1997/01/01-presentTOPOLOGY PROCEEDINGS publishes papers in all areas of topology and dynamical systems.
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Media Coverage

  1. Set-Theoretic and Geometric Topology, and their applicationsOtherResearch Institute for Mathematical Sciences, Kyoto UniversityRIMS Workshop2016/10/17
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Professional Memberships

  1. 日本数理科学協会(JAMS)
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