Алексей Басалаев

научный сотрудник / Сколковский институт науки и технологий

Профессиональные интересы
зеркальная симметрия, когомологические теории поля, теория особенностей, пространство модулей кривых, интегрируемые иерархии, теория узлов

Образование, учёные степени
2007 / Московский государственный университет / механико-математический факультет / специальность “математика”
2016 / Кандидат физико-математических наук / Институт проблем передачи информации РАН / специальность 01.01.06 “Математическая логика, алгебра и теория чисел” / тема диссертации “Зеркальная симметрия для простых эллиптических особенностей с действием группы”

Публикации

  1. A. Basalaev, "I6-dimensional FJRW theories of the simple–elliptic singularities", Asian Journal of Mathematic, v.26 (2022) 45-80, dx.doi.org/10.4310/AJM.2022.v26.n1.a3, dx.doi.org/10.4310/AJM.2022.v26.n1.a3[ PDF: English, arXiv: 1610.07428]
  2. A. Alexandrov, A. Basalaev, A. Buryak, "A construction of open descendant potentials in all genera", International Mathematics Research Notices, 2022;, rnac240, doi.org/10.1093/imrn/rnac240 [ PDF: English, arXiv: 2202.07312]
  3. A. Basalaev, A. Ionov, "Hochschild cohomology of Fermat type polynomials with non–abelian symmetries" Journal of Geometry and Physics, 2022, 174, 104450 doi.org/10.1016/j.geomphys.2021.104450
  4. A. Basalaev, "Integrable systems associated to open extensions of type A and D Dubrovin-Frobenius manifolds" Journal of Physics A: Mathematical and Theoretical, 2022, 55(29), 295202 doi 10.1088/1751-8121/ac79e4
  5. A. Basalaev, A. Takahashi, “Mirror Symmetry for a Cusp Polynomial Landau–Ginzburg Orbifold”, International Mathematics Research Notices, v.2022 (19) Oct 2022, 14865–14922, doi.org/10.1093/imrn/rnab145
  6. A. Basalaev, C. Hertling, “3-dimensional F-manifolds”, Lett Math Phys 111, 90 (2021). https://doi.org/10.1007/s11005-021-01432-y [ PDF: English, arXiv: 2012.11443]
  7. A. Basalaev, P. Dunin-Barkowski, S. Natanzon, “Integrable hierarchies associated to infinite families of Frobenius manifolds”, 2021 J. Phys. A: Math. Theor. 54 115201 doi:10.1088/1751-8121/abdd79 [ PDF: English, arXiv: 2007.11974]
  8. A. Basalaev, A. Ionov, “Mirror map for Fermat polynomial with non–abelian group of symmetries”, Theor Math Phys 209, 1491–1506 (2021). https://doi.org/10.1134/S0040577921110015 [ PDF: English, arXiv: 2103.16884]
  9. A. Basalaev, A. Buryak, “Open Saito theory for A and D singularities”, Int. Math. Res. Notices, v. 2021(7), Apr 2021, 5460–5491, doi.org/10.1093/imrn/rnz381 [ PDF: English, arXiv: 1909.00598]
  10. A. Basalaev, A. Takahashi, “Hochschild cohomology and orbifold Jacobian algebras associated to invertible polynomial”, J. of EMS, Volume 14, Issue 3, 2020, pp. 861–877, doi:10.4171/JNCG/370 [ PDF: English, arXiv: 1802.03912 ]
  11. A. Buryak, A. Basalaev, “Open WDVV equations and Virasoro constraints”, Arnold Math J. 5:2-3(2019) 145-186, doi.org/10.1007/s40598-019-00115-w [ PDF: English, arXiv: 1901.10393]
  12. A. Basalaev, N. Priddis, “Givental-Type reconstruction at a nonsemisimple point”,
    Michigan Math. J. 67:2(2018) 333-369, [ PDF: English, arXiv: 1605.07862 ]
  13. A. Basalaev, A. Takahashi, “Hochschild cohomology and orbifold Jacobian algebras associated to invertible polynomial”, [ PDF: English, arXiv: 1802.03912 ]
  14. A. Basalaev, A. Takahashi, E. Werner, “Orbifold Jacobian algebras for exceptional unimodal singularities”, [ PDF: English, arXiv: 1702.02739 ]
  15. A. Basalaev, “6-dimensional FJRW theories of the simple-elliptic singularities”, [ PDF: English, arXiv: 1610.07428 ]
  16. A. Basalaev, A. Takahashi, E. Werner, “Orbifold Jacobian algebras for invertible polynomials”, [ PDF: English, arXiv: 1608.08962 ]
  17. A. Basalaev, “SL(2,C) group action on cohomological field theories”, Lett Math Phys (2018) 108: 161 [ PDF: English, arXiv: 1405.6607 ]
  18. A. Basalaev, “Mirror symmetry for simpleelliptic singularities with a group action”, thesis, Hannover University, (2014)
  19. A. Basalaev, “SL(2, C) action on cohomological field theories and Gromov-Witten theory of elliptic orbifolds”, Oberwolfach report Nr. 22/2015, (2015).
  20. A. Basalaev, A. Takahashi, “On rational Frobenius manifolds of rank three with symmetries”, J Geom Phys, vol. 84 (2014), 73-86 [ PDF: English, arXiv: 11401.3505 ]
  21. A. Basalaev, “Orbifold GW theory as Hurwitz-Frobenius submanifold”, J Geom Phys, 77 (2014), 30-42 [ PDF: English, arXiv: 1310.3589 ]