Research Interests

Keywords:

Representation theory, Vertex operator superalgebras, Lie superalgebras, two-dimensional superconformal field theory

Employment

From Sep. 1, 2021 to Present: Program-Specific Researcher at Research Institute for Mathematical Sciences (RIMS), Kyoto University.

From Sep. 3, 2018 to Aug. 31, 2021: Postdoctoral Fellow at Institute of Mathematics, Academia Sinica.

Publications

  1. "Modular invariant representations of the N=2 superconformal algebra", Int. Math. Res. Not., IMRN, Vol. 2019, Issue 24, pages 7659–7690, 2019.

  2. "Kazama-Suzuki coset construction and its applications", Proceedings of the Meeting for Study of Number theory, Hopf algebras and related topics, pages 253–269, Yokohama Publ., Yokohama, 2019.

  3. "Kazama-Suzuki coset construction and its inverse", J. Algebra, Vol. 592, pages 435-476, 2022.

  4. "Fusion rules and Verlinde formula for N=2 vertex operator superalgebra", to appear in RIMS Kôkyûroku Bessatsu, Proceedings of 10th CFT Seminar: A Conference on Vertex Algebras and Related Topics.

  5. "Correspondences of categories for subregular W-algebras and principal W-superalgebras" (with Thomas Creutzig, Naoki Genra, Shigenori Nakatsuka), to appear in Commun. Math. Phys., preprint version arXiv:2104.00942

Preprints

  1. "Equivalences between weight modules via N=2 coset constructions", preprint, arXiv:1605.02343

  2. "On resolutions of highest weight modules over the N=2 superconformal algebra" (with Shinji Koshida), preprint, arXiv:1810.13147

Talks

  1. "On relaxed Verma modules and complex-powered twists", 17th Conference on Representation Theory of Algebraic Groups and Quantum Groups, Toyama, Jun. 4, 2014.

  2. "N=2 coset constructions and spectral flow quotients", Algebraic Lie Theory and Representation Theory 2015, Okayama, Jun. 6, 2015.

  3. "Kazama-Suzuki coset construction and logarithmic extensions of weight modules", Representation Theory Seminar, RIMS, Nov. 6, 2015.

  4. "Equivalences between logarithmic weight modules via N=2 coset constructions", University of Tsukuba, Apr. 21, 2016.

  5. "Equivalences between logarithmic weight modules via N=2 coset constructions", Algebraic Lie Theory and Representation Theory 2016, Nagano, Jun. 12, 2016.

  6. "Non-unitary highest-weight modules over the N=2 superconformal algebra", Infinite Analysis Seminar Tokyo, Graduate School of Mathematical Sciences, the University of Tokyo, Oct. 27, 2016.

  7. "On admissible modules over the N=2 superconforal algebra", Meeting for Study of Number Theory, Hopf algebras and related topics, the University of Toyama, Feb. 12, 2017.

  8. "On equivalences between $\widehat{sl}_{2}$ and the N=2 superconformal algebra", Seminar in Representation Theory, Institute of Mathematics, Academia Sinica, Taiwan, Feb. 24, 2017.

  9. "Modular transformation properties of characters of the N=2 superconformal algebra", Algebraic Lie Theory and Representation Theory 2017, Shizuoka, Jun. 10, 2017.

  10. "Modular transformation properties of characters of the N=2 superconformal algebra", Tsukuba Workshop on Pure and Applied Mathematics 2017, University of Tsukuba, Jul. 16, 2017.

  11. "Modular transformation properties of characters of the N=2 superconformal algebra", 13th Colloquium, Tokyo University of Science, Oct. 20, 2017.

  12. "Modular transformation properties of characters of the N=2 vertex operator superalgebra", 7th Regular Seminar, Research Center for Mathematical Physics, Rikkyo University, Nov. 15, 2017.

  13. "Representation theory of the N=2 superconformal algebra", Prospects of Theory of Riemann Surfaces, Yamaguchi University, Dec. 2, 2017.

  14. "Modular invariant representations of the N=2 vertex operator superalgebra", Infinite Analysis Seminar Tokyo, Graduate School of Mathematical Sciences, the University of Tokyo, Feb. 6, 2018.

  15. "Modular transformation properties and the Verlinde formula", Mathematical Society of Japan Spring Meeting 2018, the University of Tokyo, Mar. 21, 2018.

  16. "On the non-$C_{2}$-cofinite N=2 vertex operator superalgebra and the Verlinde formula", 10th CFT Seminar: A Conference on Vertex Algebras and Related Topics, RIMS, Apr. 26, 2018.

  17. "Zhu's algebra of the N=2 vertex operator superalgebra", Algebraic Lie Theory and Representation Theory 2018, Nagano, May. 28, 2018.

  18. "N=2 vertex operator superalgebras and the Verlinde formula", Kobe Seminar on Integrable Systems, Kobe University, Jun. 5, 2018.

  19. "Representation theory of the N=2 superconformal algebra", Shinshu Algebra Seminar, Shinshu University, Jul. 25 and 26, 2018.

  20. "Representation theory of the N=2 superconformal algebra", 34th Lie Algebra Summer Seminar, Toyama University, Aug. 26, 2018.

  21. "On Zhu's algebra of N=2 vertex operator superalgebras", Taipei Postdoc Seminar, Institute of Mathematics (Academia Sinica), Oct. 17, 2018.

  22. "Differential Equations Coming from Superconformal Field Theory", Prospects of Theory of Riemann Surfaces, Yamaguchi University, Dec. 2, 2018.

  23. " On Kazama-Suzuki coset construction and its inverse construction", Workshop on finite groups, vertex algebras and algebraic combinatorics, National Cheng Kung University, Mar. 25, 2019.

  24. "On Kazama-Suzuki coset construction", Algebraic Lie Theory and Representation Theory 2019, Shizuoka, May 25, 2019.

  25. "On the Kazama-Suzuki coset construction and its finite-dimensional analog", Seminar in Representation Theory, Institute of Mathematics (Academia Sinica), Jun. 12, 2019.

  26. "Logarithmic extension of the Kazama-Suzuki coset model", Seminar on Vertex Algebras, Institute of Mathematics, Academia Sinica, Nov. 27, 2019.

  27. "Commutant Constructions in Representation Theory", Colloquium, National Cheng Kung University, Dec. 12, 2019.

  28. "Logarithmic extension of the Kazama-Suzuki coset model", The 2nd Meeting for Study of Number Theory, Hopf algebras and Related Topics, the University of Toyama, Feb. 17, 2020.

  29. "Logarithmic extension of the Kazama-Suzuki coset model", (KST)2 Seminar on VOA [Online], Apr. 29, 2020.

  30. "Kazama-Suzuki coset vertex superalgebras at admissible levels", RIMS Workshop: Recent Advances in Combinatorial Representation Theory [Online], Oct. 5, 2020.

  31. "Kazama-Suzuki coset vertex superalgebras at admissible levels", Rocky Mountain Representation Theory Seminar [Online], Oct. 29, 2020.

  32. "On principal affine W-superalgebras for $\mathfrak{sl}(n|1)$", RIMS Workshop: Research on Finite Groups, Algebraic Combinatorics, and Vertex Algebras [Online], Dec. 7, 2020.

  33. "Simple Current Extensions and W-algebras", Prospects of Theory of Riemann Surfaces [Online], Dec. 13, 2020.

  34. "Feigin-Semikhatov Duality in W-superalgebras (Part II)", Algebraic Lie Theory and Representation Theory 2021 [Online], June 28, 2021.

  35. "Feigin-Semikhatov Duality in W-superalgebras", Representation Theory and Related Topics, Special Sessions in 2021 KMS Annual Meeting [Online], Oct. 21, 2021.

  36. "Feigin-Semikhatov Duality in W-superalgebras", QSMS Seminar, Center for Quantum Structures in Modules and Spaces [Online], Oct. 26 and 28, 2021.

  37. "Feigin-Semikhatov Duality in W-superalgebras", Kyoto Representation Theory Seminar [Online], Nov. 11, 2021.

  38. "Correlation functions in two-dimensional (super)conformal field theory", Prospects of Theory of Riemann Surfaces [Online], Dec. 12, 2021 (promised).

Education

  • Sep. 2017, Ph.D. in Mathematical Sciences, Graduate School of Mathematical Sciences, the University of Tokyo

Advisor: Hisayosi Matumoto and Yoshihisa Saito

  • Mar. 2014, Master of Mathematical Sciences, Graduate School of Mathematical Sciences, the University of Tokyo

Advisor: Yoshihisa Saito

  • Mar. 2012, Bachelor of Mathematical Sciences, the University of Tokyo