Yuki Arano

Teaching

京都大学
2017年度後期
解析学演義II(講読)
微分積分学演義(工T9,T12)

2018年度前期
解析学演義I
線形代数学演義A(農A4,A8)

2018年度後期
解析学入門演習
線形代数学演義B(農A4,A8)

2019年度前期
線形代数学演義A(工T5/T6)

2019年度後期
解析学演義II(演習)
線形代数学演義B(薬φ1/φ2)

2020年度前期
解析学演義I

2020年度後期
線形代数学演義B(工T18/T21)

2021年度前期
解析学演義I

2022年度前期
解析学演義I

2022年度後期
解析学入門演習

名古屋大学
2023年度前期
微分積分学I

指導学生：2022年度卒 基盤 1人、2023年度 博士1年 1人

Research

I am interested in operator algebras, mainly in quantum groups.

Papers

1. Maximalization of Quantum Group Equivariant Hilbert C*-modules, Master thesis
2. Unitary spherical representations of Drinfeld doubles, arXiv:1410.6238, Journal für die reine und angewandte Mathematik 742(2018), 157-186
3. (with Y. Kubota) A categorical perspective on the Atiyah-Segal completion theorem in KK-theory, arXiv:1508.06815, Journal of Noncommutative Geometry 12(2018) no. 2, 779-821
4. (with K. De Commer) Torsion-freeness for fusion rings and tensor C*-categories, arXiv:1511.07982, Journal of Noncommutative Geometry 13(2019) no.1, 35-58
5. (with Y. Kubota) Compact Lie group actions with continuous Rokhlin property , arXiv:1512.06333, Journal of Functional Analysis, 272(2017), no.2, 522-545
6. (with S. Vaes) C*-tensor categories and subfactors for totally disconnected groups, arXiv:1602.03047, Operator Algebras and Applications, The Abel Symposium 2015, Springer, 2016, 1-43.
7. Comparison of unitary duals of Drinfeld doubles and complex semisimple Lie groups, arXiv:1605.00866, Communications in Mathematical Physics, 351(2017), no.3, 1137-1147
8. (with T. de Laat and J. Wahl) Howe-Moore type theorems for quantum groups and rigid C*-tensor categories, arXiv:1605.08658, Compositio Mathematica, 154(2018), no.2, 328-341
9. (with T. de Laat and J. Wahl) The Fourier algebra of a rigid C*-tensor category, arXiv:1707.01778, Publication RIMS, 54(2018), no.2, 393-410
10. (with Y. Isono and A. Marrakchi) Ergodic theory of affine isometric actions on Hilbert spaces, arXiv:1911.04272, Geometric and Functional Analysis, 31(2021), 1013-1094,
11. (with A. Skalski) On the Baum--Connes conjecture for discrete quantum groups with torsion and the quantum Rosenberg Conjecture, arXiv:2008.12453, Proceedings of AMS, 149(2021), 5237-5254.

My Ph.D. thesis is Representation theory of Drinfeld doubles, which is based on 2. and 7.

Talks

1. Tannaka-Krein duality for compact quantum groups (after Woronowicz), Operator algebra seminar, Department of Mathematics, Ochanomizu university, August 2012.
2. On operator amenability of locally compact groups (after Ruan), 47th Functional analysis meeting, Sendai, August 2012.
3. On full group C*-algebras of discrete quantum groups, Operator algebra seminar, Graduate School of Mathematical Sciences, The University of Tokyo, May 2013.
4. On full group C*-algebras of discrete quantum groups, "Recent advances in operator algebras", RIMS, Kyoto university, September 2013.
5. Easy quantum groups (after Banica), 48th Functional analysis meeting, Kusatsu, September 2013.
6. Toward the classification of irreducible unitary spherical representations of the Drinfeld double of SUq(3), Operator algebra seminar, Graduate School of Mathematical Sciences, The University of Tokyo, June 2014.
7. Central property (T) for quantum groups, 49th Funcitonal analysis meeting, Gujo, August 2014.
8. Irreducible spherical unitary representations of the Drinfeld double of SU_q(3), Recent Developments in Operator Algebras, RIMS, September 2014.
9. Unitary spherical representations of Drinfeld doubles, Kansai Operator Algebra Seminars, Shirahama, November 2014.
10. Central property (T) for SUq(2n+1), Operator algebra seminar, Graduate School of Mathematical Sciences, the University of Tokyo, December 2014.
11. Unitary spherical representations of Drinfeld doubles, Operator algebra seminar, Kyushu University, December 2014.
12. Unitary spherical representations of Drinfeld doubles, 2015 East Asian Core Doctoral Forum, National Taiwan University, January 2015.
13. Central property (T) for discrete quantum groups, Seminar operator algebras, KU Leuven, February 2015.
14. Unitary spherical representations of Drinfeld doubles, TACT seminar, Vrije Universiteit Brussel, February 2015.
15. Unitary spherical representations of Drinfeld doubles, KOAS, Department of Mathematics, Kyoto University, March 2015.
16. Unitary spherical representations of Drinfeld doubles, Infinite analysis seminar, the University of Tokyo, May 2015.
17. Unitary spherical representations of Drinfeld doubles, Representation theory of groups, quantum groups, and operator algebras, University of Copenhagen, June 2015.
18. Diagrammatic method for representation theory of complex semisimple (quantum) groups (after Ghosh-Jones), 50th Functional analysis meeting, Karuizawa, September 2015.
19. Unitary spherical representations of Drinfeld doubles, Operator algebra seminar, the University of Glasgow, October 2015.
20. Unitary representations of Drinfeld doubles, Facets of quantum homogeneous spaces, Vrije Universiteit Brussel, December 2015.
21. Unitary representations of Drinfeld doubles, C*-algebra seminar, University of Oslo, February 2016.
22. Compact Lie group actions with continuous Rokhlin property, Operator algebra seminar, KU Leuven, June 2016.
23. Unitary representations of Drinfeld doubles, Séminaire d'Algèbres d'Opérateurs, Université Paris Diderot, June 2016.
24. Unitary representations of Drinfeld doubles, Workshop "Von Neumann Algebras", Hausdorff Research Institute for Mathematics, July 2016.
25. C*-tensor categories and subfactors for totally disconnected groups, Operator algebra seminar, Kyushu University, August 2016.
26. Torsion-freeness for fusion rings and tensor C*-categories, 51st Functional analysis meeting, Kusatsu, August 2016.
27. Representation theory of Drinfeld doubles, "Recent Developments in Operator Algebras", RIMS, September 2016.
28. C*-tensor categories and subfactors for totally disconnected groups, Operator algebra seminar, the University of Tokyo, October 2016.
29. Representation theory of Drinfeld doubles, Topological quantum groups and Hopf algebras, IMPAN, November 2016.
30. Torsion-freeness for fusion rings and tensor C*-categories, KOAS, RIMS, November 2016.
31. Representation theory of Drinfeld doubles, Langlands and Harmonic Analysis, Atami, March 2017.
32. Cohomology of quantum groups, KOAS, RIMS, April 2017.
33. Representation theory of Drinfeld doubles (4 lectures), Operator algebras: subfactors and their applications, Isaac Newton Institute, April-May 2017.
34. Compact Lie group actions with continuous Rokhlin property, Topological quantum groups and harmonic analysis, SNU, May 2017.
35. Rokhlin actions of fusion categories, Operator algebra seminar, the University of Tokyo, July 2017.
36. Rokhlin actions of tensor categories, Workshop on Operator theory and operator algebras, Ritsumeikan University, November 2017.
37. Rokhlin actions of tensor categories, Kansai operator algebra seminar, Osaka Kyoiku university, December 2017.
38. Rokhlin actions of tensor categories, Quantum homogeneous spaces, ICMS, June 2018.
39. Actions of tensor categories, Operator algebras and their applications, IPM, January 2019.
40. Introduction to complex quantum groups, Recent advances in tensor categories and operator algebras, RIMS, January 2019.
41. Actions of Tensor categories, MSJ Spring meeting(Invited talk), Tokyo Institute of Technology, March 2019.
42. UCT for discrete quantum groups, Mini-Workshop: Operator Algebraic Quantum Groups, Oberwolfach, October 2019.
43. Rokhlin actions of fusion categories, Subfactors and Applications, Oberwolfach, October 2019.
44. UCT for discrete quantum groups, Operator algebra seminar, SNU, November 2019.
45. Rokhlin actions of fusion categories, Korean Operator Algebra Seminar, Seoul, November 2019.
46. UCT for discrete quantum groups, Recent developments in operator algebras, RIMS, September 2020.
47. UCT for discrete quantum groups, Online quantum group seminar, November 2020.
48. Ergodic theory of affine isometric actions on Hilbert spaces, online, Wales MPPM seminar, May 2021.
49. Actions of C*-tensor categories on C*-algebras, Workshop on Operator theory and operator algebras, Kyushu, November 2021.
50. Tensor category equivariant KK-theory, Symmetry and amenability in operator algebras, RIMS, January 2022.
51. Representation theory of quantum doubles, Mathsci Freshman Seminar, Kyushu, February 2022.
52. Actions of tensor categories on C*-algebras, July 2022.
53. Actions of tensor categories on operator algebras, Colloquium, Nagoya university, May 2023.
54. Actions of tensor categories on C*-algebras, Quantum groups and interactions, Glasgow, May 2023.