Teo Banica
Professeur de Mathematiques
Universite de Cergy-Pontoise
Bureau: St-Martin E-551
Tel: +331 34 25 75 38
Working on questions from quantum physics, here is my CV.
TD fonctions plusieures variables.
For hot AI stuff, scroll all the way down.
Books
I am currently writing several math and physics books:
2026
2025
2026
2025
2026
2026
2024
2024
2026
270may
230aug
230may
2026
2025
320jun
200apr
220sep
140sep
210sep
110sep
Quantum
2023
2024
2025
2025
350oct
310jun
220aug
200apr
2024
2026
2026
210sep
350oct
230jun
200oct
220jun
210aug
220feb
200jun
210feb
Physics
2025
240jul
220jul
210feb
220jan
230jan
120feb
100jan
200feb
200jan
110jan
110feb
100nov
120jan
100jan
100nov
100nov
100dec
100dec
120jan
Random
2026
2026
50sep
50apr
2026
50oct
140oct
50sep
50sep
240jun
50sep
50sep
210jun
130aug
50aug
50jul
140jul
50jul
50sep
50aug
Life
100dec
50jul
50jul
50may
100jan
50jul
50may
50may
50apr
50apr
50apr
110mar
140nov
60dec
50may
50jan
2026
120jun
60may
50jan
Music
Each of my series of books comes with its own soundtrack:
About
I started my book projects long ago. The aim of each book is to explain, informally, the essentials of the subject.
Here are log-files 00 (status), yc (colors), zk (music), not much but that's all I have, cats doing the rest.
You can bulk download the finished books here files.zip. 23 files, updated 10/26.
Here are some slides and video presentations, made back in 2020:
Introduction to linear algebra (2020)
Real matrices and their properties > 0:19
The determinant of real matrices > 0:19
Complex matrices and diagonalization > 0:19
Linear algebra and calculus questions > 0:19
Infinite matrices and spectral theory > 0:18
Special matrices and matrix tricks > 0:17
Introduction to matrix groups (2020)
Groups of unitary matrices > 0:15
Symmetry and reflection groups > 0:17
Symmetric groups and Poisson laws > 0:12
Complex reflections and Bessel laws > 0:17
Representations of compact groups > 0:19
Probability on compact groups > 0:16
Introduction to operator algebras (2020)
Hilbert spaces and operators > 0:09
Quantum algebra explained > 0:09
Spectral measures and beyond > 0:08
Introduction to quantum groups (2020)
Operator algebras and noncommutative spaces > 0:58
Compact and discrete quantum groups > 0:52
Haar measure and Peter-Weyl theory > 0:57
Tannakian duality, diagrams and easiness > 0:58
Quantum permutations and quantum reflections > 0:58
Orientability, toral subgroups and matrix models > 0:53
Introduction to noncommutative geometry (2020)
Noncommutative spheres and tori > 0:36
Quantum isometries and reflections > 0:37
Noncommutative algebraic geometry > 0:36
Basic noncommutative geometries > 0:34
Noncommutative integration theory > 0:35
Homogeneous spaces and easy manifolds > 0:37
Introduction to subfactor theory (2020)
Von Neumann algebras and factors > 0:19
Subfactors and the Temperley-Lieb algebra > 0:18
Group actions and fixed point subfactors > 0:18
Planar algebras and spectral measures > 0:19
Commuting squares, vertex and spin models > 0:17
Subfactors of small index and big index > 0:18
Introduction to free probability (2020)
The normal and Poisson laws > 0:45
Groups and Weingarten integration > 0:45
Operator algebras and free probability > 0:44
Classical and free limiting theorems > 0:42
Quantum algebra and free Bessel laws > 0:42
Wigner and Wishart random matrices > 0:42
Introduction to Hadamard matrices (2020)
The Hadamard conjecture > 0:27
Complex Hadamard matrices > 0:27
Deformed Hadamard matrices > 0:25
Bistochastic Hadamard matrices > 0:25
Papers
Here are my old research papers, mostly in quantum algebra:
1. On the polar decomposition of circular variables, Integral Equations Operator Theory 24 (1996), 372-377.
2. The representation theory of free orthogonal quantum groups, C. R. Acad. Sci. Paris Ser. I Math. 322 (1996), 241-244.
3. The free unitary compact quantum group, Comm. Math. Phys. 190 (1997), 143-172.
4. Hopf algebras and subfactors associated to vertex models, J. Funct. Anal. 159 (1998), 243-266.
5. Representations of compact quantum groups and subfactors, J. Reine Angew. Math. 509 (1999), 167-198.
6. Fusion rules for representations of compact quantum groups, Exposition. Math. 17 (1999), 313-337.
7. Symmetries of a generic coaction, Math. Ann. 314 (1999), 763-780.
8. Compact Kac algebras and commuting squares, J. Funct. Anal. 176 (2000), 80-99.
9. Subfactors associated to compact Kac algebras, Integral Equations Operator Theory 39 (2001), 1-14.
10. Quantum groups and Fuss-Catalan algebras, Comm. Math. Phys. 226 (2002), 221-232.
11. The planar algebra of a coaction, J. Operator Theory 53 (2005), 119-158.
12. Quantum automorphism groups of small metric spaces, Pacific J. Math. 219 (2005), 27-51.
13. Quantum automorphism groups of homogeneous graphs, J. Funct. Anal. 224 (2005), 243-280.
14. with S. Moroianu, On the structure of quantum permutation groups, Proc. Amer. Math. Soc. 135 (2007), 21-29.
15. with J. Bichon, Free product formulae for quantum permutation groups, J. Inst. Math. Jussieu 6 (2007), 381-414.
16. with B. Collins, Integration over compact quantum groups, Publ. Res. Inst. Math. Sci. 43 (2007), 277-302.
17. with J. Bichon, Quantum automorphism groups of vertex-transitive graphs of order ≤ 11, J. Algebraic Combin. 26 (2007), 83-105.
18. with D. Bisch, Spectral measures of small index principal graphs, Comm. Math. Phys. 269 (2007), 259-281.
19. with J. Bichon and G. Chenevier, Graphs having no quantum symmetry, Ann. Inst. Fourier 57 (2007), 955-971.
20. with B. Collins, Integration over quantum permutation groups, J. Funct. Anal. 242 (2007), 641-657.
21. with R. Nicoara, Quantum groups and Hadamard matrices, Panamer. Math. J. 17 (2007), 1-24.
22. with J. Bichon and B. Collins, Quantum permutation groups: a survey, Banach Center Publ. 78 (2007), 13-34.
23. with J. Bichon and B. Collins, The hyperoctahedral quantum group, J. Ramanujan Math. Soc. 22 (2007), 345-384.
24. with B. Collins, Integration over the Pauli quantum group, J. Geom. Phys. 58 (2008), 942-961.
25. A note on free quantum groups, Ann. Math. Blaise Pascal 15 (2008), 135-146.
26. with R. Vergnioux, Growth estimates for discrete quantum groups, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 12 (2009), 321-340.
27. with J. Bichon, Quantum groups acting on 4 points, J. Reine Angew. Math. 626 (2009), 74-114.
28. Cyclotomic expansion of exceptional spectral measures, Internat. J. Math. 20 (2009), 275-297.
29. with R. Vergnioux, Fusion rules for quantum reflection groups, J. Noncommut. Geom. 3 (2009), 327-359.
30. with R. Speicher, Liberation of orthogonal Lie groups, Adv. Math. 222 (2009), 1461-1501.
31. with B. Collins and P. Zinn-Justin, Spectral analysis of the free orthogonal matrix, Int. Math. Res. Not. 17 (2009), 3286-3309.
32. with J. Bichon and J.M. Schlenker, Representations of quantum permutation algebras, J. Funct. Anal. 257 (2009), 2864-2910.
33. with J. Bichon, Hopf images and inner faithful representations, Glasg. Math. J. 52 (2010), 677-703.
34. with B. Collins and J.M. Schlenker, On orthogonal matrices maximizing the 1-norm, Indiana Univ. Math. J. 59 (2010), 839-856.
35. with R. Vergnioux, Invariants of the half-liberated orthogonal group, Ann. Inst. Fourier 60 (2010), 2137-2164.
36. with D. Goswami, Quantum isometries and noncommutative spheres, Comm. Math. Phys. 298 (2010), 343-356.
37. with S. Curran and R. Speicher, Classification results for easy quantum groups, Pacific J. Math. 247 (2010), 1-26.
38. The orthogonal Weingarten formula in compact form, Lett. Math. Phys. 91 (2010), 105-118.
39. with S. Curran, Decomposition results for Gram matrix determinants, J. Math. Phys. 51 (2010), 1-14.
40. with S.T. Belinschi, M. Capitaine and B. Collins, Free Bessel laws, Canad. J. Math. 63 (2011), 3-37.
41. with S. Curran and R. Speicher, Stochastic aspects of easy quantum groups, Probab. Theory Related Fields 149 (2011), 435-462.
42. with B. Collins and J.M. Schlenker, On polynomial integrals over the orthogonal group, J. Combin. Theory Ser. A 118 (2011), 778-795.
43. with J. Bichon and S. Curran, Quantum automorphisms of twisted group algebras and free hypergeometric laws, Proc. Amer. Math. Soc. 139 (2011), 3961-3971.
44. with A. Skalski, Two-parameter families of quantum symmetry groups, J. Funct. Anal. 260 (2011), 3252-3282.
45. with J.M. Schlenker, Combinatorial aspects of orthogonal group integrals, Internat. J. Math. 22 (2011), 1611-1646.
46. with S. Curran and R. Speicher, De Finetti theorems for easy quantum groups, Ann. Probab. 40 (2012), 401-435.
47. with A. Skalski, Quantum isometry groups of duals of free powers of cyclic groups, Int. Math. Res. Not. 9 (2012), 2094-2122.
48. with J. Bichon and S. Natale, Finite quantum groups and quantum permutation groups, Adv. Math. 229 (2012), 3320-3338.
49. Quantum permutations, Hadamard matrices, and the search for matrix models, Banach Center Publ. 98 (2012), 11-42.
50. with A. Skalski and P.M. Soltan, Noncommutative homogeneous spaces: the matrix case, J. Geom. Phys. 62 (2012), 1451-1466.
51. with U. Franz and A. Skalski, Idempotent states and the inner linearity property, Bull. Pol. Acad. Sci. Math. 60 (2012), 123-132.
52. with J. Bhowmick and K. De Commer, Quantum isometries and group dual subgroups, Ann. Math. Blaise Pascal 19 (2012), 17-43.
53. with I. Nechita and K. Zyczkowski, Almost Hadamard matrices: general theory and examples, Open Syst. Inf. Dyn. 19 (2012), 1-26.
54. with I. Nechita, Asymptotic eigenvalue distributions of block-transposed Wishart matrices, J. Theoret. Probab. 26 (2013), 855-869.
55. with J. Bichon, B. Collins and S. Curran, A maximality result for orthogonal quantum groups, Comm. Algebra 41 (2013), 656-665.
56. with A. Skalski, Quantum symmetry groups of C*-algebras equipped with orthogonal filtrations, Proc. Lond. Math. Soc. 106 (2013), 980-1004.
57. The defect of generalized Fourier matrices, Linear Algebra Appl. 438 (2013), 3667-3688.
58. with I. Nechita, Almost Hadamard matrices: the case of arbitrary exponents, Discrete Appl. Math. 161 (2013), 2367-2379.
59. with I. Nechita and J.M. Schlenker, Analytic aspects of the circulant Hadamard conjecture, Ann. Math. Blaise Pascal 21 (2014), 25-59.
60. First order deformations of the Fourier matrix, J. Math. Phys. 55 (2014), 1-22.
61. with I. Nechita and J.M. Schlenker, Submatrices of Hadamard matrices: complementation results, Electron. J. Linear Algebra 27 (2014), 197-212.
62. Counting results for thin Butson matrices, Electron. J. Combin. 21 (2014), 1-14.
63. Truncation and duality results for Hopf image algebras, Bull. Pol. Acad. Sci. Math. 62 (2014), 161-179.
64. with I. Nechita, Block-modified Wishart matrices and free Poisson laws, Houston J. Math. 41 (2015), 113-134.
65. with A. Skalski, The quantum algebra of partial Hadamard matrices, Linear Algebra Appl. 469 (2015), 364-380.
66. with J. Bichon, Random walk questions for linear quantum groups, Int. Math. Res. Not. 24 (2015), 13406-13436.
67. The glow of Fourier matrices: universality and fluctuations, Oper. Matrices 9 (2015), 457-474.
68. Liberations and twists of real and complex spheres, J. Geom. Phys. 96 (2015), 1-25.
69. Quantum isometries of noncommutative polygonal spheres, Munster J. Math. 8 (2015), 253-284.
70. with S. Meszaros, Uniqueness results for noncommutative spheres and projective spaces, Illinois J. Math. 59 (2015), 219-233.
71. The algebraic structure of quantum partial isometries, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 19 (2016), 1-36.
72. A duality principle for noncommutative cubes and spheres, J. Noncommut. Geom. 10 (2016), 1043-1081.
73. Half-liberated manifolds, and their quantum isometries, Glasg. Math. J. 59 (2017), 463-492.
74. Liberation theory for noncommutative homogeneous spaces, Ann. Fac. Sci. Toulouse Math. 26 (2017), 127-156.
75. Quantum isometries, noncommutative spheres, and related integrals, Banach Center Publ. 111 (2017), 101-144.
76. with I. Nechita, Flat matrix models for quantum permutation groups, Adv. Appl. Math. 83 (2017), 24-46.
77. with I. Patri, Maximal torus theory for compact quantum groups, Illinois J. Math. 61 (2017), 151-170.
78. Deformed Fourier models with formal parameters, Studia Math. 239 (2017), 201-224.
79. Quantum groups from stationary matrix models, Colloq. Math. 148 (2017), 247-267.
80. Weingarten integration over noncommutative homogeneous spaces, Ann. Math. Blaise Pascal 24 (2017), 195-224.
81. with J. Bichon, Matrix models for noncommutative algebraic manifolds, J. Lond. Math. Soc. 95 (2017), 519-540.
82. with J. Bichon, Complex analogues of the half-classical geometry, Munster J. Math. 10 (2017), 457-483.
83. with A. Chirvasitu, Thoma type results for discrete quantum groups, Internat. J. Math. 28 (2017), 1-23.
84. The planar algebra of a fixed point subfactor, Ann. Math. Blaise Pascal 25 (2018), 247-264.
85. with I. Nechita, Almost Hadamard matrices with complex entries, Adv. Oper. Theory 3 (2018), 149-189.
86. with A. Freslon, Modelling questions for quantum permutations, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 21 (2018), 1-26.
87. Complex Hadamard matrices with noncommutative entries, Ann. Funct. Anal. 9 (2018), 354-368.
88. Super-easy quantum groups: definition and examples, Bull. Pol. Acad. Sci. Math. 66 (2018), 57-68.
89. with D. Ozteke and L. Pittau, Isolated partial Hadamard matrices, and related topics, Open Syst. Inf. Dyn. 25 (2018), 1-27.
90. Tannakian duality for affine homogeneous spaces, Canad. Math. Bull. 61 (2018), 483-494.
91. Unitary easy quantum groups: geometric aspects, J. Geom. Phys. 126 (2018), 127-147.
92. with A. Chirvasitu, Quasi-flat representations of uniform groups and quantum groups, J. Algebra Appl. 18 (2019), 1-27.
93. Higher transitive quantum groups: theory and models, Colloq. Math. 156 (2019), 1-14.
94. Quantum groups, from a functional analysis perspective, Adv. Oper. Theory 4 (2019), 164-196.
95. Higher orbitals of quizzy quantum group actions, Adv. Appl. Math. 109 (2019), 1-37.
96. Quantum groups under very strong axioms, Bull. Pol. Acad. Sci. Math. 67 (2019), 83-99.
97. Block-modified Wishart matrices: the easy case, Indiana Univ. Math. J. 69 (2020), 1-34.
98. Homogeneous quantum groups and their easiness level, Kyoto J. Math. 61 (2021), 171-205.
99. with J.P. McCarthy, The Frucht property in the quantum group setting, Glasg. Math. J. 64 (2022), 603-633.
Advanced
And here are my recent papers, quite often more advanced, code at github:
1. with Claude, On the maximality conjecture for quantum permutation groups (2026).
2. with GPT, Regular complex Hadamard matrices of order 7,8 (2026).
3. with Chat GPT, On Fourier and Hadamard matrices of prime order (2026).
Contact
teo.banica@gmail.com