Teo Banica

Professeur de Mathematiques
Universite de Cergy-Pontoise

Bureau: St-Martin E-521
Tel: +331 34 25 66 80

Research

I'm interested in mathematical physics, and more specifically in math input for quantum mechanics, and for astrophysics.
I've been working on this since 1994, and wrote about 100 papers. Here is my CV, and profile at Google Scholar.

Books

I am currently writing several math books. Here is a series on quantum groups:
  1. Free quantum groups and related topics
  2. Complex Hadamard matrices and applications
  3. Quantum isometries and noncommutative geometry
  4. Quantum permutations and quantum reflections
Here is another series, on operator algebras:
  1. Linear algebra and group theory
  2. Bounded operators and von Neumann algebras
  3. Methods of classical and free probability
  4. Matrix coordinates and projective geometry
And here is a series of slide books, on various topics:
  1. Linear algebra basics (2020)
  2. Lectures on quantum algebra (2020)

Index

Here is the detailed content of my "A series" of books:
  1. Free quantum groups and related topics
  2. Complex Hadamard matrices and applications
  3. Quantum isometries and noncommutative geometry
  4. Quantum permutations and quantum reflections
Here is the detailed content of my "B series" of books:
  1. Linear algebra and group theory
  2. Bounded operators and von Neumann algebras
  3. Methods of classical and free probability
  4. Matrix coordinates and projective geometry

Videos

Here are videos for my Linear algebra basics slide book:
  1. Introduction to linear algebra (2020)
  2. Introduction to matrix groups (2020)
Here are videos for my Lectures on quantum algebra slide book:
  1. Introduction to operator algebras (2020)
  2. Introduction to quantum groups (2020)
  3. Introduction to noncommutative geometry (2020)
  4. Introduction to subfactor theory (2020)
  5. Introduction to free probability (2020)
  6. Introduction to Hadamard matrices (2020)

Papers

And here are my scientific papers, listed according to their date of online publication:
  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. Representations of compact quantum groups and subfactors, J. Reine Angew. Math. 509 (1999), 167-198.
  5. Hopf algebras and subfactors associated to vertex models, J. Funct. Anal. 159 (1998), 243-266.
  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. Subfactors associated to compact Kac algebras, Integral Equations Operator Theory 39 (2001), 1-14.
  9. Compact Kac algebras and commuting squares, J. Funct. Anal. 176 (2000), 80-99.
  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 B. Collins, Integration over the Pauli quantum group, J. Geom. Phys. 58 (2008), 942-961.
  22. with R. Nicoara, Quantum groups and Hadamard matrices, Panamer. Math. J. 17 (2007), 1-24.
  23. with R. Vergnioux, Growth estimates for discrete quantum groups, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 12 (2009), 321-340.
  24. with J. Bichon and B. Collins, Quantum permutation groups: a survey, Banach Center Publ. 78 (2007), 13-34.
  25. with J. Bichon and B. Collins, The hyperoctahedral quantum group, J. Ramanujan Math. Soc. 22 (2007), 345-384.
  26. with J. Bichon, Quantum groups acting on 4 points, J. Reine Angew. Math. 626 (2009), 74-114.
  27. A note on free quantum groups, Ann. Math. Blaise Pascal 15 (2008), 135-146.
  28. with S.T. Belinschi, M. Capitaine and B. Collins, Free Bessel laws, Canad. J. Math. 63 (2011), 3-37.
  29. Cyclotomic expansion of exceptional spectral measures, Internat. J. Math. 20 (2009), 275-297.
  30. with R. Vergnioux, Fusion rules for quantum reflection groups, J. Noncommut. Geom. 3 (2009), 327-359.

  31. with J. Bichon, Hopf images and inner faithful representations, Glasg. Math. J. 52 (2010), 677-703.
  32. with R. Speicher, Liberation of orthogonal Lie groups, Adv. Math. 222 (2009), 1461-1501.
  33. with B. Collins and P. Zinn-Justin, Spectral analysis of the free orthogonal matrix, Int. Math. Res. Not. 17 (2009), 3286-3309.
  34. with J. Bichon and J.-M. Schlenker, Representations of quantum permutation algebras, J. Funct. Anal. 257 (2009), 2864-2910.
  35. with B. Collins and J.-M. Schlenker, On orthogonal matrices maximizing the 1-norm, Indiana Univ. Math. J. 59 (2010), 839-856.
  36. with R. Vergnioux, Invariants of the half-liberated orthogonal group, Ann. Inst. Fourier 60 (2010), 2137-2164.
  37. with D. Goswami, Quantum isometries and noncommutative spheres, Comm. Math. Phys. 298 (2010), 343-356.
  38. with S. Curran and R. Speicher, Classification results for easy quantum groups, Pacific J. Math. 247 (2010), 1-26.
  39. The orthogonal Weingarten formula in compact form, Lett. Math. Phys. 91 (2010), 105-118.
  40. with S. Curran and R. Speicher, De Finetti theorems for easy quantum groups, Ann. Probab. 40 (2012), 401-435.

  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. The planar algebra of a fixed point subfactor, Ann. Math. Blaise Pascal 25 (2018), 247-264.
  44. with J. Bichon and S. Curran, Quantum automorphisms of twisted group algebras and free hypergeometric laws, Proc. Amer. Math. Soc. 139 (2011), 3961-3971.
  45. with S. Curran, Decomposition results for Gram matrix determinants, J. Math. Phys. 51 (2010), 1-14.
  46. with A. Skalski, Two-parameter families of quantum symmetry groups, J. Funct. Anal. 260 (2011), 3252-3282.
  47. with J.-M. Schlenker, Combinatorial aspects of orthogonal group integrals, Internat. J. Math. 22 (2011), 1611-1646.
  48. with A. Skalski, Quantum isometry groups of duals of free powers of cyclic groups, Int. Math. Res. Not. 9 (2012), 2094-2122.
  49. with J. Bichon and S. Natale, Finite quantum groups and quantum permutation groups, Adv. Math. 229 (2012), 3320-3338.
  50. with I. Nechita, Asymptotic eigenvalue distributions of block-transposed Wishart matrices, J. Theoret. Probab. 26 (2013), 855-869.

  51. with J. Bichon, B. Collins and S. Curran, A maximality result for orthogonal quantum groups, Comm. Algebra 41 (2013), 656-665.
  52. Quantum permutations, Hadamard matrices, and the search for matrix models, Banach Center Publ. 98 (2012), 11-42.
  53. with A. Skalski and P.M. Soltan, Noncommutative homogeneous spaces: the matrix case, J. Geom. Phys. 62 (2012), 1451-1466.
  54. with A. Skalski, Quantum symmetry groups of C*-algebras equipped with orthogonal filtrations, Proc. Lond. Math. Soc. 106 (2013), 980-1004.
  55. with U. Franz and A. Skalski, Idempotent states and the inner linearity property, Bull. Pol. Acad. Sci. Math. 60 (2012), 123-132.
  56. with J. Bhowmick and K. De Commer, Quantum isometries and group dual subgroups, Ann. Math. Blaise Pascal 19 (2012), 17-43.
  57. with I. Nechita, Block-modified Wishart matrices and free Poisson laws, Houston J. Math. 41 (2015), 113-134.
  58. with I. Nechita and K. Zyczkowski, Almost Hadamard matrices: general theory and examples, Open Syst. Inf. Dyn. 19 (2012), 1-26.
  59. The defect of generalized Fourier matrices, Linear Algebra Appl. 438 (2013), 3667-3688.
  60. with I. Nechita, Almost Hadamard matrices: the case of arbitrary exponents, Discrete Appl. Math. 161 (2013), 2367-2379.

  61. with I. Nechita and J.-M. Schlenker, Analytic aspects of the circulant Hadamard conjecture, Ann. Math. Blaise Pascal 21 (2014), 25-59.
  62. First order deformations of the Fourier matrix, J. Math. Phys. 55 (2014), 1-22.
  63. with A. Skalski, The quantum algebra of partial Hadamard matrices, Linear Algebra Appl. 469 (2015), 364-380.
  64. with I. Nechita and J.-M. Schlenker, Submatrices of Hadamard matrices: complementation results, Electron. J. Linear Algebra 27 (2014), 197-212.
  65. Counting results for thin Butson matrices, Electron. J. Combin. 21 (2014), 1-14.
  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. Truncation and duality results for Hopf image algebras, Bull. Pol. Acad. Sci. Math. 62 (2014), 161-179.
  69. The algebraic structure of quantum partial isometries, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 19 (2016), 1-36.
  70. Liberations and twists of real and complex spheres, J. Geom. Phys. 96 (2015), 1-25.

  71. Quantum isometries of noncommutative polygonal spheres, Munster J. Math. 8 (2015), 253-284.
  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. with S. Meszaros, Uniqueness results for noncommutative spheres and projective spaces, Illinois J. Math. 59 (2015), 219-233.
  76. Quantum isometries, noncommutative spheres, and related integrals, Banach Center Publ. 111 (2017), 101-144.
  77. with I. Nechita, Flat matrix models for quantum permutation groups, Adv. Appl. Math. 83 (2017), 24-46.
  78. with I. Patri, Maximal torus theory for compact quantum groups, Illinois J. Math. 61 (2017), 151-170.
  79. Deformed Fourier models with formal parameters, Studia Math. 239 (2017), 201-224.
  80. Quantum groups from stationary matrix models, Colloq. Math. 148 (2017), 247-267.

  81. Weingarten integration over noncommutative homogeneous spaces, Ann. Math. Blaise Pascal 24 (2017), 195-224.
  82. with J. Bichon, Matrix models for noncommutative algebraic manifolds, J. Lond. Math. Soc. 95 (2017), 519-540.
  83. with I. Nechita, Almost Hadamard matrices with complex entries, Adv. Oper. Theory 3 (2018), 149-189.
  84. with J. Bichon, Complex analogues of the half-classical geometry, Munster J. Math. 10 (2017), 457-483.
  85. with A. Freslon, Modelling questions for quantum permutations, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 21 (2018), 1-26.
  86. with A. Chirvasitu, Thoma type results for discrete quantum groups, Internat. J. Math. 28 (2017), 1-23.
  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. with A. Chirvasitu, Quasi-flat representations of uniform groups and quantum groups, J. Algebra Appl. 18 (2019), 1-27.
  92. Unitary easy quantum groups: geometric aspects, J. Geom. Phys. 126 (2018), 127-147.
  93. Block-modified Wishart matrices: the easy case, Indiana Univ. Math. J. 69 (2020), 1-34.
  94. Higher transitive quantum groups: theory and models, Colloq. Math. 156 (2019), 1-14.
  95. Quantum groups, from a functional analysis perspective, Adv. Oper. Theory 4 (2019), 164-196.
  96. Homogeneous quantum groups and their easiness level, Kyoto J. Math. 61 (2021), 171-205.
  97. Higher orbitals of quizzy quantum group actions, Adv. Appl. Math. 109 (2019), 1-37.
  98. Quantum groups under very strong axioms, Bull. Pol. Acad. Sci. Math. 67 (2019), 83-99.
  99. with J.P. McCarthy, The Frucht property in the quantum group setting, Glasg. Math. J., to appear.

Contact

teo.banica@gmail.com