Milen Yakimov

Publications

  1. The Poisson degeneracy locus of a flag variety, with E. Casbi and A. Masoomi, arXiv2401.04833.
  2. A Chinese remainder theorem and Carlson’s theorem for monoidal triangulated categories, with D. K. Nakano and K. B. Vashaw, arXiv:2311.17883.
  3. The lowest discriminant ideal of a Cayley-Hamilton Hopf algebra, with Z. Mi and Q. Wu, arXiv:2307.15477. 
  4. Reflective centers of module categories and quantum K-matrices, with R. Laugwitz and C. Walton, arXiv:2307.14764.

    1. Poisson geometry and Azumaya loci of cluster algebras, with G. Muller, B. Nguyen and K. Trampel, arXiv:2209.11622.
    2. A Burchnall-Chaundy-Krichever theory for fractional differential operators, with R. Casper, E. Horozov, and P. Iliev, arXiv:2108.12010.
    3. Root of unity quantum cluster algebras and discriminants, with B. Nguyen and K. Trampel, arXiv:2012.02314.
    4. On the spectrum and support theory of a finite tensor category, with D. K. Nakano and K. B. Vashaw, Math. Ann. doi:0.1007/s00208-023-02759-8, arXiv:2112.11170.
    5. Matrix valued discrete-continuous functions with the prolate spheroidal property and bispectrality, with W. R. Casper, F. A. Grünbaum, and I. Zurrián, Comm. Math. Phys. 405 (2024), Paper no. 69, 36pp., arXiv:2302.05750.
    6. Poisson trace orders, with K. A. Brown, Int. Math. Res. Not. IMRN 2024, no. 4, 2965-2998, arXiv:2211.11660.
    7. Reflective prolate-spheroidal operators and the adelic Grassmannian, with W. R. Casper, F. A. Grünbaum, and I. Zurrián, Comm. Pure Appl. Math. 76 (2023), no. 12, 3769-3810, arXiv:2003.11616.
    8. Cluster algebra structures on Poisson nilpotent algebras, with K. R. Goodearl, Memoirs Amer. Math. Soc. 290 (2023), no. 1445, v + 100pp., arXiv:1801.01963.
    9. Root of unity quantum cluster algebras and Cayley-Hamilton algebras, with S. Huang and T. T. Q. Lê, Trans. Amer. Math. Soc. 10 (2023), 6767-6798, arXiv:2107.11926.
    10. Poisson orders on large quantum groups, with N. Andruskiewitsch and I. Angiono, Adv. Math. 428 (2023), 109134, 66pp., arXiv:2008.11025.
    11. Algebras of commuting differential operators for integral kernels of Airy type, with W. R. Casper, F. A. Grünbaum, and I. Zurrián, in: Toeplitz Operators and Random Matrices, Harold Widom Memorial Volume, Operator Theory, Advances and Applications, vol. 289, eds. E. Basor et al, pp. 229–256, Birkhäuser, 2023, arXiv:2112.11639.
    12. Noncommutative tensor triangular geometry, with D. K. Nakano and K. B. Vashaw, Amer. J. Math. 144 (2022), no. 6, 1681-1724, arXiv:1909.04304.
    13. Green groupoids of 2-Calabi–Yau categories, derived Picard actions, and hyperplane arrangements, with P. Jørgensen, Trans. Amer. Math. Soc. 375 (2022), 7981-8031, arXiv:1910.05560.
    14. Noncommutative tensor triangular geometry and the tensor product property for support maps, with D. K. Nakano and K. B. Vashaw, Int. Math. Res. Not. IMRN, 2022, no. 22, 17766-17796, arXiv:2008.09924.
    15. The matrix Bochner problem, with W. R. Casper,  Amer. J. Math. 144 (2022), no.2, 1009-1065, arXiv:1803.04405.
    16. Poisson geometry and representations of PI 4-dimensional Sklyanin algebras, with C. Walton and X. Wang, Selecta Math. (N.S.) 27 (2021), no. 5, Art. 99, 60 pp., arXiv:1802.06487.
    17. Defining relations of quantum symmetric pair coideal subalgebras, with S. Kolb, Forum of Math. Sigma 9 (2021), Paper No. e67, 38pp., arXiv:2104.05625.
    18. Integral quantum cluster structures, with K. R. Goodearl, Duke Math. J. 170 (2021), 1137-1200, arXiv:2003.04434.
    19. Bivariate continuous q-Hermite polynomials and deformed quantum Serre relations, with W. R. Casper and S. Kolb, J. Algebra Appl. 20 (2021), no. 1, Art. 2140016 (issue in honor of N. Andruskiewitsch’s 60th birthday), arXiv:2002.07895.
    20. Integral operators, bispectrality and growth of Fourier algebras, with W. R. Casper, J. Reine Angew. Math. 766 (2020), 151-194, arXiv:1807.09314.
    21. The Berenstein-Zelevinsky quantum cluster algebra conjecture, with K. R. Goodearl, J. Eur. Math. Soc. (JEMS) 22 (2020), no. 8, 2453-2509, arXiv:1602.00498.
    22. Symmetric pairs for Nichols algebras of diagonal type via star products, with S. Kolb, Adv. Math. 365 (2020), 107042, 69pp., arXiv:1901.00490.
    23. C-vectors of 2-Calabi-Yau categories and Borel subalgebras of sl_infinity, with with P. Jørgensen, Selecta Math. (N.S.) 26 (2020), no. 1, Art. 1, 46 pp., arXiv:1710.06492.
    24. Reflective prolate-spheroidal operators and the KP/KdV equations, with W. R. Casper, F. A. Grünbaum, and I. Zurrián, Proc. Natl. Acad. Sci. USA 116 (2019), no. 37, 18310-18315, arXiv:1909.01448.
    25. Prime spectra of abelian 2-categories and categorifications of Richardson varieties, with K. Vashaw, in “Representations and Nilpotent Orbits of Lie Algebraic Systems, in honour of the 75th birthday of Tony Joseph,” Progr. in Math. vol. 330, eds. M. Gorelik et al, pp. 501-553, Birkhauser, 2019, arXiv:1802.00488.
    26. Poisson geometry of PI 3-dimensional Sklyanin algebras, with C. Walton and X. Wang, Proc. London Math Soc. 118 (2019), 1471-1500, arXiv:1704.04975.
    27. Prime factors of quantum Schubert cell algebras and clusters for quantum Richardson varieties, with T. H. Lenagan, J. Reine Angew. Math. 750 (2019), 123-156, arXiv:1503.06297.
    28. Azumaya loci and discriminant ideals of PI algebras, with K. A. Brown, Adv. Math. 340 (2018), 1219-1255, arXiv:1702.04305.
    29. Quantized Weyl algebras at roots of unity, with J. Levitt, Israel J. Math. 225 (2018), 681-719, arXiv:1606.02121.
    30. Recovering the topology of surfaces from cluster algebras, with E. Bucher, Math. Zeit. 288 (2018), 565-594, arXiv:1607.02131.
    31. Rigidity of quadratic Poisson tori, with J. Levitt, Bull. Inst. Math. Acad. Sinica 13 (2018), 99-142, (issue in honor of G. Lusztig’s 70th birthday), arXiv:1609.06770.
    32. Twist invariants of graded algebras, with K. R. Goodearl, in: Advances in Rings and Modules (volume in honor of B. Muller), Contemp. Math. 715 (2018), pp. 141–170, arXiv:1706.06957.
    33. Noncommutative discriminants via Poisson primes, with B. Nguyen and K. Trampel, Adv. Math. 322 (2017), 269-307, arXiv:1603.02585.
    34. Noncommutative bispectral Darboux transformations, with J. Geiger and E. Horozov, Trans. Amer. Math. Soc. 369 (2017), 5889-5919, arXiv:1508.07879.
    35. Quantum cluster algebra structures on quantum nilpotent algebras, with K. R. Goodearl, Memoirs Amer. Math. Soc. 247 (2017), no. 1169, vii + 119pp., arXiv:1309.7869.
    36. Separating Ore sets for prime ideals of quantum algebras, with S. Fryer, Bulletin London Math. Soc. 46 (2017), 202–215, arXiv:1602.05052.
    37. From quantum Ore extensions to quantum tori via noncommutative UFDs, with K. R. Goodearl, Adv. Math. 300 (2016), 672-716, arXiv:1208.6267. 
    38. Unipotent and Nakayama automorphisms of quantum nilpotent algebras, with K. R. Goodearl, in: Commutative Algebra and Noncommutative Algebraic Geometry II, eds: D. Eisenbud et al, pp 181-212, MSRI Publ. Vol 68, Cambridge Univ. Press, 2015, arXiv:1311.0278.
    39. Weak splittings of quotients of Drinfeld and Heisenberg doubles, In: Developments and retrospectives in Lie theory, geometric and analytic methods, eds: G. Mason et al, pp. 245–268, Developments in Math 37, Springer 2014, arXiv:1402.0883 .
    40. Quantum cluster algebras and quantum nipotent algebras, with K. R. Goodearl, Proc. Natl. Acad. Sci. USA 111 (2014), no. 27, 9696-9703, arXiv:1508.03086.
    41. Rigidity of quantum tori and the Andruskiewitsch-Dumas conjecture, Selecta Math. 20 (2014), no. 2, 421–464, arXiv:1204.3218.
    42. On the spectra of quantum groups, Memoirs Amer. Math. Soc. 229 (2014), no. 1078, vi + 91pp., arXiv:1106.3821.
    43. Quantum Schubert cells via representation theory and ring theory, with J. Geiger, Michigan Math. J. 63, (2014), no. 1, 125-157, arXiv:1203.3780.
    44. Spectra and catenarity of multiparameter quantum Schubert cells, Glasgow Math. J. 55A (2013), 169-194, (issue in honor of K. A. Brown’s and J. T. Stafford’s 60th birthdays), arXiv:1112.2235.
    45. The Launois-Lenagan conjecture, J. Algebra 392 (2013), 1-9, arXiv:1204.5440.
    46. Cominuscule parabolics of simple finite dimensional Lie superalgebras, with D. Grantcharov, J. Pure Appl. Algebra 217 (2013), 1844-1863, arXiv:1201.0199. 
    47. A proof of the Goodearl-Lenagan polynormality conjecture, Int. Math. Res. Not. IMRN 2013, no. 9, 2097–2132, arXiv:1109.3065.
    48. Strata of prime ideals of De Concini-Kac-Procesi algebras and Poisson geometry, in: New trends in noncommutative algebra (in honor of K. R. Goodearl’s 65th birthday), Contemp. Math. 562, pp. 265-278, Amer. Math. Soc., Providence, RI, 2012, arXiv:1103.3451.
    49. Invariant prime ideals in quantizations of nilpotent Lie algebras, Proc. London Math. Soc., 101 (2010), 454-476, arXiv:0905.0852.
    50. A classification of H-primes of quantum partial flag varieties, Proc. Amer. Math. Soc. 138 (2010), 1249-1261, arXiv:0910.0997.
    51. Cyclicity of Lusztig’s stratification of Grassmannians and Poisson geometry, in: Noncommutative structures in mathematics and physics, eds: S. Caenepeel et al, pp. 258–262, Royal Flemish Acad. of Belgium for Sciences and Arts, 2010, arXiv:0902.2181.
    52. Completeness of determinantal Hamiltonian flows on the matrix affine Poisson space, with M. Gekhtman, Lett. Math. Phys. 90 (2009), 161-173, arXiv:0809.4650.
    53. Poisson structures on affine spaces and flag varieties. II. General case, with K. R. Goodearl, Trans. Amer. Math. Soc. 361 (2009), 5753-5780, arXiv:math/0509075.
    54. Group orbits and regular partitions of Poisson manifolds, with J.-H. Lu, Comm. Math. Phys. 283 (2008), no. 3, 729-748, arXiv:math/0609732.
    55. Categories of modules over an affine Kac-Moody algebra and finiteness of the Kazhdan-Lusztig tensor product, J. Algebra 319 (2008), no. 8, 3175-3196, arXiv:math/0210180.
    56. A Deodhar type stratification on the double flag variety, with B. Webster, Transform. Groups 12 (2007), no. 4, 769-785, arXiv:math/0607374 .
    57. Partitions of the wonderful group compactification, with J.-H. Lu, Transform. Groups 12 (2007), no. 4, 695-723, arXiv:math/0606579.
    58. Modular classes of regular twisted Poisson structures on Lie algebroids, with Y. Kosmann-Schwarzbach, Lett. Math. Phys. 80 (2007), 183-197, arXiv:math/0701209.
    59. Affine Jacquet functors and Harish-Chandra categories, Adv. Math. 208 (2007), 40-74, arXiv:math/0302269.
    60. Poisson structures on affine spaces and flag varieties. I. Matrix affine Poisson space, with K. A. Brown and K. R. Goodearl, Adv. Math. 206 (2006), 567-629, arXiv:math/0501109.
    61. Triangular Poisson structures on Lie groups and symplectic reduction, with T. J. Hodges, in: Noncommutative geometry and representation theory in mathematical physics, Contemp. Math. 391, pp. 123-134, arXiv:math/0412082.
    62. On a class of double cosets in reductive algebraic groups, with J.-H. Lu, Int. Math. Res. Not. IMRN 2005, no. 13, 761-797, arXiv:math/0410006 .
    63. The prolate spheroidal phenomenon as a consequence of bispectrality, with F. A. Grünbaum, In: Workshop on superintegrability, CRM Proc. Lect. Notes 37, pp. 301-312, AMS 2004, arXiv:math-ph/0303041.
    64. Discrete Darboux transformations from Jacobi polynomials, with F. A. Grünbaum, Pacific J. Math. 204 (2002), 395-432, arXiv:math/0012191.
    65. Symplectic leaves of complex reductive Poisson-Lie groups, Duke Math. J. 112 (2002), 453-509, arXiv:math/0004102 .
    66. Quantum invariant measures, with N. Yu. Reshetikhin, Comm. Math. Phys. 224 (2001), 399-426, arXiv:math/0101048 .
    67. The double and dual of a quasitriangular Lie bialgebra, with T. J. Hodges, Math. Res. Lett. 8 (2001), 91-105, arXiv:math/0008086.
    68. Deformation quantization of Lagrangian fiber bundles, with N. Yu. Reshetikhin, In: Conference Moshé Flato 1999, vol. 2, pp. 269-288, Kluwer Acad. Publ. 2000, arXiv:math/9907164.
    69. Highest weight modules over the W1+∞ algebra and the bispectral problem, with B. Bakalov and E. Horozov, Duke Math. J. 93 (1998), no. 1, 41-72, arXiv:q-alg/9602012.
    70. Automorphisms of the Weyl algebra and bispectral operators, with B. Bakalov and E. Horozov, in: The bispectral problem, CRM Proc. Lecture Notes, pp. 3-10, AMS 1998, arXiv:q-alg/9707018. 
    71. Bispectral algebras of commuting ordinary differential operators, with B. Bakalov and E. Horozov, Comm. Math. Phys. 190 (1997), no. 2, 331-373, arXiv:q-alg/9602011.
    72. Highest weight modules of W1+∞ , Darboux transformations and the bispectral problem, with B. Bakalov and E. Horozov, Serdica Math. J. 23 (1997), 95-112, arXiv:q-alg/9601017.
    73. General methods for constructing bispectral operators, with B. Bakalov and E. Horozov, Phys. Lett. A 222 (1996), no. 1-2, 59-66, arXiv:q-alg/9605011.
    74. Tau-functions as highest weight vectors for the W1+∞  algebra, with B. Bakalov and E. Horozov, J. Phys. A 29 (1996), 5565-5573, arXiv:hep-th/9510211.
    75. Bäcklund-Darboux transformations in Sato’s Grassmannian, with B. Bakalov and E. Horozov, Serdica Math. J. 22 (1996) 571-586, arXiv:q-alg/9602010.

    Edited Proceedings:

    1. (with A. Alexeev, E. Frenkel, M. Rosso and B. Webster) Representation Theory, Mathematical Physics and Integrable Systems,
      in honor of Nicolai Reshetikhin, Progress in Math. 340, Birkhäuser, 2022.

    2. (with P. Achar, D. Jakelic and K. Misra) Recent advances in representation theory, quantum groups, algebraic geometry,
    and related topics, Contemp. Math. 623, AMS, Providence, RI, 2014.

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