Mahir Bilen Can

Office: Gibson 318 A
Office Hours: By appointment
Email: mahirbilencan at gmail dot com

I work on combinatorial algebraic geometry problems. My focus frequently shifts towards the theory of algebraic groups and algebraic monoids.

Preprints (see arXiv):

  • Toric Codes from Order Polytopes (joint with T. Hibi)
  • On the Fixed Points of a Regular Unipotent Element
  • On the Dual Canonical Monoids
  • The Betti Numbers of a Determinantal Variety
  • Complexity c Pairs in Simple Algebraic Groups
  • Adjoint Representations of the Symmetric Group (with Miles Jones)
  • Sphericality and Smoothness of Schubert Varieties (with Reuven Hodges)
  • Combinatorial Models for the Variety of Complete Quadrics (with Soumya Banerjee an Michael Joyce)
  • Equivariant K-theory of smooth projective spherical varieties (with Soumya Banerjee)

  • Published Articles:
    1. Strong Gelfand subgroups of \(F\wr S_n \) (with Liron Speyer and Yiyang She)
      International Journal of Mathematics (DOI:
    2. Diagonal Orbits in a Type A Double Flag Variety of Complexity One (with Tien Le).
      Order (DOI:
    3. Toroidal Schubert Varieties (with Reuven Hodges, Venkatramani Lakshmibai).
      Algebr. Represent. Theory 23 (2020), no. 5, 1927--1943.
    4. On the Borel Submonoid of a Symplectic Monoid (with Hayden Houser and Corey Wolfe).
      Advances in Applied Mathematics. 120 (2020)
    5. Sects (with Aram Bingham).
      Journal of Algebra. 560 (2020), 192--218.
    6. Stirling Posets (with Yonah Cherniavsky).
      Israel Journal of Mathematics. 237 (2020), no. 1, 185--219.
    7. Remarks on Enveloping Semigroups.
      Communications in Algebra 48 (2020), no. 5, 2092--2109.
    8. A Filtration on Equivariant Borel-Moore Homology (with Aram Bingham and Yıldıray Ozan).
      Forum Math. Sigma 7 (2019), e18.
    9. The rook monoid is lexicographically shellable.
      European Journal of Combinatorics, Volume 81, October 2019, 265--275.
    10. A Geometric Interpretation of the Intertwining Number (with Yonah Cherniavsky and Martin Rubey).
      Electronic Journal of Combinatorics, Volume 26, Issue 2 (2019) Article Number P2.7.
    11. The genesis of involutions, polarizations and lattice paths (with Özlem Uğurlu).
      Discrete Mathematics 342 (2019) 201--216.
    12. Classification of Reductive Monoid Spaces Over an Arbitrary Field.
      Advances in Algebra, 67--94, Springer Proc. Math. Stat., 277, Springer, Cham, 2019.
    13. Monoid embeddings of symmetric spaces (with Roger Howe and Lex Renner).
      Colloquium Mathematicum, Volume 157, no. 1, 2019.
    14. Loop-augmented forests and a variant of the Foulkes' conjecture (with Jeff Remmel).
      Algebraic Combinatorics, Volume 1 (2018) no. 5 p. 573--601
    15. Counting Borel Orbits in Symmetric Varieties of Types BI and CII (with Özlem Uğurlu).
      Arnold Mathematical Journal, 4 (2018), no. 2, 213--250.
    16. The cross section of a spherical double cone.
      Advances in Applied Mathematics. Volume 101, October 2018, Pages 215--231
    17. Wonderful symmetric varieties and Schubert polynomials (joint with Michael Joyce and Ben Wyser).
      Ars Mathematica Contemporanea. Vol 15, No 2 (2018)
    18. A representation on labeled rooted forests.
      Comm. Algebra 46 (2018), no. 10, 4273--4291.
    19. Complex G2 and associative grassmannian (with Selman Akbulut).
      Journal of Gökova Geometry Topology Volume 11 (2017) 56--79.
    20. Monodromy of torus fibrations and decomposability problem (with Mustafa Topkara).
      Topology and Its Applications 222 (2017), 165--176.
    21. An analogue of Springer fibers in certain wonderful compactifications (joint with Roger Howe and Michael Joyce).
      Journal of Algebra and Its Applications 16 (2017), no. 9.
    22. Corrigendum to ''Generators of the Hecke algebra of (S_2n,B_n)'' (with Şafak Özden).
      Adv. Math. 308 (2017), 1337--1339.
    23. Toroidal affine Nash groups.
      Journal of Lie Theory 26 (2016), no. 4, 1069--1077.
    24. Chains in weak order posets associated with involutions (with Michael Joyce and Ben Wyser).
      Journal of Combinatorial Theory Series A 137 (2016), 207--225.
    25. Divisors and specializations of Lucas polynomials (with Tewodros Amdeberhan and Melanie Jensen).
      Journal of Combinatorics 6 (2015) no 1-2, 69--89
    26. Lexicographic shellability of the Bruhat-Chevalley order on fixed point free involutions (with Yonah Cherniavsky and Tim Twelbeck)
      Israel Journal of Mathematics 207 (2015) no. 1.281--299.
    27. Omitting Parentheses from the Cyclic Notation (with Yonah Cherniavsky)
      Mediterranean Journal of Mathematics 12 (2015), no. 4, 1199--1214.
    28. Some plethystic identities and Kostka-Foulkes polynomials.
      Ars Combinatoria 122 (2015), 411--421.
    29. Bruhat order on partial fixed point free involutions. (with Yonah Cherniavsky and Tim Twelbeck)
      Electronic Journal of Combinatorics 21 (2014), no. 4, Paper 4.34, 23 pp.
    30. Branching through G2 (with Roger Howe)
      Proceedings of the Gökova Geometry-Topology Conference 2013, 41--75, Gökova Geometry/Topology Conference (GGT), Gökova, 2014.
    31. Calculating Heegaard-Floer homology by counting lattice points in tetrahedra (with Çağrı Karakurt)
      Acta Mathematica Hungarica 144 (2014), no. 1, 43--75.
    32. Lexicographic shellability of partial involutions (with Tim Twelbeck)
      Discrete Math. 335 (2014), 66--80.
    33. SL_2-regular subvarieties of complete quadrics (with Michael Joyce)
      Algebraic monoids, group embeddings, and algebraic combinatorics, 271--284, Fields Inst. Commun., 71, Springer, New York, 2014.
    34. Unipotent invariant matrices (with Roger Howe and Michael Joyce).
      Linear Algebra and its Applications, 439 (2013), no.1, 196--210.
    35. Weak order on complete quadrics (with Michael Joyce)
      Transactions of the American Mathematical Society 365 (2013), no. 12, 6269--6282.
    36. Ordered Bell Numbers, Hermite Polynomials, Skew Young Tableaux, and Borel Orbits (with Michael Joyce).
      Journal of Combinatorial Theory, Series A 119 (2012) 1798--1810.
    37. Bruhat-Chevalley Order on the Rook Monoid (with Lex Renner).
      Turkish Journal of Math. no. 36 (2012), 499--519.
    38. Irreducible representations of semisimple algebraic groups and supersolvable lattices.
      Journal of Algebra. 351 (2012), no. 1, 235--250.
    39. From Parking functions to Gelfand pairs (with K. Aker).
      Proceedings of AMS. 140 (2012), 1113--1124.
    40. Generators of the Hecke algebra of (S_2n,B_n) (with K. Aker).
      Advances in Math. 231 (2012), no. 5, 2465--2483.
    41. Broken Bracelets, Molien Series, Paraffin Wax and Elliptic Curve of Conductor 48 (with T. Amdeberhan and V.Moll).
      SIAM J. on Discrete Math. 25(4) (2011), pp. 1843--1859.
    42. Partitions, rooks, and symmetric functions in noncommuting variables (with Bruce Sagan).
      Electronic J. Combinatorics 18 (2011), no. 2, Paper 3.
    43. R-polynomials of finite monoids of Lie type (with K. Aker and M. Taskin).
      Internat. J. of Algebra and Computation, 20 (2010) no. 6, 793--805.
    44. H-polynomials and Rook Polynomials (with Lex Renner).
      Internat. J. of Algebra and Computation 18 (2008), no. 5, 935--949.
    45. Nested Hilbert schemes and the nested q,t-Catalan series.
      Discrete Mathematics and Theoretical Computer Science Proceedings (2008) 61--70.
    46. A proof of the q,t-square conjecture (with N. Loehr).
      Journal of Combinatorial Theory, Series A, 113 (2006), no. 7, 1419--1434.

    Books that I (co)edited:
  • Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics. Fields Institute Communications, Vol 71 (jointly edited with Zhenheng Li, Benjamin Steinberg, Qiang Wang).
  • Algebraic Groups: Structure and Actions. Proceedings of Symposia in Pure Mathematics series of the AMS. Volume 94.
  • Aram Bingham
  • Corey Wolfe
  • Hayden Houser
  • Yiyang She
  • Nestor Diaz Morera

  • Dejun Zhang (August 2020, MS)
  • Tien Le (May 2020, PhD)
  • Özlem Uğurlu (May 2018, PhD)
  • Tim Twelbeck (May 2013, PhD)

  • I am on the editorial board of Journal of Gökova Geometry Topology . This is a fully refereed electronic journal, specializing in articles in Geometry and Topology. Please submit your relevant papers to JGGT for rapid consideration.

  • Math 4120/6120, Abstract Algebra II (undergraduate and graduate level).