## Mahir Bilen Can

## About me

## Research

My current research interests include (but not restricted to) 14MXX, 14PXX, 17BXX, 20CXX, 20MXX, 57RXX, as well as 05XX. See MSC2010 for descriptions of these encodings.

## Preprints and the coordinates of publications

(Most of these articles are available in some form at the public domain https://arxiv.org.)

- The genesis of involutions (polarizations and lattice paths) (with Özlem Uğurlu).

- Spherical product of a partial flag variety with a symmetric space.

- The cross section of a spherical double cone.

- Combinatorial models for the variety of complete quadrics (with Soumya D. Banerjee and Michael Joyce). Here is the previous version: pdf. (I am keeping the older version here because it contains some algorithms that might be useful for some purpose.)

- An analogue of Springer fibers in certain wonderful compactifications (joint with Roger Howe and Michael Joyce).

To appear inJournal of Algebra and Its Applications.

- Monodromy of torus fibrations and decomposability problem (with Mustafa Topkara).

To appear inTopology and Its Applications.

- Equivariant K-theory of smooth projective spherical varieties (with Soumya D. Banerjee).

- Complex G2 and associative grassmannian (with Selman Akbulut).

- Toroidal affine Nash groups.

Journal of Lie Theory 26 (2016), no. 4, 1069--1077.

- Wonderful symmetric varieties and Schubert polynomials (joint with Michael Joyce and Ben Wyser).

To appear inArs Mathematica Contemporanea.

- A remarkable representation on file placements.

- Chains in weak order posets associated with involutions (with Michael Joyce and Ben Wyser).

Journal of Combinatorial Theory Series A 137 (2016), 207--225.

- Special embeddings of symmetric spaces and their Borel orbits (with Roger Howe and Lex Renner).

- Corrigendum to ''Generators of the Hecke algebra of (S_2n,B_n)'' (with Şafak Özden).

To appear inAdvances in Mathematics.

- Divisors and specializations of Lucas polynomials (with Tewodros Amdeberhan and Melanie Jensen).

Journal of Combinatorics 6 (2015) no 1-2, 69--89

- 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.

- Branching through G2 (with Roger Howe)

Proceedings of the Gökova Geometry-Topology Conference 2013, 41--75, Gökova Geometry/Topology Conference (GGT), Gökova, 2014.

- Calculating Heegaard-Floer homology by counting lattice points in tetrahedra (with Çağrı Karakurt)

Acta Mathematica Hungarica 144 (2014), no. 1, 43--75.

- 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.

- Omitting Parentheses from the Cyclic Notation (with Yonah Cherniavsky)

Mediterranean Journal of Mathematics 12 (2015), no. 4, 1199--1214.

- Lexicographic shellability of partial involutions (with Tim Twelbeck)

Discrete Math. 335 (2014), 66--80.

- The Rook Monoid is Lexicographically Shellable. pdf

- 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.

- Some plethystic identities and Kostka-Foulkes polynomials.

Ars Combinatoria 122 (2015), 411--421.

- Unipotent invariant matrices (with Roger Howe and Michael Joyce).

Linear Algebra and its Applications, 439 (2013), no.1, 196--210.

- Weak order on complete quadrics (with Michael Joyce)

Transactions of the American Mathematical Society 365 (2013), no. 12, 6269--6282.

- Ordered Bell Numbers, Hermite Polynomials, Skew Young Tableaux, and Borel Orbits (with Michael Joyce).

Journal of Combinatorial Theory, Series A 119 (2012) 1798--1810.

- Bruhat-Chevalley Order on the Rook Monoid (with Lex Renner).

Turkish Journal of Math. no. 36 (2012), 499--519.

- Irreducible representations of semisimple algebraic groups and supersolvable lattices.

Journal of Algebra. 351 (2012), no. 1, 235--250.

- From Parking functions to Gelfand pairs (with K. Aker).

Proceedings of AMS. 140 (2012), 1113--1124.

- Generators of the Hecke algebra of (S_2n,B_n) (with K. Aker).

Advances in Math. 231 (2012), no. 5, 2465--2483.

- 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.

- Partitions, rooks, and symmetric functions in noncommuting variables} (with Bruce Sagan).

Electronic J. Combinatorics 18 (2011), no. 2, Paper 3.

- 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.

- H-polynomials and Rook Polynomials (with Lex Renner).

Internat. J. of Algebra and Computation 18 (2008), no. 5, 935--949.

- Nested Hilbert schemes and the nested q,t-Catalan series.

Discrete Mathematics and Theoretical Computer Science Proceedings (2008) 61--70.

- A proof of the q,t-square conjecture (with N. Loehr).

Journal of Combinatorial Theory, Series A, 113 (2006), no. 7, 1419--1434.

## Editorial

- Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics. Fields Institute Communications, Vol 71 (jointly edited with Zhenheng Li, Benjamin Steinberg, Qiang Wang).

- Clifford Lectures on Algebraic Groups. To appear in Proceedings of Symposia in Pure Mathematics series of the AMS.

## Notes on Lie algebras, problems and solutions.

## PhD advising

- Tim Twelbeck (graduated in 2013)
- Özlem Uğurlu (expected to graduate in 2018)
- Şafak Özden (expected to graduate in 2018)
- Tien Li (expected to graduate in 2019)
- Aram Bingham (expected to graduate in 2019)

## Some past conferences and meetings