I work on combinatorial algebraic geometry problems. My focus frequently shifts towards the theory of algebraic groups and algebraic monoids.
Preprints (see arXiv):
Published Articles:

Strong Gelfand subgroups of \(F\wr S_n \) (with Liron Speyer and Yiyang She)
International Journal of Mathematics (DOI: https://doi.org/10.1142/S0129167X21500105) 
Diagonal Orbits in a Type A Double Flag Variety of Complexity One (with Tien Le).
Order (DOI: https://doi.org/10.1007/s11083020095307) 
Toroidal Schubert Varieties (with Reuven Hodges, Venkatramani Lakshmibai).
Algebr. Represent. Theory 23 (2020), no. 5, 19271943. 
On the Borel Submonoid of a Symplectic Monoid (with Hayden Houser and Corey Wolfe).
Advances in Applied Mathematics. 120 (2020) 
Sects (with Aram Bingham).
Journal of Algebra. 560 (2020), 192218. 
Stirling Posets (with Yonah Cherniavsky).
Israel Journal of Mathematics. 237 (2020), no. 1, 185219. 
Remarks on Enveloping Semigroups.
Communications in Algebra 48 (2020), no. 5, 20922109. 
A Filtration on Equivariant BorelMoore Homology (with Aram Bingham and Yıldıray Ozan).
Forum Math. Sigma 7 (2019), e18. 
The rook monoid is lexicographically shellable.
European Journal of Combinatorics, Volume 81, October 2019, 265275. 
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. 
The genesis of involutions, polarizations and lattice paths (with Özlem Uğurlu).
Discrete Mathematics 342 (2019) 201216. 
Classification of Reductive Monoid Spaces Over an Arbitrary Field.
Advances in Algebra, 6794, Springer Proc. Math. Stat., 277, Springer, Cham, 2019. 
Monoid embeddings of symmetric spaces (with Roger Howe and Lex Renner).
Colloquium Mathematicum, Volume 157, no. 1, 2019. 
Loopaugmented forests and a variant of the Foulkes' conjecture (with Jeff Remmel).
Algebraic Combinatorics, Volume 1 (2018) no. 5 p. 573601 
Counting Borel Orbits in Symmetric Varieties of Types BI and CII
(with Özlem Uğurlu).
Arnold Mathematical Journal, 4 (2018), no. 2, 213250. 
The cross section of a spherical double cone.
Advances in Applied Mathematics. Volume 101, October 2018, Pages 215231 
Wonderful symmetric varieties and Schubert polynomials (joint with Michael Joyce and Ben Wyser).
Ars Mathematica Contemporanea. Vol 15, No 2 (2018) 
A representation on labeled rooted forests.
Comm. Algebra 46 (2018), no. 10, 42734291. 
Complex G2 and associative grassmannian (with Selman Akbulut).
Journal of Gökova Geometry Topology Volume 11 (2017) 5679. 
Monodromy of torus fibrations and decomposability problem (with Mustafa Topkara).
Topology and Its Applications 222 (2017), 165176. 
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. 
Corrigendum to ''Generators of the Hecke algebra of (S_2n,B_n)'' (with Şafak Özden).
Adv. Math. 308 (2017), 13371339. 
Toroidal affine Nash groups.
Journal of Lie Theory 26 (2016), no. 4, 10691077. 
Chains in weak order posets associated with involutions (with Michael Joyce and Ben Wyser).
Journal of Combinatorial Theory Series A 137 (2016), 207225. 
Divisors and specializations of Lucas polynomials (with Tewodros Amdeberhan and Melanie Jensen).
Journal of Combinatorics 6 (2015) no 12, 6989 
Lexicographic shellability of the BruhatChevalley order on fixed point free involutions (with Yonah Cherniavsky and Tim Twelbeck)
Israel Journal of Mathematics 207 (2015) no. 1.281299. 
Omitting Parentheses from the Cyclic Notation (with Yonah Cherniavsky)
Mediterranean Journal of Mathematics 12 (2015), no. 4, 11991214. 
Some plethystic identities and KostkaFoulkes polynomials.
Ars Combinatoria 122 (2015), 411421. 
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 GeometryTopology Conference 2013, 4175, Gökova Geometry/Topology Conference (GGT), Gökova, 2014. 
Calculating HeegaardFloer homology by counting lattice points in tetrahedra (with Çağrı Karakurt)
Acta Mathematica Hungarica 144 (2014), no. 1, 4375. 
Lexicographic shellability of partial involutions (with Tim Twelbeck)
Discrete Math. 335 (2014), 6680. 
SL_2regular subvarieties of complete quadrics (with Michael Joyce)
Algebraic monoids, group embeddings, and algebraic combinatorics, 271284, Fields Inst. Commun., 71, Springer, New York, 2014. 
Unipotent invariant matrices (with Roger Howe and Michael Joyce).
Linear Algebra and its Applications, 439 (2013), no.1, 196210. 
Weak order on complete quadrics (with Michael Joyce)
Transactions of the American Mathematical Society 365 (2013), no. 12, 62696282. 
Ordered Bell Numbers, Hermite Polynomials, Skew Young Tableaux, and Borel Orbits (with Michael Joyce).
Journal of Combinatorial Theory, Series A 119 (2012) 17981810. 
BruhatChevalley Order on the Rook Monoid (with Lex Renner).
Turkish Journal of Math. no. 36 (2012), 499519. 
Irreducible representations of semisimple algebraic groups and supersolvable lattices.
Journal of Algebra. 351 (2012), no. 1, 235250. 
From Parking functions to Gelfand pairs (with K. Aker).
Proceedings of AMS. 140 (2012), 11131124. 
Generators of the Hecke algebra of (S_2n,B_n) (with K. Aker).
Advances in Math. 231 (2012), no. 5, 24652483. 
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. 18431859. 
Partitions, rooks, and symmetric functions in noncommuting variables (with Bruce Sagan).
Electronic J. Combinatorics 18 (2011), no. 2, Paper 3. 
Rpolynomials of finite monoids of Lie type (with K. Aker and M. Taskin).
Internat. J. of Algebra and Computation, 20 (2010) no. 6, 793805. 
Hpolynomials and Rook Polynomials (with Lex Renner).
Internat. J. of Algebra and Computation 18 (2008), no. 5, 935949. 
Nested Hilbert schemes and the nested q,tCatalan series.
Discrete Mathematics and Theoretical Computer Science Proceedings (2008) 6170. 
A proof of the q,tsquare conjecture (with N. Loehr).
Journal of Combinatorial Theory, Series A, 113 (2006), no. 7, 14191434.