### Preprints

**Smooth Schubert varieties in the affine flag variety of type A.**

with W. Slofstra.

preprint. arXiv:1702.02236

### Publications

**Pattern avoidance and fiber bundle structures on Schubert varieties.**

with T. Alland

J. Combin. Theory Ser. A. Vol 154 (2018), 533-550. (arXiv:1610.03535)

Slides for a talk given at FPSAC, July 2017 in London, UK.

Other verisons: FPSAC 2017**Staircase diagrams and enumeration of smooth Schubert varieties.**

with W. Slofstra.

J. Combin. Theory Ser. A. Vol 150 (2017), 328-376. (arXiv:1510.06060)

Slides for a talk given at FPSAC, July 2016 in Vancouver, BC.

Other verisons: FPSAC 2016**Billey-Postnikov decompositions and the fibre bundle structure of Schubert varieties.**

with W. Slofstra.

Math. Ann. 366 (2016), no. 1-2, 31-55. (arXiv:1408.0084)

Slides for a talk given at the AMS Sectional Meeting, November 2014 in Greensboro, NC.**Littlewood-Richardson coefficients for reflection groups**

with A. Berenstein.

Advances in Math. Vol 284 (2015), 22, 54-111. (arXiv:1012.1714)

Slides for a talk given at the JMM, January 2012 in Boston, MA.**A combinatorial characterization of tight fusion frames.**

with M. Bownik and K. Luoto.

Pacific J. Math. Vol. 275 (2015), No. 2, 257–294. (arXiv:1112.3060)

Slides for a talk given at UC-Riverside, May 2012 in Riverside, CA.

**Rationally smooth elements of Coxeter groups and triangle group avoidance.**

with W. Slofstra.

J. Algebraic Combin. 30 (2014), no. 39, 659-681. (arXiv:1206.5746)

Slides for a talk given at the JMM, January 2013 in San Diego, CA.

**Eigenvalues of Hermitian matrices and equivariant cohomology of Grassmannians.**

with D. Anderson and A. Yong.

Compositio Math. vol 149 (2013), pp 1569-1582. (arXiv:1210.5003)

Slides for a talk given at Oklahoma State, January 2013 in Stillwater, OK.

**The Belkale-Kumar cup product and relative Lie algebra cohomology. (Appendix)**

with S. Evens and W. Graham.

Int. Math. Res. Not. 2013 (2013), 1901-1933. (arXiv:1104.1415)**A multiplicative formula for structure constants in the cohomology of flag varieties.**

Michigan Math. J. 61 (2012), no. 1, 3-17. (arXiv:0812.1856)**Branching Schubert calculus and the Belkale-Kumar product on cohomology**

with N. Ressayre.

Proc. Amer. Math. Soc. 139 (2011), no. 3, 835-848. (arXiv:0909.0865)**A partial Horn recursion in the cohomology of flag varieties.**

J. Algebraic Combin. 30 (2009), no. 1, 1-17. (math/0703462)

### Thesis

**Recursive structures in the cohomology of flag varieties**

under the direction of P. Belkale.

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