Edward Richmond

My mathematical research interests include algebraic geometry, combinatorics and representation theory of Lie groups.

Here is a brief techincal summary of my research (Updated September 2024)

1. Coxeter groups and Billey-Postnikov decompositions.
   with S. Oh.
   Preprint. (arXiv:2409.03096)
   
   
2. Enumerating Permutations Avoiding Split Patterns 3|12 and 23|1.
   with T. Grigsby.
   Preprint. (arXiv:2402.17654)
   
   
3. Nil-Hecke rings and the Schubert calculus.
   with K. Zainoulline.
   Preprint. (arXiv:2310.01167)
   
   
4. The parabolic coset structure of Bruhat intervals in Coxeter groups.
   with S. Oh.
   Preprint. (arXiv:2204.11959)
   
   
5. The isomorphism problem for Schubert varieties.
   with W. Slofstra.
   Preprint. (arXiv:2103.08114)
   
   

6. The isomorphism problem for cominuscule Schubert varieties.
   with M. Tarigradschi and W. Xu.
   Sel. Math. New Ser. 30, 38 (2024) (arXiv:2302.11642)
   Other verisons: FPSAC 2023
   
   
7. Demazure product of permutations and hopping.
   with T. Li, S. Oh, G. Yan and K. You
   Electron. J. Combin, Vol 31(1) (2024). (arXiv:2303.03618)
   
   
8. On the generating function for intervals in Young's lattice.
   with F. Azam.
   Electron. J. Combin, Vol 4(2) (2023). (arXiv:2107.09149)
   
   
9. An equivariant basis for the cohomology of Springer fibers.
   with M. Precup.
   Trans. Amer. Math. Soc., Series B, no. 8 (2021), 481-509. (arXiv:1912.08892)
   Slides for a talk given at AMS Sectional Meeting, March 2022 in Medford, MA.
   
   
10. Noncommutative LR coefficients and crystal reflection operators.
    with V. Tewari.
    Algebraic Combinatorics, Vol 4 (2021) no 1, 145-162. (arXiv:1905.10942)
    
    
11. The Nash blow-up of a cominuscule Schubert variety.
    with W. Slofstra and A. Woo.
    J. Algebra. Vol 559 (2020), 580-600. (arXiv:1808.05918)
    
    
12. Smooth Schubert varieties in the affine flag variety of type A.
    with W. Slofstra.
    European J. of Combin. Vol 71 (2018), 125-138. (arXiv:1702.02236)
    
    
13. 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
    
    
14. 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
    
    
15. 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.
    
    
16. 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.
    
    
17. 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.
    
    
18. 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.
    
    
19. 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.
    
    
20. 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)


21. A multiplicative formula for structure constants in the cohomology of flag varieties.
    Michigan Math. J. 61 (2012), no. 1, 3-17. (arXiv:0812.1856)


22. 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)


23. A partial Horn recursion in the cohomology of flag varieties.
    J. Algebraic Combin. 30 (2009), no. 1, 1-17. (math/0703462)

24. Recursive structures in the cohomology of flag varieties
    under the direction of P. Belkale.
    Click here to view.