Research 

LIST OF PUBLICATIONS     (*)=joint projects with undergraduates.

• You can square a cubic segment, (with Rathbun), in preparation.
• Upper bounds for the Hausdorff dimensions of Weierstrass curves (with Alexander), The PUMP Journal of Undergraduate Research, 5, (2022), 199-205 (*).
• 3-symmetric spaces, Ricci solitons and homogeneous structures, (with Nagy), in preparation.
• Quasi-Einstein metrics on sphere bundles ( with Huang and Phan),  Involve,  Vol. 15 (2022), No. 3, 507–514  (*).
• Rigidity  of SU(n)-type symmetric spaces (with Batat, Hall and Waldron), Int.  Math. Res. Not.,(2024) no 3, 2066-2098
• Bounding the invariant spectrum when the scalar curvature is non-negative ,  (with Hall),  Contemp. Math. (AMS), 756 (2020), 136-139.
• Compact Hermitian symmetric spaces, coadjoint orbits, and the dynamical stability of the Ricci flow, (with Hall and Waldron), J. Geom. Anal. 31, (2021), no. 6, 6195-6218.
•  Optimal Rectangle Packing for the 70 square , (with Laverty), Recreational Math. Mag., 5 (2019), no 9. 5-47 (*).
• Numerically destabilizing minimal discs , (with Brubaker and Negron), Exp. Math., 31 (2022), no 3, 794-805 (*). 
• Random manifolds have no totally geodesic submanifolds, (with Wilhelm), Michigan Math. J., 68 (2019), 323-335.
•  Destabilising compact warped product Einstein manifolds , (with Batat and Hall),  Comm. Anal. Geom. 29 (2021), no. 5, 1061-1094.
•  Complex Riemannian foliations of open Kaehler manifolds, (with Nagy), Trans. Amer. Math. Soc. 371 (2019), no. 7, 4895-4910.
•  Approximating Ricci solitons and quasi-Einstein metrics on toric surfaces , (with Hall), New York Jour. Math.,22 (2016) 615 -635.
• Bounding the first invariant eigenvalue of toric Kaehler manifolds  (with Hall),  Math. Res. Lett., 24 (2017), 67 -81.
•  Conformally Kaehler geometry and quasi-Einstein metrics , (with Batat, Jizany, and Hall), Muenster Jour. Math., 8 (2015), 211- 228.
• Numerical Approximations to extremal toric Kaehler metrics with arbitrary Kaehler class . (with Hall), Proc. Edinburgh Math. Soc., 60 (2017), 1-18.
• Rigidity results for Hermitian-Einstein manifolds, (with Hall), Math. Proc. Roy. Irish Acad., 116, No. 1 (2016), 35-44.
•  Bounding $\lambda_2$ for Kaehler-Einstein manifolds with large symmetry groups, (with Hall), Ann. Glob. Anal. Geom., 46 (2014), 145-158.
•  Riemannian foliations of projective space admitting complex leaves ,  Rend. Semin. Mat. Univ. Politec. Torino 70 (2012), no. 4, 449-461.
•  On the spectrum of the Page and Chen-LeBrun-Weber metrics, (with Hall), Ann. Glob. Anal. Geom., 46 No. 1 (2014) 87-101.
• Variations of complex structures and linear stability of Kaehler-Ricci solitons,  (with Hall), Pacific J. Math., 265 No. 2 (2013), 331-454.
•  Real hypersurfaces of complex and quaternionic hyperbolic spaces , Adv. Geom,  14 No. 1 (2014), 1-10.
• Curvature-adapted submanifolds of symmetric spaces , Indiana U. Math. J., 61 No.2 (2012), 831-847.
• Totally geodesic submanifolds of regular Sasakian manifolds, Osaka J. Math., 49 No.1 (2012), 125-132.
• On the linear stability of Kaehler-Ricci solitons, (with Hall), Proc Amer. Math. Soc., 139 No. 9 (2011), 3327- 3337.