I am primarily interested in manifolds of non-negative and positive sectional curvature, especially those somehow involving Lie groups.
Here are my papers:
1. The classification of compact simply connected biquotients in dimension 4 and 5 (arXiv pdf) - Diff. Geom. Appl., Vol. 34 (2014), 128-138
2. The classification of compact simply connected biquotients in dimension 6 and 7 (arXiv pdf - Math. Ann. Vol. 368, Issue 3-4 (2017), 1493-1541)
3. The classification and curvature on biquotients of the form $Sp(3)//Sp(1)^2$ (Joint with undergrads Robert DeYeso III, Michael Ruddy, and Philip Wesner) (arXiv pdf) - Ann. Glob. Anal. Geo , Vol. 46 (2014), No. 4, 389-407
4. The classification of $SU(2)^2$ biquotients of rank $3$ Lie groups (Joint with undergrad Robert DeYeso III) (arXiv pdf - Topol. and Appl., Vol. 198 (2016), 86-100
5. Rationally $4$-periodic biquotients (arXiv pdf) (To appear in Geometriae Dedicata)
6. Quasi-positive curvature on a biquotient of $Sp(3)$ (Joint with undergrad Wesley Martin) ( arXiv pdf) - Involve, a Journal of Mathematics 11-5 (2018), 787-801. DOI 10.2140/involve.2018.11.787
7. Cohomogeneity one manifolds with singly generated rational cohomology ring (Joint with Lee Kennard) (In preparation)
8. Almost positive curvature on an irreducible compact symmetric space of rank 2 (Joint with undergrad Ezra Nance) ( arXiv pdf) (To appear in International Mathematics Research Notices)
- Due to IMRN copyright policies, the arXiv version will not be updated until a year after the article appears online.
9. Highly connected manifolds with singly generated rational cohomology ring (In preparation)
10. Low dimensional manifolds admitting a double disc bundle decomposition (Joint with Fernando Galaz-García and Martin Kerin) (In preparation)