Education:
Ph.D., University of Maryland - College Park - 2012 (Mathematics)
B.A., Yale University - 2005 (Mathematics)
Areas of Expertise:
Professor Aulicino's research concerns the long-term behavior of a trajectory on the surface of a (rational) solid or a billiard trajectory in a (rational) polygon. It addresses these systems through the study of the geometry and dynamics of a space of related objects known as the moduli space of translation surfaces.
Books and Publications
D. Aulicino and Duc-Manh Nguyen, Rank 2 Affine Manifolds in Genus 3. J. Differential Geom. 116 (2020), no. 2, 205-280. (Books and Publications: Article (Peer-reviewed)) 2020
D. Aulicino, A new approach to the automorphism group of a Platonic surface. Rocky Mountain J. Math. 50 (2020), no. 1, 9-23. (Books and Publications: Article (Peer-reviewed)) 2020
D. Aulicino, and Chaya Norton, Shimura-Teichmüller Curves in Genus 5. J. Mod. Dyn. 16 (2020), 255-288. (Books and Publications: Article (Peer-reviewed)) 2020
Jayadev S. Athreya, David Aulicino, W. Patrick Hooper & with an appendix by Anja Randecker (2020) Platonic Solids and High Genus Covers of Lattice Surfaces, Experimental Mathematics, DOI: 10.1080/10586458.2020.1712564 (Books and Publications: Article (Peer-reviewed)) 2020
Jayadev S. Athreya and D. Aulicino, A Trajectory from a Vertex to Itself on the Dodecahedron. The American Mathematical Monthly, 126:2, 161-162 (2019). (Books and Publications: Article (Peer-reviewed)) 2019
D. Aulicino, Affine Invariant Submanifolds with Completely Degenerate Kontsevich-Zorich Spectrum. Ergodic Theory Dynam. Systems 38 (2018), no. 1, 10-33. (Books and Publications: Article (Peer-reviewed)) 2018
D. Aulicino, The Cantor-Bendixson Rank of Certain Bridgeland-Smith Stability Conditions. Comm. Math. Phys. 357 (2018), no. 2, 791-809. (Books and Publications: Article (Peer-reviewed)) 2018
D. Aulicino and Duc-Manh Nguyen, Rank two affine submanifolds in H(2,2) and H(3,1). Geom. Topol. 20 (2016), no. 5, 2837-2904. (Books and Publications: Article (Peer-reviewed)) 2016
D. Aulicino, Duc-Manh Nguyen, and Alex Wright, Classification of higher rank orbit closures in Hodd(4). J. Eur. Math. Soc. (JEMS) 18 (2016), no. 8, 1855-1872. (Books and Publications: Article (Peer-reviewed)) 2016
D. Aulicino, Affine Manifolds and Zero Lyapunov Exponents in Genus 3. Geometric and Functional Analysis 25 (2015), no. 5, 1333-1370. (Books and Publications: Article (Peer-reviewed)) 2015
D. Aulicino, Teichmüller Discs with Completely Degenerate Kontsevich-Zorich Spectrum. Commentarii Mathematici Helvetici 90 (2015), no. 3, 573-643. (Books and Publications: Article (Peer-reviewed)) 2015
Awards, Honors and Fellowships
NSF Standard Grant $120,000 July 2016 - June 2019 DMS - 1738381 (Originally DMS - 1600360) (Grants and Fellowships) 2016
NSF PostDoctoral Research Fellowship $150,000 September 2012 - August 2016 DMS - 1204414 (Grants and Fellowships) 2012
Conferences, Seminars and Symposiums
"Shimura-Teichmueller Curves in Genus 5." Geometry & Topology Seminar. Yale University. New Haven, CT, January 14. (Conferences, Seminars and Symposiums: Invited Talk) 2020
"Trajectories on the Platonic Solids." Geometry & Topology Seminar. Brown University. Providence, RI, March 6. (Conferences, Seminars and Symposiums: Invited Talk) 2019
"Saddle Connections on Meromorphic Differentials." Learning seminar on stability conditions. Mathematical Sciences Research Institute. Berkeley, CA, October 7. (Conferences, Seminars and Symposiums: Invited Talk) 2019
"Trajectories on the Platonic Solids." Graduate School on Geometry of Teichmuller Spaces. Simons Center. Stony Brook, New York, April 15. (Conferences, Seminars and Symposiums: Conference Presentation) 2019
