# Sam Ballas

I am currently an an assistant professor in the Department of Mathematics at Florida State University.

Previously I was an RTG visiting assistant professor at UC Santa Barbara. Before that I was a graduate student at The University of Texas at Austin under the supervision of Alan Reid.

## Research

My research is primarily concerned with understanding various types of geometric structures on manifolds. Studying these structures typically involves the interplay of techniques from algebra, geometry, and topology.

My research is currently supported by the National Science Foundation (DMS-1709097)

### Papers

1. Generalized cusps in real projective manifolds: classification
joint with Daryl Cooper and Arielle Leitner, arXiv:1710.03132
2. Rank 1 deformations of non-compact hyperbolic lattices
joint with Julien Paupert and Pierre Will, arXiv:1702.00508
3. Convex projective bendings of hyperbolic manifolds
joint with Ludovic Marquis, arXiv:1609.03046
4. Convex projective structures on non-hyperbolic three-manifolds
joint with J. Danciger and G.-S. Lee, To appear in Geom. Topol.
5. Constructing thin subgroups commensurable with the figure-eight knot group
joint with Darren Long, Algebr. Geom. Topol. 15 (2015), no. 5, 3011–3024

### Work in progress

Copies may be available upon request

1. Generalized cusps in real projective manifolds: deformations
joint with Daryl Cooper and Arielle Leitner
2. Constructing convex projective 3-manifolds with generlized cusps
A Sage Notebooks containing some computations regarding the $$5_2$$ knot and the $$6_3$$ knot

## Teaching

### Current Courses

• Fall 2018: MAP2302 Oridinary Differential Equations

### Outreach

Math Fun Day 2017

• Wisdom of the masses: a talk about using probability to calculate $$\pi$$.

## Activities

### Upcoming Travel

1. Thin groups in Number Theory, Geometry and Topology
Darren Long 60th birthday conference
(Houston, TX 5/2018)
2. Representation varieties and geometric structures in low dimensions
(University of Warwick, 7/2018)

### Invited Talks

1. Convex projective structures on low dimensions
(University of Georgia, Topology Seminar, 4/9/2018)
2. Generalized Cusps in Convex Projective Manifolds (Slides,Video)
(GEAR Retreat, Stanford Univeristy, 8/7/2017)
3. Generalized Cusps in Convex Projective Manifolds
(Workshop on Dynamics on Character Varieties, University of Rennes I, 6/29/2017)
4. Rank 1 Deformations of Non-cocompact Hyperbolic Lattices
(University of Texas at Austin, Topology Seminar, 3/6/2017)
5. Geometric Structures on Manifolds
(UF/FSU Topology and Dynamics Meeting, University of Florida, 2/25/2017)

### Things I've Organized

1. GEAR Junior Retreat 2017
(Stanford University, 7/31-8/5/2017)

## Contact

321 Love Building