Sam Ballas

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About me

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.

If you want to learn more about my research check out my short Research Statement or CV. You may also be interested in this artice featuring my research written for school aged children. This article was produced by Futurum, a magazine and online platform aimed at inspiring young people to follow a career in the sciences, research and technology.

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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 (grant DMS-1709097)


  1. The moduli space of marked generalized cusps in real projective manifolds
    joint with Daryl Cooper and Arielle Leitner, arXiv:2008.09553
  2. Gluing equations for real projective structures on 3-manifolds
    joint with Alex Casella, arXiv:1912.12508
  3. Thin subgroups isomorphic to Gromov--Piatetski-Shapiro lattices
    Pacific J. Math. 309 (2020), no 2, 257--266.
  4. Constructing thin subgroups of SL(n+1,R) via bending
    joint with Darren Long, Algebr. Geom. Topol. 20-4 (2020), 2071--2093
  5. Constructing convex projective 3-manifolds with generalized cusps
    to appear in J. London Math. Soc.
    Supplemental Sage notebooks related to this work can be found here

Work in progress

Copies may be available upon request

  1. Properly convex Dehn filling
    joint with Jeff Danciger, Gye-Seon Lee, and Ludovic Marquis
  2. Complex projective structures on thrice punctured spheres
    joint with Phil Bowers, Alex Casella, and Lorenzo Ruffoni
  3. Neumann-Zagier relations for projective gluing equations
    joint with Alex Casella


  1. A Geometric Description of (P)SL(4,R) Hitchin Representations
    notes from workshop on higher teichmuller theory


Current Courses

Older Courses

Ireland Sunrise


Math Fun Day

  • Wisdom of the masses: a talk about using probability to calculate \(\pi\).
    (Fall 2017)
  • Measuring lengths with the Steinhaus Longimeter
    (Spring 2020)

Soccer Analytics

Recently I helped the analytics team for the FSU Women's Soccer Team. I was able to use projective geometry to help them turn 2D shot data into 3D shot charts.

Together, we were able to turn pictures like these...

...into 3D shot charts like these.

Abby and Eli Math Fun Day


Upcoming Travel

    Travel currently suspended due to COVID-19

Invited Talks

  1. Triangulations in low dimensional geometry
    (Cal Poly, Colloquium, 2/19/2021)
  2. Gluing equations in low dimensional geometry (Slides)
    (Oklahoma State Topology Seminar, 11/4/2020)
  3. Gluing equations for projective structures on 3-manifolds (Slides, Video)
    (Trends in Low Dimensional Topology, Online Seminar, 6/23/2020)
  4. Gluing equations for projective structures on 3-manifolds
    Cancelled due to COVID-19
    (Oklahoma State Topology Seminar, 4/13/2020)
  5. Gluing equations for projective structures on 3-manifolds
    Cancelled due to COVID-19
    AMS Sectional Meeting, Charlottesville, VA 3/14/2020)

Things I'm Organizing/Have Organized

  1. AMS Sectional Meeting
    on Geometric Structures on Manifolds
    (University of Florida, 11/2-11/3/2019)
  2. UF/FSU Topology and Geometry Meeting
    (Florida State University, 2/8-2/9/2019)
  3. GEAR Junior Retreat 2017
    (Stanford University, 7/31-8/5/2017)

Topology and Geometry Seminar

I will be organizing the Topology and Geometry Seminar this semester.

Unless otherwise noted below, our meetings this semester will take place this on Tuesdays at 3:05 and our meetings will take place at the following this Zoom link. The password for our meetings is the name of the only knot with crossing number 3.

The schedule can be found below. Please contact me if you are interested in giving a talk.

Palace Korea

Castle Heidelberg Little Eli


321 Love Building
1017 Academic Way
Tallahassee, FL 32306-4510
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