Sam Ballas

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About me

I am currently an an associate 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. Tame and relatively elliptic CP1-structures on the thrice-punctured sphere
    joint with Phil Bowers, Alex Casella and Lorenzo Ruffoni, arXiv:2107.06370
  2. The moduli space of marked generalized cusps in real projective manifolds
    joint with Daryl Cooper and Arielle Leitner, Conf. Geom. & Dyn. vol 26 (2022) 111-164
  3. Gluing equations for real projective structures on 3-manifolds
    joint with Alex Casella, Geom. Dedicata 215 (2021), 69-131.
  4. Thin subgroups isomorphic to Gromov--Piatetski-Shapiro lattices
    Pacific J. Math. 309 (2020), no 2, 257--266.
  5. Constructing thin subgroups of SL(n+1,R) via bending
    joint with Darren Long, Algebr. Geom. Topol. 20-4 (2020), 2071--2093

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. 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

Invited Talks

  1. A convex projective Dehn filling theorem (Slides)
    (AMS Southwest Sectional Meeting, GA Tech , 3/18/2023)
  2. Complex projective structures on surfaces (Slides)
    (University of Florida, Colloquium, 2/11/2022)
  3. Properly convex Dehn fillings (Slides)
    (University of Virginia, Topology Seminar, 10/26/2021)
  4. Triangulations in low dimensional geometry (Slides)
    (Cal Poly, Colloquium, 2/19/2021)
  5. Gluing equations in low dimensional geometry (Slides)
    (Oklahoma State Topology Seminar, 11/4/2020)
  6. Gluing equations for projective structures on 3-manifolds (Slides, Video)
    (Trends in Low Dimensional Topology, Online Seminar, 6/23/2020)

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 in LOV 105 on Tuesdays at 3:05. This semester, the seminar will be a hybrid with a combination of in person and virtual talks. Zoom links for virtual talks will be listed in the talk abstract. If you are interested in giving a talk either in person or virtually please send me an email.

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Castle Heidelberg Little Eli



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