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Franco Vargas Pallete

Franco Vargas Pallete


Department of Mathematics
Yale University
New Haven, CT 06511, USA

Office: 735 Kline Tower
Email: [My first name] DOT [My TWO last names] AT yale DOT edu
Curriculum Vitae (December 2023)

ABOUT ME

I am a Gibbs Assistant professor at Yale University, and from 2020-2023 I was a NSF Postdoctoral Fellow there as well. I was a graduate student in Mathematics at the University of California, Berkeley, where I received my PhD in May 2018.  My advisor was Ian Agol.
My interests are Geometry and Topology in low-dimension, mainly geometric aspects of hyperbolic 3-manifolds. Some interests and keywords are Renormalized volume, Teichmüller theory, minimal surfaces, isoperimetric problems, systoles and extremal length.   I passed my qual on March 20, 2014. Here is the transcript of what I was asked.
I also graduated from the Pontificia Universidad Católica del Perú in 2011 with a BA .  I am originally from Lima, Perú.
In Summer 2018 (UC Berkeley) and Summer 2022 (Yale) I lead research groups for undergraduates, focusing on Fundamental Domains of Hyperbolic 3-manifolds and on Minimal area disks, respectively.

Here are some slides I used for my talk at the Nearly Carbon Neutral Geometric Topology Conference: June 1-14, 2020. You can see the video here

This Fall 2023 I am teaching Math 255.

RESEARCH

  1. W-volume of planar domains with circular boundary (j. with Jeffrey Brock).
  2. Universal Liouville action as a renormalized volume and its gradient flow (j. with Martin Bridgeman, Ken Bromberg and Yilin Wang).
  3. Cheeger constant of convex co-compact hyperbolic 3-manifolds (j. with Celso Viana) (Submitted).
  4. On the topology and index of minimal/Bryant framed surfaces (j. with Davi Maximo) (Submitted).
  5. Uniform spectral gap and orthogeodesic counting for strong convergence of Kleinian groups (j. with Beibei Liu) (Accepted, Forum of Mathematics, Sigma)
  6. Peripheral birationality for 3-dimensional convex co-compact PSL2ℂ varieties (j. with Ian Agol) (Submitted)
  7. Besse projective spaces with many diameters (j. with Ian Adelstein) (Accepted, Journal of Geometric Analysis)
  8. Volume bounds for the canonical lift complement of a random geodesic (j. with Tommaso Cremaschi, Yannick Krifka, Dídac Martínez-Granado) (Accepted, Transactions of the American Mathematical Society)
  9. Isoperimetric interpretation for the renormalized volume of convex co-compact hyperbolic 3-manifolds (j. with Celso Viana) (Accepted, American Journal of Mathematics)
  10. Mean curvature flow in homology and foliations of hyperbolic 3-manifolds (j. with Marco A. M. Guaraco, Vanderson Lima) (Submitted)
  11. The extremal length systole of the Bolza surface (j. with Maxime Fortier Bourque, Dídac Martínez-Granado) (Submitted)
  12. Minimal area surfaces and fibered hyperbolic 3-manifolds (j. with James Farre) Proc. Amer. Math. Soc. 150 (2022), 4931-4946
  13. The Weil-Petersson gradient flow of renormalized volume on a Bers slice has a global attracting fixed point (j. with Martin Bridgeman and Ken Bromberg) (Accepted, Compositio Mathematica)
  14. The length of the shortest closed geodesic on positively curved 2-spheres (j. with Ian Adelstein) Mathematische Zeitschrift arxiv
  15. Hyperbolic limits of Cantor set complements in the sphere (j. with Tommaso Cremaschi) Bull. Lond. Math. Soc. 54 (2022) no. 3, 1104-1119.
  16. Comparing hyperbolic and extremal lengths for shortest curves (j. with Dídac Martínez-Granado) (submitted)
  17. Upper bounds on Renormalized Volume for Schottky groups (submitted)
  18. A differential form approach to the genus of Open Riemann surfaces (j. with Jesus Zapata Samanez) (arxiv)
  19. Embedded Delaunay triangulations for point clouds of surfaces in R^3 Proceedings of the American Mathematical Society arxiv
  20. Additive continuity of the renormalized volume under geometric limits (arxiv)
  21. Continuity of the renormalized volume under geometric limits (arxiv)
  22. Local convexity of renormalized volume for rank-1 cusped manifolds Mathematical Research Letters arxiv
  23. Hyperbolic groups with few linear representations (A non-published argument of William Thurston) Pro Mathematica, 32(63), 73-81.

CONTACT

[My first name] DOT [My TWO last names] AT yale DOT edu
735 Kline Tower, 219 Prospect St
Department of Mathematics
Yale University
Kline Tower Floors 7-9
219 Prospect St.
New Haven, CT 06511