Eliot Bongiovanni

eliot.bonge@gmail.com
Google Scholar
ORCID
Research Gate

Click here to download my full CV as a PDF.


I am currently a PhD candidate at Rice University’s department of mathematics. My advisor is Chris Leininger. My research is in geometric group theory and makes frequent use of the terms “hyperbolicity”, “flat surface”, and “Veech group”.

Last update: November 8, 2024

Research

I am interested in “geometry” in a broad sense, but I mainly focus on geometric analysis and low-dimensional topology. Most of my papers listed below address questions of surface area minimization under various constraints. The most recent paper represents my current work in geometric group theory.

Preprints

Extensions of finitely generated Veech groups. Eliot Bongiovanni; preprint (2024). Full text on arXiv.

Abstract: Given a closed surface S with finitely generated Veech group G and its extension Γ, there exists a hyperbolic space Ê on which Γ acts isometrically and co-compactly. The space Ê is obtained by collapsing some regions of the surface bundle over the convex hull of the limit set of G. Next Γ is shown to be hierarchically hyperbolic. This generalizes results from Dowdall-Durham-Leininger-Sisto, who assume in addition that G is a lattice. Because finitely generated Veech groups are among the most basic examples of subgroups of mapping class groups which are expected to qualify as geometrically finite, this result is evidence for the development of a broader theory of geometric finiteness.

Papers

The least-area tetrahedral tile of space. Eliot Bongiovanni, Alejandro Diaz, Arjun Kakkar, Nat Sothanaphan; Geometriae Dedicata (2019). Full text on springer.com.

Isoperimetry in surfaces of revolution with density. Eliot Bongiovanni, Alejandro Diaz, Arjun Kakkar, Nat Sothanaphan; Missouri Journal of Mathematical Sciences: Vol. 30, Iss. 2 (2018), 150-165. Full text on projecteuclid.org.

Double bubbles on the real line with log-convex density. Eliot Bongiovanni, Leonardo Di Giosia, Alejandro Diaz, Jahangir Habib, Arjun Kakkar, Lea Kenigsberg, Dylanger Pittman, Nat Sothanaphan, Weitao Zhu; Analysis and Geometry in Metric Spaces: Vol. 6: Iss. 1, 64-88 (2018). Full text on degruyter.com.

The convex body isoperimetric conjecture in R^2. John Berry, Eliot Bongiovanni, Wyatt Boyer, Bryan Brown, Matthew Dannenberg, Paul Gallagher, David Hu, Jason Liang, Alyssa Loving, Zane Martin, Maggie Miller, Byron Perpetua, Sarah Tammen, and Yingyi Zeng; Rose-Hulman Undergraduate Mathematics Journal: Vol. 18: Iss. 2 (2017). Full text on scholar.rose-hulman.edu.