Sergio Zamora

PhD Student

Penn State University

Department of Mathematics

sxz38@psu.edu

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Research

Under the direction of Professor Anton Petrunin, I perform research in the areas of metric geometry, geometric group theory, and arithmetic combinatorics. However, my interests also include geometric analysis, geometric probability, index theory, and geometric topology. Here is my full Research Statement and my CV.

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Texts (click to enlarge)

• Fundamental groups and group presentations with bounded relator lengths
  (preprint)
• Tori can't collapse to an interval
  Electronic Research Archive 2020
• Limits of almost homogeneous spaces and their fundamental groups
  (preprint)
• Moon in a puddle and the four vertex theorem
  American Mathematical Monthly 2021
  with Anton Petrunin and artwork by Ana Cristina Chavez Caliz
• Fundamental groups of aspherical manifolds that collapse
  (preprint)
• Notes on Hyperbolic Geometry
• Notes on Alexandrov Geometry
• Notes on Almost Flat Manifolds

Talks and Posters (click to enlarge)

• Limites de espacios homogeneos discretos (slides)
  Talk. Jornada de Topologia, Geometria y Dinamica. 2022
• On collapse of tori under lower sectional curvature bounds (slides)
  Talk. Alexandrov Seminar in Geometry. Euler Institute. 2022
• On limits of almost homogeneous spaces (slides)
  Talk. University of Copenhagen. 2022
• Structure of Collapse on Aspherical Manifolds
  Talk. University of Toronto. 2021
• Global shape of Galois covers (slides)
  Talk. UCSB. 2021
• Global shape of universal covers
  Talk. Vanderbilt University. 2021
• Structure of Collapse and Fundamental Groups (slides)
  Talk. CUNY Geometric Analysis Seminar. 2021
• Universal Covers of Manifolds with Ricci Curvature Bounded Below (slides)
  Talk. UNCG ANT-CoG. 2021
• Lower Semi-continuity of the Fundamental Group (slides)
  Talk. Friday Lunch Seminar. Penn State University. 2021
• Lower Semi-continuity of the Fundamental Group and Convergence with Discrete Symmetry
  Talk. Virtual Workshop on Ricci and Scalar Curvature in honor of Misha Gromov. 2020
• Fundamental Groups and Limits of Almost Homogeneous Spaces (slides)
  Talk. Metric Measure Spaces and Convergence Seminar. 2020
• Amenable Groups and Ultrafilters. Different takes on Probability (notes)
  Talk. Student Directed Colloquium. Penn State University. 2019
• Amenability
  Talk. MSRI Summer School. Geometric Group Theory. 2019
• Geometry of Universal Covers through Cayley Graphs
  Poster. Sub-Riemannian Geometry and Beyond II. Jyvaskyla. 2019
• On Diameters of Universal Covers (slides)
  Talk. Geometry Seminar. Penn State University. 2018
• Non-Smooth Curvature (slides)
  Talk. Student Directed Colloquium. Penn State University. 2018
• Curvature and the Paper Sphere
  Talk. Mathematical Coven. UNAM. 2015
• Lines in the plane and decomposition of graphs
  Talk. Seminar Proofs from the book. UNAM. 2013

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Teaching

• My Teaching Philosophy
• Calculus of Several Variables
• What is Differential Geometry textbook (collaboration with Anton Petrunin)