Ralph R. Gomez
Associate Professor of Mathematics
Swarthmore College

500 College Avenue, Swarthmore PA 19081. Office: Science Center 152. Phone: (610)690-5727. email: rgomez1(at)swarthmore(dot)edu

Research Interests

My area of research is in differential geometry. I am interested in geometric structures that are related to ideas from physics. In particular, my focus is in Sasaki-Einstein geometry as well as generalized contact (and complex) geometry. More recently, I have become interested in the possible interplay between BHK mirror symmetry and Sasaki-Einstein geometry.

Publications and Preprints

*=undergraduate collaboration

  • (with *Nana Brobbey and *Xiuming Zhang) Berglund-Hübsch Duals and Sasaki-Einstein 5-Manifolds, in progress
  • (with Jaime Cuadros Valle and Joe Lope Vicente) Non-Existence of Extremal Sasaki Metrics via Berglund- Hübsch Transpose arXiv:2409.09720, submitted for publication.
  • (with Jaime Cuadros Valle and Joe Lope Vicente) Berglund-Hübsch Transpose Rule and Sasaki-Einstein Rational Homology 7-spheres, Commun. Math. Phys. 405, 199 (2024)
  • Berglund-Hübsch Transpose Rule and Sasakian Geometry, Ann Glob Anal Geom 65, 2 (2024).
  • Sasaki-Einstein 7-Manifolds, Orlik Polynomials And Homology. Symmetry. 11 (7) 947 (2019).
  • A Note on Smale Manifolds and Lorentzian Sasaki-Einstein Geometry, Bull. Math. Soc. Sci. Math. Roumanie, (107) no. 2, (2016), 151-158.
  • (with Janet Talvacchia) Generalized CoK\”ahler Geometry and an Application to Generalized K\”ahler Structures, J. Geom. Phys. 98 (2015) , 493-503.
  • (with Janet Talvacchia) On Products of Generalized Geometries, Geom. Dedicata 175 (2015), 211-218.
  • Lorentzian Sasaki-Einstein Metrics on Connected Sums of S² ×S³, Geom. Dedicata 150 (2011), 249-255.
  • Thesis: On Lorentzian Sasaki-Einstein Geometry. Advisor: Charles P. Boyer.

Resource: Homology of links This resource calculates the homology of links coming from hypersurfaces in weighted projective space.

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Teaching

  • Fall 2024: Math 28 Honors Linear Algebra, Math 65 Topics in Geometry: Differential Geometry of Curves and Surfaces
  • Spring 2024: Math 35 Honors Multivariable Calculus, Math 67 Introduction to Modern Algebra
  • Fall 2023: Math 15 Single-Variable Calculus, Math 39 Discrete Mathematics with an  Introduction to Proof
  • Sabbatical 2022-2023
  • Spring 2022: Math 101 Real Analysis II Seminar
  • Fall 2021: Math 15 Single-Variable Calculus, Math 15SP STEM Scholars Program
  • Spring 2021: Math 34 Several-Variable Calculus
  • Fall 2020: Math 63 Real Analysis, Math 27 Linear Algebra
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about me

  • Here is an interview I did with the Swarthmore College newspaper “The Phoenix”. In the first part of the interview, I discuss my mathematical research and in the second part of the interview, I share my journey in becoming a mathematician.
  • I was also featured in Lathisms.
  • There is a much more detailed description of my journey in becoming a mathematician which is available here. It is also available in the book “Testimonios: Stories of Latinx and Hispanic Mathematicians“.
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