Professor Sandoval is a Professor in the Department of Mathematics.   Her specialty is Global Analysis, which is the study of partial differential equations on abstract spaces, with particular interest in the connection between the nature of the solutions of these equations and the underlying geometry of the abstract space in question.  This area has applications to many fundamental questions in mathematical physics.

Professor Sandoval particularly enjoys teaching mathematics courses that highlight the connections ot other areas of mathematics and physics such as linear algebra, multivariable calculus, and topics courses in special relativity, Lie theory, differential geometry and topology. Teaching such courses allows her to show students how mathematics can be used to solve interesting problems in the fields of engineering and physics. She is also interested in pedagogical innovations and has flipped two of her courses in linear algebra and multivariable calculus.

Prior to joining Trinity College, Professor Sandoval served as a visiting professor at Purdue University. She graduated from Yale University in 1989 with a B. A. in Mathematics. She earned a Masters of Science from the University of Michigan in 1993, and her Ph. D. in  Mathematics in 1997.  She also worked as a government mathematician for the Department of Energy's Energy Information Administration from 1989 to 1991.  While there, she helped develop mathematical models that were  used to analyze proposed revisions to the Clean Air Act of 1990, some of which eventually came into law.

Selected Publications:

• "Do the Hodge Spectra distinguish Orbifolds from Manifolds? Part 1." Joint work with Katie Gittens, Carolyn Gordon, Magda Khalile, Ingrid Membrillo-Solis, and Liz Stanhope (Women In Geometry 2 Spectral Theory Team). Accepted 2021, to appear in Michigan Mathematics Journal.
  
• "Leaf Space Isometries of Singular Riemannian Foliations and Their Spectral Properties." Joint work with I. Adelstein. Sao Paolo Journal of Mathematical Sciences, vol. 15, 2021, pp. 3--19.
  
• "The G-Invariant Spectrum and Non-orbifold Singularities," (Joint work with I. Adelstein), Archiv der Mathematik, vol. 109, No. 6, (2017): 563-573.
  
• "The Wave Trace of the Basic Laplacian of a Riemannian Foliation at a Non-zero Period." Annals of Global Analysis and Geometry 44, no. 2, (2013): 217-244.
• Sandoval, Mary. "Wave Invariants of the Spectrum of the G-Invariant Laplacian and the Basic Laplacian of a Riemannian Foliation."  Communcations in Partial Differential Equations 33 (2008): 1818-1846.
• "The Singularities of the Wave Trace of the Basic Laplacian of a Riemannian Foliation."  Journal of Functional Analysis 243, no. 1 (2007): 1-27.

Recent Presentations:

• "Using Heat Invariants to Distinguish Orbifolds from Manifolds,"Women In Geometry 2. Banff International Research Station-Casa Matematica de Oaxaca, Oaxaca, Mexico, June 26, 2019.
• "Spectral Theory via Quotients," Geometry and Topology Seminar, Dartmouth University, May 15th, 2018.
  
• "Leaf Spaces of Singular Riemannian Foliations and Applications to Spectral Geometry," EGEO 2016, VI Workshop in Differential Geometry in La Falda, Argentina, August 2016.
  
• "Wave Trace Singular Spaces," Geometry and Topology Seminar. Dartmouth University, May 26, 2015.

• Senior mentor/researcher for Women In Geometry II Team in Spectral Geometry, 2019-present.
  
• Visiting Member, Mathematical Sciences Research Institute, Berkeley, Fall 2008.
• Visiting Member, Mathematical Sciences Research Institute, Berkeley, March 2001.
• Visiting Member, Fields Institute, 1997.
• Recipient of Mathematical Sciences Research Institute Travel Grants, March 2001, August-November, 2008.
• Project NEXT Fellow, 1997-1998, a professional development program for new Ph.D.'s who are interested in improving the teaching of undergraduate mathematics.