The author of over 100 research articles (many with undergraduate coauthors) and four books, Professor Garcia works in operator theory, complex variables, matrix analysis, number theory, and discrete geometry. He serves on the editorial board of several well-known journals and has received four National Science Foundation (NSF) grants as principal investigator. He was the inaugural winner of the American Mathematical Society's Dolciani Prize for Excellence in Research (2019) and he is a Fellow of the American Mathematical Society.
- Operator Theory
- Complex Analysis
- Matrix Analysis
- Number Theory
- Discrete Geometry
100 Years of Math Milestones: The Pi Mu Epsilon Centennial Collection (with Steven J. Miller). American Mathematical Society, 2019.
Finite Blaschke Products and Their Connections (with Javad Mashreghi and William Ross), Spinger, 2018.
A Second Course in Linear Algebra with Roger Horn. Cambridge University Press, 2017.
Introduction to Model Spaces and Their Operators with Javad Mashreghi, William Ross.
Cambridge Studies in Advanced Mathematics, Cambridge University Press, 2016.
Garcia, S.R., Omar, M., O’Neill, C., Yih, S. (’18), Factorization length distribution for affine semigroups II: asymptotic behavior for numerical semigroups with arbitrarily many generators, J. Combin. Theory Ser. A, 178 (2021), 105358.
Garcia, S.R., Yu, J. (’23), Udell, G. (’21), Multidimensional Schinzel-type theorems for multiplicative functions near prime tuples, J. Number Theory, 219 (2021), 212-227.
Böttcher, A., Garcia, S.R., Omar, M., O’Neill, C., Weighted means of B-splines, positivity of divided differences, and complete homogeneous symmetric polynomials, Lin. Alg. Appl. 608 (2021), 68-83
Aletheia-Zomlefer, S.L. (’18), Fukshansky, L., Garcia, S.R., The Bateman–Horn conjecture: history, heuristics, and applications, Expo. Math, 38 (2020), 430-479.
Garcia, S.R., Lateral movement in undergraduate research: case studies in number theory, in “A Project-Based Guide to Undergraduate Research in Mathematics: Starting and Sustaining Accessible Undergraduate Research,” Foundations for Undergraduate Research in Mathematics (eds. P. Harris, E. Insko, A. Wootton), Springer (2020), 203-234.
Garcia, S.R., Hu, J., Miller, S.J., Upper level mathematics and statistics courses shared across campuses (invited book chapter), Chapter 5 in “Teaching and Learning Mathematics Online,” (eds. J.P. Howard II, J.F. Beyers), Chapman and Hall / CRC, 2020.
Garcia, S.R., Horn, R.A., Block matrices in linear algebra, Problems, Resources, and Issues in Mathematics Undergraduate Studies (PRIMUS), 30 (2020), no. 3, 285- 306.
Eischen, E., Garcia, S.R., A gallery of Gaussian periods, Proceedings of Bridges 2020: Mathematics, Music, Art, Architecture, Culture, 243-8.
Awards & Honors
Awards & Honors
Member-at-Large, American Mathematical Society Council (2020-)
National Science Foundation (NSF) Research Grant (principal investigator) DMS-1800123: “Opportunities in Operator Theory,” $179,998, (2019-2021)
Elected to Pi Mu Epsilon (National Mathematics Honor Society), (2019)
Elected to Sigma Xi (Scientific Research Honor Society) (2019)
Fellow of the American Mathematical Society (2019)
Member of the editorial board of Notices of the American Mathematical Society (2019)
Senior participant: Institute for Pure and Applied Mathematics (IPAM) program on Quantitative Linear Algebra (2018)
Member of the editorial board of the American Mathematical Monthly (2017-2022)
David L. Hirsch III and Susan H. Hirsch Research Initiation Grant, $10,000 (2017-2019 )
Director’s Mathematician in Residence (DMiR), Budapest Semesters in Mathematics (DMS) Program (2017)
Member of the editorial board of Proceedings of the American Mathematical Society (2016-2020)
Member of the editorial board of Involve (2011-)
National Science Foundation (NSF) Research Grant (principal investigator) DMS-1265973: "Operators on Hilbert Space," 2013-2016.
Member of the Research Experiences for Undergraduate Faculty (REUF) Advisory Board (2013-)
Member of the editorial board of Annals of Functional Analysis (2013-2020)
Pomona College Nominee, CASE US Professors of the Year Award (2012)
Pomona College Nominee, CASE US Professors of the Year Award (2011)
National Science Foundation (NSF) Research Grant (principal investigator) DMS-1001614: "Complex symmetric operators - theory and applications," 2010-14
Pomona College, Wig Distinguished Professorship Award for Excellence in Teaching, 2009, 2019
American Institute of Mathematics (AIM), Member, Human Resources Board, Palo Alto, CA, 2008-present
National Science Foundation (NSF) Research Grant (principal investigator) DMS-0638789: "Complex symmetric operators and function theory," 2006-10.
University of California, Santa Barbara; Mochizuki Memorial Fund Award, 2005; Outstanding Educator, 2004
University of California, Berkeley; Nikki Kose Memorial Teaching Prize, 2003; Outstanding Graduate Student Instructor, 1999