Stephan Ramon Garcia

The author of over 100 research articles (many with undergraduate coauthors) and five books, Garcia works in operator theory, complex variables, matrix analysis, number theory, analytic combinatorics and discrete geometry. He has served on the editorial board of several well-known journals and has received five 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 is a Fellow of the American Mathematical Society.

Books

Operator Theory by Example with Javad Mashreghi and William T. Ross, Oxford University Press, 2023.

Matrix Mathematics: A Second Course in Linear Algebra with Roger Horn, Cambridge University Press, 2023 (second edition of A Second Course in Linear Algebra)

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.

Recent Papers

Frobenius-Rieffel norms on finite-dimensional C*-algebras (with Konrad Aguilar, Elena Kim ’21) Oper. Matrices 16 (2022), no. 3, 733-758.

Norms on complex matrices induced by complete homogeneous symmetric polynomials (with Konrad Aguilar, Ángel Chávez, Jurij Volćić) Bull. London Math. Soc. 54 (2022), no. 6, 2045-2584.

Factorization length distribution for affine semigroups IV: a geometric approach to weighted factorization lengths in three-generator numerical semigroups (with Christopher O'Neill, Gabe Udell ’21) Comm. Algebra 8 (2022), no. 50, 3481-3497.

Explicit estimates for Artin L-functions: Duke's short-sum theorem and Dedekind zeta residues (with Ethan Simpson Lee) J. Number Theory (2022), no. 238, 920-943.

Powers of rational matrices (with Roger A. Horn, Florian Luca, Kuldeep Sarma) Amer. Math. Monthly 129 (2022), no. 2, 177.

Unconditional explicit Mertens' theorems for number fields and Dedekind zeta residue bounds (with Ethan Simpson Lee) Ramanujan J. 57 (2022), 1169–1191.

Factorization length distribution for affine semigroups III: modular equidistribution for numerical semigroups with arbitrarily many generators (with Mohamed Omar, Christopher O'Neill, Tim Wesley ’21) J. Austral. Math. Soc 113 (2022), no. 1, 21-35.