معرفی
Sharon M. Frechette is an Associate Professor in the Department of Mathematics & Computer Science at the College of the Holy Cross, where she teaches across the undergraduate curriculum and develops innovative interdisciplinary seminars.
Her educational background includes:
- Ph.D. in Mathematics from Dartmouth College (1997), thesis: "Decomposition of Spaces of Half-Integral Weight Cusp Forms" under Thomas Shemanske
- A.M. from Dartmouth College (1994)
- B.A. from Boston University (1988) with senior thesis advised by Paul Blanchard
Frechette's research bridges number theory and combinatorics, with deep investigations into modular forms, L-functions, multiple Dirichlet series, and hypergeometric functions over finite fields. She explores connections between algebraic combinatorics and representation theory, and examines the relationship between elliptic curves and modular forms. Her work often reveals combinatorial structures within analytic number theory problems, particularly through the lens of Hecke operators and their traces.
Analysis of her publication timeline (2000-2018) shows evolution from foundational work on half-integral weight modular forms to sophisticated studies of multiple Dirichlet series and finite-field hypergeometric functions, with consistent emphasis on combinatorial interpretations of number-theoretic objects.
As an educator, Frechette has created the distinctive Montserrat cryptology sequence combining historical narrative with mathematical rigor, and regularly teaches advanced courses like Modern Algebra and Number Theory. Her commitment to undergraduate research is evident through supervision of senior theses and development of course-based research opportunities.
