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Sharon M. FrechetteView profile

Associate Professor

• Number Theory
• Modular Forms
• Algebraic Combinatorics
• +4 more

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.

Özlem ImamogluView profile

Adjunct Professor

• Number Theory
• Modular Forms
• Mock Modular Forms
• +5 more

Özlem Imamoglu is an Adjunct Professor in the Department of Mathematics at ETH Zurich, a position she has held since 2005. Her academic journey includes prior appointments as Assistant Professor at ETH Zurich (2002-2005), Associate Professor at UC Santa Barbara (2003-2004), and Visiting Professor at Sabanci University (2000-2001). She teaches core undergraduate courses including Complex Analysis and Algebra II, with upcoming instruction scheduled through 2025. Her educational background features a B.S. in Electrical Engineering from Middle East Technical University (1987), followed by M.Sc. and Ph.D. in Mathematics from UC Santa Cruz (1992). Ph.D. Mathematics, UC Santa Cruz (1992) M.Sc. Mathematics, UC Santa Cruz B.S. Electrical Engineering, Middle East Technical University (1987) Professor Imamoglu's research centers on number theory with emphasis on modular forms , mock modular forms , and cycle integrals . She investigates connections between automorphic forms and geometric invariants, particularly through special values of modular functions on hyperbolic spaces and applications to real quadratic fields. Her work bridges analytic and algebraic number theory, often revealing deep relationships between L-functions and dynamical systems like Lyapunov exponents. Analysis of her 15 most recent publications reveals intensifying focus on hyperbolic 3-space geometry and modular function dynamics since 2018, with 6 publications in 2024 alone exploring twisted traces, Lyapunov exponents, and Kaneko's conjectures. Her research maintains strong connections to classical number theory through Hurwitz's method while incorporating modern geometric perspectives. As an active participant in the ETH Number Theory Seminar and co-organizer of the triannual Number Theory Days conference (EPFL/ETH/UniBasel), she provides students with collaborative research opportunities. Her international co-authorship network—including researchers from UCLA, Eötvös Loránd University, and University of Luxembourg—facilitates global academic exchange despite no formal lab structure. Professor Imamoglu remains a vital contributor to ETH Zurich's mathematics community through both her sustained research output and commitment to undergraduate education, with courses scheduled through 2025 demonstrating ongoing academic engagement.

• Analytic Number Theory
• Random Matrix Theory
• Zeta and L-Functions
• +4 more

Peter Sarnak is the Eugene Higgins Professor of Mathematics at Princeton University and a permanent faculty member at the Institute for Advanced Study's School of Mathematics. His research revolutionizes analytic number theory, with seminal contributions to L-functions, random matrix theory, and spectral geometry. Key affiliations include Princeton, IAS, UC Berkeley, and Stanford. Sarnak's work explores deep connections between automorphic forms, ergodic theory, and quantum chaos. His publications—like studies on zeta function zeros and quantum unique ergodicity—have redefined modern number theory. Recent papers address crystalline measures (2020) and quantum simulation lattices (2019), demonstrating interdisciplinary impact. As editor of Annals of Mathematics and Shaw Prize adjudicator, he shapes global mathematical discourse. While no lab or students are specified, his influence extends through collaborations and foundational theories.

• Number Theory
• Uniform Distribution Theory
• Discrepancy Theory
• +3 more

Christoph Baxa is an Associate Professor in the Department of Mathematics at the University of Vienna, where he has been a faculty member since 2000. His academic career at the University of Vienna began in 1990 as an Assistant Professor in the Department of Statistics, then moved to the Department of Mathematics in 1992, where he was promoted to Associate Professor in 2000. He maintains an active research profile and teaching load, with courses scheduled through 2025. Dr. Baxa completed his academic training at the University of Vienna, earning his M.A. in 1990 with a thesis on prime representing functions and Hilbert's Tenth Problem, his Ph.D. in 1994 on the discrepancy of sequences (nα), and his Habilitation in 2000 on estimates for discrepancies of special uniformly distributed sequences. His research focuses on Number Theory, particularly Uniform Distribution Theory, Discrepancy Theory, Continued Fractions, and Diophantine Approximation. His work often connects number theory with mathematical logic, as evidenced by his early research on Diophantine representations. His recent scholarly activity is dominated by book reviews for Monatsh. Math., covering diverse areas including algebraic geometry, number theory, history of mathematics, and mathematical education. Dr. Baxa has received several prestigious awards including the Ph.D. sub auspiciis Praesidentis rei publicae, the Würdigungspreis from the Austrian Ministry of Science and Research, the Jubiläums-Studienpreis from the Austrian Mathematical Society, and the Edmund und Rosa Hlawka Preis from the Austrian Academy of Sciences. He has held research grants from the Austrian Science Fund and was an Erwin Schrödinger Fellow at the University of Colorado at Boulder from 2001-2003. As a professional service, he has been a regular reviewer for Mathematical Reviews since 1996 and reviews books for Monatsh. Math. He is a member of numerous mathematical societies including the AMS, DMV, EMS, LMS, ÖMG, and SMF.

Harald GrobnerView profile

Professor

• Automorphic Forms
• Number Theory
• L-functions
• +3 more

Harald Grobner is a Professor at the Department of Mathematics within the Faculty of Mathematics at the University of Vienna, Austria. His office is located in Room 11.139 at Oskar-Morgenstern-Platz 1, 1090 Wien. He holds a Privatdozent qualification and serves as Principal Investigator for multiple major research projects including the ongoing FWF project 'New aspects of automorphic and smooth-automorphic forms' (2024-2028). His primary research focuses on automorphic forms—particularly cohomological ones—and their applications to number theory. He investigates the arithmetic and analytic theory of L-functions, with emphasis on representation theory (both local and global) and the geometry of arithmetically defined varieties. His work bridges deep theoretical constructs with concrete arithmetic problems, often exploring connections between automorphic representations and special values of L-functions. Grobner's recent publications demonstrate a sustained focus on automorphic cohomology, L-value rationality, and representation-theoretic structures. His research increasingly examines smooth-automorphic forms, the Franke filtration, and Deligne's conjecture for various L-functions, reflecting both technical sophistication and expanding conceptual scope. Key recurring themes include period relations, rationality phenomena, and the interplay between automorphic forms and arithmetic geometry. Edmund and Rosa Hlawka Award for Mathematics (2024, 4K €) START-Prize of the Austrian Science Fund (Y-966, 1.2 Mio €, 2016-2022) FWF Stand-alone research project (P-32333, 355K €, 2020-2024) FWF Stand-alone research project (P-25974, 228K €, 2013-2016) Erwin Schrödinger Grant (J-3076, 143K €, 2010-2013) Grobner actively supervises research through multiple funded projects including the current FWF Principal Investigator project (443K €) and a Croatian Science Foundation collaboration. He co-organizes the Wiener Seminar für Logik und Recht and maintains significant teaching responsibilities including Algebra, Number Theory, and advanced research seminars at the University of Vienna.