Number Theory Research Unit

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Number Theory Research Unit

The Number Theory Research Unit (NTRU) brings together AUB number theorists, their students, and collaborators with the aim of strengthening research and teaching in number theory, and fostering regional collaborations at the service of the field. The unit is established under the Center for Advanced Mathematical Sciences (CAMS) at the American University of Beirut, with founding members who between them have benefited from CAMS support for more than two decades now, advancing the Center's mission through international collaborations and associated activities, all the while rooting their respective research programs at AUB.

NTRU will focus on current research topics in number theory and modular forms. Unit members will host specialists in their respective research areas, organizing extended thematic programs, workshops and international conferences. Number theorists in the region will be invited to join the Unit's efforts, stimulating interest in number theory in general and sustaining focused research in fields of mutual interest. The Unit will partner with international programs to strengthen its local projects, expand its network of associated scholars, and work to secure extramural funds for collaborative projects. In due course, the Unit will, in collaboration with CAMS, announce openings for postdoctoral positions.

Members

Founding Members

Kamal Khuri-Makdisi, Professor, Department of Mathematics, AUB, Lebanon
Wissam Raji, Professor, Department of Mathematics, AUB, Lebanon

External Members

Ahmad El Guindy, Assistant Professor, Department of Mathematics, Texas A&M University, Qatar
Alia Hamieh, Assistant Professor, Department of Mathematics, University of Northern British Columbia , Canada
Ghaith Hiary, Associate Professor, Department of Mathematics, Ohio State University, USA

Select Publications

Diamantis, N., Lee M., Raji W. Rolen L. 2022. "L-Functions of Harmonic Maass Forms and a Summation Formula for Harmonic Lifts", International Mathematics Research Notices.
Ono, K. and Raji, W. 2021. "Class numbers and self-conjugate 7-cores", Journal of Combinatorial Theory. Series A, vol.180
Khuri-Makdisi, K., Kohnen, W., and Raji, W. 2020. "Values of L-series of Hecke eigenforms", Journal of Number Theory, vol.211, pp-28-42
Kohnen, W. and Raji, W. 2018. "Special values of Hecke L-functions of modular forms of half-integral weight and cohomology", Research in Mathematical Sciences, vol.5, no.2
Kohnen, W. and Raji, W. 2017. "Non-vanishing of L-functions associated to cusp forms of half-integral weight in the plus space", Research in Number Theory, vol.3, no.1
Raji, W. 2013. "Eichler cohomology of generalized modular forms of real weights", Proceedings of the American Mathematical Society, vol.141, no.2, pp-383-392
Mühlenbruch, T. and Raji, W. 2013. "Generalized maass wave forms", Proceedings of the American Mathematical Society, vol.141, no.4, pp-1143-1158
Mühlenbruch, T. and Raji, W. 2013. "Eichler integrals for maass cusp forms of half-integral weight", Illinois Journal of Mathematics, vol.57, no.2, pp-445-475
Khuri-Makdisi, K. 2012. "Moduli Interpretation of Eisenstein series", International Journal of Number Theory 8, no. 3, 715-748
Kilford, L.J.P. and Raji, W. 2012. "On generalized modular forms supported on cuspidal and elliptic points", Ramanujan Journal, vol.27, no.3, pp-285-295
Khuri-Makdisi, K. 2007. "Asymptotically fast group operations on Jacobians of general curves", Mathematics of Computation 76, 2213-2239
Khuri-Makdisi, K. 2004. "Linear algebra for divisors on an algebraic curve", Mathematics of Computation 73, 333-357

NTRU Associates

NTRU Associates are distinguished number theorists who have generously accepted to join the unit in an advisory capacity, helping Unit members (and CAMS along with them) fulfill the strategic objectives of the Unit, as they catalyze collaborative and funding opportunities within their international network. Profiles of current associates can be accessed via the links below:

Ken Ono, Department of Mathematics, University of Virginia, USA
Nikos Diamantis, School of Mathematical Sciences, University of Nottingham, UK
Ozlem Imamoglu, Department of Mathematics, ETH Zurich, CH
Michel Waldschmidt, Department of Mathematics, Université Pierre et Marie Curie (Paris 6), FR
YoungJu Choie, Department of Mathematics, Pohang University of Science and Technology, ROK

Upcoming Events

CIMPA 2024: L-Functions and Modular Forms in Number Theory

Previous Events

Solomon Friedberg (Boston College, USA) - [Poster]

Title: "The Langlands Program: An Introduction and Recent Progress"
Date and time: March 21, 2023 at 4:00pm (Beirut time)
Venue: online via Zoom
Recorded Lecture: https://youtu.be/q5eGAG0CUN4

Nikolaos Diamantis (The University of Nottingham, UK)

Title: "L-series of weakly holomorphic forms and their values"
Date and time: December 5, 2022 at 6:00pm (Beirut time)

William Duke (University of California Los Angeles UCLA, USA) - [Poster]

Title: "The Representation of Integeres by Quadratic Forms"
Date and time: November 21, 2022 at 4:00pm (Beirut time)
Venue: College Hall, Auditorium B1
Recorded Lecture: https://youtu.be/_P3ouTQ9P74

Alvaro Lozano-Robledo (University of Connecticut, USA) - [Poster]

Title: "From Diophantus to Bitcoin: Why Are Elliptic Curves Everywhere?"
Date and time: November 1, 2022 at 6:00pm (Beirut time)
Recorded Lecture: https://youtu.be/JJ3s1MMDxv0

Ghaith Hiary (The Ohio State University, USA): Mini-course on "The Riemann Zeta Function: Conjectures and Computations" - [Poster]

Date and time: October 18, 19 and 20, 2022 (4:00pm - 5:00pm), College Hall, Auditorium B1
Lecture I recording: Link
Lecture II recording: Link
Lecture III recording: Link

Ghaith Hiary (Department of Mathematics, The Ohio State University) - [Poster]

Title: "How to Verify the Riemann Hypothesis for the First 1,000 Zeta Zeros"
Date and time: April 12, 2022 at 4:00pm (Beirut time)
Recorded Lecture: https://youtu.be/6fg7BJTR9Gw

Kathrin Bringmann (Department of Mathematics, University of Cologne) - [Poster]

Title: "Aysmptotic Properties of Modular Type Properties"
Date and time: April 1, 2022 at 4:00pm (Beirut time)

Michel Waldschmidt (Department of Mathematics, Université Pierre et Marie Curie (Paris 6))

TItle: Transcendental Number Theory: Recent Results and Open Problems
Date and time: January 18, 2022
Recorded Lecture: https://youtu.be/1q47G3oG83Y

Kenneth Ribet (Department of Mathematics, University of California, Berkeley) - [Poster]

Title: "A Brief History of Fermat's Last Theorem"
Date and time: November 8, 2021 at 7:00pm (Beirut time)
[Presentation slides]
Recorded Lecture: https://youtu.be/eFPUFMD4yjs

Ken Ono (Department of Mathematics, University of Virginia) - [Poster]

Title: "What is the Riemann Hypothesis and Why Does It Matter?"
Date and time: October 14, 2021 at 6:00pm (Beirut time)
Recorded Lecture: https://youtu.be/rDfCRGWVQRU

Mathematics Summer Research Camp - June & July 2022

Undergraduate Students: Ali Saraeb and Maher Memneh
Published papers:

A New Proof of the Transformation laws of Jacobi Theta Functions. (Link)
Generalization of Siegel's Method to Jacobi's theta_1 and theta_3. (Link)
A Generalization of Iseki's Formula and the Transformation Law of\theta_1 (z,\tau). (Link)

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