Department of Mathematics-American University of Beirut

The PhD in Mathematics is now officially launched at AUB.

Don't miss your chance and apply before June 16, 2026!! https://tinyurl.com/gradadmi

Apply for Fall 2026–27 and take the next step in your academic journey at the heart of science and technology.

The PhD in Mathematics is now officially launched—opening new pathways for advanced research, innovation, and academic excellence.

📅 Submission deadline: June 16, 2026
🎓 Fellowships with stipends are available

Apply now https://tinyurl.com/gradadmi

The next talk at the AUB Mathematics Seminar will be on Tuesday, May 5, from 11:30 to 12:30 in Bliss Hall 205. Everyone interested is warmly welcome.

Speaker: Joe Germany (Department of Mathematics, AUB)

Title: Approximation Theory for Exactly Periodic, Divergence-Free Neural Networks and Application to the Navier-Stokes and Nonlocal Advection-Diffusion PDEs

Abstract: Many physically relevant models have properties such as periodic boundary conditions or incompressibility. Standard neural network architectures do not enforce these properties exactly, creating difficulties in carrying out high-regularity analysis and energy estimates.

In this talk, we introduce neural network architectures that are exactly periodic and/or exactly divergence-free, by construction, and we establish approximation theories for these methods.

Our networks display abundant analytical advantages for carrying out energy estimates and allow for the approximation of nonlocal, periodic operators like the fractional Laplacian and the Riesz transform. We apply our techniques to study the convergence analysis of such networks for the incompressible Navier-Stokes equations and a family of fractional nonlocal advection-diffusion equations.

Finally, we present an a posteriori framework to rigorously translate empirically observed decay rates of neural network approximations into decay rates for the true PDE solution, providing a novel bridge between physics-informed neural networks and rigorous numerics.

This is joint work with Elie Abdo (AUB), Xu Yang (UCSB), Ruimeng Hu (UCSB), and Lihui Chai (Sun Yat-sen University).

About the speaker: Joe Germany is an undergraduate student in Math and Physics at AUB. His interests lie at the intersection of machine learning, physics, and partial differential equations, particularly in the study of structure-preserving neural architectures and the mathematical analysis of machine learning algorithms.

Up-to-date information regarding the upcoming talks can be found on the website of the seminar:
https://www.aub.edu.lb/fas/math/Pages/ags.aspx

This seminar series is supported by the FAS Dean's Office.

We will resume the AUB Mathematics Seminar with a talk on Tuesday, April 21, from 16:00 to 17:00 online through Webex. Everyone interested is warmly welcome.

Tuesday, April 21, 16:00, Online
Speaker: Quyuan Lin (Clemson University, US)

Title: Well-posedness and ill-posedness of the fractional dissipative primitive equations

Abstract: The primitive equations (PE) are widely used in the study of geophysics, in particular when the aspect ratio of the domain is small, such as the ocean and atmosphere in the planetary scale. They are derived from the Navier-Stokes equations or Euler equations by taking the hydrostatic limit. The viscosity plays an important role in the properties of the PE. While the full viscous PE is globally well-posed in 3D, the inviscid PE is ill-posed in Sobolev spaces and its analytic solutions can form singularity in finite time. I will discuss some recent works on the investigation of fractional dissipative PE, focusing on well-posedness and ill-posedness for different fractional powers of viscosity.

About the speaker: Quyuan Lin is an Assistant Professor in the School of Mathematical and Statistical Sciences at Clemson University. He earned his Ph.D. from Texas A&M University in 2021 and then spent two years at the University of California, Santa Barbara as a Visiting Assistant Professor. His research focuses on nonlinear partial differential equations arising in fluid dynamics, particularly in geophysical flows and electrohydrodynamics.

Up-to-date information regarding the upcoming talks can be found on the website of the seminar:
https://www.aub.edu.lb/fas/math/Pages/ags.aspx

This seminar series is supported by the FAS Dean's Office.

The next talk at the AUB Mathematics Seminar will be on Tuesday, March 3, from 11:00 to 12:00 in Bliss Hall 205. Everyone interested is warmly welcome.

Speaker: Faruk F. Abi-Khuzam (Department of Mathematics, AUB)

Title: Minimum Modulus Oscillation and ratios of successive zeros of entire functions

Abstract: The maximum modulus M(r) of a transcendental entire function is monotone increasing while the minimum modulus m(r) oscillates in the presence of zeros. But if f is of order 0, then the ratio m(r)/M(r) can approach the value 1 along some sequence of values of r tending to infinity. We present a study of the oscillation of the minimum modulus in relation to ratios of successive zeros of f. The connection is made through the second logarithmic derivative of log M(r): This leads to a simple proof of a conjecture on the growth of the ratio m(r)/M(r), and to the determination of explicit sequences, defined in terms of the zeros, where the upper limit of m(r)/M(r) attains the value 1.

About the speaker: Faruk Abi-Khuzam is Professor of Mathematics at the American University of Beirut. His fields of interest are Analysis and Geometry; in particular the study of growth and distribution of zeros of entire functions, and the study of geometric inequalities, where “The Abi-Khuzam Inequality” was used in the proof of Yff's conjecture. His research also includes occasional excursions into the structure of minimal surfaces and prime number distribution. He is the recipient of a Research Award, a Teaching Excellence Award, and an award for durable and dedicated service to the University.

Up-to-date information regarding the upcoming talks can be found on the website of the seminar:
https://www.aub.edu.lb/fas/math/Pages/ags.aspx

This seminar series is supported by the FAS Dean's Office.

Whether you graduated recently or years ago, join us on campus on June 11 to reconnect with classmates and meet the next generation of mathematicians.

We hope you can join us; Let us know if you’ll be there!
https://alumni.aub.edu.lb/s/1716/bp20/Interior.aspx?sid=1716&gid=2&pgid=4198&cid=13929&post_id=0

February = Review Month!

Ace your Quiz 1 with our MATH review sessions!

Check the schedule, pick your course, and join us!

Spots are limited. Register now!

The next talk at the AUB Mathematics Seminar will be on Tuesday, February 17, from 14:00 to 15:00 in Bliss Hall 204. Everyone interested is warmly welcome.

Speaker: Georgios Charalambous (AUB - Mediterraneo)

Title: On the internal symmetries of mathematical universes

Abstract: Classification is a central theme in mathematics: in everyday mathematical practice we seek to organize complex structures into manageable families. Traditionally, one of the most successful strategies for achieving this is to translate ``hard'' geometric problems into “easy” algebraic ones, using algebraic invariants. However, a deeper question arises: can we find a systematic way to perform this translation that works across diverse mathematical settings? In this talk, we explore Grothendieck’s (and his school's) approach to this problem - an approach that shifts attention from individual objects to the global architecture of the “mathematical universe” they inhabit. Through this perspective, we illustrate how powerful, systematic tools emerge, building bridges between classical foundations and more recent developments and reshaping the way many classification problems are understood.

About the speaker: Dr Georgios Charalambous (AUB - Mediterraneo) holds a PhD in Mathematics from the University of Cambridge, where he specialized in higher dimensional algebraic geometry. His research explores the use of homotopical and categorical tools - such as fundamental groups, higher stacks, and derived structures - to study the intrinsic geometry of schemes and related moduli spaces. He is the Teaching and Learning Coordinator of the University and leads the Academy of Mathematical Excellence and Innovation. Beyond his institutional roles, he serves as the Organizing Secretary of the Cyprus Mathematical Society and is a Board Member of the European Mathematical Society's Young Academy (EMYA).

Up-to-date information regarding the upcoming talks can be found on the website of the seminar:
https://www.aub.edu.lb/fas/math/Pages/ags.aspx

This seminar series is supported by the FAS Dean's Office.

The next talk at the AUB Mathematics Seminar will be on Tuesday, February 10, from 11:00 to 12:00 in Bliss Hall 205. Everyone interested is warmly welcome.

Speaker: Malak Diab (University of Wuppertal, Germany)

Title: Structure-preserving computation of linear systems arising in port-Hamiltonian DAEs

Abstract: We consider structure-preserving computational techniques for the pencil Padé approximation and the generalized Cayley transform, arising in the numerical integration of port-Hamiltonian differential-algebraic equations (pH-DAEs) via Gauss–Legendre schemes. We analyze how FOM-based Krylov subspace methods can be designed to inherit structure-induced properties such as energy preservation and dissipativity.

About the speaker: Malak Diab is a postdoctoral researcher in Mathematics at the University of Wuppertal, Germany, and an associate member of the CRC-1701 project on port-Hamiltonian systems (PHS). She obtained her Ph.D. in applied mathematics in 2022 from Humboldt University of Berlin, Germany, within the Marie Skłodowska-Curie STIMULATE program. Her research interests focus on operator splitting methods for DAEs, structure-preserving numerical methods for PHS and applications in electric circuit modeling and mechanical systems.

Up-to-date information regarding the upcoming talks can be found on the website of the seminar:
https://www.aub.edu.lb/fas/math/Pages/ags.aspx

The next talk at the AUB Mathematics Seminar will be on Tuesday, January 20, from 11:00 to 12:00 in Bliss Hall 205. Everyone interested is warmly welcome.

Speaker: Faruk Abi-Khuzam (Department of Mathematics, AUB)

Title: A Jacobian Group Structure on a hyperbolic pencil and its applications

Abstract: Using Jacobian Elliptic Functions we introduce a group structure A on a Hyperbolic Pencil of Coaxal circles. We then use this to obtain new proofs of the Poncelet closure theorems, and in particular we prove: Given two circles of the pencil, an inter scribed polygon of n sides exists for these two circles if and only if the inside circle is an element of order n in the group A.

About the speaker: Faruk Abi-Khuzam is Professor of Mathematics at the American University of Beirut. His fields of interest are Analysis and Geometry; in particular the study of growth and distribution of zeros of entire functions, and the study of geometric inequalities, where "The Abi-Khuzam Inequality" was used in the proof of Yff's conjecture. His research also includes occasional excursions into the structure of minimal surfaces and prime number distribution. He is the recipient of a Research Award, a Teaching Excellence Award, and an award for durable and dedicated service to the University.

Up-to-date information regarding the upcoming talks can be found on the website of the seminar:
https://www.aub.edu.lb/fas/math/Pages/ags.aspx

This seminar series is supported by the FAS Dean's Office.

📘 Need a Calculus Boost This Semester?

If concepts like inverse trigonometric functions, derivative rules, or integration techniques feel rusty, you’re not alone. These tools are often assumed in Calculus and Differential Equations courses, making it hard to keep up.

Our Calculus Foundations Workshops are designed to help you review, consolidate, and gain confidence in the core skills you need to succeed — all aligned with what you’re covering in class.

🗓 Workshop Schedule
📍 Location: Nicely 415
🕔 Time: 5:00–7:00 p.m.
• Thursday, January 15: Inverse Trigonometric Functions
• Tuesday, January 20: Derivative Rules
• Thursday, January 22: Integration Rules
⚠️ Limited spots available — registration is first come, first served.

👉 Register here: https://forms.office.com/r/HMvk3rkiQG

📩 Questions? Email [email protected] or DM on Instagram .aub

We’re excited to support you this semester and help you succeed in your calculus courses!