LUMS provides its PhD students with opportunities to engage with academic communities worldwide. Two students from the Department of Mathematics, Muhammad Ameer Hamza and Mughees Ghayas, recently participated in a staff exchange initiative at the University of Valencia, Spain, under the EU-funded CaLIGOLA program. This exchange, held from November 13 to December 28, 2024, aimed to promote international collaboration and advance research in areas such as Cartan Geometry, Lie Theory, Integrable Systems, and Quantum Groups.

Muhammad Ameer Hamza's Research on Topological Data Analysis

Hamza, a PhD student specializing in Topological Data Analysis under the supervision of Dr. Haniya Azam (Assistant Professor, Mathematics) and Dr. Hassan Mohy-Ud-Din (Assistant Professor, Electrical Engineering), focused on the topological regularization of image segmentation using deep learning methods. His project aimed to improve methods for segmenting 3D MRI scans, particularly in distinguishing cardiac structures like the left ventricle, right ventricle, and myocardium. To support this work, Hamza used computational tools such as Google Colab with A100 GPUs to calculate Wasserstein distances between persistence diagrams of predicted segmentation and the ground truth, a necessary step in diagnosing cardiovascular diseases.

During his visit, Hamza gave a talk on "Topological Data Analysis: A Naïve Introduction," discussing its applications in areas like string theory, biology, and chemistry. He also collaborated with Dr. María Antonia Lledó Barrena on double geometry, which allowed him to explore complex linear algebra and the structure of manifolds. After his time in Valencia, Hamza extended his research journey to Aarhus University in Denmark, where he worked with Dr. Simon Kristensen and Nikita Shugla on Diophantine approximation theory, exploring problems in continued fractions.

Mughees Ghayas' Research on Algebraic and Combinatorial Properties

Mughees Ghayas, a PhD student under the supervision of Dr. Imran Anwar, focused on the asymptotic behavior of Inc(N) invariant monomial ideals, particularly their algebraic and combinatorial properties. His research lies at the intersection of algebraic geometry and combinatorics, revealing patterns in infinite algebraic structures. During the visit, Mughees concentrated on conjectures about Cohen-Macaulay properties of simplicial complexes and the asymptotic behavior of ideals under combinatorial constraints.

Mughees presented his research weekly to Professor Marian Lledó at the University of Valencia. These presentations led to discussions that helped refine his research, including exploring applications in theoretical physics. He also delivered a seminar at Universidad Autónoma de Madrid, where he had discussions with faculty members such as Dr. Beatriz Pascual, Dr. Ana Bravo, and Dr. Adolfo Quirós, which opened potential future research opportunities.

Collaborations and Research Development

The visit to the University of Valencia provided both Hamza and Mughees with the chance to deepen their research and engage in international collaborations.

Both students expressed appreciation for the support of their supervisors, Dr. Haniya Azam and Dr. Imran Anwar, and thanked Dr. Walther Schwarzacher, Dean of SBASSE, for facilitating the funding and support that made their exchange possible.

This initiative reflects LUMS’ commitment to fostering global research connections, enabling students to advance their work and bring valuable international experience back to the institution.
 

On Friday, 24th January 2025, Syed Babar Ali School of Science and Engineering (SBASSE) organized Programme Day, bringing together faculty, students, and staff for a collaborative and engaging experience. 

The event provided freshmen with a chance to explore the departments, their research areas, and career pathways in an atmosphere that was as informative as it was fun.

Interactive models, live demonstrations, and lab tours were a key part of the day, offering students hands-on insights into areas such as recycling, electroplating, fingerprinting techniques, ferrofluids, and dye-sensitized solar cells. Each department showcased concise and well-organized displays, highlighting their research areas, placement opportunities, and academic offerings. 

Faculty members were actively present throughout the event, guiding and mentoring undergraduate students, answering questions in an informal capacity. The approachable atmosphere made it easy for students to connect, seek advice, and learn more about the opportunities ahead.

Adding to the excitement, the Electrical Engineering lobby became a central hub of activity with a live DJ performance by one of our talented EE students (highlights here). The student’s project—a device capable of producing the sound of any musical instrument—was a crowd favorite, showcasing the innovative potential of SBASSE students. 
Food stalls, including a peanut station (developed by one of our students, learn about the project here) at the EE booths, added a touch of comfort and warmth to the lively gathering.
 

A unique feature of Programme Day was the introduction of the "Passport to SBASSE," where students were encouraged to collect stamps at every department and activity they visited. 

The initiative not only added a sense of adventure but also inspired friendly competition as students compared their stamped passports, the more stamps, the cooler you were! 

At the end of the day, stamped passports were collected in a box for the lucky draw. Dean SBASSE selected the winner, who received the opportunity to dine with the Dean. This added a sense of anticipation and engagement to the event.

In the Mathematics Department, the collaborative spirit was on full display as the department chair challenged Lead Academic Affairs SBASSE to a game of Tower of Liré. The lighthearted competition sparked laughter and underscored the engaging nature of the day (highlights). Meanwhile, students enjoyed solving puzzles, engaging in activities, and exploring how mathematics connects to various industries.

Programme Day was a celebration of learning, collaboration, and creativity, with students sharing their excitement and positive feedback. Many expressed their appreciation for the experience, with emails to the Dean reflecting the enthusiasm generated by the event.

It was an inspiring and enjoyable day for the entire SBASSE community, reaffirming the school’s commitment to fostering curiosity, innovation, and a sense of belonging.  A heartfelt thank you to all the faculty, staff, academic staff, and organizers of Programme Day 2025 for making this event such a memorable and successful experience for everyone involved.

We are pleased to announce that Dr. Haniya Azam, Assistant Professor in Mathematics at the Syed Babar Ali School of Science and Engineering (SBASSE), has been promoted to Associate Professor with Tenure.

Dr. Haniya earned her PhD in Mathematics from the Abdus Salam School of Mathematical Sciences (ASSMS), GCU, Lahore, in 2013. During her PhD, she was awarded the French Embassy Split-PhD Fellowship, which enabled her to conduct research at the Institut de Mathématiques de Jussieu (IMJ) in Paris.

Before joining LUMS, Dr. Haniya worked as a Teaching Fellow at the Information Technology University in Lahore and as a Postdoctoral Fellow at ASSMS. Her research interests include Algebraic and Geometric Topology, Floer Homology, and Lower Dimensional Topology.

Beyond her research, Dr. Haniya has been actively involved in outreach activities, including the LUMS Math Circles, which aim to make mathematics accessible and engaging for school children. She received the Vice Chancellor’s Award for Teaching Excellence (2021-22) and has been serving as the Associate Dean for Undergraduate Education since 2023.

We extend our heartfelt congratulations to Dr. Haniya Azam on this well-deserved achievement and wish her continued success at LUMS!

On the 13th and 15th of May 2024, mathematics senior year students geared up to present their projects as part of the Math Senior Project (Sproj) exhibition. Sproj is a degree requirement at SBASSE, where students apply everything, they have learned  in their respective disciplines during their four years at LUMS and present a final research project. For mathematics this year, the topics for the projects were diverse, ranging from presentations of models of financial and sales  data, to philosophical discussions regarding the historical interpretations of mathematics.

The first of these projects was “Value of Risk”, presented by Marium Shahid, Mahnoor Sheikh, and Raheema Naeem. Value of Risk (VaR) is a measure used in finance to quantify the potential risk (measured as potential loss in value) of a portfolio (collection of financial investments) over a specified time interval. This project investigated the accuracy of the Historic, Parametric and Monte Carlo methods of calculating VaR. Under the guidance of Dr. Adnan Khan, the students began working on the project in fall 2023, spending the first month determining the scope of their project, and then devoting the rest of their time researching and running simulations using Python and Excel.  

Another project presented was “Revolutions in Mathematics: A Case Study”, by Muhammad Tayyab and Ahmed Shaheer Rathore. This project took a philosophical approach to mathematics, exploring the history of the field and highlighting ‘eureka’ moments in mathematics, referring to how ‘scientific revolution’ was defined by Thomas Kuhn, and why studying such moments in retrospect is important to mathematics. They also discussed how Imre Lakatos used a historical approach to mathematics, and how it questions the idea of timeless mathematics. By building on the work of other mathematicians and philosophers such as Michael Crowe, Caroline Dunmore, and Viktor Blasjo, the team looked at cases such as that of Cartesian and Non-Euclidean Geometry. In developing the project, Muhammad Tayyab concentrated on the philosophical underpinnings of the study while Ahmed Rathore worked on the mathematics. They were both guided by Dr. Sultan Sial, who gave his students the freedom to go beyond the mathematics and pursue the philosophical aspects of the project.

Another project included at the exhibition was Abdul Basit’s “An Empirical Analysis of Amazon Product Sales; A Comprehensive Study on the Applicability of Zipf’s”. Also being supervised by Dr. Sultan Sial, Abdul Basit analyzed the data from over a million Amazon products by applying Zipf’s Law.  Specific categories were examined, including sports and baby products, and the analysis showed that the baby products category exhibited a greater deviation from Zipf’s Law than the sports product category. This implied that customers purchasing baby products converged on a few popular items while in the sports products category, customers might have more diverse preferences based on their interests.

Meanwhile, Arhum Naseem Khawaja’s “The Geometry and Topology of Brower's Fixed-Point Theorem”, under the guidance of Dr. Haniya Azam, explored Brower’s theorem and its application in Nash equilibrium and game theory; both of which are important concepts in economics.
 

Many of these students decided the topic of their projects after being inspired by certain courses they took. The team behind the “Value of Risk" project took it on after all three completed a course in Quantitative Finance, Abdul Basit pursued his Amazon project after taking a course in Operations Research, while Arhum Naseem Khawaja explored algebraic topology as part of a directed research project following his completion of General Topology.

Why Maths: Senior Students’ Reflections  

When these students were asked why they chose math as a major, everyone had different reasons. Some had excelled in the subject in school and in their first year at LUMS, while others originally intended to pursue different disciplines before engaging with mathematics.

Arhum Khawaja, for example, was originally an Economics major who did not enjoy math in school due to its computational nature and focus on solving past papers. However, as he took math courses at LUMS, he realized his interest in the theoretical aspect of the subject and transferred to the Department of Mathematics at SBASSE. Abdul Basit had a similar experience; he had originally declared Electrical Engineering as his major but switched to Mathematics because it was his true passion, and it gave him a sense of inner peace.

With their graduation imminent, each of these math majors have different plans moving forward. Some are focused on the industry pathway, such as Abdul Basit, who intends to work on a startup for the next year. Meanwhile, others have been accepted into graduate schools, including Marium Shahid, who will be attending the University of Kent for Actuarial Sciences, and Arhum Khawaja, who will be pursuing a master's in mathematics at the University of Illinois Urbana-Champaign. Regardless of the different career paths these students take, they are united by their commitment to mathematics and the determination to keep their passion alive.
 

The Department of Mathematics at SBASSE, LUMS, in collaboration with the International Center for Theoretical Physics (ICTP) in Trieste, Italy, is hosting the International Mathematics Masters (IMM). This two-year intensive program connects students and professors from all across the world right inside LUMS. 

The mathematics program covers core areas of mathematic to help students gain a deeper insight in the subject before they decide on their specialization. In Fall 2023, the maths department welcomed their first batch. We were able to chat with Abderrahmane Labane and Radhwane Hassane Habra, hailing from Algeria, about their experiences with IMM and LUMS so far.

Each course within this program is delivered by a trio of faculty members: two well-renowned experts from outside Pakistan alongside one from LUMS, who collaboratively teach the course modules. This distinctive arrangement ensures that students are exposed to a variety of teaching styles, fostering a seamless understanding of the subject matter without any confusion. The international faculty members open doors to global research opportunities while their counterparts at LUMS lay a solid foundation, equipping students with the necessary skills to navigate the demanding teachings of the International Mathematics Masters program. The fusion of globally distinguished faculty with the esteemed LUMS faculty in this fully funded program distinguishes it as a truly unparalleled educational experience.
“The same topic is taught by different teachers so you get different teaching styles and ways of learning the same thing”, they emphasized. "What sets this program apart from others,” Radhwane adds, “is being in the department, which is open 24/7, and discussing mathematics with students”.

They further noted the immense passion for mathematics among the program's students, which fosters a healthy environment for discourse and learning. “It's surprising how mathematics can be learned from such diverse perspectives!”, they share. 

Adding to the program, their experience on-campus and in Pakistan has been a pleasant one. Staying on a campus with multiple facilities, they are thoroughly enjoying their student life. The convenience of a nearby mosque to their hostel and the availability of numerous cuisines, in addition to well-equipped sports facilities and healthcare canters on campus, make their daily life rather easy. Abderrahmane says, 'In Ghana, my university experience was just about taking classes and going home, but here, with all facilities on campus, it's really good.' Additionally, the students mention the similarity between the culture of their home country and Pakistan, which fosters a sense of belonging.
 
Finding this sense of belonging away from home is a universal aspiration for students studying abroad. Abderrahmane, who was studying Quantum Field Theory and theoretical physics in Ghana, discovered this program through a professor after expressing his interest in the mathematical foundations of quantum physics.

Radhwane, in his second year of a Masters program in France, applied through the ICTP, which then assigned him to the IMM at LUMS. Through their diverse experiences within the program, students form a passionate community around mathematics. For them, the pleasant surprises of a familiar culture and a welcoming community significantly eased their adjustment. This could well be described as finding a home away from home on their academic journey.

Apply now: https://www.internationalmathematicsmaster.org/