Dr Duygu Sap

I am a mathematician conducting both mathematical and interdisciplinary research. I develop structure-preserving methods for partial differential equations and construct theoretical frameworks for problems in computer science and engineering.

My expertise lies in theoretical numerical analysis and scientific computing, with a particular focus on finite element exterior calculus (FEEC). My doctoral research centered on finite element analysis, partial differential equations, and differential geometry. In my Ph.D. dissertation, I developed finite element methods for the Stokes problem on n-dimensional cubical and general quadrilateral meshes that yield divergence-free velocity fields.

Education

• Ph. D. and M.Sc. in (General) Mathematics, Faculty of Science & Letters, University of Pittsburgh, USA.
• M.Sc. in Electronics and Communication Engineering, Faculty of Electrical & Electronics Engineering, Istanbul Technical University, Turkey.
• B.Sc. in Mathematical Engineering, Faculty of Science & Letters, Istanbul Technical University, Turkey, and Department of Mathematical Sciences, Durham University, UK.

Brief Academic History

Prior to joining CAMaCS, I was a postdoc at the University of Oxford (first, at the Department of Engineering Science; then, at the Mathematical Institute). During my time at Engineering, I was a member of the Impact Engineering Lab and the Solid Mechanics Group, and worked on the ASiMoV project. During my time at Maths, I was a member of the Numerical Analysis Group and funded by the project PRISM. Before I moved to Oxford, I also conducted postdoctoral research in Berkeley as a member of the Research Initiatives Group at the International Computer Science Institute.

Please visit my personal website for more about me, my research and teaching experience.

Research Areas

• Numerical Analysis and Scientific Computing:
  Numerical Methods for PDEs, Finite Element Exterior Calculus, Finite Element Analysis, Isogeometric Analysis, Hybrid Methods, Quadrature.
• Applied Geometry and Topology:
  Discrete Differential Geometry, Applied Algebraic Topology, Geometric Modeling, Topological Data Analysis.
• Artificial Intelligence:
  Geometric Deep Learning, Graph Neural Networks, Graph Attention Networks.
• Applications in Engineering and Physics:
  Fluid Mechanics, Solid Mechanics, Electromagnetism.
• Computer-Aided Systems:
  Interoperability of CAD Systems, CAD-CAE Integration

Interdisciplinary Research Projects at CAMaCS

• Image Categorization and Retrieval

This project aimed at categorizing second-hand garments and retrieving a given garment from large datasets. I introduced a novel approach based on representative models, which capture the key features of each image, and applied it to image sets using GATs. We also utilized this approach for the categorization of second-hand garments with visual transformers.

• Sensor Visualization

This project aimed at applying topological data analysis and statistical techniques to multi-sensor data obtained from a railway system. I derived various correlations of the sensors measuring two distinct quantities and offered physical interpretations of topological signatures of the dynamical system to enable assessing the structural integrity of the system.

• 3D Visualization via Morgan Panel Maps (MPMs)

This project aimed at supporting strategic decision-making across complex supply chains. I offered strategies and methods to enhance 3D visualization panels and storylines to support this objective via three distinct applications.

• GDP Nowcasting

This project aims at offering the UK Office for National Statistics (ONS) the optimal GNAR (Generalized Network Autoregressive) model for GDP nowcasting.

• Heat Battery Applications of Composite Phase-Change Material Modeling (Upcoming)

Knowledge Exchange Activities

• AI in Mathematical Sciences, KE Hub Sandpit, (Academic and Panelist), 2026.
• Scientific Machine Learning, KE Hub Workshop, (Attendee), 2026.
• Multi-dimensional Sensing, KE Hub Sandpit, (Academic), University of Manchester, 2026.
• Dynamical Systems and TDA, KE Hub Working Group, (Academic), University of Oxford, 2025.

Thinkubators

I participated in the following Thinkubators at CAMaCS:

• Warwickshire Police, 2025.
• Platform Housing, 2025.
• BarberBoss, 2025.
• Bosch, 2025.

Other Interdisciplinary Activities

• Co-organizing the FSEM (Faculty of Science, Engineering, and Medicine) Symposium, University of Warwick, 2026.
• Participated in the ESGI (European Study Group with Industry), University of Bristol, 2025.