Dilan Karaguler

I am a Ph.D. candidate in Mathematics at Michigan State University, advised by Prof. Ekaterina Rapinchuk and Prof. Guo-Wei Wei. I expect to graduate in May 2027.

My work sits between applied algebraic topology and machine learning. I develop new homology theories for directed graphs and path complexes, most recently Mayer path homology, and turn them into topological features that graph neural networks can use on molecular, dynamical and engineering data. I also bring these tools to industry: at Intel I have built graph and GNN pipelines for chip-layout analysis and yield workflows.

Before MSU, I earned my M.S. (2021) and B.S. (2019, honor student) in Mathematics at Middle East Technical University (METU) in Ankara, where my master’s thesis, supervised by Assoc. Prof. Semra Pamuk, surveyed multidimensional persistence theory.

Research interests

• Applied algebraic topology and topological data analysis (TDA)
• Path homology and Mayer (N-nilpotent) homology of directed graphs and path complexes
• Persistent homology
• Topology-informed graph machine learning and geometric deep learning, with applications to molecular, dynamical and engineering data

Timeline

• May 2027Expected Ph.D. completion.
• Jul 2026Mayer Path Homology (with G.-W. Wei) accepted to Foundations of Data Science.
• May 2026Started my second Intel internship: Software Engineer Intern in Oregon, extracting schematic topology from chip layout files.
• May 2026Program evaluator for the AI for Advanced Semiconductor Manufacturing Workshop at MSU.
• Sep 2025Poster at the SIAM Great Lakes Section Meeting, Illinois Institute of Technology.
• May 2025Started my first Intel internship: Graduate Technical Intern, applying graph neural networks to chip-layout pattern analysis.
• May 2025Received the Excellence in Teaching Award, MSU Department of Mathematics.
• Mar 2025Poster at the Mathematics of Data, Dynamics, and Life Sciences Conference, UC Irvine.
• Summer 2024Colleges Online Learning Academy (COLA) Fellowship, Michigan State University.
• Apr 2024Co-organized the Graduate Student Topology and Geometry Conference at MSU.
• Aug 2023Became Lead Teaching Assistant in the MSU Department of Mathematics.
• May 2023Research Mentor for the Topology RTG at MSU.
• Aug 2022Started my Ph.D. in Mathematics at Michigan State University; joined the AWM MSU Chapter board.
• Sep 2021Completed my M.S. in Mathematics at METU with the thesis A Survey on Multidimensional Persistence Theory.