Welcome to my webpage!

I am a PhD candidate in Biomathematics at Florida State University, advised by Tom Needham. My research spans both the theoretical and applied aspects of Topological Data Analysis. Looking ahead, I aim to pursue a research or data scientist role, with a focus on developing and applying geometric and topological methods to challenging problems in data science.

CV Google Scholar GitHub

Interests: Topological Data Analysis, Metric Geometry, Optimal Transport, Data Science

Publications

Preprints

A Persistent Homology Pipeline for the Analysis of Neural Spike Train Data

C Ayhan, AN Nash, R Vincis, M Bauer, R Bertram, T Needham

arXiv preprint (2025)

arXiv Code

Equivalence of Landscape and Erosion Distances for Persistence Diagrams

Cagatay Ayhan and Tom Needham

arXiv preprint (2025)

arXiv

Talks

Highlighted talks

A Persistent Homology Pipeline for the Analysis of Neural Spike Train Data
AMS Spring Southeastern Sectional Meeting, Georgia Southern University — Mar 2026
Equivalence of Landscape and Erosion Distances for Persistence Diagrams
Topological Data Analysis Conference 2025 (Talk + Poster), University of Missouri — Nov 2025
Equivalence of Landscape and Erosion Distances for Persistence Diagrams
ComPer 2025: Workshop on Computational Topology (Online talk), University at Albany (SUNY) — Oct 2025
Topological Optimization Techniques
Machine Learning/Data Science Seminar, Florida State University — Mar 2025
TDA in Simultaneously Recorded Neural Spike Train Datasets
AMS Spring Southeastern Sectional Meeting, Florida State University — Mar 2024
Multiple Neuron Spike Train Data Analysis Using Persistent Homology
ICERM (Lightning talk), Brown University — Oct 2023

Service

Professional and community contributions.

Co-organizer, with Tom Needham and Martin Bauer, Special Session on Geometric Methods for Data Science
2026 Spring Southeastern Sectional Meeting of the American Mathematical Society
Georgia Southern University, Armstrong Campus — Savannah, GA
March 28–29, 2026

Teaching

Instructional roles at Florida State University.

Course Instructor
- MAC2313 — Calculus with Analytic Geometry III (Fall 2025)
- MAC2312 — Calculus with Analytic Geometry II (Spring 2025)
- MAC2311 — Calculus with Analytic Geometry I (Spring 2024)
- MAC1140 — Precalculus Algebra (Spring 2023)
Recitation Instructor
- MAD2104 — Discrete Mathematics I (Fall 2023)
- MAC2311 — Calculus with Analytic Geometry I (Fall 2022)
Teaching / Lab Assistant
- MAC2233 — Business Calculus (Fall 2021, Summer 2023)
- MGF1107, MAC1140, MAC1105 (Spring 2022, Summer 2022)
Grader
- MAC5301, MAC2302 (Spring 2022, Fall 2021)
Research Assistant
- Supported by NSF Grant DMS-2324962 (Summer 2024, Fall 2024, Summer 2025, Spring 2026)

Contact

Emailhca21a@fsu.edu

OfficeMCH, 402F