معرفی
Esma Dirican Erdal serves as an Assistant Professor in the Department of Mathematics within the Faculty of Engineering and Natural Sciences at Istanbul Kültür University. Her academic profile combines rigorous research in geometric and algebraic topology with dedicated undergraduate instruction across foundational mathematics courses.
Her educational journey includes:
- BSc in Mathematics from Hacettepe University (2008-2013)
- MSc in Mathematics from Hacettepe University (2013-2015)
- PhD in Mathematics from Izmir Institute of Technology (2017-2021)
- Postdoctoral research at Istanbul Technical University (2022-2023)
Dr. Erdal's research centers on topological invariants and their geometric applications, with particular expertise in Reidemeister torsion, discrete topological complexity, and representation varieties. Her work bridges abstract topological concepts with concrete geometric structures, focusing on surfaces and 3-manifolds through techniques like pants decomposition and volume form analysis. She investigates how torsion invariants behave under manifold operations such as connected sums and boundary gluings, revealing deep connections between algebraic topology and differential geometry.
Analysis of her publication record reveals two dominant research trajectories: (1) The systematic development of Reidemeister torsion theory for surfaces and 3-manifolds, including multiplicative properties under connected sums and applications to representation varieties; (2) The extension of discrete topological complexity to higher analogues, providing new theoretical frameworks for motion planning problems. Her recent work increasingly integrates geometric structures with topological invariants, particularly in the context of Kahler manifolds and moduli spaces.
Dr. Erdal actively contributes to academic instruction through courses including Discrete Mathematics (Turkish, 2021-2024), Linear Algebra (English, 2022-2024), Calculus-I (English, 2020-2022), and Basic Mathematics (English, 2020-2021). Her research projects encompass investigations into Reidemeister torsion's multiplicative properties on unique factorization monoids, applications to Kahler manifolds, and connections between Lefschetz numbers and the Cartan determinant conjecture.
