Ian Zemke

Ian Zemke is an Assistant Professor in the Department of Mathematics at the University of Oregon's College of Arts and Sciences. His research focuses on low-dimensional topology and symplectic geometry, with a particular emphasis on Heegaard Floer homology and knot theory.

Education:

• PhD in Mathematics from University of California, Los Angeles (2017) - Advisor: Ciprian Manolescu

Research Interests:

Zemke's work bridges symplectic geometry and low-dimensional topology, using Heegaard Floer homology as a primary tool. His research explores fundamental questions in knot theory, 3- and 4-dimensional manifold theory, and the interplay between different Floer-theoretic invariants. Key areas include:

• Development of surgery formulas in Heegaard Floer homology
• Study of concordance and cobordism invariants for knots and links
• Investigation of involutive Floer homologies and their applications
• Analysis of exotic smooth structures on 4-manifolds

Recent Research Trends:

Zemke's recent publications demonstrate a concentrated focus on advancing the theoretical foundations of Heegaard Floer homology, particularly through the development of new surgery formulas and the study of involutive invariants. His work consistently addresses fundamental questions about knot concordance and the structure of 3- and 4-manifolds, with significant contributions to understanding the relationship between different Floer-theoretic invariants.

Scientific Awards:

• Sloan Research Fellowship

Funding and Support:

Zemke's research is partially supported by:

• National Science Foundation grants DMS-1703685 and DMS-2204375
• Sloan Research Fellowship

Teaching and Service:

Currently teaching Math 690: Morse Theory in Autumn 2025 at the University of Oregon. He maintains an active website with research materials, including Python and Sage code for computational topology, lecture notes, and slides from various conferences and summer schools.