Matthew Edward Hedden

Matthew Edward Hedden is a Professor in the Department of Mathematics at Michigan State University's College of Natural Science, where he maintains an active research program in low-dimensional topology. His office is located in D325 Wells Hall, and he holds regular office hours via Zoom on Wednesdays and Thursdays. Hedden has established himself as a leading researcher in Heegaard Floer homology and its applications to knot theory and 4-manifold topology.

Hedden's research centers on low-dimensional topology, with emphases on Heegaard Floer homology, knot concordance, and connections between symplectic topology and gauge theory. His work explores deep relationships between knot invariants, 3- and 4-manifold structures, and complex curves in Stein domains. He has made significant contributions to understanding how Floer-theoretic invariants detect geometric properties of knots and 3-manifolds, particularly through his investigations of cabling operations, satellite constructions, and concordance invariants. His research often bridges abstract topological frameworks with concrete computational techniques in knot theory.

Hedden's publication record demonstrates consistent innovation in low-dimensional topology over the past two decades. His work shows a clear trajectory from foundational studies in knot Floer homology toward increasingly sophisticated applications in 4-manifold topology and connections with symplectic geometry. Key thematic developments include the systematic exploration of concordance invariants, the geometric interpretation of Floer homology through pillowcase geometry, and the extension of these techniques to study complex curves in Stein domains. His collaborative work spans multiple subfields, reflecting the interdisciplinary nature of modern geometric topology.

Hedden has received significant recognition for his research, most notably the prestigious Alfred P. Sloan Research Fellowship (2011-2013). His work has been supported by multiple National Science Foundation grants, including a CAREER award.

Hedden has directed substantial research funding through six National Science Foundation grants spanning 2005-2020, including the CAREER grant DMS-1150872 on Floer Homology and Low-Dimensional Topology (2012-2018) and the research grant DMS-1709016 on Floer Homology, Concordance, and Complex Curves (2017-2020). His research program has fostered numerous collaborations across the topology community, resulting in over 30 publications in top mathematics journals. Through his extensive lecture notes and resource compilations on Heegaard Floer homology, Hedden has significantly contributed to the education and training of new researchers in the field.