Erik Carlsson

Erik Carlsson is a Professor in the Mathematics department at the University of California, Davis. His research spans multiple areas of pure and applied mathematics, connecting deep theoretical concepts with practical computational applications.

He received his Ph.D. from Princeton University under Professor Andrei Okounkov in 2008, and a B.S. in Mathematics with honors and a minor in Computer Science from Stanford University in 2003.

Carlsson's research focuses on representation theory, algebraic geometry, algebraic combinatorics, computational topology, and connections with nonconvex optimization. He is particularly interested in connections between Goresky-Kottwitz-Macpherson (GKM) spaces and applications to Macdonald theory and combinatorics. His work also includes computational topology, especially persistent homology, which he develops in collaboration with John Carlsson. One of his recent developments is a method for constructing the alpha complex in high dimension using the powerful duality principle in mathematical optimization.

His recent publications show a clear trend toward bridging theoretical mathematics with computational applications. His work spans from proving deep conjectures in algebraic combinatorics (like the shuffle conjecture) to developing practical algorithms for topological data analysis. The interdisciplinary nature of his work connects pure mathematical theory with applications in data science, computer vision, and optimization problems.

Carlsson has made significant contributions to multiple fields of mathematics through his collaborations and independent work. His research has implications for both theoretical mathematics and practical computational problems, with recent publications as of 2024 demonstrating his continued active research program.