Irving Dai

E-mail: Office: PMA 12-160

Hi! I am an assistant professor at the University of Texas at Austin. I am primarily interested in low-dimensional topology, Floer homology, and gauge theory.

My recent papers have focused on studying symmetries of knots and manifolds through tools such as Heegaard Floer homology and instanton Floer homology. These have had several exciting applications to questions involving corks and exotic phenomena, as well as providing new sliceness obstructions. You can read about part of my research in the following Quanta article.

I am also interested in lattice homology, a rather mysterious invariant with connections to singularity theory and algebraic geometry. Some of my work has involved understanding the connection between lattice homology and Seiberg-Witten-Floer homotopy.

I was previously an NSF Postdoctoral Fellow at Stanford working with Ciprian Manolescu; before that, I was an NSF Postdoctoral Fellow at MIT working with Tomasz Mrowka. I received my PhD in 2019 from Princeton under the direction of Zoltán Szabó.