Email: artofkot [at] iu.edu
I am a math postdoc at Indiana University, working in low-dimensional topology. Before that I was a graduate student at Princeton, under the supervision of Zoltán Szabó. Take a look at my CV below for more information.
My work is at the crossroads of symplectic geometry and low-dimensional topology. In particular, I use methods from bordered Heegaard Floer homology and Fukaya categories to study invariants of such objects as 3-manifolds, knots, mapping classes of surfaces. Currently, I mostly think about immersed curve invariants of four-ended tangles. Take a look at this brief introduction to my research, and papers below for more details.
Slides and talks:
- The earring correspondence on the pillowcase. (video)
Workshop at BIRS "Interactions of Gauge Theory with Contact and Symplectic Topology in dimensions 3 and 4", June 2020.
Content: traceless character varieties, Pillowcase homology, immersed Lagrangian correspondences, quilts and an example of a figure eight bubble.
- Heegaard Floer and Khovanov theories through the lens of immersed curves, I. (video)
Virtual seminar Trends in Low-Dimensional topology, May 2020.
Content: brief introduction to Khovanov homology, Heegaard Floer theory, and Lagrangian Floer homology of curves on surfaces.
- Knot homologies through the lens of immersed curves.
Joint LA topology seminar, April 2020.
Content: overview of all existing immersed curve invariants, criterion for when a type D structure can be thought of as an immersed curve, a glimpse into mnemonic paper, and an overview of immersed curves paper.