I work in low-dimensional topology, specifically in invariants of 3- and 4-dimensional manifolds defined using gauge theory. I am especially interested in the constructions of Floer theories, which involves the study of topology of infinite-dimensional spaces equipped with functions (e.g., the Chern-Simons-Dirac functional or the Chern-Simons functional). This involves the study of:

• specific elliptic PDEs (e.g. Seiberg-Witten or Yang-Mills equations), especially in a low-regularity setting,
• Morse theory in infinite-dimensions and the related "semi-infinite dimensional" versions of geometric homology,
• constructions of equivariant Floer theories,
• algebraic and differential topology of infinite-dimensional manifolds.

I obtained my PhD in Mathematics in 2020 from Massachusetts Institute of Technology under the guidance of Tomasz S. Mrowka. My thesis was on the topic of Semi-infinite Homology of Floer Spaces.

Publications:

1. Słomka J., Suwara S., Dunkel J., The nature of triad interactions in active turbulence, J. Fluid Mech. 841 (2018), doi:10.1017/jfm.2018.108.
2. Suwara P., Minimal Generating Sets of Directed Oriented Reidemeister Moves, J. Knot Theory Ramifications 26, 1750016 (2017), doi:10.1142/S021821651750016X.
3. Oszmaniec O., Suwara P., Sawicki A., Geometry and Topology of CC and CQ states, J. Math. Phys. 55, 062204 (2014), doi:10.1063/1.4883879.