Research interests

My interests lie at the intersection between algebra and geometry. I try to tackle geometric problems with the use of algebraic tools such as homological algebra, dg-categories, and so on.

During the first year of my PhD, I worked on spherical twists around spherical functors and equivalences of derived categories arising from a flop, the so called "flop-flop" autoequivalences. From the studies I have undertaken during this period, the preprints "On the composition of two spherical twists"  and "Spherical functors and the flop-flop autoequivalence" have developed.

After that, I delved into the topic of categorical dynamical systems, and together with Dr Jongmyeong Kim we wrote two preprints: "Entropy of the composition of two spherical twists" and "On Gromov-Yomding type theorems and a categorical interpretation of holomorphicity".

The last works of my PhD were focused on categories of matrix factorisations: Serre functors of residual categories via hybrid models, and autoequivalences of K3 surfaces: Spherical twists, relations and the center of autoequivalence groups of K3 surfaces.

I am also interested in topics such as 

Preprints

Spherical twists, relations and the center of autoequivalence groups of K3 surfaces, with Kohei Kikuta, arXiv:2210.00228 

Serre functors of residual categories via hybrid models, with Ed Segal, arXiv:2205.04793; published (online) in Bull. LMS

On Gromov-Yomdin type theorems and a categorical interpretation of holomorphicity, with Jongmyeong Kim, arXiv:2110.12597 

Entropy of the composition of two spherical twists, with Jongmyeong Kim, arXiv:2107.06709; to appear in Osaka Math Journal, Vol 60 No. 3 (July 2023)

Spherical functors and the flop-flop autoequivalence, arXiv:2007.14415

This paper has three versions on the arXiv. Here is a roadmap to the differences between the versions:

On the composition of two spherical twists, Published (online) in IMRN; arXiv:2006.06016

This paper also has three versions; here's a road map to the differences: