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".

I am also interested in topics such as

  • Hochschild (co)homology and its applications in algebraic geometry

  • language of infinity categories

  • derived algebraic geometry

Preprints

Serre functors of residual categories via hybrid models, with Ed Segal, arXiv:2205.04793

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

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:

  • v1: this was the first version, you can find here both the theoritical part and the examples.

  • v2: this version is the first half of v1 because the second half was moved to arXiv:2103.02555; however, I have now merged them back together.

  • v3: this is the most recent version; I have merged the examples back, but most importantly I have heavily rewritten most of the paper. The main result is unchanged (it is actually strengthened, in that I prove it for compactly generated, enhanced triangulated categories), but the proofs are simplified and the exposition is improved. The strategy to carry out the computation in the Mukai flop case has changed, but if you want to read through many pages of involved computations you can still have a look at the appendix of v1. :)

On the composition of two spherical twists, arXiv:2006.06016

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

  • v1: this is the first version, nothing much to say.

  • v2: I just added some funder acknowledgement.

  • v3: the biggest difference (apart from some rewriting that simplified many proofs and improved the exposition) is that in this version I have implemented the framework of bar categories as defined in [Anno-Logvinenko, arXiv:1612.09530 ]. This helped me to simplify the proofs and made it possible to strengthen the initial result: not only I can glue spherical functors, I can also describe explicitly the cotwist of the glued spherical functor (something that in v1 I could do only in the example of gluing of spherical objects).