Arkadij Bojko

Bio

My research field is enumerative algebraic geometry where I have mainly focused on sheaf-counting theories thus far. Through my work, I help to advance our understanding of invariants and structures of moduli spaces of sheaves. I enjoy finding new approaches to existing problems that borrow tools from representation theory and differential geometry. I dedicated most of my time to two main areas: sheaf-counting on Calabi-Yau fourfolds and Virasoro constraints for linear categories. Here, I used vertex algebras and their formal families combined with wall-crossing to prove multiple existing conjectures. Returning to my roots, I am beginning to dabble in various topics of mathematical physics.My research field is enumerative algebraic geometry where I have mainly focused on sheaf-counting theories thus far. Through my work, I help to advance our understanding of invariants and structures of moduli spaces of sheaves. I enjoy finding new approaches to existing problems that borrow tools from representation theory and differential geometry. I dedicated most of my time to two main areas: sheaf-counting on Calabi-Yau fourfolds and Virasoro constraints for linear categories. Here, I used vertex algebras and their formal families combined with wall-crossing to prove multiple existing conjectures. Returning to my roots, I am beginning to dabble in various topics of mathematical physics.

Education Experience

• 2018.10 – 2021.5  University of Oxford     DPhil in Mathematics
• 2016.6 – 2018.9  University of Vienna MSc in Physics
• 2017.2 – 2018.5  University of Vienna MSc in Mathematics
• 2013.10-2016.6   University of Vienna    BSc in Physics

Work Experience

• 2021.9 – 2023.8 ETH Zurich     Postdoctoral researcher
• 2023.09 – 2025.2 Academia Sinica Institute research scholar

Honors and Awards

• 2023-2028 Institute Research Scholarship at Academia Sinica (left for assistant professorship at SIMIS)
• 2021 Commendation for PhD thesis from Merton College
• 2021 Commendation for PhD thesis from the Division of Mathematical, Physical and Life Sciences Graduate School Office
• 2018–2021 Clarendon Scholarship at the University of Oxford

Publications

1. A. Bojko, W. Lim, and M. Moreira, Virasoro constraints for moduli of sheaves and vertex algebras, Invent. Math. 236 (2024), no. 1, 387–476.
2. A. Bojko, Hilbert schemes of points on Calabi–Yau 4-folds via wall-crossing, Adv. Math. 448 (2024), Paper No. 109715.
3. A. Bojko, Application of Lagrange inversion to wall-crossing for Quot schemes on surfaces, Port. Math. 81 (2024), no. 1-2, 97–106.
4. A. Bojko, Orientations for DT invariants on quasi-projective Calabi-Yau 4-folds, Adv. Math. 388 (2021), Paper No. 107859, 59.