I am a Postdoctoral Fellow at the Max Planck Institute of Mathematics in Bonn, mainly interested in all things related to tensor-triangulated geometry and Quillen model categories. My mentor is Tobias Barthel.
I completed my Ph.D. at the University of Leicester in 2017 under the supervision of Frank Neumann. Following this I was a postdoc at the University of Sheffield and the University of Warwick with John Greenlees working on the project "Adelic models, rigidity and equivariant cohomology".
email: balchin@mpim-bonn.mpg.de
Publications
Accepted Papers
- S. Balchin, D. Barnes and C. Roitzheim, "$N_\infty$-operads and associahedra", 18pp To appear in Pacific Journal of Mathematics, (2021).
- S. Balchin, J. P. C. Greenlees, L. Pol and J. Williamson "Torsion models for tensor-triangulated categories: the one-step case ". 35pp. To appear in Algebraic & Geometric Topology, (2021).
- S. Balchin and J. P. C. Greenlees, "Adelic models of tensor-triangulated categories". 45pp. Advances in Mathematics, Vol 375, (2020).
- S. Balchin, D. Bearup, C. Pech and C. Roitzheim, "Equivariant homotopy commutativity for $G=C_{pqr}$". 11pp. Tbilisi Mathematical Journal, Special Issue on Homotopy Theory, Spectra, and Structured Ring Spectra, 17-31, 2020. (2020).
- S. Balchin and F. Neumann, "On the number of rational points of classifying stacks for Chevalley group schemes". Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants - Interactions between Geometry, Topology, Number Theory and Algebra, Springer Proceedings in Mathematics & Statistics, Springer (2020).
- S. Balchin and R. Garner, "Bousfield localisation and colocalisation of one-dimensional model structures", Applied Categorical Structures, Vol 27, no. 3, 1-21 (2019).
- S. Balchin, "Homotopy of Planar Lie Group Equivariant Presheaves", Journal of Homotopy and Related Structures, Vol 13, no. 3, 555-580 (2018).
- S. Balchin, "Crossed Simplicial Group Categorical Nerves", Applied Categorical Structures, Vol 28, no.3, 545-558 (2018).
- S. Balchin and D. Rust, "Computations for Symbolic Substitutions", Journal of Integer Sequences, Vol. 20, 36pp (2017).
Submitted Papers
- S. Balchin and J. P. C. Greenlees, "Separated and complete adelic models for one-dimensional Noetherian tensor-triangulated categories". 37pp. (2021).
Books
- S. Balchin "A Handbook of Model Categories". xiv+304. Algebra and Applications, Vol 27. (2021).
Edited Volumes
- S. Balchin, D. Barnes, M. Kędziorek, M. Szymik, "Equivariant Topology and Derived Algebra". xviii+338. To appear in London Mathematical Society Lecture Notes, (2021).