I am a Lecturer at Queen's University Belfast.
Prior to this I was a Postdoctoral Fellow at the Max Planck Institute of Mathematics in Bonn where my mentor was 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: s.balchin@qub.ac.uk
Publications
Accepted Papers
- S. Balchin, E. MacBrough and K. Ormsby, "Composition closed premodel structures and the Kreweras lattice", European Journal of Combinatorics, Vol. 116 (2024).
- S. Balchin, E. MacBrough and K. Ormsby, "Lifting $N_\infty$ operads from conjugacy data", Tunisian Journal of Mathematics, Vol. 5, no.3, 479-504 (2023).
- S. Balchin, K. Ormsby, A. Osorno and C. Roitzheim, "Model structures on finite total orders", Mathematische Zeitschrift , Vol. 3-, no.3, 45pp (2023).
- S. Balchin and J. P. C. Greenlees, "Separated and complete adelic models for one-dimensional Noetherian tensor-triangulated categories". 37pp. Journal of Pure and Applied Algebra, Vol. 226, no. 12 (2022).
- S. Balchin, D. Barnes and C. Roitzheim, "$N_\infty$-operads and associahedra", Pacific Journal of Mathematics, Vol 315, no. 2, 285-304 (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, D. Barnes and T. Barthel, " Profinite equivariant spectra and their tensor-triangular geometry ". 88pp. (2024).
- S. Balchin, T. Barthel and J.P.C. Greenlees "Prismatic decompositions and rational G-spectra ". 61pp. (2023).
- S. Balchin, C. Roitzheim and J. Williamson, " Tensor-triangular rigidity in chromatic homotopy theory ". 16pp. (2023).
- S. Balchin and G. Stevenson, "Big categories, big spectra". 27pp. (2021).
- S. Balchin, E. MacBrough and K. Ormsby, "The combinatorics of $N_\infty$ operads for $C_{qp^n}$ and $D_{p^n}$". 20pp. (2022).
Books
- S. Balchin, "A Handbook of Model Categories". XV+326. Algebra and Applications, Vol 27. (2021).
Edited Volumes
- S. Balchin, D. Barnes, M. Kędziorek and M. Szymik, "Equivariant Topology and Derived Algebra". XVIII+338. London Mathematical Society Lecture Notes, Vol 474. (2021).