Preprints/Theses
- Algorithmic Computation of Reidemeister Torsion bachelors thesis, 17 pages, PDF
- Formal Group Laws and Stable Homotopy Theory over Compactly Metrizable Groups masters thesis, 76 pages, PDF
- Gros Topoi as Partially Lax Limits of Petit Topoi (joint with Qi Zhu) preprint, 15 pages, arXiv:2609.35119, PDF
Detailed Descriptions
- Gros Topoi as Partially Lax Limits of Petit Topoi joint with Qi Zhu
We prove that the sheaf $\infty$-topos associated to a geometric site in the sense of Lurie can be written as a partially lax limit of smaller sheaf $\infty$-topoi. This is thus a formalization of Lurie's vision for fractured $\infty$-topoi to axiomatize the relation between gros and petit topoi. As a consequence, we realize the $\infty$-topos of $\kappa$-small condensed anima as a partially lax limit of sheaf $\infty$-topoi over extremally disconnected spaces, marked at the open embeddings. Moreover, we deduce a gros version of the étale exodromy theorem.
- Formal Group Laws and Stable Homotopy Theory over Compactly Metrizable Groups Masters Thesis in Chromatic Equivariant Homotopy Theory
We extend the theory of complex-oriented cohomology theories to the setting of A-equivariant homotopy theory, where A is a compact metrizable abelian group. We identify the homotopy groups of the A-equivariant complex bordism spectrum with the A-equivariant Lazard ring, and we factor the chromatic character map via geometric fixed points through p-adic equivariant Borel–Lubin–Tate theory.
- Algorithmic Computation of Reidemeister Torsion Bachelors Thesis in Computational Algebraic Topology
We develop an algorithm that computes the Reidemeister Torsion of the geometric realization of a simplicial set. We compute the Reidemeister Torsions of the Poincare Homology 3-Sphere.