Notes and Publications

Notes, talks and Writings

• Nerves,oo-categories and the Boardman-Vogt construction
• Here is my project report from my Summer 2022 reading project. (Comments: The report is expository in nature, mostly based on work by Mike Shulman and Nima Rasekh. A paper is currently in progress, which has been motivated by some of the later parts of this report.)
• Kan Fibrations and the Kan-Quillen Model Structure
• Non-Presentable Higher Topos Semantics of HoTT and a proposed realizability model
• The Joyal Model Structure
• The Henry Model Structure
• A (function) realizability model of HoTT
• Homotopy Groups of Kan Complezes and Serre’s Long Exact Sequence of a fibration
• A 2-categorical Quillen’s Theorem A (Part 1)
• A 2-categorical Quillen’s Theorem A (Part 2)
• An intro to Thom Spectra and Thom spectra as Orthogonal spectra
• Lazard’s Theorem and Complex Oriented Cohomology Theories
• Flatness over M_FG and Landweber Exactness
• Elementary Higher Topoi. Why should the Topologist care?
• Lubin-Tate Theory
• Extended Reflection Positivity for Invertible Topological Quantum Field Theories (Part 1)
• Extended Reflection Positivity for Invertible Topological Quantum Field Theories (Part 2)
• The May spectral Sequence for AdSS E2 page computations: In these notes, I try to motivate the May SS and compute the stable homotopy groups of the sphere and the AdSS E2 page of ko using two approaches: using minimal $\mathcal{A}(1)$-resolutions and the May SS.
• A (function) realizability model of HoTT: This time I had a different audience compared to last time’s Octoberfest, so the content is a bit different.

Publications, Preprints and Works in Progress

• A Realizability Model of HoTT (work in progress with Ulrik Buchholtz)
• Generalised N_∞ operads (in progress)
• $\mathbb{E}_n$-algebras in $(m+1)$-categories (in progress with Leon Liu) *