# 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) *