---
date: 2021-11-05
tags: [ web/quick-notes ]
---

# 2021-11-05

Tags:
#web/quick-notes

Refs:
?

## 01:31

Differential forms on (derived) [Projects/2022 Algebraic Geometry Oral Exam/500 Stacks and Moduli](Projects/2022%20Algebraic%20Geometry%20Oral%20Exam/500%20Stacks%20and%20Moduli.md):

![](figures/2021-11-05_01-32-03.png)


![](figures/2021-11-05_01-33-08.png)



![](figures/2021-11-05_01-37-40.png)



What is non-commutative geometry?

![](figures/2021-11-05_02-10-53.png)


Category of singularities:

![](figures/2021-11-05_02-11-49.png)



Bloch's conductor conjecture:


![](figures/2021-11-05_02-13-37.png)



# Other Stuff

On harmonic bundles:


![](figures/2021-11-05_10-22-50.png)



![](figures/2021-11-05_10-50-57.png)


![](figures/2021-11-05_10-52-20.png)


![](figures/2021-11-05_10-52-33.png)


![](figures/2021-11-05_10-58-02.png)


## 13:41

Existence of spin and string structures: kind of like applying a functor to the Whitehead tower and asking for sections of the image tower:

\begin{tikzcd}
	{\B\String_n} & \vdots && \vdots \\
	{\B\Spin_n} & {\BO_n\gens{2}} && {[X, \BO_n\gens{2}]} \\
	{\B\SO_n} & {\BO_n\gens{1}} && {[X, \BO_n\gens{1}]} \\
	{\B \O_n} & {\BO_n\gens{0}} && {[X, \BO_n\gens{0}]}
	\arrow[from=1-2, to=2-2]
	\arrow[""{name=0, anchor=center, inner sep=0}, from=2-2, to=3-2]
	\arrow[from=3-2, to=4-2]
	\arrow[""{name=1, anchor=center, inner sep=0}, from=2-4, to=3-4]
	\arrow[from=3-4, to=4-4]
	\arrow["{s_0}"', curve={height=12pt}, dashed, from=4-4, to=3-4]
	\arrow["{s_1}"', curve={height=12pt}, from=3-4, to=2-4]
	\arrow[from=1-4, to=2-4]
	\arrow["{[X, \wait]}", shorten <=20pt, shorten >=20pt, Rightarrow, from=0, to=1]
\end{tikzcd}

> [Link to Diagram](https://q.uiver.app/?q=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)