Added AG and CA

.github/workflows/pdf.yml

@@ -14,6 +14,8 @@ jobs:
       # one filename per line, including directory if in a subdirectory
       FILES: |
         F4D1-Analysis-and-Geometry-on-Manifolds/Analysis_on_Manifolds_Notes.tex
+        V4A1-Algebraic-Geometry-I/Algebraic_Geometry_I_Notes.tex
+        V5B1-Advanced-Topics-in-Complex-Analysis/Advanced_Complex_Analysis_Notes.tex
     steps:
       - name: Checkout
         uses: actions/checkout@v4

.gitignore

@@ -303,6 +303,6 @@ TSWLatexianTemp*
 # option is specified. Footnotes are the stored in a file with suffix Notes.bib.
 # Uncomment the next line to have this generated file ignored.
 #*Notes.bib
-*.bbl-SAVE-ERROR
-F4D1-Analysis-and-Geometry-on-Manifolds/Analysis_on_Manifolds_Notes.pdf
+V4A1-Algebraic-Geometry-I/Algebraic_Geometry_I_Notes.pdf
 F4D1-Analysis-and-Geometry-on-Manifolds/Analysis_on_Manifolds_Notes.pdf
+V5B1-Advanced-Topics-in-Complex-Analysis/Advanced_Complex_Analysis_Notes.pdf

F4D1-Analysis-and-Geometry-on-Manifolds/Analysis_on_Manifolds_Notes.tex

@@ -43,7 +43,7 @@
 \urladdr{https://wgabrielong.github.io/}
 \maketitle
 \section*{Preliminaries}
-These notes roughly correspond to the course \textbf{F4D1 -- Analysis and Geometry on Manifolds} taught by Prof. Laurent C\^{o}t\'{e} at the Universit\"{a}t Bonn in the Winter 2024/25 semester. These notes are \LaTeX-ed after the fact with significant alteration and are subject to misinterpretation and mistranscription. Use with caution. Any errors are undoubtedly my own and any virtues that could be ascribed to these notes ought be attributed to the instructor and not the typist. x
+These notes roughly correspond to the course \textbf{F4D1 -- Analysis and Geometry on Manifolds} taught by Prof. Laurent C\^{o}t\'{e} at the Universit\"{a}t Bonn in the Winter 2024/25 semester. These notes are \LaTeX-ed after the fact with significant alteration and are subject to misinterpretation and mistranscription. Use with caution. Any errors are undoubtedly my own and any virtues that could be ascribed to these notes ought be attributed to the instructor and not the typist. 
 \tableofcontents
 \include{Lecture 1}
 \newpage

V4A1-Algebraic-Geometry-I/Algebraic_Geometry_I_Notes.tex

@@ -0,0 +1,51 @@
+\documentclass{amsart}
+\usepackage[margin=1.1in]{geometry} 
+\usepackage{amsmath}
+\usepackage{tcolorbox}
+\usepackage{amssymb}
+\usepackage{amsthm}
+\usepackage{lastpage}
+\usepackage{fancyhdr}
+\usepackage{accents}
+\usepackage{hyperref}
+\usepackage{xcolor}
+\usepackage{color}
+\input{shortcuts.tex}
+\setlength{\headheight}{40pt}
+
+
+\newenvironment{solution}
+  {\renewcommand\qedsymbol{$\blacksquare$}
+  \begin{proof}[Solution]}
+  {\end{proof}}
+\renewcommand\qedsymbol{$\blacksquare$}
+
+\usepackage{amsmath, amssymb, tikz, amsthm, csquotes, multicol, footnote, tablefootnote, biblatex, wrapfig, float, quiver, mathrsfs, cleveref, enumitem, upgreek,stmaryrd}
+\addbibresource{refs.bib}
+\theoremstyle{definition}
+\newtheorem{theorem}{Theorem}[section]
+\newtheorem{lemma}[theorem]{Lemma}
+\newtheorem{corollary}[theorem]{Corollary}
+\newtheorem{exercise}[theorem]{Exercise}
+\newtheorem{question}[theorem]{Question}
+\newtheorem{example}[theorem]{Example}
+\newtheorem{proposition}[theorem]{Proposition}
+\newtheorem{conjecture}[theorem]{Conjecture}
+\newtheorem*{remark}{Remark}
+\newtheorem{definition}[theorem]{Definition}
+\numberwithin{equation}{section}
+\begin{document}
+\large
+\title[Algebraic Geometry I]{V4A1 -- Algebraic Geometry I \\ Winter Semester 2024/25}
+\author{Wern Juin Gabriel Ong}
+\address{Universit\"{a}t Bonn, Bonn, D-53111}
+\email{[email protected]}
+\urladdr{https://wgabrielong.github.io/}
+\maketitle
+\section*{Preliminaries}
+These notes roughly correspond to the course \textbf{V4A1 -- Algebraic Geometry I} taught by Prof. Daniel Huybrechts at the Universit\"{a}t Bonn in the Winter 2024/25 semester. These notes are \LaTeX-ed after the fact with significant alteration and are subject to misinterpretation and mistranscription. Use with caution. Any errors are undoubtedly my own and any virtues that could be ascribed to these notes ought be attributed to the instructor and not the typist. 
+\tableofcontents
+\include{Lecture 1}
+\newpage
+\printbibliography
+\end{document}

V4A1-Algebraic-Geometry-I/Lecture 1.tex

@@ -0,0 +1 @@
+\section{Lecture 1}

V4A1-Algebraic-Geometry-I/quiver.sty

@@ -0,0 +1,40 @@
+% *** quiver ***
+% A package for drawing commutative diagrams exported from https://q.uiver.app.
+%
+% This package is currently a wrapper around the `tikz-cd` package, importing necessary TikZ
+% libraries, and defining a new TikZ style for curves of a fixed height.
+%
+% Version: 1.2.2
+% Authors:
+% - varkor (https://github.com/varkor)
+% - AndréC (https://tex.stackexchange.com/users/138900/andr%C3%A9c)
+
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{quiver}[2021/01/11 quiver]
+
+% `tikz-cd` is necessary to draw commutative diagrams.
+\RequirePackage{tikz-cd}
+% `amssymb` is necessary for `\lrcorner` and `\ulcorner`.
+\RequirePackage{amssymb}
+% `calc` is necessary to draw curved arrows.
+\usetikzlibrary{calc}
+% `pathmorphing` is necessary to draw squiggly arrows.
+\usetikzlibrary{decorations.pathmorphing}
+
+% A TikZ style for curved arrows of a fixed height, due to AndréC.
+\tikzset{curve/.style={settings={#1},to path={(\tikztostart)
+    .. controls ($(\tikztostart)!\pv{pos}!(\tikztotarget)!\pv{height}!270:(\tikztotarget)$)
+    and ($(\tikztostart)!1-\pv{pos}!(\tikztotarget)!\pv{height}!270:(\tikztotarget)$)
+    .. (\tikztotarget)\tikztonodes}},
+    settings/.code={\tikzset{quiver/.cd,#1}
+        \def\pv##1{\pgfkeysvalueof{/tikz/quiver/##1}}},
+    quiver/.cd,pos/.initial=0.35,height/.initial=0}
+
+% TikZ arrowhead/tail styles.
+\tikzset{tail reversed/.code={\pgfsetarrowsstart{tikzcd to}}}
+\tikzset{2tail/.code={\pgfsetarrowsstart{Implies[reversed]}}}
+\tikzset{2tail reversed/.code={\pgfsetarrowsstart{Implies}}}
+% TikZ arrow styles.
+\tikzset{no body/.style={/tikz/dash pattern=on 0 off 1mm}}
+
+\endinput

V4A1-Algebraic-Geometry-I/refs.bib

@@ -0,0 +1,148 @@
+@misc{Rezk,
+  author       = {Rezk, Charles},
+  title        = {Introduction to Quasicategories}, 
+  url = {https://people.math.rochester.edu/faculty/doug/otherpapers/Rezk-quasicats-intro.pdf}
+}
+
+@Book{Riehl,
+ Author = {Riehl, Emily},
+ Title = {Category theory in context},
+ ISBN = {978-0-486-80903-8},
+ Year = {2016},
+ Publisher = {Mineola, NY: Dover Publications},
+ Language = {English},
+ Keywords = {18-01,18A05,18A15,01A75},
+ zbMATH = {6649061},
+ Zbl = {1348.18001}
+}
+
+@misc{kerodon,
+  author       = {Jacob Lurie},
+  title        = {Kerodon},
+  howpublished = {\url{https://kerodon.net}},
+  year         = {2023},
+}
+
+@misc{stacks-project,
+  author       = {The {Stacks project authors}},
+  title        = {The Stacks project},
+  howpublished = {\url{https://stacks.math.columbia.edu}},
+  year         = {2023},
+}
+
+@misc{Cisinski,
+      title={The universal coCartesian fibration}, 
+      author={Denis-Charles Cisinski and Hoang Kim Nguyen},
+      year={2022},
+      eprint={2210.08945},
+      archivePrefix={arXiv},
+      primaryClass={math.CT}
+}
+
+@Book{LurieHTT,
+ Author = {Lurie, Jacob},
+ Title = {Higher topos theory},
+ FSeries = {Annals of Mathematics Studies},
+ Series = {Ann. Math. Stud.},
+ Volume = {170},
+ ISBN = {978-0-691-14049-0; 978-0-691-14048-3},
+ Year = {2009},
+ Publisher = {Princeton, NJ: Princeton University Press},
+ Language = {English},
+ DOI = {10.1515/9781400830558},
+ Keywords = {18-02,18B25,18G30,18G55,18F20},
+ zbMATH = {5497319},
+ Zbl = {1175.18001}
+}
+
+@Book{Land,
+ Author = {Land, Markus},
+ Title = {Introduction to infinity-categories},
+ FSeries = {Compact Textbooks in Mathematics},
+ Series = {Compact Textb. Math.},
+ ISSN = {2296-4568},
+ ISBN = {978-3-030-61523-9; 978-3-030-61524-6},
+ Year = {2021},
+ Publisher = {Cham: Birkh{\"a}user},
+ Language = {English},
+ DOI = {10.1007/978-3-030-61524-6},
+ Keywords = {18-01,18Nxx},
+ zbMATH = {7332844},
+ Zbl = {1471.18001}
+}
+
+@misc{AyalaFrancis,
+      title={The cobordism hypothesis}, 
+      author={David Ayala and John Francis},
+      year={2017},
+      eprint={1705.02240},
+      archivePrefix={arXiv},
+      primaryClass={math.AT}
+}
+
+@misc{GradyPavlov,
+      title={The geometric cobordism hypothesis}, 
+      author={Daniel Grady and Dmitri Pavlov},
+      year={2022},
+      eprint={2111.01095},
+      archivePrefix={arXiv},
+      primaryClass={math.AT}
+}
+
+@Article{Freed,
+ Author = {Freed, Daniel S.},
+ Title = {The cobordism hypothesis},
+ FJournal = {Bulletin of the American Mathematical Society. New Series},
+ Journal = {Bull. Am. Math. Soc., New Ser.},
+ ISSN = {0273-0979},
+ Volume = {50},
+ Number = {1},
+ Pages = {57--92},
+ Year = {2013},
+ Language = {English},
+ DOI = {10.1090/S0273-0979-2012-01393-9},
+ Keywords = {57R56,81T45},
+ zbMATH = {6157475},
+ Zbl = {1280.57025}
+}
+
+@Article{CalaqueScheimbauer,
+ Author = {Calaque, Damien and Scheimbauer, Claudia},
+ Title = {A note on the {{\((\infty,n)\)}}-category of cobordisms},
+ FJournal = {Algebraic \& Geometric Topology},
+ Journal = {Algebr. Geom. Topol.},
+ ISSN = {1472-2747},
+ Volume = {19},
+ Number = {2},
+ Pages = {533--655},
+ Year = {2019},
+ Language = {English},
+ DOI = {10.2140/agt.2019.19.533},
+ Keywords = {18D05,57R56},
+ zbMATH = {7075111},
+ Zbl = {1420.18012}
+}
+
+@misc{LuriHopkinsAmbi,
+  author       = {Hopkins, Michael J. and Lurie, Jacob},
+  title        = {Ambidexterity in $K(n)$-Local Stable Homotopy Theory},
+  year         = {2013},
+  url          = {https://www.math.ias.edu/~lurie/papers/Ambidexterity.pdf}
+}
+
+@Article{HarpazAmbi,
+ Author = {Harpaz, Yonatan},
+ Title = {Ambidexterity and the universality of finite spans},
+ FJournal = {Proceedings of the London Mathematical Society. Third Series},
+ Journal = {Proc. Lond. Math. Soc. (3)},
+ ISSN = {0024-6115},
+ Volume = {121},
+ Number = {5},
+ Pages = {1121--1170},
+ Year = {2020},
+ Language = {English},
+ DOI = {10.1112/plms.12367},
+ Keywords = {55U35,57R56,18B35,18N10,18Mxx},
+ zbMATH = {7242523},
+ Zbl = {1479.55031}
+}

V4A1-Algebraic-Geometry-I/shortcuts.tex

@@ -0,0 +1,103 @@
+% Fields
+\newcommand{\CC}{\mathbb{C}}
+\newcommand{\RR}{\mathbb{R}}
+\newcommand{\QQ}{\mathbb{Q}}
+\newcommand{\ZZ}{\mathbb{Z}}
+\newcommand{\NN}{\mathbb{N}}
+\newcommand{\FF}{\mathbb{F}}
+\newcommand{\PP}{\mathbb{P}}
+
+% mathcal letters
+\newcommand{\Acal}{\mathcal{A}}
+\newcommand{\Bcal}{\mathcal{B}}
+\newcommand{\Ccal}{\mathcal{C}}
+\newcommand{\Dcal}{\mathcal{D}}
+\newcommand{\Ecal}{\mathcal{E}}
+\newcommand{\Fcal}{\mathcal{F}}
+\newcommand{\Gcal}{\mathcal{G}}
+\newcommand{\Hcal}{\mathcal{H}}
+\newcommand{\Ical}{\mathcal{I}}
+\newcommand{\Jcal}{\mathcal{J}}
+\newcommand{\Kcal}{\mathcal{K}}
+\newcommand{\Lcal}{\mathcal{L}}
+\newcommand{\Mcal}{\mathcal{M}}
+\newcommand{\Ncal}{\mathcal{N}}
+\newcommand{\Ocal}{\mathcal{O}}
+\newcommand{\Pcal}{\mathcal{P}}
+\newcommand{\Qcal}{\mathcal{Q}}
+\newcommand{\Rcal}{\mathcal{R}}
+\newcommand{\Scal}{\mathcal{S}}
+\newcommand{\Tcal}{\mathcal{T}}
+\newcommand{\Ucal}{\mathcal{U}}
+\newcommand{\Vcal}{\mathcal{V}}
+\newcommand{\Wcal}{\mathcal{W}}
+\newcommand{\Xcal}{\mathcal{X}}
+\newcommand{\Ycal}{\mathcal{Y}}
+\newcommand{\Zcal}{\mathcal{Z}}
+
+% abstract categories
+\newcommand{\Asf}{\mathsf{A}}
+\newcommand{\Bsf}{\mathsf{B}}
+\newcommand{\Csf}{\mathsf{C}}
+\newcommand{\Dsf}{\mathsf{D}}
+\newcommand{\Esf}{\mathsf{E}}
+\newcommand{\Ssf}{\mathsf{S}}
+
+% algebraic geometry
+\newcommand{\spec}{\operatorname{Spec}}
+\newcommand{\proj}{\operatorname{Proj}}
+
+% categories 
+\newcommand{\id}{\mathrm{id}}
+\newcommand{\Obj}{\mathrm{Obj}}
+\newcommand{\Mor}{\mathrm{Mor}}
+\newcommand{\Hom}{\mathrm{Hom}}
+\newcommand{\Aut}{\mathrm{Aut}}
+\newcommand{\Sets}{\mathsf{Sets}}
+\newcommand{\SSets}{\mathsf{SSets}}
+\newcommand{\kVect}{\mathsf{Vect}_{k}}
+\newcommand{\Vect}{\mathsf{Vect}}
+\newcommand{\Alg}{\mathsf{Alg}}
+\newcommand{\Ring}{\mathsf{Ring}}
+\newcommand{\Mod}{\mathsf{Mod}}
+\newcommand{\Grp}{\mathsf{Grp}}
+\newcommand{\AbGrp}{\mathsf{AbGrp}}
+\newcommand{\PSh}{\mathsf{PSh}}
+\newcommand{\Sh}{\mathsf{Sh}}
+\newcommand{\PSch}{\mathsf{PSch}}
+\newcommand{\Sch}{\mathsf{Sch}}
+\newcommand{\Top}{\mathsf{Top}}
+\newcommand{\Com}{\mathsf{Com}}
+\newcommand{\Coh}{\mathsf{Coh}}
+\newcommand{\QCoh}{\mathsf{QCoh}}
+\newcommand{\Opens}{\mathsf{Opens}}
+\newcommand{\Opp}{\mathsf{Opp}}
+\newcommand{\Cat}{\mathsf{Cat}}
+\newcommand{\NatTrans}{\mathrm{NatTrans}}
+\newcommand{\pr}{\mathrm{pr}}
+\newcommand{\Fun}{\mathrm{Fun}}
+\newcommand{\colim}{\mathrm{colim}}
+\newcommand{\lifts}{\boxslash}
+\DeclareMathOperator\squarediv{\lifts}
+\newcommand{\Kan}{\mathsf{Kan}}
+\newcommand{\Path}{\mathsf{Path}}
+\newcommand{\SPSh}{\mathsf{SPSh}}
+\newcommand{\SSh}{\mathsf{SSh}}
+\newcommand{\Bord}{\mathsf{Bord}}
+
+% simplicial sets
+\newcommand{\DDelta}{\Updelta}
+\newcommand{\Sing}{\operatorname{Sing}}
+
+% ideal theory
+\newcommand{\mfrak}{\mathfrak{m}}
+\newcommand{\afrak}{\mathfrak{a}}
+\newcommand{\bfrak}{\mathfrak{b}}
+\newcommand{\pfrak}{\mathfrak{p}}
+\newcommand{\qfrak}{\mathfrak{q}}
+
+% number theory
+\newcommand{\Tr}{\mathrm{Tr}}
+\newcommand{\Nm}{\mathrm{Nm}}
+\newcommand{\Gal}{\mathrm{Gal}}
+\newcommand{\Frob}{\mathrm{Frob}}