\(
\newcommand{\mcl}[1]{\mathcal{#1}}
\newcommand{\mbb}[1]{\mathbb{#1}}
\newcommand{\mbf}[1]{\mathbf{#1}}
\newcommand{\msc}[1]{\mathscr{#1}}
\newcommand{\mfk}[1]{\mathfrak{#1}}
\newcommand{\mit}[1]{\mathit{#1}}
% Standard number sets.
\newcommand{\N }{\mbb{N}} % Natural
\newcommand{\Z }{\mbb{Z}} % Integer
\newcommand{\Q }{\mbb{Q}} % Rational
\newcommand{\R }{\mbb{R}} % Real
\newcommand{\C }{\mbb{C}} % Complex
\newcommand{\F }{\mbb{F}} % Finite
\newcommand{\K }{\mbb{K}} % Generic
\DeclareMathOperator{sl}{\mfk{sl}}
\DeclareMathOperator{SL}{SL}
\DeclareMathOperator{\ad}{ad} % adjoint
\DeclareMathOperator{\Ad}{Ad} % Big Adjoint
\DeclareMathOperator{\id}{id}
\newcommand{\acts}{{}^\curvearrowright} % Action
\DeclareMathOperator{\End}{End}
\DeclareMathOperator{\Aut}{Aut}
\newcommand{\dual}[1]{{#1}^*}
\newcommand{\uea}[1]{\mathfrak{U}(#1)}
\newcommand{\diffdchar}{d}
% or {ⅆ}, or {\mathrm{d}}, or whatever standard you’d like to adhere to
\newcommand{\dd}{\mathop{\diffdchar\!}}
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\Gl}{\mfk{gl}}
\DeclareMathOperator{\SL}{SL}
\DeclareMathOperator{\SP}{Sp}
\DeclareMathOperator{\Sp}{\mfk{sp}}
\DeclareMathOperator{\Sl}{\mfk{sl}} % Why is this capitalized?
\DeclareMathOperator{\SO}{SO}
\DeclareMathOperator{\U}{U}
\DeclareMathOperator{\SU}{SU}
\DeclareMathOperator{\Or}{O}
\DeclareMathOperator{\So}{\mfk{so}}
\newcommand{\inv}[1]{{#1}^{-1}}
\)
This is a daily log of my work as a grad student. This is partially to give
others a sense of what a graduate student in math does, and partially to hold
myself accountable to my job as a mathematician.