Make progress on first proper slide

Makefile

@@ -26,6 +26,7 @@ $(addsuffix .py,${SAGEPLOTFILES}): $(addsuffix .sage,${SAGEPLOTFILES})
 
 .PHONY: clean
 clean:
+	rm -rf **/__pycache__
 	latexmk -C
 	git clean -xf || echo no git repo to use for cleaning
 

main.tex

@@ -26,6 +26,8 @@
 \newcommand\coh{\operatorname{Coh}}
 \newcommand\rank{\operatorname{rk}}
 \newcommand\degree{\operatorname{deg}}
+\newcommand\realpart{\mathfrak{Re}}
+\newcommand\imagpart{\mathfrak{Im}}
 
 \begin{document}
 
@@ -36,22 +38,6 @@
 \section{Transitioning to Stab on Triangulated Categories}
 
 \begin{frame}{Central Charge}
-	\begin{column}{.5\textwidth}
-		\centering
-		one
-		\\
-		one
-		\\
-		one
-		\\
-		one
-		\\
-	\end{column}
-
-	\begin{column}{.4\textwidth}
-		\centering
-		two
-	\end{column}
 \end{frame}
 
 \begin{sagesilent}
@@ -60,44 +46,52 @@
 
 \begin{frame}{Central Charge for Mumford Stability}
 	\begin{align*}
-		\centralcharge \colon \coh(X) &\to \CC \\
-		E &\mapsto - \degree(E) + i \rank(E)
+		&\centralcharge \colon \coh(X) \to \CC \\
+		&\centralcharge (E) = - \degree(E) + i \rank(E)
 	\end{align*}
 
-
-	\begin{column}{.5\textwidth}
-		\centering
-		one
-	\end{column}
-
-	\begin{column}{.4\textwidth}
-		\centering
-		two
-	\end{column}
-
 	\resizebox{1\hsize}{!}{
 		\sageplot{sagetexscripts.fig1.plot()}
 	}
 
-	\begin{column}{.5\textwidth}
-		\centering
-		one
-		\\
-		one
-		\\
-		one
-		\\
-		one
-		\\
-	\end{column}
-
-	\begin{column}{.4\textwidth}
-		\centering
-		two
-	\end{column}
+	\begin{columns}[T] % align columns
+	\begin{column}{.48\linewidth}
+		\[
+			\centralcharge (E) = r(E) e^{i\pi \varphi(E)}
+		\]
+		$\varphi$ called "phase"
+	\end{column}%
+	%\hfill%
+	\begin{column}{.48\linewidth}
+		\[
+			\mu(E) =
+			\frac{
+				- \realpart(\centralcharge(E))
+			}{
+				\imagpart(\centralcharge(E))
+			}
+			\quad
+			\text{(allow for $+\infty$)}
+		\]
+	\end{column}%
+	\end{columns}
 
 \end{frame}
 
+
+\begin{frame}
+	\begin{columns}[T] % align columns
+	\begin{column}{.48\linewidth}
+	Left Part
+	\end{column}%
+	\hfill%
+	\begin{column}{.48\linewidth}
+
+	Right Part
+	\end{column}%
+	\end{columns}
+\end{frame}
+
 \section{Section 1}
 
 \section{Section 2}

sagetexscripts/fig1.sage

@@ -25,14 +25,14 @@ def plot():
         return point(
             Z,
             marker = "o",
-            size = 600,
+            size = 800,
             rgbcolor = "white",
             #markeredgecolor = "purple",
             zorder = 100
         ) + point(
             Z,
             marker = name,
-            size = 500,
+            size = 700,
             rgbcolor = "red",
             zorder = 101
         ) + line(
@@ -53,11 +53,11 @@ def plot():
     p = sum(
         plot_central_charge(chern, name)
         for chern, name in [
-            (O1, r"$\mathcal{O}(1)$"),
-            (O, r"$\mathcal{O}_X$"),
-            (O1inv, r"$\mathcal{O}(-1)$"),
-            (O2, r"$\mathcal{O}(2)$"),
-            (O_x, r"$\mathcal{O}_p$")
+            (O1, r"$\mathcal{Z}(\mathcal{O}(1))$"),
+            (O, r"$\mathcal{Z}(\mathcal{O}_X)$"),
+            (O1inv, r"$\mathcal{Z}(\mathcal{O}(-1))$"),
+            (O2, r"$\mathcal{Z}(\mathcal{O}(2))$"),
+            (O_x, r"$\mathcal{Z}(\mathcal{O}_p)$")
         ]
     )