From 0f2a0b73d1b76221a0e7c4f2df801b10869e0f56 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Thu, 10 Jun 2021 13:41:19 +0200
Subject: Changed section titles.

---
 stokes.tex | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

(limited to 'stokes.tex')

diff --git a/stokes.tex b/stokes.tex
index fdc8e69..f417f07 100644
--- a/stokes.tex
+++ b/stokes.tex
@@ -74,7 +74,7 @@ landscapes, which are typically constructed from the limits of series or
 integrals of analytic functions which are not themselves analytic
 \cite{Cavagna_1999_Energy}.
 
-\section{Dynamics}
+\section{Integration by Lefschetz thimble}
 
 Consider an $N$-dimensional hermitian manifold $M$ and a Hamiltonian $H:M\to\mathbb C$. The partition function
 \begin{equation}
@@ -111,6 +111,8 @@ Morse theory provides the universal correspondence between contours and thimbles
 Each of these integrals is very well-behaved: convergent asymptotic series
 exist for their value about the critical point $\sigma$, for example. One must know the integer weights $n_\sigma$.
 
+\section{Gradient descent dynamics}
+
 For a holomorphic Hamiltonian $H$, dynamics are defined by gradient descent on
 $\operatorname{Re}H$. In hermitian geometry, the gradient is given by raising
 an index of the conjugate differential, or
-- 
cgit v1.2.3-70-g09d2

