New side-gigs
Starting two new positions this month — founding president of the Columbia chapter of Pi Mu Epsilon (PME).
PME is a premier math honor society I’m helping bring back to campus. The project site is here.
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Representation of the Riemann Sphere
A clean-ish picture of the Riemann sphere projected onto the plane. In this model, \(\infty\) is adjoined to \(\mathbb{C}\).
When Möbius maps start feeling overwhelming, I come back to this picture to reset intuition.
riemann sphere
stereographic projection
static diagram
static diagram
Formally, we think of \(\mathbb{C}_\infty = \mathbb{C} \cup \{\infty\}\) as a sphere.
The point \(\infty\) is the north pole.
Soft colors are just a visual cue:
blue lives on the sphere side,
green lives on the plane side,
and the red line is the projection path.
When \(f=u+iv\) is holomorphic: \(\partial_x u=\partial_y v\) and \(\partial_y u=-\partial_x v\).
Jane Street support of CES
Quick appreciation post for Jane Street, newest corporate sponsor of Columbia Economics Society.
If any Streeter is reading this: thank you for backing students who are trying to take the work seriously.
Jane Street × Columbia Economics Society
First post
Keeping this one short while I continue testing layout and spacing.