Caltech Undergraduate Research Journal

CURJ is Caltech's award-winning undergraduate research journal, dedicated to highlighting the accomplishments of the numerous undergraduates conducting research at Caltech during the SURF program and throughout the academic year.

Featured Article

Proof by Picture: The Poincare-Hopf Index Theorem For Surfaces

Steve Paik and Rahul Pandharipande

An image for the article on display.

SUPPOSE YOU ARE AN ANT LIVING ON A SPHERE. FROM YOUR PERSPECTIVE the world is two-dimensional: you can move back and forth, left and right, but not up or down. You settle into a comfortable life on the sphere when suddenly the wind starts to blow. Air currents develop and begin to circulate around the globe much the same way they do here on earth. In an effort to escape the torrid winds, you decide to journey across the desolate plains of the globe in search of a land where the air is perfectly still. Is it possible to find such a calm place? Fortunately, the answer is always yes - there will be at least one point on the sphere where the wind speed is zero....