This is a "vintage" (i.e. pre-ipad ownership) animation I made of an isotopy.
I sometimes use pipecleaners to model knots and surfaces.
Quanta Magazine has some great articles on developments in topology, including the triangulation and geometrization conjectures.
This article by Lee Rudolph and Bill Menasco on the unknotting number features some gorgeous pictures!
My PhD advisor, Josh Greene, wrote a beautiful survey on Heegaard Floer homology.
Andrew Lobb's AMS Notices article, A Feeling for Khovanov Homology, describes how low-dimensional topologists often approach research.
BEAM founder Dan Zaharopol explains his thought process for designing STEM outreach programs for students from groups historically excluded from mathematics.
Reva Kasman's thoughts on being a teaching mentor.
Justin Lanier and Marissa Loving discuss goals to keep in mind while designing equity-minded online programs.
This blog post by Jasmine Kwasa provides some great guidance for first time fellowship applicants (I wish it existed when I was a grad student!).
Allison N. Miller's thoughtful piece disability and chronic illness in mathematics.
This video by Henry Segerman features lots of trefails!
Andy Putnam has a great collection of notes, including a slick proof of the classification of surfaces.
Milnor has some great (somewhat technical, depending on your background) surveys on various topics, including the Poincaré conjecture in all dimensions, the Poincaré conjecture in dimension 3, and infinite cyclic covers.
This interview with Candice Price contains many nuggets of teaching wisdom.
Ravi Vakil's suggestions for graduate students (it is pitched as advice for students who want to work for him, but it is very widely applicable).
This historical overview of the (3D) Poincaré Conjecture by Stillwell is fantastic!
Inspired by Liam Watson's @mathonmydeskrightnow, I started my own topologically inclined instagram account: @knotoffthepress.
As lead organizers of the Nearly Carbon Neutral Geometric Topology Conference 2021, we (Martin Bobb, Allison N. Miller, and myself) solicited mathematical postcards from the participants. Here's mine!
("Amma" and "Appa" mean "mom" and "dad", respectively, in my mother tongue.)
I'm better friends with Elizabeth Warren than Kyle Hayden is.