Dr. Allison Miller headshot

WEBSITE(S)| Mathematics | Swarthmore Faculty page

  • BA in Mathematics, Pomona College (2012)
  • MA in Mathematics, UT Austin (2014)
  • PhD in Mathematics, UT Austin (2018)

My work is in the area of topology, so I study properties of spaces that don’t change under continuous deformations like stretching, twisting, or rotating. More specifically, I use algebraic and geometric techniques to understand the 4-dimensional properties of knots in 3-dimensional space (i.e. I study knot concordance.) My current work focuses on understanding how an operation called the satellite construction, which combines two knots into a generally more complicated knot, interacts with various 4-dimensional properties. For example, one might ask what conditions are necessary for two complicated knots to combine into a knot which, from the 4-dimensional perspective, is completely uninteresting.

I am excited to be part of a broader academic community as part of the Rice Academy of Fellows, and look forward to the professional development and mentorship opportunities ahead.

When I’m not teaching or doing research, I greatly enjoy playing basketball, reading science-fiction and fantasy novels, and gardening.