Allison N. Miller
I'm a low-dimensional topologist researching questions related to knot concordance, the study of 4-dimensional properties of knots.
I've just started as a G.C. Evans Instructor in the Department of Mathematics at Rice University, after receiving my PhD in May 2018 from the University of Texas at Austin, where my advisor was Cameron Gordon. During my PhD, I spent four months at the Hausdorff Institute in Bonn, Germany participating in the Knot Concordance and 4-manifolds group of the Junior Trimester in Topology in fall 2016.
Disambiguation/ Disclaimer: I am not Allison Moore, also once a student of Cameron Gordon at UT Austin, also once a postdoc at Rice in HBH 456, but now a Krener Assistant Professor at UC Davis. Nor am I Alison Miller, a postdoctoral fellow at Harvard who works in number theory. I can be distinguished from the many other Allison Millers in the world (who the reader can go out and discover for themselves) by my middle name- so far as I know I am the only Allison Northey Miller.
Recent and upcoming invited talks:
Satellite operators and knot concordance, at UT Austin for The topology and geometry of low-dimensional manifolds: a celebration of the mathematics of Bob Gompf (July 2018), at the University of Georgia Topology seminar (September 2018), and at the Tech Topology Conference (December 2018)
Abstract: The classical satellite construction behaves nicely with respect to concordance, since if K and J are concordant then P(K) and P(J) are concordant for any pattern P. It is therefore natural to ask about the properties of satellite-induced maps on the collection of knots modulo concordance. I will briefly survey results in this area, focusing on differences between the smooth and topological categories. I will then describe Gompf and Miyazaki's construction of dualizable patterns, which induce invertible functions on the concordance group, and discuss joint work with Lisa Piccirillo which smoothly distinguishes certain dualizable pattern operators from any connected sum operator.
Satellite operators on knot concordance, in Dubrovnik, Croatia for Geometric structures on 3 and 4 manifolds (June 2018)
Winding number of satellite operators and concordance at NC State University's Topology/ Geometry Seminar (Feb. 2018)
Knot traces and concordance, at the Séminaire de géométrie et topologie of CIRGET, Montreal (March 2017), the Princeton University topology seminar (March 2017), Low-dimensional topology on Skye (June 2017), and Thirty Years of Floer Theory for 3-Manifolds at Casa Matematica Oaxaca, Mexico (August 2017).
The topological sliceness of 3-strand pretzel knots, at the Séminaire de géométrie et topologie of CIRGET, Montreal (March 2016)
Distinguishing mutant pretzel knots in concordance, at the Special Session on Spatial Graphs, AMS Western Fall Sectional Meeting at CSU Fullerton. (October 2015), the Special Session on Geometric Perspectives in Knot Theory, AMS Central Fall Sectional Meeting at Loyola University. (October 2015), and Topology Seminar of Rice University (September 2015).
(Abstracts and notes available upon request.)