Samantha Allen

About me

I am currently a postdoc in mathematics at Dartmouth College. My research interests lie in the field of low-dimensional topology. In particular, I am interested in knot theory in dimensions 3 and 4.

Before coming to Dartmouth, I completed my PhD in mathematics at Indiana University advised by Charles Livingston.

Click here to view my CV.

Publications

Concordances from differences of torus knots to L-space knots. arXiv. (To appear, Proc. Amer. Math. Soc.)

Using secondary Upsilon invariants to rule out stable equivalence of knot complexes. arXiv. (To appear, Algebraic and Geometric Topology.)

Teaching

In the spring term, I will be teaching Math 17 An Introduction to Mathematics Beyond Calculus.

In previous terms at Dartmouth College, I have taught:

Math 8 Calculus of Functions of One and Several Variables.
Math 22 Linear Algebra with Applications.
Math 25 Number Theory
Math 31 Topics in Algebra

At Indiana University, I taught a variety of courses:

D116 Introduction to Finite Mathematics I.
D117 Introduction to Finite Mathematics II.
T101 Mathematics for Elementary Teachers.
J010 Introduction to Algebra.
J110 Introductory Problem Solving.
J111 Introduction to College Math I.
M014 Basic Algebra.

Talks

Unknotting with a single twist, AMS-AWM Special session on Women in Topology, Joint Mathematics Meetings, January 2020, Denver, CO.

Unknotting with a single twist, Special Session on Invariants of Knots, Links, and Low-dimensional Manifolds, AMS Sectional Meeting, October 2019, Binghamton, NY.

Nonorientable surfaces bounded by knots: a geography problem, Knot concordance and low-dimensional manifolds, June 2019, Le Croisic, France.

The geography of nonorientable surfaces bounded by knots, Special Session on Invariants of Knots, Links, and Low-dimensional Manifolds, AMS Sectional Meeting, April 2019, Hartford, CT.

Nonorientable surfaces bounded by knots, Special Session on Algebraic, Combinatoric, and Quantum Invariants of Knots and Manifolds, AMS Sectional Meeting, March 2018, Columbus, OH.

The nonorientable four-genus of knots, University of Virginia Geometry Seminar, February 2018, Charlottesville, VA.

The nonorientable four-genus of knots, University of Oregon Topology Seminar, January 2018, Eugene, OR.

Nonorientable surfaces bounded by knots, Graduate Student Topology and Geometry Conference, April 2017, East Lansing, MI.

Professional Development

Attended the ICERM workshop Perspectives on Dehn Surgery (July 2019, Providence, RI).

Attended the Workshop in Geometric Topology at Calvin College (June 2018, Grand Rapids, MI).

Attended the Joint Mathematics Meetings of the AMS and MAA (January 2018, San Diego, CA).

Attended the UCLA Topology Conference 2018 (January 2018, Los Angeles, CA).

Attended the Banff workshop on Thirty Years of Floer Theory for 3-Manifolds. (July/August 2017, Oaxaca, Mexico)

Recent Outreach

Presenter at The Governor's Institute of Vermont in Mathematical Sciences, June 2019. I had the opportunity to teach a group of high school students some basic knot theory.

Co-organizer of Sonia Kovalevsky Day at Dartmouth, May 2019. Here are slides from a workshop I co-organized.

Selection committee member for Dartmouth's Biographies of Contemporary Women in Mathematics essay contest, Winter 2019.

Contact details

My email address is samantha.g.allen [𝔞𝔱] dartmouth [𝔡𝔬𝔱] edu.