Contact Information
Biography
Dr. Samantha Allen is an Assistant Professor in the Department of Mathematics & Computer
Science. She received her PhD in Mathematics from Indiana University in 2018, following
which she pursued postdoctoral work at Dartmouth College and the University of Georgia.
Her research interests lie in the field of geometric topology. More specifically,
she studies knot theory in dimensions 3 and 4 and is particularly interested in using
knot invariants arising from Heegaard Floer theory to study knot concordance, problems
related to unknotting operations, and other knot-theoretic problems.
Education
Ph.D. Mathematics, Indiana University
B.S., Mathematics, High Point University
B.S., Computer Science, High Point University
Research Interests
Dr. Allen's research interests lie in the field of low-dimensional topology, the study of manifolds in dimensions up to four. More specifically, she studies knot theory in dimensions 3 and 4 and is particularly interested in using knot invariants arising from Heegaard Floer theory to study knot concordance, problems related to unknotting operations, and other knot-theroetic problems.
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About
- Nonorientable surfaces bounded by knots: a geography problem. New York J. Math. 29 (2023) 1038–1059. (http://nyjm.albany.edu/j/2023/29-41.html)
- Do Link Polynomials Detect Causality In Globally Hyperbolic Spacetimes? Joint with Jacob H. Swenberg. J. Math. Phys. 62 (2021), no. 3, 032503. (https://doi.org/10.1063/5.0040956)
- Unknotting with a single twist. Joint with Charles Livingston. Enseign. Math. 66 (2020), no. 3-4, 541-589. (https://doi.org/10.4171/lem/66-3/4-10)
- Concordances from differences of torus knots to L–space knots. Proc. Amer. Math. Soc. 148 (2020), no.4, 1815–1827. (https://doi.org/10.1090/proc/14833)
- Using secondary Upsilon invariants to rule out stable equivalence of knot complexes. Algebr. Geom. Topol. 20 (2020), no. 1, 29–48. (https://doi.org/10.2140/agt.2020.20.29)