topology and geometry, group theory, non-commutative
Publications and Preprints (with downloads)
Preprints from arXiv.org
Google scholar page
Mathematical Reviews at MathSciNet
My mathematical genealogy
Carolyn Otto, Ph.D. May 2011
Thesis: The (n)-solvable filtration of the link concordance group and Milnor's invariants
Taylor Martin, Ph.D. May 2013
Thesis: Lower order solvabilty of links
Taylor McNeill, Ph.D. May 2013
Thesis: A new filtration of the Magnus kernel
Katherine Vance, Ph.D. May 2016
Thesis: Tau invariants of spatial graphs
JungHwan Park, Ph.D. May 2017
Thesis: Derivatives of genus one and three knots
Anthony Bosman, Ph.D. May 2017
Thesis: Shake slice and shake concordant links
Miriam Kuzbary, Ph.D. May 2019
Thesis: Link concordance and groups
Sarah Seger, Ph.D. May 2019
Thesis: Lower order solvability, Seifert forms, and Blanchfield forms of links
Shawn Williams, Ph.D. expected May 2022
Alex Manchester, Ph.D. expected May 2024
Teaching (Spring 2021):
Math 445/540 - Algebraic Topology
Math 541 - Topics in Topology: Concordance and 4-manifolds
RTG: Math 699 - Current Topics in Topology
The CompuTop.org Software Archive
Low-Dimensional Topology Conferences
Lecture Notes from courses (may be imcomplete and may contain mistakes):
L2 Invariants in Topology and Geometry
Conferences and special sessions (co)organized:
AIM workshop on "Distinguishing smooth concordance classes of topologically slice
knots and links," June 3–7, 2019.
2019 AWM Research Symposium, Rice University, April 6-7, 2019.
in Dimension 3.5: A conference in memory of Tim Cochran, June 1-4,
AWM Research Symposium 2015, University of Maryland, College Park,
April 11-12, 2015.
Special Session on Low-Dimensional Topology at the AWM Research Symposium, University of Maryland, College Park, April 11-12, 2015.
AMS Special Session on Knot Theory at the Joint Math Meetings, San Antonio, TX, January 12–13, 2015.
"Hempelfest" 3-Manifolds: Heegaard Splittings, the Curve Complex, and Hyperbolic geometry, Rice
University, April 19-21, 2013.
Special Session on Low-Dimensional Topology at the AWM Research Symposium, Santa Clara, CA, March 16-17, 2013
AMS Special Session on Knot Theory at the Joint Math Meetings, Boston, MA, January 4-7, 2012.
Special Session on Low Dimensional Topology and Geometry at the AMS Fall Southeastern Section Meeting, Winston-Salem, NC, September 24-25, 2011.
AMS Special Session on Knot Theory at the Joint Math Meetings, New Orleans, LA, January 8-9, 2011.
Special Session on Low Dimensional Topology at the AMS Fall Eastern Section Meeting, Middletown, CT, October 11-12, 2008.
3rd Annual Louisiana Texas Topology Retreat, Rice University, February
9-10, 2008 (Pictures)
Louisiana-Texas-Topology-Retreat (LTTR), February 3-4, 2007
2006 Texas Geometry and Topology Conference at Rice University, Oct 27-29, 2006
Selected Research Talks:
A non discrete metric on the group of topologically slice knots; Conference on Topology in Dimensions 3, 3.5, and 4 (in honor of Abby Thompson, Marty Scharleman, and Rob Kirby), UC Berkeley, June 2018.
Fractal nature of the space of knotted curves; Colloquium, Monash University, Melbourne,
Australia, March 2018.
The geometry of knot concordance spaces; Topology Seminar, UC Berkeley, September 2014.
4-dimensional equivalence relations on knots; Invited Address at the AMS Southeastern Sectional Meeting in Winston-Salem, NC, September 2011.
Knots and link
concordance; Connections for Women: Homology Theories of Knots and
Links at MSRI, January 2010.
Torsion in the knot concordance group; Cascade Topology Seminar, University of Oregon, October 2009.
Torsion in the knot concordance group; 2009 Georgia
International Topology Conference, May 2009.
A survey of knot theory and its
combinatorial invariants; CombinaTexas: Combinatorics in the
South-central US conference, University of Houston, April 2009.
Subgroups of the mapping class group and higher-order
signature cocycles; Colloquium, University of Indiana,
Bloomington, March 2009.
Subgroups of the mapping
class group and higher-order signature cocycles; Texas Geometry and Topology Conference, University of Houston, February 2009.
Filtrations of the Knot Concordance Group; Colloquium at University of Riverside,
Classical Knot Concordance and
Blanchfield Duality; "Geometric Topology Conference," Beijing 2007.
New Phenomena in Knots and Links; "4-Dimensional
Manifolds," Oberwolfach 2006.
Group theoretic invariants of
links and 3-manifolds; "3-manifolds after Perelman," Edinburgh,
Scotland, March 2006.
Homology Equivalence of Groups and
Spaces; "Knots and their manifold stories" held at BIRS in May 2004.
Department of Mathematics, MS 136
P.O. Box 1892
Houston, TX 77251-1892