Interests
I am interested in low dimensional topology and geometry, including
geometric group theory and dynamics. I am less officially interested in
algorithm analysis and optimization.
CV
My (somewhat out of date) CV is available
here.
Papers
In preparation
- With Danny Calegari - Circle actions on the boundary of Schottky space
Preprints
Published and to appear
- J. Taback and A. Walker, Conjugation Curvature in Solvable Baumslag-Solitar Groups Jour. Top. An. 15 no. 2 (2023)
- J. Taback and A. Walker, A new proof of the growth rate of the solvable Baumslag-Solitar groups Geom. Ded. 216 (2022)
- D. Calegari and A. Walker, Extreme points in limit sets Proc. Amer. Math. Soc. 147 (2019), 3829-3837
- A. Gamst, J. Reyes, and A. Walker, Estimating the operating characteristics of ensemble methods, Presented at the Conference on Neural Information Processing Systems (NIPS), Workshop on Challenges in Machine Learning, Long Beach, December 2017.
- A. Gamst and A. Walker, The energy landscape of a simple neural network, Presented at the Conference on Neural Information Processing Systems (NIPS), Workshop on Optimization (OPT-ML), Long Beach, December 2017.
- K. K. Chen, A. Gamst, and A. Walker, Knots in random neural networks, Presented at the Conference on Neural Information Processing Systems (NIPS), Workshop on Bayesian Deep Learning, Barcelona, Spain, December 2016.
- J. Bavard and A. Walker, The Gromov boundary of the ray graph, Trans. Amer. Math. Soc. (2018)
- D. Calegari, S. Koch, and A. Walker, Roots, Schottky Semigroups, and a proof of Bandt's Conjecture, Ergodic Theory and Dynamical Systems 37 (2017), 2487-2555.
- A. Walker, Stable immersions in orbifolds, Alg. Geom. Top. 15 (2015) 1877-1908.
- D. Calegari and A. Walker, Surface subgroups from linear programming, Duke Math. Jour. 164 no. 5 (2015), 933-972. (old, unabridged version)
- D. Calegari and A. Walker, Random groups contain surface subgroups, Jour. Amer. Math. Soc. 28 (2015), 383-419
- Sean A. Weaver, Katrina J. Ray, Victor W. Marek, Andrew J. Mayer, and Alden Walker, Satisfiability-based set membership filters, Journal on Satisfiability, Boolean Modeling and Computation 8 (2014), 129-148.
- A. Walker, Stable commutator length in free products of cyclic groups, Experimental Math 22 (2013), no. 3, 282-298.
- D. Calegari and A. Walker, Random rigidity in the free group, Geometry and Topology 17 (2013), no. 3, 1707-1744.
- D. Calegari and A. Walker, Integer hulls of linear polyhedra and scl in families, Trans. Amer. Math. Soc. 365 (2013), no. 10, 5085-5102.
- A. Walker Surface maps into free groups, Ph.D. thesis, (contains material from several published and upcoming papers).
- D. Calegari and A. Walker, Ziggurats and rotation numbers, Journal of Modern Dynamics 5 (2011), no. 4, 711-746
- D. Calegari and A. Walker, Isometric endomorphisms of free groups, New York Journal of Math 17 (2011) 713-743
- G. Civan, J. Etnyre, P. Koprowski, J. Sabloff, and A. Walker, Product Structures for Legendrian Contact Homology, Math. Proc. Camb. Phil. Soc. 150 (2011), no. 2, 291-311
Slides
- Topologically minimal surface maps (an overview of scl).
- Actions of big mapping class groups from the AIM workshop
- As part of the 2015 UChicago topology summer school,
I gave a minicourse about surfaces in low-dimensional topology.
The course notes are available here.
- Roots, Schottky semigroups, and a proof of Bandt's conjecture:
- An introduction to fatgraphs and stable
commutator length at Seoul National University: slides.
- A very concise talk about surface subgroups of random groups:
slides.
- Stable immersions in orbifolds: slides.
- Stable commutator length in free products of cyclic groups:
slides.
- As part of the 2013 UChicago geometry REU, I gave an introduction to fatgraphs and stable
commutator length.
- Random HNN extensions contain surface subgroups: slides.
- An introduction to scl at Haverford College: slides.
Invited Talks
- Bowdoin Math Seminar, September, 2019
Topologically minimal surface maps
- Wasatch topology conference, August, 2019
Actions on the boundary of the loop graph
- AIM surfaces of infinite type workshop, April, 2019
Actions of big mapping class groups
- CMS Winter Meeting, December, 2016
Circle actions on the boundary of Schottky space
- Topology and Computer workshop, Akita, Japan, October, 2016
Certifying surface subgroups
- Tokyo Institute of Technology Topology Seminar, October, 2016
The Gromov Boundary of the Ray Graph
- Duke Geometry/Topology Seminar, September, 2015
Topologically minimal surface maps
- UChicago summer school in geometry and topology, UChicago, June, 2015
Finding surface subgroups (minicourse)
- Young Geometric Group Theory Conference, Spa, Belgium, January, 2015
Surface subgroups of random groups
- Seoul National University, Seoul, November, 2014
Visiting lecturer on random groups
- UMichigan Dynamics Seminar, October, 2014
Roots, Schottky semigroups, and a proof of Bandt's conjecture
- UW Madison Geometry and Topology Seminar, October, 2014
Roots, Schottky semigroups, and a proof of Bandt's conjecture
- Uchicago Dynamics Seminar, October, 2014
Roots, Schottky semigroups, and a proof of Bandt's conjecture
- Orderable Groups, Cajon del Maipo, Chile, September, 2014
Transfers of quasimorphisms
- Geometry on Groups and Spaces, Daejeon, South Korea, August, 2014
Homologically essential surface subgroups of random groups
- Research Cluster in Random Groups, Tufts, June, 2014
Visiting lecturer
- AMS/IMU Joint Meetings, Tel Aviv, June, 2014
Schottky semigroups
- Redbud Topology Conference, OU, April, 2014
Constructing quasimorphisms
- Geometric Groups on the Gulf Coast, Pensacola, March, 2014
Constructing quasimorphisms
- Spring Topology and Dynamics Conference, Richmond, March, 2014
Stable immersions in orbifolds
- IU Bloomington, December, 2013
Surface subgroups of random groups
- CMS Winter Meeting, December, 2013
Surface subgroups of random groups
- Topology, Geometry, and Group Theory, Informed by Experiment, ICERM, October, 2013
Surface maps into orbifolds
- Bi-College Colloquium, Haverford College, April, 2013
Topologically minimal surface maps
- Hot topics: surface subgroups and cube complexes, MSRI, March, 2013
Surface subgroups from linear programming
- UChicago dynamics seminar, January, 2013
Surface subgroups from linear programming
- Caltech Topology and Geometry Seminar, May, 2012
Traintracks and endomorphisms
- The Park School of Baltimore, April, 2012
Math for fun and profit
- IHP trimestor on surface group representations, Paris, March 2012
Ziggurats and rotation numbers
- IDA/CCR-La Jolla, November, 2011
Stable commutator length in free products of cyclic groups
- Caltech combinatorics seminar, November, 2011
Integer hulls of linear polyhedra and scl in families
- U Chicago dynamics seminar, November, 2011
Ziggurats and rotation numbers
- Caltech graduate student seminar, November, 2011
Rotation numbers of positive words
- Max Dehn Seminar, U of Utah, September, 2011
Random rigidity in the free group
- Geometry and Topology Down Under (Hyamfest), University of Melbourne, August 2011
Teaching assistant (five one-hour problem sessions) for the short course:
Ergodic Theory of Hyperbolic Groups by Danny Calegari
- AMS Spring Western Section Meeting,
Special Session on Geometric Group Theory and Dynamics, Las Vegas, May 2011
Isometric endomorphisms of free groups
- Caltech Geometry and Topology Seminar, April 2011
Random rigidity in the free group
- Conference on geometry, analysis, and surfaces, Autrans, March 2011
Random rigidity in the free group
- U Chicago Geometry and Topology Seminar, January 2011
Isometric endomorphisms of free groups
- Caltech Geometry and Topology Seminar, January 2011
Isometric endomorphisms of free groups
- Caltech Geometry and Topology Seminar, January 2011
Integer hulls of linear polyhedra and scl in families
- UC Santa Barbara Topology Seminar, November 2010
Integer hulls of linear polyhedra and scl in families
- Caltech Geometry and Topology Seminar, February 2009
Product Structures for Legendrian Contact Homology
- Conference at IDA/CCR-Princeton, October, 2007
- Bryn Mawr College CS Colloquium, May 2007
Natural Language Interaction with Robots
- Seminar at IDA/CCR-La Jolla, March 2007
(Covering essentially my undergraduate thesis)
- Haverford College Math Colloquium, December 2006
Lower Bounds on Algorithm Complexity Using Topology.