### 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My (somewhat out of date) CV is available here.### Papers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

- (With Danny Calegari) Extreme points in limit sets
- (With Juliette Bavard) Two simultaneous actions of big mapping class groups
- (with Kevin K. Chen and Anthony Gamst) The empirical size of trained neural networks

#### Published and to appear

- 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

- 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

- 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*.