Research

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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My (somewhat out of date) CV is available here.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 Juliette Bavard) Two simultaneous actions of big mapping class groups (to appear in TAMS)


• (with Kevin K. Chen and Anthony Gamst) The empirical size of trained neural networks

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:
  • Slides 1
  • Slides 2 (covering different material)


• 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.
  • Week 1 class slides.
  • Week 2 class slides.
  • Week 3 class slides.
  • Exercises.


• 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.

Alden Walker
Contact: (first name) at (this website)