Genevieve Walsh

Mathématicienne (Professor)

Department of Mathematics
Tufts University

Spring 2023 CRM-Simons Scholar, Thematic Program in GGT
Spring 2018 Chaire Jean-Morlet CIRM

Paper mail:
Genevieve Walsh, Department of Mathematics
Tufts University
Medford, MA 02155
E-mail: genevieve.walsh@tufts.edu

CV, Current as of Nov 2020
Office: 565 JCC (Joyce Cummings Center, by the Green Line Tufts stop)
Fall 2022 Office hours (in person) TBA.
Geometric Group Theory and Topology Seminar
Tufts AWM email list


February 2023 Young Geometric Group Theory XI (mini-course speaker)

January - July 2023 Thematic Program in Geometric Group Theory, CRM Montreal Canada

July 16-27 2023 Women in Groups, Geometry and Dynamics, Ashton, Idaho

August 2023 Groups, Actions, and Geometries (Tufts)

October 2023 AIM: Rigidity properties of free-by-cyclic groups

March 11-15 and April 22-26 AIM Squares: Pasadena, CA.

July 2024 Geometry in Groups, ICTS, Bangaluru, India.

Some limit set pictures:

A punctured torus group with a square root adjoined

An orbifold generated by reflections with interesting characteristic suborbifold


Spring semester 2024 I am teaching Graduate Algebra, Math 245. Please e-mail me with any questions.

Research Articles:

Papers on the arXiv

P. Haissinsky, L. Paoluzzi, G.S. Walsh, On groups with Schotty set boundary, arXiv:2309.08735, Submitted.

R. Kropholler, S. Vidussi, G.S. Walsh, Virtual algebraic fibrations of surface-by-surface groups and orbits of the mapping class group, arXiv:2103.06930, Submitted.

G. C. Hruska and G. S. Walsh, Planar boundaries and parabolic subgroups,, To Appear, Math. Research Letters. arXiv:2008.07639

"Right-angled Coxeter groups with non-planar boundary" Joint with Pallavi Dani and Matthew Haulmark. arxiv:arXiv:1902.01029. Groups Geom. Dyn. 17 (2023), no. 1, 127--155.

R. Kropholler, G. S. Walsh, Incoherence and fibering of many free-by-free groups, Ann. Inst. Fourier (Grenoble) 72 (2022), no. 6, 2385--2397. arXiv:1910.09601

S.-H. Kim and G. S. Walsh, Some groups with planar boundaries, Surv. Differ. Geom., 25 International Press, Boston, MA, 2022, 253--280. arXiv:1907.06898.

"On groups with S^2 Bowditch boundary" Joint with Bena Tshishiku. Groups Geom. Dyn. 14 (2020), no. 3, 791--811. arXiv:1710.09018.

"Erratum to groups with S^2 Bowditch boundary" Joint with Bena Tshishiku. Groups Geom. Dyn. 15 (2021), no. 3, 1133--1137.

"Boundaries of Kleinian groups" . Joint with P. Haïssinsky and L. Paoluzzi. Illinois Journal of Mathematics (Special Haken Issue) Vol 60, no. 1 (2016) 353--364.

"Right-angled Coxeter groups, hyperbolic cubes, and acute triangulations". Joint with S.-H. Kim. Journal of Topology Vol. 9 (2016) 117--142 Link to on-line article

"Big Dehn surgery space and the link of $S^3$ . Joint with N. Hoffman. Proceedings of the American Mathematical Society, Series B . Vol. 2 (2015) 17--34.

"Knot complements, hidden symmetries, and reflection orbifolds" . Joint with M. Boileau, S. Boyer, and R. Cebanu. Annales de la Faculté des Sciences de Toulouse Vol. 6 (2015) no.5 1179--1201.

"The bumping set and the characteristic submanifold" . Algebraic and Geometric Topology. , Vol 14 (2014) 283--297.

"Knot commensurability and the Berge conjecture" . Joint with M. Boileau, S. Boyer and R. Cebanu. Geometry and Topology, Vol 16 (2012) 625--664.

"Orbifolds and commensurability". "Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory" Contemporary Mathematics Vol 541 (2011) 221--231.

"Incompressible surfaces and spunnormal form" . Geometriae Dedicata Vol 151 (2011) 221--231.

"The automorphism group of the free group of rank two is a CAT(0) group" . Joint with Kim Ruane and Adam Piggott. Michigan Math. J. Vol 59, (2010), 297--302.

"Commensurability classes of 2-bridge knots". Joint with Alan Reid. Algebraic and Geometric Topology Vol 8 (2008) 1031--1057.

"Three-manifolds, virtual homology, and group determinants" . Joint with Daryl Cooper. Geometry and Topology Vol. 10 (2006) 2247-2269.

"Virtually Haken filings and semi-bundles" . Joint with Daryl Cooper. Geometry and Topology Vol 10 (2006) 2237-2245.

"Great circle links and virtually fibered knots". Topology, Vol 44 (2005) No. 5, pp. 947--958.

"Double bubbles in the three-torus". Joint with M. Carrion Alvarez, J. Corneli, and S. Beheshti. Experimental Mathematics Vol 12 (2003) No. 1, pp. 79-89.

Other papers/stuff

BOOK REVIEW: Review of ``Mostly Surfaces", by R. E. Schwartz, American Mathematical Monthly , Vol 121 (2014) 954--956.

"Big Dehn surgery space and the link of $S^3" uses the computer program Orb, details of which can be found here.

"Surfaces in finite covers and the group determinant" . In: Low Dimensional Manifolds. Oberwolfach Reports Vol. 2 (2005). (non-refereed)

The topic of my dissertation is geodesic links in the 3-sphere.


More Math Links

MathSciNet Search
Thurston's notes Here you can download Thurston's notes "The Geometry and Topology of 3-Manifolds", from his 1979 course at Princeton.
Mazes by Weeks Everyone needs this.
American Math Society
Links to people in Low-Dimensional Topology

Partially supported by NSF grant DMS - 2005353 (2020-2023)