Professor at University of Rennes 1 Institut de Recherche Mathématique de Rennes (IRMAR) Campus Beaulieu 35042 Rennes Cedex France Building: B023 Office: 8 - 835 Phone: (+33) (0)2 23 23 60 28 Email: mark dot baker at univ-rennes1 dot fr |

- Research areas: low-dimensional topology, hyperbolic manifolds, and arithmetic groups.

Papers | Talks | Invitations |
Teaching/Seminars |

**All principal congruence link groups**

(with M. Goerner and A. Reid), to appear J. of Algebra

**Technical Report: All principal congruence link groups**

(with M. Goerner and A. Reid), arXiv: 1902.04722

**All known principal congruence links**

(with M. Goerner and A. Reid), arXiv: 1902.04426

**Congruence link complements-- a 3-dimensional Rademacher conjecture,**

(with A. Reid). In: Cohomology of Arithmetic Groups, 177-200, Springer Proc. Math. Stat. 245, 2018

**Principal congruence links: class number greater than one**

(with A. Reid). Experimental Math, 27(4), 395-413 (2018)

(appeared online: DOI:10.1080/10586458.2017.1289867) pdf- Finite volume hyperbolic
3-manifolds contain immersed quasi-fuchsian surfaces

(with D. Cooper). Algebr Geom Topol 15 (2015), no 2, 1199-1228

**Principal congruence link complements**

(with A. Reid). Ann Sci Fac Toulouse Math 23 (2014), no 5, 1037-1066

**Restricting the topology of 1-cusped arithmetic 3-manifolds**

(with A. Reid). Algebr Geom Topol 13 (2013), no 3, 1273-1298**Conservative subgroup seperability for surfaces with boundary**

(with D. Cooper). Algebr Geom Topol 13 (2013), no 1, 115-125**A combination theorem for convex hyperbolic manifolds with applications to surfaces in 3-manifolds**

(with D. Cooper). J of Topology 1 (2008), 603-642**Arithmetic knots in closed 3-manifolds**

(with A. Reid). J Knot Theory and Ramifications 11 (2002), 903-920

**All links are sublinks of arithmetic links**

Pacific J Math 203 (2002), 257-263

- Towers of covers of hyperbolic
3-manifolds

(with M. Boileau, S. Wang). Rend Instit Mat Univ Trieste Supp Vol XXXII (2001), 1-9 - Commensurability classes of
arithmetic link complements

J Knot Theory and Ramifications 10 (2001), 943-957 **Link complements and the Bianchi modular groups**

Trans Amer Math Soc 353 (2001), 3229-3246**Immersed, virtually embedded boundary slopes**

(with D. Cooper) Topology Appl 102 (2000), 239-252**On boundary slopes of immersed incompressible surfaces**

Annales Inst Fourier 46 (1996), 1443-1449**The figure eight knot is congruence**

Preprint (1992)**Link complements and integer rings of class number greater than one**

Topology '90, Proceedings of the research semester in low-dimensional topology

at Ohio State University, De Gruyter Verlag (1992), 55-59**On coverings of figure eight knot surgeries**

Pacific J Math 150 (1991), 215-228**Covers of Dehn fillings on once-punctured torus bundles II**

Proc Amer Math Soc 110 (1990), 1099-1108**Covers of Dehn fillings on once-punctured torus bundles**

Proc Amer Math Soc 105 (1989), 747-754**On the homology of subgroups of PSL(2,O)**

Preprint (1988)**The virtual Z-representability of certain 3-manifold groups**

Proc Amer Math Soc 103 (1988), 996-998**On certain branched covers of S^3**

Geometry and Topology: Proceedings of U. Georgia Topology Conference 1985,

Marcel Dekker, New York, 1987, 43-46**Seminar on Conformal and Hyperbolic Geometry**

Given by D. Sullivan at the IHES, Fall 1981. Notes prepared by Mark Baker and Jose Seade.

Preprint IHES/M/82/42**Ramified primes and the homology of the Bianchi groups**

Preprint IHES/M/82/57**Link complements and the homology of arithmetic subgroups of PSL(2,C)**

Preprint IHES/M/82/41- Link complements and imaginary
quadratic number fields

Advances in Math (accepted)

- Topology Seminar, Monash U., Melbourne, August 2018
- Seminaire GDT, Marseille, December 2017
- Seminaire Quimperiodique, Quimper, April 2016
- IV Atlantic Geometry Seminar, CIEM Castro-Urdiales, Spain
October 2013 (3 lecture mini-course on

essential surfaces in cusped 3-manifolds)

- Conference "Low dimensional topology and geometry" (M. Boileau
60th), Toulouse, June 2013

- Topology Seminar, U. Toulouse 3, June 2012
- Analytic geometry seminar, U. Rennes 1, December 2011
- Conference "Singularities, knots, and mapping class groups, Dijon, September 2010
- Conference "From braids to Teichmuller spaces", CIRM Luminy, June 2009
- Topology Seminar, U. California Santa Barbara, May 2009
- Topology Seminar, U. Texas-Austin, March 2009
- Conference "Braids, groups and manifolds", Toulouse, September 2007
- Journees GDR "Tresses et topologie en basse dimension",
Clermont-Ferrand, September 2006

- Conference "Knots, groups and 3-manifolds", Marseille, June 2006
- Conference "Geometry and topology of 3-manifolds, ICTP Trieste,
June 2005

- AMS Meeting 1007: Session on "Geometric methods in three dimensions", Santa Barbara, April 2005

- CIRM Conference "Structure of 3-manifold groups", CIRM, Luminy, February 26-March 2 2018
- CIRM Conference "Geometry of groups and geometry of 3-manifolds", CIRM, Luminy, February 19-23 2018
- Computation in Geometric Topology Workshop, University of Warwick, December 11-15 2017
- Geometric Topology in Low Dimensions Workshop, University of Warwick, September 18-22 2017
- Advanced School on Geometric Group Theory and Low Dimensional Topology, ICTP, Trieste, May 23 - June 3 2016
- University of Texas-Austin, September-October 2015 (3 weeks)
- MFO Meeting "New perspectives on interplay between discrete groups in low dimensional topology and arithmetic lattices", Oberwolfach, June 21-27, 2015
- Uni Firenze, Thesis committee, Florence, April 2014
- CIRM Conference "Low dimensional topology, knots, and orderable groups", CIRM Luminy, July 1-5 2013
- CNRS/JSPS Joint Seminar "Aspects of representation theory in low dimensional topology and 3-dimensional invariants" Carrey le Rouet, November 5-9, 2012
- CIRM Conference "Rigidity and flexibility in dimensions 2,3,4", CIRM Luminy, May 14-18, 2012
- IHP Trimester "Geometry and analysis of surface group representations", Paris, January- March 2012
- LMS Symposium "Geometry and arithmetic of lattices", Durham University, July 4-13, 2011
- University of Texas-Austin, April 2011 (2 weeks)
- University
of California Santa Barbara, May 2009 (1 month).

- University of Texas-Austin, March 2009 (2 weeks)

- University of California Santa Barbara, April- May 2008 (2 weeks)
- University of Texas-Austin, August 2006 (1 week)
- ICMS- University of Edinburg, March 2006 (1 week)
- MFO Workshop "Low-dimensional manifolds", Oberwolfach, September 2005 (1 week)

Cours polycopié ici

Feuilles de TD ici

Feuilles de TD ici

Jeudi 16h15-17h15, B22 Salle 016

Mercredi 13h00-14h00, B22 Salle 004