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), J. of Algebra 528 (2019), 497-504

**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)

Polycopié ici

Cours ici

Feuilles de TD ici

Corriges des TD ici

Cours ici

Feuilles de TD ici

Corriges des TD ici

Jeudi 16h15-17h15, B22 Salle 016

Mercredi 13h00-14h00, B22 Salle 004