Mark Baker

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

• Infinitely many arithmetic alternating links: class number greather than one
  (with A. Reid), J Knot Theory and Ramifications, to appear pdf


• Infinitely many arithmetic alternating links
  (with A. Reid), Algeb. Geom. Topol., 23:6 (2023), 2857-2866
  (appeared online: DOI 10.2140/agt.2023.23.2857) pdf


• 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)

Recent talks

• Topology Seminar, Monash U., Melbourne, July 26, 2023
• Topology Seminar, Max Planck Institute Math., Bonn, May 2, 2022
• Topology Seminar, Monash U., Melbourne, August 1, 2018
• Seminaire GDT, Marseille, December 4, 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

Research/Conference Invitations

• Rice University, April 6-14, 2023
• Conference: Arithmetic groups and 3-manifolds, MPIM Bonn, May 16-20, 2022 (online)
• Max Planck Institute Math, Bonn, May 1-7, 2022
• Conference: Low Dimensional Actions of 3-Manifold Groups, University of Bourgogne (Dijon), November 4-8, 2019
• Conference on Geometric Structures, University of Nice, January 14-18, 2019
• 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)

Teaching

Miscellaneous (Divers)