Prof. em. Dr. Marc Burger

Publications

Title Place of publication / Abstract
ℓ2-stability and homomorphisms into the mapping class group (PDF, 1 MB) (with A. Iozzi) IRMA Lect. Math. Theor. Phys., 34. Abstract MR
The Hopf-Tsuji-Sullivan dichotomy in higher rank and applications to Anosov subgroups (PDF, 334 KB) (with O. Landesberg, M. Lee and H. Oh) J. Mod. Dyn. 19 (2023), 301–330. Abstract MR
Currents, systoles and compactifications of character varieties (PDF, 647 KB) (with A.I ozzi, A. Parreau and M.B. Pozzetti) Proceedings of the London Mathematical Society, 123(6):565-596, 2021. Abstract MR
Integrality of volumes of representations (PDF, 448 KB) (with M. Bucher and A. Iozzi) Math. Ann. no. 1-2:209-242, 2021. Abstract MR
The real spectrum compactification of character varieties: characterizations and applications (PDF, 676 KB) (with A. Iozzi, A. Parreau and M.B. Pozzetti) C. R. Acad. Sci. Paris, 359:439-463, 2021. Abstract MR
The bounded Borel class and 3-manifold groups (PDF, 294 KB) (with M. Bucher and A. Iozzi) Duke Math. J., 167(17):3129-3169, 2018. Abstract MR
On the role of totally disconnected groups in the structure of locally compact groups. New directions in locally compact groups. 1–8, London Math. Soc. Lecture Note Ser., 447, Cambridge Univ. Press, Cambridge, 2018. (Reviewer: Bruno Duchesne). Abstract MR
Maximal representations, non-Archimedean Siegel spaces, and buildings (with M.B. Pozzetti) Geom. Topol. 21(6):3539–3599, 2017. Abstract MR
On weakly maximal representations of surface groups (with G. Ben Simon, T. Hartnick A. Iozzi and A. Wienhard) J. Differential Geom., 105(3):375–404, 2017. Abstract MR
On order-preserving representations (with G. Ben Simon, T. Hartnick A. Iozzi and A. Wienhard) J. Lond. Math. Soc., 94(2):525–544, 2016. Abstract MR
Higher Teichmüller spaces: from SL(2,R) to other Lie groups. Handbook of Teichmüller theory (with A. Iozzi and A. Wienhard). Vol. IV, 539-618, IRMA Lect. Math. Theor. Phys., 19, 2014. Abstract MR
Lattices in products of trees and a theorem of H. C. Wang (PDF, 145 KB) (with S. Mozes) Bull. Lond. Math. Soc., 46:1126-1132, 2014. Abstract MR
Isometric embeddings in bounded cohomology (PDF, 328 KB) (with M. Bucher, R. Frigerio, A. Iozzi, C. Pagliantini and B. Pozzetti) J. Topol. Anal., 1-25, 2014. Abstract MR
A dual interpretation of the Gromov-Thurston proof of Mostow rigidity and volume rigidity for representations of hyperbolic lattices (PDF, 761 KB) (with M. Bucher and A. Iozzi) Springer INdAM Ser., 3, 47-76, 2013. Abstract MR
On Ulam stability (PDF, 272 KB) (with N. Ozawa and A. Thom) Israel J. Math., 193:109-129 2013. Abstract MR
Bounded cohomology and totally real subspaces in complex hyperbolic geometry (PDF, 160 KB) (with A. Iozzi) Ergod. Th. & Dynam. Sys., 32:467-478, 2012. Abstract MR
Fundamental groups of Kähler manifolds and geometric group theory (PDF, 180 KB) Séminaire Bourbaki, vol. 2009/2010, Exposé 1022, Astérisque, 339:305-321, 2011. Abstract MR
An extension criterion for lattice actions on the circle (PDF, 222 KB) Geometry, rigidity, and group actions, 3-31, Chicago Lectures in Math., Univ. Chicago Press, Chicago, IL, 2011. Abstract MR
Surface group representations with maximal Toledo invariant (PDF, 1.6 MB) (with A. Iozzi and A. Wienhard) Ann. Math., 172(1):517-566, 2010. Abstract MR
A useful formula from bounded cohomology (PDF, 1023 KB) (with A. Iozzi) Géométries à courbure négative ou nulle, groupes discrets et rigidités, 243-292, Sémin. Congr., 18, Soc. Math. France, Paris, \2009.** Abstract MR
Linear representations and arithmeticity of lattices in products of trees (PDF, 269 KB) (with S. Mozes and R.J. Zimmer) Essays in geometric group theory. Ramanujan Mathematical Society Lecture Notes Series, 9:1-25, 2009. Abstract MR
Tight homomorphisms and Hermitian symmetric spaces (PDF, 565 KB) (with A. Iozzi and A. Wienhard) Geom. Funct. Anal., 19(3):678-721, 2009. Abstract
Bounds for cohomology classes (PDF, 30 KB) (with A. Iozzi, N. Monod, A. Wienhard) L'enseignement Mathématique (2) 54, pp.52-54, 2008.
Bounded cohomology and applications: a panorama (PDF, 86 KB) Oberwolfach Reports, Vol. 5, No.1, pp.252-255, EMS Publishing, 2008.
A measurable Cartan theorem and applications to deformation rigidity in complex hyperbolic geometry (PDF, 278 KB) (with A. Iozzi) Pure Appl. Math. Q. 4 (2008), no. 1, part 2, 181-202. Abstract MR
Preface [Special issue in honor of Grigory Margulis. Part 1] (with L. Ji, A. Lubotzky, H. Oh and S.T. Yau) Pure Appl. Math. Q. 3 (2007), no. 4, Special Issue: In honor of Grigory Margulis. Part 1, i-vii. Abstract MR
Bounded differential forms, generalized Milnor-Wood inequality and an application to deformation rigidity (PDF, 422 KB) (with A. Iozzi) Geom. Dedicata, 125:1-23, 2007. Abstract MR
Hermitian symmetric spaces and Kähler rigidity (PDF, 320 KB) (with A. Iozzi and A. Wienhard) Transform. Groups, 12(1):5-32, 2007. Abstract MR
Maximal representations of surface groups: symplectic Anosov structures (PDF, 394 KB) (with A. Iozzi, F. Labourie, A. Wienhard) Pure Appl. Math. Q. 1 (2005), no. 3, Special Issue: In memory of Armand Borel. Part 2, 543-590. Abstract MR
Equivariant embeddings of trees into hyperbolic spaces (PDF, 383 KB) (with A. Iozzi and N. Monod) Int. Math. Res. Not., 2005(22):1331-1369, 2005. Abstract MR
Bounded Kähler class rigidity of actions on Hermitian symmetric spaces (PDF, 287 KB) (with A. Iozzi) Ann. Sci. École Norm. Sup. (4), 37(1):77-103, 2004. Abstract MR
Surface group representations with maximal Toledo invariant (PDF, 101 KB) (with A. Iozzi and A. Wienhard) C. R. Math. Acad. Sci. Paris 336(5):387--390, 2003. Abstract MR
Counting hyperbolic manifolds (PDF, 168 KB) (with T. Gelander, A. Lubotzky and S. Mozes) Geom. Funct. Anal., 12(6):1161-1173, 2002. Abstract MR
On and around the bounded cohomology of SL (2, R) (PDF, 1 MB) (with N. Monod) Rigidity in dynamics and geometry. (Cambridge, 2000), 19-37, Springer, Berlin, 2002. Abstract MR
Boundary maps in bounded cohomology. Appendix to: "Continuous bounded cohomology and applications to rigidity theory'' (PDF, 184 KB) (with A. Iozzi) Geom. Funct. Anal., 12(2):219-280, 2002. Abstract MR
Continuous bounded cohomology and applications to rigidity theory (PDF, 563 KB) (with N. Monod) Geom. Funct. Anal., 12(2):219-280, 2002. Abstract MR
Lattices in products of trees (PDF, 3.8 MB) (with S. Mozes) ubl. I.H.E.S., 92:151-194, 2000. Abstract MR
Groups acting on trees: from local to global structure (PDF, 3.5 MB) (with S. Mozes) Publ. I.H.E.S., 92:113-150, 2000. Abstract MR
Erratum to the below (PDF, 23 KB) (with N. Monod) J. Eur. Math. Soc., 1(3):338-338, 1999. Abstract MR
Bounded cohomology of lattices in higher rank Lie groups (PDF, 237 KB) (with N. Monod) J. Eur. Math. Soc., 1(2):199-235, 1999, Abstract MR
Idempotents in complex group rings: theorems of Zalesskii and Bass revisited (PDF, 5.2 MB) (with A. Valette). J. of Lie Theory, 8(2):219-228, 1998. Abstract MR
Finitely presented simple groups and products of trees (PDF, 463 KB) (with S. Mozes) C. R. Acad. Sci. Paris, 324:747-752, 1997. Abstract MR
Constructing irreducible representations of discrete groups (PDF, 643 KB) (with P. de la Harpe) Proc. Indian Acad. Sci., 107(3):223-235, 1997. Abstract MR
CAT(-1)-spaces, divergence groups and their commensurators (PDF, 578 KB) (with S. Mozes) J. of the Amer. Math. Soc. 9(1):57-93, 1996. Abstract MR
Rigidity properties of group actions on CAT(0)-spaces (PDF, 1 MB) Proc. ICM Zürich, Switzerland 1994, 761-769 ; Birkhäuser 1995. Abstract MR
Alower bound on λ0 for geometrically finite hyperbolic n-manifolds (PDF, 2.5 MB) (with D. Canary) J. reine angew. Math., 454 (1994), 37-57. Abstract MR
Réseaux arithmétiques et commensurateur d'après G. A. Margulis (PDF, 1.2 MB) (with N. A'Campo) Invent. Math., 116:1-25, 1994. Abstract MR
Intersection, the Manhattan curve, and Patterson-Sullivan theory in rank 2 (PDF, 718 KB) Int. Math. Res. Not., 993(7):217-225, 1993. Abstract MR
Ramanujan duals and automorphic spectrum (PDF, 526 KB) (with P. Sarnak) Bull. Am. Math. Soc., New Ser., 26(2):253-257, 1992. Abstract MR
Ramanujan duals. II (PDF, 478 KB) (with P. Sarnak) Invent. Math., 106(1):1-11, 1991. Abstract MR
Kazhdan constants for SL(3,Z) (PDF, 2.7 MB) J. Reine Angew. Math., 413:36-67, 1991. Abstract MR
Horocycle flow on geometrically finite surfaces (PDF, 1.4 MB) Duke Math. J., 61(3):779-803, 1990. Abstract MR
Small eigenvalues of Riemann surfaces and graphs (PDF, 1 MB) Math. Z., 205(3):395-420, 1990. Abstract MR
Asymptotics of small eigenvalues of Riemann surfaces (PDF, 198 KB) Bull. Am. Math. Soc., New Ser., 18(1):39-40, 1988. Abstract MR
Spectre du Laplacien, graphes et topologie de Fell (PDF, 29.5 MB) Comment. Math. Helv., 63(2):226-252, 1988. Abstract MR
Riemann surfaces of large genus and large \lambda_1 (PDF, 392 KB) (with P. Buser and J. Dodziuk) In: "Geometry and analysis on manifolds", Lectures Notes in Math., 1339, Springer, 54-63, 1988. Abstract MR
Volume, diameter and the first eigenvalue of locally symmetric spaces of rank one (PDF, 937 KB) (with V. Schröder) J. Differ. Geom., 26(2):273-284, 1987. Abstract MR
Amenable groups and stabilizers of measures on the boundary of a Hadamard manifold (PDF, 589 KB) (with V. Schröder) Math. Ann., 276(3):505-514, 1987. Abstract MR
Estimation de petites valeurs propres du laplacien d'un revêtement de variétés riemanniennes compactes C.R. Acad. Sci. Paris, Sér. I, 302(5):191-194, 1986. Abstract MR
Petites valeurs propres du laplacien et topologie de Fell Thesis, Lausanne, 1986.
A propos de la multiplicité de la première valeur propre du laplacien d'une surface de Riemann (with B. Colbois) C.R. Acad. Sci. Paris, Sér. I, 300:247-249, 1985. Abstract MR
Analyse harmonique sur les groupes de Heisenberg généralisés (PDF, 515 KB) Monatsh. Math., 98(1):29-40, 1984. Abstract MR