Marc Burger

Prof. Dr. Marc Burger

*31.10.1959 Neuchâtel (Switzerland)

Marc Burger studied mathematics at the University of Lausanne (Switzerland); having completed his diploma (1983) he earned a doctorate (1986) with the thesis "Petites valeurs propres du laplacien et topologie de Fell". His Habilitation (1990) at Basle University (Switzerland) was followed by a three-year stay in the USA as an Invited Assistant Professor at Stanford University (CA, 1989-1990), then as a Member of the Institute for Advanced Study, Princeton (NJ, 1990-1991) and finally as an Invited Professor at the Graduate Center of the City University of New York (NY, 1991-1992). In 1992 he followed a call as Professeur Ordinaire to the University of Lausanne; from there he was appointed as a full professor to the Mathematics Department at the Swiss Federal Institute of Technology (ETH) in Zurich (Switzerland) in 1997. In 1999 he was appointed as director of the Forschungsinstitut für Mathematik (FIM) at the ETH; he held this position until 2009. He has been a research council member of the Swiss National Science Foundation since 2005.

Marc Burger's main research interest focuses on the study of discrete subgroups of Lie groups, in the broadest sense. In collaborations with P. Sarnak he developed a method for estimating the spectrum of the laplacian on locally symmetric spaces which is based on ideas from dynamical systems. In collaborations with S. Mozes he developed a structure theory for groups acting on trees and product of trees which lead to a new class of examples of infinite simple groups. In collaboration with A. Iozzi and A. Wienhard he developed a structure theory for actions of surface groups on hermitian symmetric space which lead to a full geometric understanding of maximal representations; these works are based on the theory of continuous bounded cohomology which he developed with N. Monod in order to prove a conjecture of R. Zimmer.

Since 2012 he is fellow of the American Mathematical Society and member of the Leopoldina.

Publications (a selection):

- BURGER, M., and SARNAK, P.: Ramanujan duals II. lnvent. Math. 106, 1-11 (1991)

- BURGER, M.,: Rigidity properties of group actions on CAT (0)-spaces, Proc. ICM, Zürich1994

- BURGER, M., and MOZES, S.: Lattices in products of trees. Inst. Hautes Etudes Sci. Pub.

  Math. 92, 151-194 (2000)

- BURGER, M., IOZZI, A., and WIENHARD, A.: Surface group representations withmaximal Toledo 

  invariant. Ann. Math., 517-566 (2010)