This volume contains articles based on talks given at the Robert Brooks Memorial Conference on Geometry and Spectral Theory and the Workshop on Groups, Geometry and Dynamics held at Technion - the Israel Institute of Technology (Haifa). Robert Brooks' (1952 - 2002) broad range of mathematical interests is represented in the volume, which is devoted to various aspects of global analysis, spectral theory, the theory of Riemann surfaces, Riemannian and discrete geometry, and number theory. A survey of Brooks' work has been written by his close colleague, Peter Buser. Also included in the volume are articles on analytic topics, such as Szego's theorem, and on geometric topics, such as isoperimetric inequalities and symmetries of manifolds. The book is suitable for graduate students and researchers interested in various aspects of geometry and global analysis.
On the mathematical work of Robert Brooks by P. Buser Moduli spaces of homotopy theory by D. Blanc K-regular graphs and Hecke surfaces by R. Brooks and M. Monastyrsky Isospectrality and spectral rigidity of surfaces with small topology by P. Buser and K.-D. Semmler Topics in isoperimetric inequalities by I. Chavel Hidden symmetries and arithmetic manifolds by B. Farb and S. Weinberger Variants of the $3N 1$ conjecture and multiplicative semigroups by H. M. Farkas Energy capacity inequalities via an action selector by U. Frauenfelder, V. Ginzburg, and F. Schlenk On non-bounded generation of discrete subgroups in rank-1 Lie group by K. Fujiwara Isospectral and isoscattering manifolds: A survey of techniques and examples by C. Gordon, P. Perry, and D. Schueth Filling area conjecture, optimal systolic inequalities, and the fiber class in abelian covers by M. G. Katz and C. Lescop An invitation to Deninger's work on arithmetic zeta functions by E. Leichtnam Some more non-arithmetic rigid groups by A. Lubotzky On domain monotonicity for the principal eigenvalue of the Laplacian with a mixed Dirichlet-Neumann boundary condition by R. G. Pinsky The sharp form of the strong Szego theorem by B. Simon.