CONFERENCE IN ERGODIC THEORY,GEOMETRY AND ARITHMETIC Erwin Schroedinger Institute, Vienna, February 3-14,1997 Organizers: A. Katok (Penn State) and G. Margulis (Yale) ALL TALKS WILL TAKE PLACE IN THE LECTURE ROOM N3 IN THE CORRIDOR LEADING TO THE ESI FACILITIES AND NOT IN THE ESI LECTURE ROOM THE FIRST DAY OF THE CONFERENCE (FEBRUARY 3) WILL FOLLOW THE SPECIAL SCHEDULE (SEE BELOW) Starting from TUESDAY FEBRUARY 4 MORNING SESSIONS will feature one-hour lectures beginning at 9:30am and 11am. All of these will be parts of series listed below. In addition on Thursday February 6 and Wednesday February 12 there will be one-hour survey talks. There will be no afternoon sessions on there days. AFTERNOON SESSIONS will feature three 45-minutes talks beginning at 3:30pm, 4:30pm and 5:30pm. SATURDAY FEBRUARY 8 will be a full working day. There will be no talks on SUNDAY FEBRUARY 9. CONFERENCE SCHEDULE: Monday FEBRUARY 3. MORNING Special pre-conference event 10am M.Ya.Antonovskii 1965 School in Ergodic Theory at Humsan, Uzbekistan. Reflections and recollections of the organizer. 10:45am A.Katok Ergodic theory from Humsan to Vienna. There will also be probably be some remarks by G.Margulis. AFTERNOON 3:45pm. Opening of the Conrefence on Ergodic Theory, Geometry and Arithmetic. 4pm-5pm H. Furstenberg Stiffness of group actions 5:15-6:15pm G. Knieper Volume growth and the distribution of closed geodesics in manifolds of nonpositive curvature. ----------------------------------------------------- LECTURE SERIES AND SURVEY TALKS Flows on homogeneous spaces and number theory. G.Margulis, D.Kleinbock, A.Eskin, N.Shah. 6 lectures: Feb 5,6,7,11,12,13. Actions of higher--rank abelian groups and rigidity. A.Katok, K.Schmidt. 4 lectures: Feb.4,5,7,8. Lattices in the automorphism group of a product of trees. M.Burger, S.Mozes. 3 lectures: Feb.4,6,8. Topological surerrigidity and its applications. R.Feres. 3 lectures: Feb. 10,12,13. Minimal entropy and rigidity of symmetric spaces. G.Besson, G.Courtois. 3 lectures: Feb.10,11,14. Groups quasi-isometric to symmetric spaces. B.Leeb (one talk) Feb 6 Quasi--isometry and rigidity: latices and beyond. B.Farb (one talk) Feb 12. ---------------------------------------------------------- AFTERNOON TALKS ON FEBRUARY 4,5,7,8,10,11,13,14. Please notice that exact times have been scheduled only for some of these talks. Complete schedule will be provided shorty after the begining of the conference. E.Ghys (ENS-Lyon) Smooth linearizations of SL(n) actions around a fixed point I.Benoist (Paris VII) Linear groups with positive eigenvalues G.Tomanov (U.Lyon) On the quadratic and unitary inequalities in the S-adic case. P.Foulon (Strasbourg) Dynamical rigidity in Finsler geometry. Y.Guivarch (Rennes) TBA V.Kaimanovich (Rennes) Singularity of the harmonic measure on symmetric spaces. H. Abels (Bielefeld) A quantitative version of finite generatedness for lattices. W.Ballmann (Bonn) Property T for groups acting on complexes. U.Hamenstaedt (Bonn) Cocycles, cross-ratios and eigenfunctions in negative curvature. F. Grunewald (Dusseldorf) On ternary quadratic forms. P de la Harpe (Geneva) Pierre Growth on root lattices and Ehrhart polynomials. I.Goldsheid (london) Zariski dense semi-groups of Lie groups: propertoes of eigenvalues and invariant sets. A.Starkov (Istra) Closures of horospherical leaves on hyperbolic manifolds G.Soifer (Bar-Ilan) Discontinuous groups of affine transformations with orthogonal linear part S.Katok (Penn State) Automorphic forms of the complex hyperbolic space S.Hurder (Illinois-Chicago) Boundary Chaos for open manifolds S.Adams (Minnesota) Dynamics on Lorentz manifolds. C-B.Yue (Penn State) On the representation variety of complex hyperbolic Kleinian groups. Y. Gao (Yale) Superrigidity for isometric group actions on CAT(-1) spaces A.Torok (Princeton) Regularity and rigidity of cocycles V.Nitica (Indiana) Cocycles over Anosov actions. N.Qian (Yale) Tangential flatness and local rigidity of higher rank lattice actions. A.Wilkinson (Norstwestern) Prevalence of non-Lipschitz Anosov foliations and conjugacies. A.Iozzi (Maryland) TBA E.Gutkin (USC) Polygonal billiards and cofinite lattices. ------------------------------------------------------ DAILY SCHEDULES NOTE: Some of the afternoon talks have not been scheduled for particular time slots. The principal reason is to provide some flexibility in view of uncertainty of arrival and departure dates of several participants. TUESDAY FEBRUARY 4, MORNING 9:30am. Actions of higher--rank abelian groups and rigidity.I A.Katok.Anosov actions and hyperbolic measures on compact manifolds; a survey. 11am. Lattices in the automorphism group of a product of trees.I M.Burger, S.Mozes AFTERNOON 3:30pm Dynamics on Lorentz manifolds. S.Adams 4:30pm Cocycles over Anosov actions V.Nitica 5:30pm Regularity and rigidity of cocycles A.Torok WEDNESDAY FEBRUARY 5, MORNING 9:30am. Flows on homogeneous spaces and number theory. G.Margulis. A survey. 11am.Actions of higher--rank abelian groups and rigidity.II K.Schmidt. Actions with positive entropy; a survey. AFTERNOON 3:30pm On ternary quadratic forms. F.Grunewald 4:30pm TBA 5:30pm TBA THURSDAY FEBRUARY 6, MORNING 9:30am. Flows on homogeneous spaces and number theory. D.Kleinbock. Metric theory of Diophantine approximation via flows on SL(n,R)/SL(n,Z).I 11am. Lattices in the automorphism group of a product of trees.II M.Burger, S.Mozes 12:15pm Groups quasi-isometric to symmetric spaces. B.Leeb NO TALKS IN THE AFTERNOON FRIDAY FEBRUARY 7, MORNING 9:30am. Flows on homogeneous spaces and number theory. D.Kleinbock. Metric theory of Diophantine approximation via flows on SL(n,R)/SL(n,Z).II 11am. Actions of higher--rank abelian groups and rigidity.III A.Katok. Local rigidity of Anosov actions and applications AFTERNOON 3:30pm Tangential flatness and local rigidity of higher rank lattice actions. N.Qian 4:30pm A quantitative version of finite generatedness for lattices. H.Abels 5:30pm Property T for groups acting on complexes. W.Ballmann SATURDAY FEBRUARY 8, MORNING 9:30am.Actions of higher--rank abelian groups and rigidity,IV. K.Schmidt. Cohomological rigidity for algebraic actions and topological Markov chains 11am. Lattices in the automorphism group of a product of trees.III M.Burger, S.Mozes AFTERNOON 3:30pm On the representation variety of complex hyperbolic Kleinian groups. C-B. Yue 4:30pm Dynamical rigidity in Finsler geometry. P.Foulon 5:30pm Boundary Chaos for open manifolds. S.Hurder NO TALKS ON SUNDAY FEBRUARY 9. MONDAY FEBRUARY 10, MORNING 9:30am. Minimal entropy and rigidity of symmetric spaces,I. G.Besson, G.Courtois 11am. Topological surerrigidity and its applications,I. R.Feres AFTERNOON 3:30pm Cocycles, cross-ratios and eigenfunctions in negative curvature. U.Hamestaedt 4:30pm Automorphic forms on the complex hyperbolic space. S.Katok 5:30pm Singularity of the harmonic measure on symmetric spaces. V.Kaimanovich TUESDAY FEBRUARY 11, MORNING 9:30am. Minimal entropy and rigidity of symmetric spaces" G.Besson, G.Courtois 11am. Flows on homogeneous spaces and number theory. N.Shah.Counting of integral points on homogeneous varieties. AFTERNOON 3:30pm TBA 4:30pm TBA 5:30pm TBA WEDNESDAY FEBRUARY 12, MORNING 9:30am. Flows on homogeneous spaces and number theory. A.Eskin. Quantitative version of Oppenheim conjecture and eigenvalue spacing for the flat tori,I 11am. Topological surerrigidity and its applications,II R.Feres 12:15pm Quasi--isometry and rigidity: lattices and beyond. B.Farb NO TALKS IN THE AFTERNOON THURSDAY FEBRUARY 13, MORNING 9:30am. Flows on homogeneous spaces and number theory. A.Eskin Quantitative version of Oppenheim conjecture and eigenvalue spacing for the flat tori,II. 11am. Topological surerrigidity and its applications,III R.Feres AFTERNOON 3:30pm TBA 4:30pm TBA 5:30pm TBA FRIDAY FEBRUARY 14, MORNING 9:30am. Minimal entropy and rigidity of symmetric spaces.III G.Besson, G.Courtois 11am. TBA AFTERNOON 3:30pm TBA 4:30pm TBA 5:30pm TBA