*Seifert Bundles and Orlik's Conjecture on the Topology of Hypersurface Singularities,*geometry seminar at the University of Texas,**Austin,**Texas, U.S.A; May 3, 2007.*Obstructions in Kähler-Einstein and Sasaki-Einstein Geometry,*geometry seminar at the University of Cologne,**Cologne,**Germany; January 12, 2007.*Wonderworld of Sasakian Manifolds,**Riemannian Topology*conference, University of New Mexico,**Albuquerque**, New Mexico, USA; October 13, 2006.*Real Monge-Ampère Equations on Contact Manifolds,*Oberseminar Globale Analysis, University of Bonn,**Bonn**, Germany; June 20, 2006.*Sasakian Geometry: Past, Present, and Future Perspectives,*University of Glasgow,**Glasgow**, United Kingdom; May 19, 2006.*Einstein Metrics on Spheres,*Colorado State University,**Fort Collins**, Colorado, USA; April 24, 2006.*Einstein Metrics on Spheres,*University of Leeds,**Leeds**, United Kingdom; March 29, 2006.*Geometric Structures on 5-Manifolds,*Ohio State University colloquium,**Columbus**, Ohio, USA; January 26, 2006.*Geometric Structures on 5-Manifolds,*geometry seminar at the University of Cologne,**Cologne,**Germany; December 18, 2005.*Geometric Structures on 5-Manifolds,*Humboldt Universität geometry seminar,**Berlin**, Germany; November 22, 2005.*Geometric Structures on 5-Manifolds,*invited seminar at the Jagiellonian University,**Kraków**, Poland; November 14, 2005.*Seifert Bundles and Contact Structures,*invited lecture at the**International Erwin Schrödinger Institute**in the program*Geometry of Pseudo-Riemannian Manifolds with Applications in Physics,***Vienna**, Austria; November 1, 2005.*Manifolds with Positive Ricci Curvature,*invited talk at the Arthur L. Besse seminar, Ecole Polytechnique,**Palaiseau**, France; October 10, 2005.*Sasakian Structures in Mathematics and Physics,*invited lecture at the conference*Géométrie Pseudo-Riemannienne at Supersymétrie; September 22-24, 2005*,**Strasbourg**, France; September 23, 2005.*Geometric Structures on 5-Manifolds,*Max-Planck-Institut Oberseminar, MPI,**Bonn**, Germany; September 1, 2005.*Geometric Structures on 5-Manifolds,*invited lecture at the SFB 478 workshop*Curvature and Global Shape, 31 July -- 7 August, 2005*,**Münster**, Germany; August 3, 2005.*Geometric Structures on 5-Manifolds,*geometry seminar at the Università di Cagliari,**Caglilari,**Italy; July 21, 2005.*Geometric Structures on 5-Manifolds,*lecture given at Università di Roma, ``La Sapienza",**Roma**, Italy; July 14, 2005.*Geometric Structures on 5-Manifolds,*lecture given at Università di Bari,**Bari**, Italy; July 6, 2005.*Sasakian Geometry I-III*, invited series of**three**lectures at the Institut Élie Cartan, Université Henri Poincaré Nancy 1,**Nancy**, France; June 7,14, 2005.*Sasakian Geometry of 5-Manifolds,*invited colloquium at the Arthur L. Besse seminar, Ecole Polytechnique,**Palaiseau**, France; June 13, 2005.*Einstein Metriken auf Exotischen Sphären,*Universität Hamburg,**Hamburg**, Deutschland; 10. Dezember, 2004.*Einstein Metrics on Brieskorn Manifolds*, invited colloquium at the University of Bochum,**Bochum**, Germany; November 19, 2004.*Einstein Metrics on Brieskorn Manifolds*, geometry seminar at the University of Hamburg,**Hamburg**, Germany; November 2, 2004.*Seifert Bundles, Log Del Pezzo Surfaces, and Einstein 5-Manifolds,*Oberseminar Topologie, MPI,**Bonn**, Germany; October 25, 2004.*Einstein Metrics on Boothby-Wang Fibrations,*differential geometry seminar at the University of Bonn,**Bonn**, Germany; October 21, 2004.*Sasakian Geometry and Einstein Metrics, Lectures I-III,*invited series of**three**lectures at the Differential Geometry and Topology Workshop, Centro di Ricerca Matematica ``Ennio De Giorgi",**Pisa**, Italy; October 11-16, 2004.*Transverse Fano Structures and Einstein Metrics on Exotic Spheres,*invited colloquium, University of Bucharest,**Bucharest**, Romania; May 12, 2004.*Transverse Fano Structures and Einstein Metrics on Exotic Spheres,*invited colloquium, University of Göttingen,**Göttingen**, Germany; April 22, 2004.*Transverse Fano Structures and Einstein Metrics on Exotic Spheres*, invited lecture at the**International Erwin Schrödinger Institute**in the in the program*Geometric and analytic problems related to Cartan connections,***Vienna**, Austria; April 6, 2004.*Transverse Fano Structures and Einstein Metrics on Exotic Spheres*, Max-Planck-Institut Oberseminar, MPI,**Bonn**, Germany; March 18, 2004.*Einstein Metrics on Spheres*, invited lecture at the*Positive scalar curvature and related topics*conference at LMU München,**München**, Germany; February 28, 2004.*Transverse Fano Structures and Einstein Metrics on Spheres*, geometry seminar at the University of Oxford,**Oxford**, England; February 2, 2004.*Contact Structures, Complex Singularities, and Einstein Metrics, Lectures I-III*, a series of**three**invited plenary lectures at the*XXIV Winter School in Geometry and Physics*,**Srni**, Chech Republic; January 18-24,2004.*Transverse Fano Structures, Ricci Curvature, and Einstein Metrics*, geometry seminar at the Università di Cagliari,**Caglilari,**Italy; July 21, 2003.*Negative Self-Dual Einstein Metrics as Quotients*, lecture given at Università di Roma, ``La Sapienza",**Roma**, Italy; July 4, 2003.*Transverse Fano Structures, Ricci Curvature, and Einstein Metrics*, geometry seminar at the Università di L'Aquila,**L'Aquila**, Italy; June 24, 2003.*Transverse Fano Structures, and Einstein Metrics*, geometry seminar at the University of California,**Riverside**, California, USA; May 2, 2003.*Transverse Fano Structures and Positive Ricci Curvature*, colloquium at the University of California,**Riverside**, California, USA; April 30, 2003.*Transverse Fano Structures, Ricci Curvature, and Einstein Metrics*, colloquium at the Oregon State University,**Corvalis**, Oregon, USA; April 8, 2003.*Transverse Fano Structures, Ricci Curvature, and Einstein Metrics*, geometry seminar at the University of Oregon,**Eugene**, Oregon, USA; April 8, 2003.*Transverse Fano Structures, Positive Ricci Curvature, and Einstein Metrics,*invited lecture at the Erwin Schrödinger Institute,**Vienna**, Austria; November 22, 2002.*On the Geometry of Sasakian-Einstein 5-Manifolds*, invited lecture at the Joint International AMS/UMI Meeting in Pisa, June 12-16,**Pisa**, Italy; June 15, 2002.*Sasakian Manifolds and Einstein Metrics in Dimension 5*, invited lecture at the EDGE meeting on*Special and Low-dimensional Geometries*, June 3-7,**Luminy**, France; June 6, 2002.*Contact Structures, Einstein Metrics and Positive Ricci Curvature*, invited lecture at Institut Elie Cartan, Université Henri Poincaré,**Nancy**, France; May 28, 2002.*Sasakian Manifolds and Einstein Metrics*, Arthur Besse seminar, Ecole Polytechnique,**Palaiseau**, France; May 27, 2002.-
*Metrics Cones, Holonomy, and Special Metrics*, the SFB 288*Differentialgeometrie und Quantenphysi Kolloquium*, Freie Universität Berlin,**Berlin**, Germany; December 6, 2001. *Constact Structures and Algebraic Geometry*, invited lecture at the conference*Recent trends in mathematics*, November 23-25, 2001,**Schloss Klink**, Germany; November 24, 2001.*On Sasakian-Einstein 5-Manifolds,*Humboldt Universität geometry seminar,**Berlin**, Germany; November 19, 2001.*New Einstein Metrics in Dimensions Five and Seven,*lecture given at the Università di Roma, ``La Sapienza",**Rome**, Italy; September 26, 2001.*3-Sasakian Geometry, Nilpotent Orbits, and Exceptional Quotients*, invited lecture at the LMS Durham Symposium*Special Structures in Differential Geometry*, July 30 - August 9, 2001, University of Durham,**Durham**, England; August 2, 2001.*Algebraic Geometry and Einstein Manifolds in Dimension Five*, invited lecture at the Forschunginstitut Oberwolfach,*Differentialgeometrie im Grossen*, June 11 - 15, 2001,**Oberwolfach**, Germany; June 11, 2001.*Algebraic Geometry and Compact Einstein 5-Manifolds,*invited lecture at the University of Bonn Differential Geometry Seminar,**Bonn**, Germany; May 22, 2001.*Sasakian-Einstein Geometry of 5-Manifolds,*lecture given at Università di Roma, ``La Sapienza",**Roma**, Italy; March 21, 2001.*New Einstein Metrics in Dimension Five*, Arthur Besse Seminar at Ecole Polytechnique,**Palaiseau**, France; May 29, 2000.*Killing Spinors, Einstein Manifolds, and Contact Geometry,*invited lecture at the conference on*Generalized Dirac Operators and Their Geometric Scattering Theory*,**Warsaw**, 23 August - 4 September, 1999; International Stefan Banach Center of the Polish Academy of Sciences.*Sasakian-Einstein Manifolds, Killing Spinors, and Near Horizon Geometries*, Humboldt Universität geometry seminar,**Berlin**, Germany, July 13, 1999.*Sasakian-Einstein Manifolds, Killing Spinors, and Near Horizon Geometries*, München Universität geometry seminar,**München**, Germany; June 17, 1999.*From Archimedes to Newton -- A Beginner's Guide to Symplectic Reduction*, lecture at the West Washington University,**Bellingham**, Wxiashington, U.S.A.; February 24, 1999.*Cones, Holonomy, and Einstein Manifolds*, lecture at the West Washington University,**Bellingham**, Washington, U.S.A.; February 24, 1999.*New Families of Einstein 7-manifolds*, invited colloquium talk at Università di Bari,**Bari**, Italy; June 18, 1998.*A Short Introduction to 3-Sasakian Manifolds I-IV,*series of**four**lectures given at Università di Roma, ``La Sapienza",**Roma**, Italy; June 2,4,9,12, 1998.*Quaternionic Geometry and Einstein Manifolds*, invited joint colloquium at the Max-Planck-Institut für Mathematik and Leipzig Universität,**Leipzig**, Germany; December 9, 1997.*Hypercomplex Structures on Toral Quotients*, lecture given in the Special Session of the AMS Meeting,**Albuquerque**, New Mexico, U.S.A.; November 9, 1997.*Einstein Manifolds From Spheres*, report on my research presented to the Fachbeirat at the Max-Planck-Institut für Mathematik in Bonn,**Bonn**, Germany; October 9, 1997.*Quaternionic Geometry and Einstein Manifolds*, lecture given in the ICMS conference 18-29 August, 1997,**Edinburgh**, Scotland; August 18, 1997.*Quaternionic Geometry and Einstein Manifolds*, lecture given in the MPI Faltings-Harder-Manin-Zagier Oberseminar, MPI,**Bonn**, Germany; July 10, 1997.*Making Einstein Manifolds Out of Spheres*, geometry seminar at the Jagiellonian University,**Kraków**, Poland; June 9, 1997.*On Betti Numbers of 3-Sasakian Manifolds*, lecture given in in the MPI Oberseminar Topologie, MPI,**Bonn**, Germany; April 7, 1997.*Einstein 7-manifolds of Positive Scalar Curvature and Arbitrary Second Betti Number*and*3-Sasakian Geometry and Killing Spinors*, invited**two**lecture at the*Meeting on Dirac Operators and Geometry*, Warsaw, 16 February -- 1 March, 1997; International Stefan Banach Center of the Polish Academy of**Warsaw**, Poland; February 25,27, 1997.*Einstein 7-manifolds of Positive Scalar Curvature and Arbitrary Second Betti Number*, geometry seminar at seminar at Universität Bonn,**Bonn**, Germany; February 4, 1997.*Einstein 7-manifolds of Positive Scalar Curvature and Arbitrary Second Betti Number*, invited colloquium talk at the University of California at Riverside,**Riverside**, California; November 13, 1996.*Geometry and Topology of 3-Sasakian Manifolds, I-III*, invited**three**lectures at the ICMS Workshop*Interplays Between Geometry and Topology*, June 3-29, 1996,**Edinburgh**, Scotland; June 4,6,27, 1996.*Hypercomplex manifolds and 3-Sasakian geometry*, contributed paper in a Special Session at the AMS meeting, April 13-14, 1996,**New York**, New York, U.S.A.; April 14, 1996.*On Betti Numbers of 3-Sasakian Manifolds*, contributed paper in a Special Session at the second joint meeting of AMS and SMM, November 29 -- December 2, 1995,**Guanajuato**, Mexico; December 1, 1995.*Geometry and Topology of 3-Sasakian Manifolds: On Betti Numbers of 3-Sasakian Spaces*, Humboldt Universität geometry seminar,**Berlin**, Germany; November 21, 1995.*Quaternionic Geometry, Supergravity, and Einstein Manifolds*, colloquium at Universität Augsburg,**Augsburg**, Germany; November 16, 1995.*Geometry and Topology of 3-Sasakian Manifolds: Quotient Construction*, Humboldt Universität geometry seminar,**Berlin**, Germany; November 14, 1995.*Quaternionic Geometry, 3-Sasakian Manifolds, and Supergravity*, SFB 288*Differentialgeometrie und Quantenphysik*Kolloquium, Freie Universität Berlin,**Berlin**, Germany; November 9, 1995.*3-Sasakian Manifolds*, Mathematisches Forschunginstitut Oberwolfach,*Differentialgeometrie im Grossen*June 12 -- 16,**Oberwolfach**, Germany; June 12, 1995.*Geometry and Topology of 3-Sasakian Manifolds*Max-Planck-Institut,**Bonn**, Germany; June 9, 1995.*Geometry and Topology of 3-Sasakian Manifolds*, Arthur Besse Seminar at Ecole Polytechnique,**Palaiseau**, France; May 22, 1995.*3-Sasakian Manifolds*, University of Adelaide,**Adelaide**, Australia; January 10, 1995.*Einstein Metrics and 3-Sasakian Geometry*, Erwin Schrödinger Institute,**Vienna**, Austria; September 28, 1994.*On 3-Sasakian manifolds*, lecture presented at the Meeting Meeting on*Quaternionic structures in mathematics and physics*, September 5-9, 1994; SISSA,**Trieste**, Italy; September 9, 1994.*On strongly inhomogeneous Einstein manifolds with positive scalar curvature and 3-Sasakian structure*, Columbia University,**New York**, New York, U.S.A.; November 17, 1993.*On strongly inhomogeneous Einstein manifolds with positive scalar curvature and 3-Sasakian structure*, SUNY@Stony Brook,**Stony Brook**, New York, U.S.A.; November 16, 1993.*On strongly inhomogeneous Einstein manifolds with positive scalar curvature and 3-Sasakian structure*, Institute for Advanced Study,**Princeton**, New Jersey, U.S.A.; November 15, 1993.*A construction of strongly inhomogeneous Einstein manifolds with 3-Sasakian structure*, Max-Planck-Institut Oberseminar, MPI,**Bonn**, Germany; July 1, 1993.*Rozmaitosci Einsteina w róznych teoriach z supersymetria¸,*Wroclaw University,**Wroclaw**, Poland; June 4, 1993.*O pewnych siedmiowymiarowych rozmaitosciach Einsteina*, Wroclaw University,**Wroclaw**, Poland; May 26, 1992.*Quaternionic Reduction and Einstein Manifolds*, The New Mexico Geometry and Topology Symposium,**Las Cruces**, New Mexico, U.S.A; February 29, 1992.*Group Actions, Quotients, and Quaternionic Manifolds*, SUNY@Stony Brook,**Stony Brook**, New York, U.S.A.; February 12, 1991.*Group Actions, Quotients, and Quaternionic Manifolds*, Institute for Advanced Study,**Princeton**, New Jersey, U.S.A.; January 27, 1991.*Self-dual Einstein Metrics with Nonzero Scalar Curvature*, University of Warwick,**Warwick**, England; May 14, 1990.*Quaternionic Käahler Reduction and Self-Dual Einstein Orbifolds*, Washington University,**St. Louis**, Missouri, U.S.A; February 6, 1990.*Quaternionic Käahler Reduction and Self-Dual Einstein Orbifolds*, the University of New Mexico,**Albuquerque**, New Mexico, U.S.A.; February 1, 1990.*Quaternionic Käahler Reduction and Self-Dual Einstein Orbifolds*, University of British Columbia,**Vancouver**, BC, Canada; January 29, 1990.*Quaternionic Käahler Reduction and Self-Dual Einstein Orbifolds*, University of California at Davis,**Davis**, California, U.S.A.; January 26, 1990.*Quaternionic Käahler Reduction and Self-Dual Einstein Orbifolds*, Oregon State University,**Corvalis**, Oregon, U.S.A.; January 25, 1990.*Quaternionic Käahler Reduction and Self-Dual Einstein Orbifolds*, Oklahoma State University,**Stillwater**, Oklahoma, U.S.A.; January 23, 1990.*Quaternionic Käahler Reduction and Self-Dual Einstein Orbifolds*, SUNY@Buffalo,**Buffalo**, New York, U.S.A.; January 11, 1990.*Quotient Constructions of Special Riemannian Geometries*, Odense University,**Odense**, Denmark; August 25, 1989.*Quotient Constructions of Special Riemannian Geometries*, Danmarks Tekniske Hskole,**Copenhagen**, Denmark; August 23, 1989.*Generalized Symplectic Reduction*, Max-Planck-Institut für Mathematik,**Bonn**, Germany; June 16, 1989.*Generalized Symplectic Reduction*, University of California,**Santa Barbara**, California, U.S.A.; February 21, 1989.*New metrics with Sp(n)Sp(1) holonomy*, Tulane University,**New Orleans**, Louisiana, U.S.A.; December 8, 1988.*Quaternionic reduction and quaternionic orbifolds*, the Second Meeting on Applications of Group Theory to Math-Physics, University of Georgia,**Athens**, Georgia, U.S.A.; July 6-15, 1988.*Quaternionic reduction and quaternionic orbifolds*, SUNY at Stony Brook,**Stony Brook**, New York, U.S.A.; February 27, 1988.*A generalization of moment map in quaternionic geometry*, Texas A&M University,**College Station**, Texas, U.S.A.; October 12, 1987.*Quaternionic manifolds and local supersymmetry*, University of Georgia,**Athens**, Georgia, U.S.A.; April 28, 1985.