* Einstein Metrics, Minimizing Sequences,
and the Differential Topology of Four-Manifolds. *

International Conference on Differential Geometry,

Münster, Germany,

August 15, 2006.

* Optimal Metrics, Curvature Functionals, and
the Differential Topology of Four-Manifolds. *

Geometry Conference in Honor of Nigel Hitchin,

Madrid, Spain,

September 5, 2006.

* On Conformally Kähler, Einstein Manifolds. *

Einstein Manifolds and Beyond:

Variétés d'Einstein aujourd'hui et demain,

Luminy, France.

June 21, 2007.

* Einstein Metrics
and Global
Conformal Geometry, I & II.*

NZIMA Summer School,

Nelson, New Zealand.

January 8 & 10, 2008.

* On
Four-Dimensional Einstein Manifolds.
*

7

Harvard University, Cambridge, MA,

May 3, 2008.

* On
Four-Dimensional Optimal Metrics.
*

Conformal Geometry:

Invariant Theory and Variational Methods,

Roscoff, France,

June 30, 2008.

*The Einstein-Weyl Equations, Scattering Maps, and Holomorphic Disks.
*

Geometry of Einstein Metrics,

Nantes, France,

June 29, 2009.

*Einstein Manifolds and Extremal Kähler Metrics.
*

Fifth Yamabe Memorial Symposium:

"Geometry and Low-Dimensional Topology,"

University of Minnesota,

Minneapolis, MN, October 8, 2010.

*On Hermitian, Einstein 4-Manifolds.*

26th Annual Geometry Festival,

University of Pennsylvania,

Philadelphia, PA,

April 16, 2011.

*Hermitian Metrics, Einstein Manifolds, and Conformal Geometry.*

7th Pacific Rim Complex Geometry Conference,

Kyoto University,
Kyoto, Japan,

August 6, 2012.

*Instantons, Quotient Singularities, and the Geometrization of Four-Manifolds.*

The Interaction of Geometry and Representation Theory,

Erwin Schrödinger International Institute,

Vienna, Austria,

September 10, 2012.

Five-Part Minicourse:

* Curvature Functionals, Kähler Metrics,
& the Geometry of 4-Manifolds, I, II, III, IV & V.*

Institut Henri Poincaré, Paris, France,

December 3-7, 2012.

*Curvature, Cones, and Characteristic Numbers.*

AMS Eastern Section Meeting,

Boston College,

Chestnut Hill, MA,

April 6, 2013.

*Edges, Orbifolds, and Seiberg-Witten Theory.*

IMPA Conference,

Encounters in Geometry,

Cabo Frio, Brazil,

June 3, 2013.

*Four-Manifolds,
Einstein Metrics
& Differential Topology.*

IMPA Seminar,
Rio de Janeiro, Brazil,

June 11, 2013.

*Edges, Orbifolds, and Seiberg-Witten Theory.*

Differential Geometry Section,

Mathematical Congress of the Americas,

Guanajuato, Mexico,

August 9, 2013.

*The Einstein-Weyl Equations, Scattering Maps,
& Holomorphic Disks.*

Clay Mathematics Conference,

Mathematics of CCC: Mathematical Physics with Positive Lambda,

Oxford, England,

September 13, 2013.

*Curvature Functionals, Einstein Metrics, & the Geometry of 4-Manifolds.*

Union College Mathematics Conference,

Union College, Schenectady, NY, October 19, 2013.

*Einstein Metrics, Curvature Functionals, & Conformally Kähler Geometry.*

AMS/MAA Annual Joint Meeting,

Baltimore, MD, January 15, 2014.

*Weyl Curvature, Einstein Metrics, & 4-Dimensional Geometry.*

Geometric Analysis Conference,

Lisbon, Portugal, July 9, 2014.

*Einstein Metrics, Harmonic Forms, & Symplectic Four-Manifolds.*

New Trends in Differential Geometry 2014,

Villasimius (Sardinia), Italy, September 20, 2014.

*The Einstein-Maxwell Equations
and Conformally Kähler Geometry.*

Recent Advances in Kähler Geometry,

Vanderbilt Univ, Nashville, TN, May 18, 2015.

*Einstein Metrics, Harmonic Forms, and Symplectic Four-Manifolds.*

Relativity Seminar,

University of Oxford, July 22, 2015.

*Mass in Kähler Geometry.*

Metric and Analytic Aspects of Moduli Spaces,

Isaac Newton Institute,

Cambridge, England,
July 31, 2015.

*Mass in Kähler Geometry.*

Differential Geometry Seminar,

Harvard University, September 15, 2015.

*Four-Manifolds, Einstein Metrics, and Differential Topology.*

Colloquium, Ohio State University,

Columbus, Ohio, October 22, 2015.

*Einstein Metrics, Weyl Curvature, and Symplectic Manifolds;*

*Mass in Kähler Geometry.*

Geometric Analysis in Geometry and Topology,

Tokyo, Japan, November 9 & 10, 2015.

*Mass in Kähler Geometry.*

New Perspectives in Differential Geometry,

Università di Roma "La Sapienza," November 19, 2015.

*Mass in Kähler Geometry;*

*The Einstein-Maxwell Equations and Conformally Kähler Geometry.*

Complex Geometry and Lie Groups,

Nara, Japan, March 22 & 23, 2016.

*Mass in Kähler Geometry.*

31^{st} Annual Geometry Festival &

Princeton Mathematics Colloquium,

Princeton University, April 8, 2016.

*Mass in Kähler Geometry.*

Differential Geometry in the Large.

Florence, Italy, July 15, 2016.

*Mass in Kähler Geometry.*

Trends in Modern Geometry.

Tokyo, Japan, July 24, 2016.

*Four-Manifolds, Einstein Metrics, & Differential Topology,* I, II, & III.

Rademacher Lecture Series.

University of Pennsylvania,

Philadelphia, PA, October 19-21, 2016.

*Mass in Kähler Geometry.*

New Horizons in Twistor Theory,

University of Oxford, January 5, 2017.

*The Einstein-Maxwell Equations &Conformally Kähler Geometry.*

Relativity Seminar,

University of Oxford, July 31, 2017.

*Einstein Metrics, Symplectic 4-Manifolds, and Smooth Topology.*

Interactions of Symplectic and Algebraic Geometry,

University of Warwick, August 2, 2017.

*Mass, Scalar Curvature,
Kähler Geometry, and All That.*

Analysis, Geometry, and Topology of Positive-Scalar-Curvature Metrics,

Mathematisches Forschungsinstitut Oberwolfach, August 7, 2017.

*Bach-Flat Kähler Surfaces.*

Third Pacific Rim Mathematical Association
Congress,

Oaxaca, Mexico, August 17, 2017.

*Einstein Metrics, Weyl Curvature, and Conformally Kähler Geometry.*

ÖMG-DMV
Joint Congress,

Salzburg, Austria, September 11, 2017.

*Mass, Scalar Curvature,
Kähler Geometry, and All That.*

Mathematics Colloquium,
Rutgers-Newark, October 11, 2017.

*Anti-Self-Dual 4-Manifolds,
Quasi-Fuchsian Groups, and
Almost-Kähler Geometry.*

Conformal and Symplectic Geometry,

Auckland, New Zealand, February 7, 2018.

*Anti-Self-Dual 4-Manifolds,
Quasi-Fuchsian Groups, and
Almost-Kähler Geometry.*

Shanks Workshop on Complex Differential Geometry,

Vanderbilt University, March 2, 2018.

*Mass in Kähler Geometry.*

Workshop on Mass in General Relativity,

Simons Center for Geometry and Physics,

Stony Brook, NY, March 30, 2018.

*Anti-Self-Dual 4-Manifolds,
Quasi-Fuchsian Groups, and
Almost-Kähler Geometry.*

Differential Geometry & Geometric Analysis Seminar,

Princeton University, April 23, 2018.

Three-Part Lecture Series:

* Mass, Scalar Curvature, and Kähler Geometry, I, II, & III.*

Extremal Metrics and Relative K-Stability,

Institut de Mathématiques de Jussieu, Sorbonne Université,

Paris, France, September 5-7, 2018.

*Anti-Self-Dual 4-Manifolds,
Quasi-Fuchsian Groups, and
Almost-Kähler Geometry.*

Séminaire d'Analyse et Géométrie,

Jussieu, September 25, 2018.

*Anti-Self-Dual 4-Manifolds,
Quasi-Fuchsian Groups, and
Almost-Kähler Geometry.*

Oberseminar Geometrie und Topologie,

Stuttgart, Germany, October 9, 2018.

*Anti-Self-Dual 4-Manifolds,
Quasi-Fuchsian Groups, and
Almost-Kähler Geometry.*

Seminario de Geometría Diferencial,

La Laguna, Tenerife, Spain, October 16, 2018.

Three-Part Lecture Series:

* Mass, Scalar Curvature, and Kähler Geometry, I, II, & III.*

Instituto de Ciencias Matemáticas (ICMAT),

Cantoblanco, Madrid, Spain,

October 29-November 8, 2018.

Seven-Part Lecture Series:

*Autumn School on Zoll Metrics and Holomorphic Disks,*

Schloss Rauischholzhausen,

Justus-Liebig-Universität Gießen, Germany

November 15-18, 2018.

*Bach-Flat 4-Manifolds, Quasi-Fuchsian Groups, and Almost-Kähler Geometry.*

School and Workshop on
Special Metrics and Gauge Theory,

Instituto de Ciencias Matemáticas (ICMAT),

Cantoblanco, Madrid, Spain,

December 10, 2018.

*Mass, Kähler Manifolds, and Symplectic Geometry.*

Workshop on
Global Aspects of Projective and Kähler Geometry,

Tsinghua Sanya International Mathematics Forum,

Sanya, Hainan Province, China,

January 4, 2019.

*Mass, Kähler Manifolds, and Symplectic Geometry.*

CUNY Workshop on Kähler Geometry,

New York City College of Technology,

Brooklyn, NY,

January 20, 2019.

*Mass, Kähler Manifolds, and Symplectic Geometry.*

Australian-German Workshop on Differential Geometry in the Large,

MATRIX Institute, University of Melbourne,

Creswick,VIC, Australia, February 7, 2019.

*Einstein Metrics, Harmonic Forms, &
Conformally Kähler Geometry.*

Seminario de Geometría,
ICMAT, Cantoblanco,

Madrid, Spain, March 7, 2019.

*Einstein Metrics, Harmonic Forms, &
Conformally Kähler Geometry.*

Seminário Geometria em Lisboa,

Instituto Superior Técnico,

Lisbon, Portugal, March 12, 2019.

*Mass, Kähler Manifolds, and Symplectic Geometry.*

Differential Geometry Seminar,

University of California at Irvine,

Irvine, CA, April 2, 2019.

*Mass, Scalar Curvature,
Kähler Geometry, and All That.*

Mathematics Colloquium,

University of Florida,

Gainesville, FL, April 15, 2019.

*Einstein Metrics, Harmonic Forms, & Conformally Kähler Geometry.*

Séminaire de Géométrie,

Institut Fourier, Université de Grenoble,

Grenoble, France, April 30, 2019.

*Mass, Scalar Curvature, Kähler Geometry, and All That.*

Colloquium de Mathématiques,

Institut Fourier, Université de Grenoble,

Grenoble, France, May 2, 2019.

*Mass, Kähler Manifolds, and Symplectic Geometry.*

Séminaire joint Gaston Darboux/AGATA,

Institut Montpelliérain Alexander Grothendieck,

Université de Montpellier, France, May 9, 2019.

*Einstein Metrics, Complex Surfaces, and Symplectic Geometry.*

Colloquium de Mathématiques,

Université Paul Sabatier,

Toulouse, France, May 10, 2019.

*Mass, Scalar Curvature, Kähler Geometry, and All That.*

Colloquium di Matematica e Fisica,

Università degli Studi Roma Tre,

Rome, Italy, May 22, 2019.

*Einstein Metrics, Harmonic Forms, & Conformally Kähler Geometry.*

Seminario di Geometria,

Università degli Studi Roma Tre,

Rome, Italy, May 23, 2019.

*Bach-flat Kähler Surfaces.*

Seminario de Geometría,

ICMAT, Cantoblanco,

Madrid, Spain, May 28, 2019.

*Mass, Kähler Manifolds, and Symplectic Geometry.*

Current Developments in Complex and Analytic Geometry,

Incontro INdAM al Palazzone,

Cortona, Italy, June 5, 2019.

*Einstein Metrics, Harmonic Forms, & Conformally Kähler Geometry.*

Séminaire de Géométrie,

Université Libre de Bruxelles,

Brussels, Belgium, June 26, 2019.

*Mass, Kähler Manifolds, and Symplectic Geometry.*

Differentialgeometrie im Großen,

Mathematisches Forschungsinstitut Oberwolfach,

Oberwolfach, Germany, July 2, 2019.

*Mass, Kähler Manifolds, and Symplectic Geometry.*

Relativity Seminar,

Mathematical Institute, University of Oxford,

Oxford, England, July 19, 2019.

*Einstein Manifolds, Self-Dual Weyl Curvature,
and Conformally Kähler Geometry.*

Differential Geometry & Geometric Analysis Seminar,

Princeton University, October 9, 2019.

*Einstein Metrics, Complex Surfaces, and Symplectic 4-Manifolds.*

Mathematics Department Colloquium,

Stony Brook University, October 17, 2019.

*Einstein Manifolds,
Weyl Curvature, &
Anti-Holomorphic Involutions.*

Geometry and Topology of (Almost) Complex Structures,

Geometry & TACoS Web Conference, July 7, 2020.

*Anti-Self-Dual 4-Manifolds,
Quasi-Fuchsian Groups, and
Almost-Kähler Geometry.*

Brussels-Oxford-Warwick-London

BOWL Geometry Seminar, February 16, 2021.

*Einstein Manifolds,
Conformal Curvature, and
Anti-Holomorphic Involutions.*

Irish Geometry Seminar,

NUI Galway & Maynooth,

February 23, 2021.

*Mass, Kähler Manifolds, and Symplectic Geometry.*

SCGP Weekly Talk in Mathematics,

Stony Brook, March 25, 2021.

*Métriques d'Einstein, Courbure de Weyl, et Involutions Antiholomorphes,*

Atelier sur la Géométrie Différentielle et l'Analyse Globale,

Centre Interuniversitaire de Recherches en Géométrie et Topologie, Montréal, May 26, 2021.

*Kodaira Dimension and the Yamabe Problem, Revisited,*

Analysis, Geometry and Topology of Positive Scalar Curvature Metrics,

Mathematisches Forschungsinstitut Oberwolfach, Germany, June 29, 2021.

*Twistors, Self-Duality, and Spin ^{c} Structures,*

RP90: Twistors, from Geometry to Physics,

University of Oxford, July 23, 2021.

*Einstein Manifolds,
Conformal Curvature, and
Anti-Holomorphic Involutions.*

Twistor Theory and Beyond,

University of Cambridge, September 27, 2021.

*Einstein Manifolds, Kähler Metrics, and Conformal Geometry,*

Workshop on Special Geometries on Riemannian Manifolds,

Centre de Recherches Mathématiques, Montréal, October 13, 2021.

*Einstein Manifolds, Self-Dual Weyl Curvature, and Conformally
Kähler Geometry,*

Interactions in Complex Geometry,

Vanderbilt University, December 12, 2021.

*Yamabe Invariants, Weyl Curvature,
and the
Differential Topology of 4-Manifolds,*

Gromov's Not Only Scalar Curvature seminar,

Paris/Augsburg/New York, May 13, 2022.

*Kodaira Dimension
and the
Yamabe Problem,
Revisited.*

Rutgers Geometric Analysis Conference,

New Brunswick, NJ, May 17, 2022.

*Curvature in the Balance:
The Weyl Functional and
Scalar Curvature of
4-Manifolds,*

Special Metrics in Complex Geometry,

University of Texas at Dallas, May 19, 2022.

*Four-Manifolds,
Conformal Curvature, and
Differential Topology,*

2022 Union Mathematical Conference

Union College, Schenectady, NY, June 4, 2022.

Three-Part Lecture Series:

*Geometry of 4-Manifolds: Curvature in the Balance,*

Centro di Ricerca Matematica Ennio De Giorgi,

Pisa, Italy, June 8-10, 2022.

*Kodaira Dimension and the Yamabe Problem, Revisited,*

Conference in Honor of Robin Graham:

Conformal Geometry, Analysis, and Physics,

Seattle, Washington, June 16, 2022.

*Kodaira Dimension and the Yamabe Problem, Revisited,*

Simons Center for Geometry and Physics Workshop:

Recent Advances on Scalar Curvature Problems,

Stony Brook, NY, June 28, 2022.

*Four-Manifolds,
Conformal Curvature, and
Differential Topology,*

Pure Mathematics Colloquium,

Waterloo, ON, Canada, September 12, 2022.

*Curvature in the Balance:
The Weyl Functional and
Scalar Curvature of
4-Manifolds,*

Informal Complex Geometry & PDE Seminar,

Columbia University, October 6, 2022.

*Geometry of 4-Manifolds:
Curvature in the Balance,
Lehigh Journal of Differential Geometry Conference
in honor of the 70*

*Curvature in the Balance:
The Weyl Functional and
Scalar Curvature of
4-Manifolds,*

Pacific Northwest Geometry Seminar,

Seattle University, November 6, 2022.

*Twistors, Hyper-Kähler Manifolds,
and Complex Moduli,*

Special Session on Complex Geometry and Moduli Spaces,

Canadian Mathematical Society Winter Meeting,

Toronto, ON, Canada, December 3, 2022.

*Einstein Manifolds, Self-Dual Weyl Curvature, and Conformally
Kähler Geometry,*

Seminário Geometria em Lisboa,

Instituto Superior Técnico,

Lisbon, Portugal, March 16, 2023.

*Einstein Manifolds, Self-Dual Weyl Curvature, and Conformally
Kähler Geometry.*

Topology and Dynamics Seminar,

University of Florida,

Gainesville, FL, April 18, 2023.

*Einstein Manifolds, Self-Dual Weyl Curvature, and Conformally
Kähler Geometry.*

Special Colloquium,

Florida International University,

Miami, FL, April 20, 2023.

*Einstein Manifolds, Weyl Curvature, and Conformally
Kähler Geometry.*

Differentialgeometrie im Großen,

Mathematisches Forschungsinstitut Oberwolfach, Germany, July 4, 2023.

*Einstein Metrics, Four-Manifolds, and Conformally
Kähler Geometry.*

Einstein Metrics and Special Geometry,

Institut Mittag-Leffler,

Djursholm, Sweden, July 10, 2023.

*Einstein 4-Manifolds, Weyl Curvature, and Orbifold Limits.*

Curvature and Global Shape,

Westfälische Wilhelms-Universität Münster,

Muenster, Germany, August 4, 2023.

*Gravitational Instantons, Weyl Curvature, and Conformally Kähler Geometry.*

Analytic Methods in Complex Geometry,

Westfälische Wilhelms-Universität Münster,

Muenster, Germany, August 7, 2023.

*On Four-Dimensional Einstein Manifolds*,

Mathematics Colloquium,

Brown University, September 27, 2023.

*Gravitational Instantons, Weyl Curvature, and Conformally Kähler Geometry.*

Centre Interuniversitaire de Recherches en Géométrie et Topologie,

Université du Québec à Montréal,

Montreal, QC, Canada, October 6, 2023.

*Gravitational Instantons, Weyl Curvature, and Conformally Kähler Geometry.*

Differential Geometry Seminar,

University of California, Berkeley,

Berkeley, CA, October 21, 2023.

*Gravitational Instantons, Weyl Curvature, and Conformally Kähler Geometry.*

Differential Geometry and Geometric Analysis Seminar,

Department of Mathematics, Princeton University,

Princeton, NJ, November 15, 2023.

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Research supported in part by grants

from the National Science Foundation.