* 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.

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slides (PDF) or videos.

Research supported in part by grants

from the National Science Foundation.