Valentino TOSATTI Curriculum Vitae (December 2017)

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1 Valentino TOSATTI Curriculum Vitae (December 2017) Personal Data Born in Trieste, Italy; Italian citizen, US permanent resident Married, 1 child Current address: Northwestern University, Department of Mathematics, Room Sheridan Road, Evanston IL 60208, USA tosatti@math.northwestern.edu Member of: American Mathematical Society, Unione Matematica Italiana, European Mathematical Society, New York Academy of Sciences, Italian Scientists and Scholars in North America Foundation. Employment Professor, Northwestern University, 2015-present. Associate Professor, Northwestern University, Joseph Fels Ritt Assistant Professor, Columbia University, Education Harvard University, USA M.A. on 9 June 2005 Ph.D. on 4 June 2009, thesis title Geometry of complex Monge-Ampère equations Advisor: Prof. Shing-Tung Yau University of Pisa, Italy Italian Laurea on 10 June 2004, grade 110/110 cum laude Scuola Normale Superiore of Pisa, Italy Italian Diploma on 15 June 2004, grade 70/70 cum laude Awards Invited Address, AMS Eastern Section Meeting, Northeastern University, April Poincaré Chair, Institut Henri Poincaré and Clay Mathematics Institute 2015 Kavli Frontiers of Science Fellow, selected by the National Academy of Sciences Alfred P. Sloan Research Fellowship (extended to 2016) 2011 Blavatnik Award for Young Scientists, given by the New York Academy of Sciences Prize Premio Giuseppe Bartolozzi 2009, given by the Italian Mathematical Union Harvard Merit Fellowship Prize Premio Franco Tricerri 2005, given by the Italian Mathematical Union 1

2 Grants NSF Grant DMS , Geometric Analysis on Complex Manifolds, September August NSF Conference Grant DMS , Emphasis Year in Geometric Analysis at Northwestern University, January December NSF Grant DMS , Geometry and Analysis on Calabi-Yau and Hermitian Manifolds, September August NSF Conference Grant DMS , Great Lakes Geometry Conference 2013, December November Alfred P. Sloan Research Fellowship (extended to 2016) NSF Grant DMS , Partial Differential Equations on Complex and Symplectic Manifolds, July June Research Interests General research areas: Differential Geometry, Geometric Analysis, Complex Algebraic Geometry, PDEs. Some specific topics: Kähler Geometry, Calabi-Yau manifolds, complex Monge-Ampère equations, almost-complex, symplectic and Hermitian geometry, geometric flows, transcendental methods in algebraic geometry. Publications and Preprints 53. Smooth and rough positive currents (with S. Filip), preprint Collapsing hyperkähler manifolds (with Y. Zhang), preprint Restricted volumes on Kähler manifolds (with T. Collins), preprint C 1,1 regularity for degenerate complex Monge-Ampère equations and geodesics rays (with J. Chu and B. Weinkove), to appear in Comm. Partial Differential Equations Gauduchon metrics with prescribed volume form (with G. Székelyhidi and B. Weinkove), to appear in Acta Math The Monge-Ampère equation for non-integrable almost complex structures (with J. Chu and B. Weinkove), to appear in J. Eur. Math. Soc. (JEMS) The Aleksandrov-Bakelman-Pucci estimate and the Calabi-Yau equation (with B. Weinkove), to appear in Harvard CMSA Series in Math Regularity of envelopes in Kähler classes to appear in Math. Res. Lett Hermitian metrics, (n 1, n 1) forms and Monge-Ampère equations (with B. Weinkove), to appear in J. Reine Angew. Math The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits (with B. Weinkove and X. Yang), to appear in Amer. J. Math KAWA lecture notes on the Kähler-Ricci flow 2

3 to appear in Ann. Fac. Sci. Toulouse Math Finite time collapsing of the Kähler-Ricci flow on threefolds (with Y. Zhang), to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci Orthogonality of divisorial Zariski decompositions for classes with volume zero to appear in Tohoku Math. J Nakamaye s Theorem on complex manifolds to appear in Proc. Sympos. Pure Math An extension of a theorem of Wu-Yau (with X. Yang), J. Differential Geom. 107 (2017), no.3, On the C 1,1 regularity of geodesics in the space of Kähler metrics (with J. Chu and B. Weinkove), Ann. PDE 3 (2017), no.2, 3: Uniqueness of CP n Expo. Math. 35 (2017), no.1, The Monge-Ampère equation for (n 1)-plurisubharmonic functions on a compact Kähler manifold (with B. Weinkove), J. Amer. Math. Soc. 30 (2017), no.2, Inoue surfaces and the Chern-Ricci flow (with S. Fang, B. Weinkove and T. Zheng), J. Funct. Anal. 271 (2016), no.11, The Calabi-Yau Theorem and Kähler currents Adv. Theor. Math. Phys. 20 (2016), no.2, Gromov-Hausdorff collapsing of Calabi-Yau manifolds (with M. Gross and Y. Zhang), Comm. Anal. Geom. 24 (2016), no.1, A singular D ly-Păun theorem (with T. Collins), C. R. Math. Acad. Sci. Paris 354 (2016), no.1, Remarks on the collapsing of torus fibered Calabi-Yau manifolds (with H.-J. Hein), Bull. Lond. Math. Soc. 47 (2015), no.6, Kähler currents and null loci (with T. Collins), Invent. Math. 202 (2015), no.3, Families of Calabi-Yau manifolds and canonical singularities Int. Math. Res. Not. IMRN (2015), no.20, Infinite time singularities of the Kähler-Ricci flow (with Y. Zhang), Geom. Topol. 19 (2015), no.5, C 2,α estimates for nonlinear elliptic equations in complex and almost complex geometry (with Y. Wang, B. Weinkove and X. Yang), Calc. Var. PDE 54 (2015), no.1, Non-Kähler Calabi-Yau manifolds Contemp. Math. 644 (2015), Collapsing of the Chern-Ricci flow on elliptic surfaces (with B. Weinkove and X. Yang), Math. Ann. 362 (2015), no.3-4, On the evolution of a Hermitian metric by its Chern-Ricci form (with B. Weinkove), J. Differential Geom. 99 (2015), no.1, Triviality of fibered Calabi-Yau manifolds without singular fibers (with Y. Zhang), Math. Res. Lett. 21 (2014), no.4, An extension theorem for Kähler currents with analytic singularities (with T. Collins), Ann. Fac. Sci. Toulouse Math. 23 (2014), no.4, The Chern-Ricci flow on complex surfaces (with B. Weinkove), Compos. Math. 149 (2013), no.12, Collapsing of abelian fibred Calabi-Yau manifolds (with M. Gross and Y. Zhang), Duke Math. J. 162 (2013), no. 3, Blowup behavior of the Kähler-Ricci flow on Fano manifolds Univ. Iagel. Acta Math. 50 (2012), Calabi-Yau manifolds and their degenerations 3

4 Ann. N.Y. Acad. Sci (2012), Plurisubharmonic functions and nef classes on complex manifolds (with B. Weinkove), Proc. Amer. Math. Soc. 140 (2012), no. 11, The K-energy on small deformations of constant scalar curvature Kähler manifolds in Advances in Geometric Analysis, , Adv. Lect. Math. (ALM) 21, International Press, Kähler-Einstein metrics on Fano surfaces Expo. Math. 30 (2012), no.1, Regularity of weak solutions of a complex Monge-Ampère equation (with G. Székelyhidi), Anal. PDE 4 (2011), no.3, Degenerations of Calabi-Yau metrics Acta Phys. Polon. B Proc. Suppl. 4 (2011), no.3, The Calabi-Yau equation on the Kodaira-Thurston manifold (with B. Weinkove), J. Inst. Math. Jussieu 10 (2011), no.2, The Calabi-Yau equation, symplectic forms and almost complex structures (with B. Weinkove), in Geometry and Analysis, Vol. I, , Adv. Lect. Math. (ALM) 17, International Press, The complex Monge-Ampère equation on compact Hermitian manifolds (with B. Weinkove), J. Amer. Math. Soc. 23 (2010), no.4, Estimates for the complex Monge-Ampère equation on Hermitian and balanced manifolds (with B. Weinkove), Asian J. Math. 14 (2010), no.1, Adiabatic limits of Ricci-flat Kähler metrics J. Differential Geom. 84 (2010), no.2, Kähler-Ricci flow on stable Fano manifolds J. Reine Angew. Math. 640 (2010), Limits of Calabi-Yau metrics when the Kähler class degenerates J. Eur. Math. Soc. (JEMS) 11 (2009), no.4, Taming symplectic forms and the Calabi-Yau equation (with B. Weinkove and S.-T. Yau), Proc. London Math. Soc. 97 (2008), no.2, A general Schwarz Lemma for almost-hermitian manifolds Comm. Anal. Geom. 15 (2007), no.5, The Calabi flow with small initial energy (with B. Weinkove), Math. Res. Lett. 14 (2007), no.6, On the Critical Points of the E k Functionals in Kähler Geometry Proc. Amer. Math. Soc. 135 (2007), no.12, Explaining the uneven distribution of numbers in nature (with L. Pietronero, E. Tosatti, and A. Vespignani), Phys. A 293 (2001), Fellowships and Visiting Positions September-December Visiting Fellow at the École Normale Supérieure of Paris, France. September Cooper-Siegel Graduate Student Fellowship Fund, Harvard University. August Juan Carlos Fellow, to attend the ICM November de Valpine Graduate Student Fellowship Fund, Harvard University. April-May Visiting Student at UCLA, USA June-August Visitor of the Morningside Center of Mathematics, Beijing, China. July-August Visitor of the Morningside Center of Mathematics, Beijing, China. June US Junior Oberwolfach Fellow, MFO Oberwolfach, Germany. June-August Visitor of the MSC, Tsinghua University, Beijing, China. May-June Visitor of the MSC, Tsinghua University, Beijing, China. 4

5 August Visitor of the MSC, Tsinghua University, Beijing, China. June-August Visitor of the YMSC, Tsinghua University, Beijing, China. August-September Visitor of the Simons Center for Geometry and Physics, Stony Brook University. February-April Visitor of the Center of Mathematical Sciences and Applications, Harvard University. July 2017-June Visitor of the Center of Mathematical Sciences and Applications, Harvard University. March 2018-August Poincaré Chair at the Institut Henri Poincaré, Paris, France. Invited Talks 1. Differential Geometry Seminar, ICTP, Trieste, Italy (September 2005), Constant scalar curvature Kaehler metrics and geometric stability of polarized algebraic varieties 2. Differential Geometry Seminar, Indian Institute of Science, Bangalore, India (July 2006), Constant scalar curvature Kaehler metrics and the Calabi flow 3. Chennai Mathematical Institute, Chennai, India (July 2006), Constant scalar curvature Kaehler metrics and the Calabi flow 4. Geometry Seminar, Differential Geometry Seminar, Harvard University, USA (October 2006), The Calabi flow with small initial energy 5. Differential Geometry Seminar, Peking University, China (January 2007), The Calabi flow with small initial energy 6. Differential Geometry Seminar, ICTP, Trieste, Italy (March 2007), The Calabi-Yau equation on symplectic manifolds 7. Symposia on Analysis of Geometric Evolution, Austin, USA (May 2007), The Calabi flow with small initial energy 8. Morningside Center of Mathematics, Beijing, China (June 2007), Series of lectures The Calabi-Yau equation on symplectic manifolds 9. Lehigh University Geometry and Topology Conference, Lehigh University, USA (October 2007), The Calabi-Yau equation on symplectic manifolds 10. Differential Geometry Seminar, Ohio State University, USA (February 2008), Kähler Degenerations of Calabi-Yau manifolds 11. Geometric Evolution Equations, CRM, Montreal, Canada (April 2008), The Calabi-Yau equation on symplectic manifolds 12. Giornate di Geometria Algebrica ed Argomenti Correlati IX, Trento University, Italy (May 2008), Degenerazioni di varietà Calabi-Yau 13. School and Conference on Differential Geometry, ICTP, Trieste, Italy (June 2008), The Calabi- Yau equation on symplectic manifolds 14. London topology and geometry seminar, Imperial College, London (June 2008), The Calabi-Yau equation on symplectic manifolds 15. Ricci flow and related topics, IHP, Paris, France (June 2008), The Calabi-Yau equation on symplectic manifolds 16. ECNU Geometric Analysis Workshop, Shanghai, China (July 2008), Kähler Degenerations of Calabi-Yau manifolds 17. Differential Geometry Seminar, Harvard University, USA (October 2008), Kähler-Ricci flow and stability 18. AMS Eastern Section Meeting, Wesleyan University, USA (October 2008), Degenerations of Calabi-Yau metrics 19. Analysis Seminar, Cornell University, USA (November 2008), Kähler-Ricci flow and stability 20. Analysis and PDE Seminar, Johns Hopkins University, USA (November 2008), Kähler-Ricci flow 5

6 and stability 21. Complex Analysis and Geometry Seminar, Rutgers University, USA (November 2008), Kähler- Ricci flow and stability 22. Geometric Analysis Seminar, MIT, USA (December 2008), Kähler-Ricci flow and stability 23. Geometry Seminar, UC San Diego, USA (February 2009), Kähler-Ricci flow and stability 24. Differential Geometry Seminar, Harvard University, USA (March 2009), Large Kähler limits of Calabi-Yau metrics 25. Extremal Kähler metrics, BIRS, Canada (June 2009), Degenerations of Calabi-Yau metrics 26. Differential Geometry Seminar, CUNY, USA (September 2009), Degenerations of Calabi-Yau metrics 27. Complex Monge-Ampère Equation, BIRS, Canada (October 2009), Complex Monge-Ampère equations on symplectic and Hermitian manifolds 28. Complex Geometry: A Conference Honoring Simon Donaldson, Northwestern University, USA (October 2009), Kähler-Ricci flow with bounded curvature 29. Graduate Student Colloquium, Northwestern University, USA (October 2009), The Calabi Conjecture 30. AMS Western Section Meeting, UC Riverside, USA (November 2009), Degenerations of Calabi- Yau metrics 31. Geometry Seminar, UC San Diego, USA (November 2009), Collapsing of Ricci-flat metrics 32. Differential Geometry Seminar, Lehigh University, USA (November 2009), Complex Monge- Ampère equations on symplectic and Hermitian manifolds 33. Geometric Analysis Seminar, MIT, USA (November 2009), Collapsing of Ricci-flat metrics 34. Geometry and Analysis Seminar, Columbia University, USA (February 2010), The Calabi-Yau equation and symplectic 4-manifolds 35. Differential Geometry & Geometric Analysis Seminar, Princeton University, USA (April 2010), Complex Monge-Ampère equations on symplectic and hermitian manifolds 36. Differential Geometry Seminar, Ohio State University, USA (May 2010), Collapsing of Ricci-flat metrics 37. AMS Eastern Section Meeting, Newark, USA (May 2010), Complex Monge-Ampère equations on compact manifolds 38. Workshop Geometrie, MFO Oberwolfach, Germany (June 2010), The Calabi-Yau equation on symplectic four-manifolds 39. The Fifth Pacific Rim Complex and Symplectic Geometry Conference, Nagoya, Japan (July 2010), The Calabi-Yau equation on symplectic four-manifolds 40. Geometry and Physics in Cracow, Jagiellonian University, Poland (September 2010), Degenerations of Calabi-Yau metrics 41. Geometry/Topology Seminar, Duke University, USA (October 2010), The Calabi-Yau equation on symplectic four-manifolds 42. Geometry/Topology Seminar, SUNY Stony Brook, USA (October 2010), How do Calabi-Yau manifolds degenerate? 43. Geometry and Topology Seminar, UQAM, Montreal, Canada (December 2010), How do Calabi- Yau manifolds degenerate? 44. Colloquium, Northwestern University, USA (January 2011), Symplectic forms and almost-complex structures in 4 dimensions 45. Geometry and Physics Seminar, Northwestern University, USA (January 2011), How do Calabi- Yau manifolds degenerate? 46. Geometry Seminar, University of Texas, Austin, USA (February 2011), Calabi-Yau manifolds and complex Monge-Ampère equations th Southern California Geometric Analysis Seminar, UC San Diego, USA (February 2011), How do Calabi-Yau manifolds degenerate? 6

7 48. Workshop on Extremal Kähler Metrics, Simons Center for Geometry and Physics, Stony Brook, USA (March 2011), Degenerations of Calabi-Yau manifolds 49. Differential Geometry Seminar, CUNY, USA (March 2011), Symplectic forms and almost-complex structures in 4 dimensions 50. Geometry Seminar, University of Michigan, USA (April 2011), The Calabi-Yau equation on symplectic four-manifolds 51. Complex Geometry and Analysis Seminar, Rutgers University, USA (April 2011), The Calabi-Yau equation on symplectic 4-manifolds 52. Geometry Seminar, Università di Trieste, Italy (May 2011), Degenerazioni di varietà Calabi-Yau 53. Differential Geometry Seminar, ICTP, Trieste, Italy (May 2011), How do Calabi-Yau manifolds degenerate? 54. Differential Geometry Seminar, Capital Normal University, Beijing, China (June 2011), The Calabi-Yau theorem for Hermitian manifolds 55. Mathematical Sciences Center, Tsinghua University, Beijing, China (June-August 2011), Series of lectures Topics in Kähler geometry 56. Algebraic Geometry Seminar, Università di Pavia, Italy (September 2011), Collapsing di varietà di Calabi-Yau fibrate in tori e simmetria speculare hyperkahleriana 57. Geometric Structures in Mathematical Physics, Golden Sands, Bulgaria (September 2011), Collapsing of abelian fibred Calabi-Yaus and hyperkähler mirror symmetry 58. Geometric structures on complex manifolds, Laboratory of Algebraic Geometry, Moscow, Russia (October 2011), Collapsing of abelian fibred Calabi-Yaus and hyperkähler mirror symmetry 59. Colloquium, Northwestern University, USA (October 2011), Ricci curvature and complex geometry 60. Geometry/Topology Seminar, Duke University, USA (November 2011), Collapsing of Calabi-Yau manifolds 61. Geometry Seminar, Florida International University, Miami, USA (November 2011), The Calabi- Yau Theorem for Hermitian Manifolds 62. Geometry Seminar, University of Texas, Austin, USA (November 2011), Ricci curvature and complex geometry 63. Colloquium, Rice University, USA (December 2011), Ricci curvature and complex geometry 64. Colloquium, Northeastern University, USA (December 2011), Ricci curvature and complex geometry 65. Colloquium, UCLA, USA (December 2011), Ricci curvature and complex geometry 66. Geometric Analysis Seminar, MIT, USA (December 2011), Collapsing of abelian fibred Calabi- Yaus and hyperkähler mirror symmetry 67. Algebraic Geometry Seminar, Università di Roma, Italy (January 2012), Collapsing of Calabi-Yau manifolds 68. Analysis Seminar, Cornell University, USA (January 2012), The Chern-Ricci flow 69. Colloquium, Stanford University, USA (February 2012), Ricci curvature and complex geometry 70. Colloquium, Medgar Evers College, CUNY, USA (February 2012), Complex manifolds and spheres 71. Colloquium, Rutgers University Newark, USA (February 2012), Ricci curvature and complex geometry 72. L 2 (Lafayette-Lehigh) Geometry-Topology Seminar, Lafayette College, USA (March 2012), Degenerations of Calabi-Yau manifolds and mirror symmetry Great Lakes Geometry Conference, Ohio State University, USA (April 2012), The evolution of a Hermitian metric by its Chern-Ricci curvature 74. Special Day on Complex Geometry and PDE, Columbia University, USA (April 2012), Collapsing of solutions of complex Monge-Ampère equations 75. Geometric PDEs, CRM, Montreal, Canada (April 2012), Collapsing of Calabi-Yau manifolds th Annual Geometry Festival, Duke University, USA (April 2012), The evolution of a Hermitian 7

8 metric by its Chern-Ricci curvature 77. Mathematical Sciences Center, Tsinghua University, Beijing, China (May-June 2012), Series of lectures The Kähler-Ricci flow and the Minimal Model Program 78. Differential Geometry Seminar, Capital Normal University, Beijing, China (May 2012), The Chern-Ricci Flow 79. Analysis Seminar, Peking University, China (June 2012), Collapsing of Ricci-flat Kähler metrics 80. Geometric and Nonlinear Partial Differential Equations, Xi An Jiaotong University, China (June 2012), Parabolic complex Monge-Ampère equations on compact complex manifolds 81. Felix Klein Seminar, University of Notre Dame, USA (September 2012), The Chern-Ricci Flow 82. Differential Geometry Seminar, UC Berkeley, USA (November 2012), Degenerations of Calabi- Yau manifolds and mirror symmetry 83. Geometry Seminar, Florida International University, Miami, USA (December 2012), The Chern- Ricci Flow Great Lakes Geometry Conference, Northwestern University, USA (April 2013), The boundary of the Kähler cone 85. Analysis, Complex Geometry and Mathematical Physics, Columbia University, USA (May 2013), The Chern-Ricci Flow 86. Annual Undergraduate Prize Lecture, Northwestern University, USA (May 2013), Metric sociology 87. Workshop on Curvature and Global Shape, University of Münster, Germany (July 2013), Collapsing of Calabi-Yau manifolds 88. Summer School in Complex Geometry, Rutgers, USA (August 2013), Series of lectures Calabi-Yau manifolds 89. Differential Geometry Seminar, Capital Normal University, Beijing, China (September 2013), Finite time singularities of the Kähler-Ricci flow 90. Geometry and Physics Seminar, Boston University, USA (October 2013), Degenerations of Calabi- Yau manifolds 91. Mini-School on K-stability, Stony Brook, USA (December 2013), Introduction to K-Stability 92. Algebraic Geometry Seminar, UIC, USA (February 2014), Nakamaye s theorem on complex manifolds 93. Geometry and Topology Seminar, University of Waterloo, Canada (March 2014), Calabi-Yau theorems for non-kähler metrics 94. Complex Monge-Ampère Equations on Compact Kähler Manifolds, BIRS, Canada (April 2014), Collapsing of Ricci-flat Calabi-Yau manifolds 95. Mirror symmetry, enumerative geometry and related topics, Università di Pavia, Italy (May 2014), Collapsing of Calabi-Yau metrics near a large complex structure limit 96. Workshop Geometrie, MFO Oberwolfach, Germany (June 2014), Finite-time singularities of the Kähler-Ricci flow th Pacific Rim Conference on Complex Geometry, Gunsan, Korea (July 2014), Kähler currents, null loci and the formation of singularities in complex geometry years of Calabi conjecture, Tsinghua University, Beijing, China (August 2014), Calabi-Yau theorems for non-kähler complex manifolds 99. Mathematical Sciences Center, Tsinghua University, Beijing, China (August 2014), Series of lectures The Calabi-Yau Theorem and some generalizations 100. Differential Geometry Seminar, UC Santa Barbara, USA (September 2014), Collapsing of Calabi- Yau manifolds 101. Joint Johns Hopkins-University of Maryland Complex Geometry Seminar, Johns Hopkins University, USA (November 2014), The Kähler-Ricci flow and its singularities 102. Metro Area Differential Geometry Seminar, University of Maryland, USA (November 2014), Long-time behavior of the Kähler-Ricci flow 8

9 103. Geometry Seminar, Florida International University, Miami, USA (December 2014), The Kähler- Ricci flow and its singularities 104. Colloquium, SISSA, Trieste, Italy (December 2014), The Kähler-Ricci flow and its singularities 105. Komplex Analysis Winter School-KAWA 2015, Centro de Giorgi, Pisa, Italy (March 2015), Series of lectures The Kähler-Ricci flow 106. Special Day in Geometry and PDE, Columbia University, USA (April 2015), Complex Monge- Ampère type equations on Hermitian manifolds 107. Differential Geometry Seminar, Harvard University, USA (May 2015), Degenerations and collapsing of Ricci-flat Calabi-Yau manifolds 108. Conference Recent advances in Kähler geometry, Vanderbilt University, USA (May 2015), The Kähler-Ricci flow: finite-time singularities and long-time behavior 109. Yau Mathematical Sciences Center, Tsinghua University, Beijing, China (June 2015), Series of lectures The Kähler-Ricci flow 110. Geometric Analysis Seminar, Peking University, China (June 2015), Kähler currents and the formation of singularities of geometric PDEs 111. Summer School in Geometric Analysis, Northwestern University, USA (July 2015), Series of lectures The Kähler-Ricci flow 112. AMS Summer Institute in Algebraic Geometry, University of Utah, USA (July 2015), Nakamaye s theorem on complex manifolds 113. Beihang University, Beijing, China (July 2015), The Kähler-Ricci flow and its singularities 114. Chinese Academy of Sciences, Beijing, China (July 2015), Degenerations of Calabi-Yau metrics 115. Chinese Academy of Sciences, Beijing, China (July 2015), Kähler currents in complex geometry 116. Colloquium, Stony Brook, USA (September 2015), Metric limits of Calabi-Yau manifolds 117. Colloquium, University of Oregon, USA (September 2015), The Kähler-Ricci flow and its singularities 118. Geometric Analysis Seminar, University of Oregon, USA (September 2015), Complex Monge- Ampère type equations on Hermitian manifolds 119. Geometry Seminar, Purdue University, USA (October 2015), Kähler currents in complex geometry 120. Geometric Analysis Colloquium, Fields Institute, Toronto, Canada (October 2015), Holomorphic sectional curvature 121. Colloquium, UCLA (December 2015), From base loci of line bundles to geometric PDEs 122. Colloquium, University of Michigan, USA (January 2016), The Ricci flow on compact Kähler manifolds 123. Differential Geometry Seminar, UC Berkeley, USA (January 2016), Monge-Ampère equations and the geometry of Calabi-Yau manifolds 124. Algebraic Geometry Seminar, University of Bonn, Germany (February 2016), Nakamaye s theorem on complex manifolds 125. Hausdorff-Kolloquium, University of Bonn, Germany (February 2016), The Ricci flow on compact Kähler manifolds 126. Geometric Analysis Seminar, CMSA, Harvard University, USA (February 2016), Non-Kähler Calabi-Yau manifolds 127. AMS Eastern Section Meeting, Stony Brook, USA (March 2016), Compact Kähler manifolds with nonpositive holomorphic sectional curvature 128. AMS Eastern Section Meeting, Stony Brook, USA (March 2016), Collapsing of the Kähler-Ricci flow 129. Workshop Kähler Geometry, Einstein Metrics, and Generalizations, MSRI, USA (March 2016), Holomorphic fibrations on Calabi-Yau manifolds and collapsing 130. Nonlinear Equations Conference, CMSA, Harvard University, USA (April 2016), Adiabatic limits of Ricci-flat Kähler metrics 9

10 131. Algebraic and Kähler Geometry Workshop, Institut Fourier, Grenoble, France (May 2016), Monge-Ampère equations for (n 1, n 1) forms Lehigh University Geometry and Topology Conference, Lehigh University, USA (May 2016), The Ricci flow on compact Kähler manifolds 133. Conference Differential Geometry in the large, University of Florence, Italy (July 2016), The Ricci flow on compact Kähler manifolds 134. Algebra and Geometry Seminar, University of Grenoble, France (September 2016), Adiabatic limits of Ricci-flat Kähler metrics 135. KASS Seminar, Chalmers University, Sweden (September 2016), On and around Nakamaye s Theorem 136. Introduction to Modern Mathematics Lecture, Yau Mathematical Sciences Center, Tsinghua University, Beijing, China (October 2016), Compact complex surfaces and the Chern-Ricci flow 137. Colloquium, Beijing Normal University, China (November 2016), Metric limits of Calabi-Yau manifolds 138. Geometry, Physics and Representation Theory Seminar, Northeastern University, USA (November 2016), Metric SYZ for hyperkähler manifolds 139. Minischool on Nonlinear Equations, Harvard University (December 2016), Series of lectures Complex Monge-Ampère equations 140. CMSA Colloquium, Harvard University (December 2016), Metric limits of hyperkähler manifolds 141. School Kähler Geometry : flows and limits, Universitè de Nantes, France (April 2017), Metric limits of Calabi-Yau manifolds 142. Workshop on Complex Geometry, University of Notre Dame, USA (April 2017), Collapsing hyperkähler manifolds 143. Conference in honor of J.-P. D ly s 60 th birthday, Grenoble, France (June 2017), C 1,1 estimates for complex Monge-Ampère equations 144. Summer school Current developments and new directions in Kähler geometry, University of Notre Dame, USA (June 2017), Metric limits of Calabi-Yau manifolds 145. Conference Current developments and new directions in Kähler geometry, University of Notre Dame, USA (June 2017), C 1,1 estimates for complex Monge-Ampère equations 146. Chinese Academy of Sciences, Beijing, China (August 2017), Semipositive line bundles and (1, 1) classes 147. Differential Geometry Seminar, Harvard University, USA (October 2017), Special Kähler geometry and collapsing 148. Differential Geometry Seminar, UC Berkeley, USA (October 2017), Collapsing hyperkähler manifolds 149. Geometric Analysis Seminar, CUNY, USA (October 2017), Collapsing hyperkähler manifolds 150. Conference Geometric and Nonlinear Partial Differential Equations, Murramarang, Australia (February 2018) 151. Seminar, Université Paris-Sud (March 2018) 152. Séminaire danalyse et Géométrie, Jussieu, Paris, France (March 2018) 153. French-German conference on Algebraic Geometry, CIRM, Luminy, France (April 2018) 154. Invited Address, AMS Eastern Section Meeting, Northeastern University, USA (April 2018), Metric limits of Calabi-Yau manifolds 155. Workshop Geometrie, MFO Oberwolfach, Germany (June 2018) Teaching At Northwestern University Fall Quarter Differential Calculus of Multivariable Functions 10

11 Fall Quarter Partial Differential Equations Winter Quarter Differential Geometry Winter Quarter Geometry/Topology Spring Quarter Geometry/Topology Fall Quarter Introduction to Differential Geometry Winter Quarter Geometry/Topology Spring Quarter Geometry/Topology Fall Quarter Differential Geometry Fall Quarter Algebraic Geometry Winter Quarter Partial Differential Equations Spring Quarter Introduction to Topology Spring Quarter Analysis At Columbia University Spring Term Instructor of Calculus IV, Multivariable Calculus, two sections Fall Term Instructor of Calculus III, Multivariable Calculus Spring Term Instructor of Calculus IV, Multivariable Calculus, two sections Fall Term Instructor of Complex Analysis and Riemann Surfaces I Spring Term Instructor of Complex Analysis and Riemann Surfaces II and Calculus IV, Multivariable Calculus At Harvard University Fall Term Instructor of Math 21a, Multivariable Calculus Fall Term Instructor of Math 21a, Multivariable Calculus Fall Term Course Assistant of Math 231a, Algebraic Topology Fall Term Instructor of Math 21a, Multivariable Calculus, two sections Summer School Course Assistant of Math 1ab, Intensive Calculus Mentoring PhD students: Greg Edwards (Northwestern co-advised with Ben Weinkove, ), Nick Mc- Cleerey (Northwestern, 2016-present). PhD Thesis defense committees: Jakob Hultgren (Chalmers, 2018), Tat Dat Tô (Toulouse, 2018), Lei Wu (Northwestern, 2017), Jian Xiao (Grenoble, 2016), Zhenan Wang (Northwestern, 2015), Xiangwen Zhang (McGill, 2012), Adam Jacob (Columbia, 2012). Postdoctoral mentoring: Jian Xiao (2016-present), Yashan Zhang (2017), Jianchun Chu ( ), Xiaokui Yang ( ), Yu Wang ( ), Tao Zheng ( ), Shouwen Fang (2014), Northwestern postdocs and visitors. Services Editor of Universitatis Iagellonicae Acta Mathematica (2012-present) Editor of Lecture Notes of the Unione Matematica Italiana (2013-present) Director of Graduate Studies, Northwestern University, Spring quarter

12 Referee for: Acta Mathematica, Acta Mathematica Sinica, Advances in Mathematics, American Journal of Mathematics, Analysis & PDE, Annales scientifiques de l École Normale Supérieure, Annali della Scuola Normale Superiore di Pisa, Annali di Matematica Pura ed Applicata, Annals of Mathematics, Archiv der Mathematik, Asian Journal of Mathematics, Bulletin de la Société Mathématique de France, Bulletin of the Australian Mathematical Society, Bulletin of the London Mathematical Society, Calculus of Variations and Partial Differential Equations, Canadian Journal of Mathematics, Communications in Analysis and Geometry, Communications in Contemporary Mathematics, Communications in Mathematical Physics, Communications in Partial Differential Equations, Communications in Pure and Applied Mathematics, Complex Manifolds, Compositio Mathematica, Comptes Rendus Mathematique, Duke Mathematical Journal, Frontiers of Mathematics in China, Geometric and Functional Analysis, Geometry & Topology, International Journal of Mathematics, International Mathematics Research Notices, Inventiones Mathematicae, Journal de l École polytechnique, Journal für die reine und angewandte Mathematik, Journal of the American Mathematical Society, Journal of Differential Equations, Journal of Differential Geometry, Journal of the European Mathematical Society, Journal of Functional Analysis, Journal of Geometric Analysis, Journal of Geometry and Physics, Journal of Mathematical Analysis and Applications, Manuscripta Mathematica, Mathematica Scandinavica, Mathematical Research Letters, Mathematische Annalen, Mathematische Nachrichten, Nonlinear Analysis: Theory, Methods & Applications, Nuclear Physics B, Pacific Journal of Mathematics, Proceedings of the American Mathematical Society, Quarterly Journal of Mathematics, Science in China, Surveys in Differential Geometry, Tokyo Journal of Mathematics, Transactions of the American Mathematical Society. Reviewer for Math Reviews and Zentralblatt MATH. Co-organizer of the workshop Nonlinear PDEs in real and complex geometry at the American Institute of Mathematics (August ). Co-organizer of the workshop Young Geometric Analysts Forum 2018 at the Tsinghua Sanya International Mathematics Forum (January 2018). Co-organizer of the summer school Summer at Northwestern Analysis Program - SNAP at Northwestern University (July 2017). Co-organizer of the workshop Analytic Methods in Algebraic Geometry at Northwestern University (March ). Co-organizer of the workshop Young Geometric Analysts Forum 2017 at the Tsinghua Sanya International Mathematics Forum (January ). Co-organizer of the workshop The complex Monge-Ampère Equation at the American Institute of Mathematics (August ). Co-organizer of section Geometric Partial Differential Equations at AMS Meeting in Chicago (October ). Co-organizer of the program Moduli spaces and singularities in algebraic and Riemannian geometry at Stony Brook University (August 17 - November ). Co-organizer of the workshop Collapsing Calabi-Yau manifolds at Stony Brook University (August 12

13 31 - September ). Co-organizer of the Emphasis Year in Geometric Analysis at Northwestern University ( ). Co-organizer of the Summer School in Geometric Analysis at Northwestern University (July ). Co-organizer of the Workshop on Ricci curvature at Northwestern University (May ). Co-organizer of the Special Day on Analytic Methods in Algebraic Geometry at Northwestern University (April ). Co-organizer of the Special Day on Complex Geometry and Analysis on real analytic Riemannian manifolds at Northwestern University (February ). Co-organizer of the Special Day on Eigenfunctions of the Laplacian on Manifolds at Northwestern University (October ). Co-organizer of the 73 rd Midwest PDE Seminar at Northwestern University (May ). Co-organizer of the Summer School in Complex Geometry at Rutgers University (August ). Co-organizer of the Great Lakes Geometry Conference 2013 at Northwestern University (April ). Co-organizer of section Complex Geometry and Partial Differential Equations at AMS Meeting in Akron, Ohio (October ). Co-organizer of the Special Day on Complex Geometry and PDE at Columbia University (April ). Co-organizer of the Special Day on Complex Geometry and PDE at Columbia University (October ). Co-organizer of the Informal Complex Geometry Reading Seminar at Northwestern University (October 2012-present). Co-organizer of the Informal Complex Geometry and PDE Seminar at Columbia University (September 2009-May 2012). Member of the International Committee for the oral examinations of the S.-T. Yau College Mathematics Contests, Member of the Jury of the ISSNAF Award for Young Investigators Annamaria Molteni Award, Italian Embassy in Washington DC, Grant Proposal Reviewer for NSF (USA), Simons Foundation (USA), ERC (Europe), NSERC (Canada), BSF (US-Israel), FWF (Austria), PRIN, INdAM, SNS, CINECA (Italy), ANR (France), RGC (Hong Kong), NCN (Poland). 13