Valentino TOSATTI Curriculum Vitae (August 2014)

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1 Valentino TOSATTI Curriculum Vitae (August 2014) Personal Data Born in Trieste, Italy on April 1981, Italian citizen, US permanent resident Married, 1 child Current address: Northwestern University, Department of Mathematics, Room Sheridan Road, Evanston IL 60208, USA 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 Associate Professor, Northwestern University, 2012-present. 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 and Grants 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 Blavatnik Award for Young Scientists, given by the New York Academy of Sciences Prize Premio Giuseppe Bartolozzi 2009, given by the Italian Mathematical Union NSF Grant DMS , Partial Differential Equations on Complex and Symplectic Manifolds, July June Harvard Merit Fellowship

2 Prize Premio Franco Tricerri 2005, given by the Italian Mathematical Union Research Interests General research areas: Differential Geometry, Geometric Analysis, Complex Geometry, PDEs. Some specific topics: Kähler Geometry, Calabi-Yau manifolds, complex Monge-Ampère equations, almost-complex, symplectic and Hermitian geometry, geometric flows. Publications and Preprints 34. The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits (with B. Weinkove and X. Yang), preprint Remarks on the collapsing of torus fibered Calabi-Yau manifolds (with H.-J. Hein), preprint C 2,α estimates for nonlinear elliptic equations in complex and almost complex geometry (with Y. Wang, B. Weinkove and X. Yang), preprint Families of Calabi-Yau manifolds and canonical singularities preprint Hermitian metrics, (n 1, n 1) forms and Monge-Ampère equations (with B. Weinkove), preprint The Monge-Ampère equation for (n 1)-plurisubharmonic functions on a compact Kähler manifold (with B. Weinkove), preprint Kähler currents and null loci (with T. Collins), preprint Gromov-Hausdorff collapsing of Calabi-Yau manifolds (with M. Gross and Y. Zhang), preprint Collapsing of the Chern-Ricci flow on elliptic surfaces (with B. Weinkove and X. Yang), preprint An extension theorem for Kähler currents (with T. Collins), to appear in Ann. Fac. Sci. Toulouse Math Triviality of fibered Calabi-Yau manifolds without singular fibers (with Y. Zhang), to appear in Math. Res. Lett On the evolution of a Hermitian metric by its Chern-Ricci form (with B. Weinkove), to appear in J. Differential Geom Non-Kähler Calabi-Yau manifolds to appear in Contemp. Math 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 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 2

3 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. August Visitor of the MSC, Tsinghua University, Beijing, China. Invited Talks 3

4 1. ICTP, Trieste, Italy (Sept 2005), Constant scalar curvature Kaehler metrics and geometric stability of polarized algebraic varieties 2. 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. Differential Geometry Seminar, Harvard University, USA (October 2006), The Calabi flow with small initial energy 5. Peking University, China (January 2007), The Calabi flow with small initial energy 6. 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. 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. Cornell University, USA (November 2008), Kähler-Ricci flow and stability 20. Johns Hopkins University, USA (November 2008), Kähler-Ricci flow and stability 21. Rutgers University, USA (November 2008), Kähler-Ricci flow and stability 22. MIT, USA (December 2008), Kähler-Ricci flow and stability 23. 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. 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 4

5 31. UC San Diego, USA (November 2009), Collapsing of Ricci-flat metrics 32. Lehigh University, USA (November 2009), Complex Monge-Ampère equations on symplectic and Hermitian manifolds 33. MIT, USA (November 2009), Collapsing of Ricci-flat metrics 34. Columbia Geometry and Analysis Seminar (February 2010), The Calabi-Yau equation and symplectic 4-manifolds 35. Princeton University, USA (April 2010), Complex Monge-Ampère equations on symplectic and hermitian manifolds 36. 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. 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? 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. Università di Trieste, Italy (May 2011), Degenerazioni di varietà Calabi-Yau 53. ICTP, Trieste, Italy (May 2011), How do Calabi-Yau manifolds degenerate? 54. 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. 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 5

6 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. 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. 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. 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 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. Capital Normal University, Beijing, China (May 2012), The Chern-Ricci Flow 79. 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. 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. 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. Capital Normal University, Beijing, China (September 2013), Finite time singularities of the Kähler-Ricci flow 6

7 90. 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. 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. UC Santa Barbara, USA (September 2014) 101. KAWA 2015, Centro de Giorgi, Pisa, Italy (March 2015), Series of lectures The Kähler-Ricci flow Teaching At Northwestern University Fall Quarter Differential Calculus of Multivariable Functions and 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 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 7

8 Services Editor of Universitatis Iagellonicae Acta Mathematica (2012-present) Editor of Lecture Notes of the Unione Matematica Italiana (2013-present) Referee for: Acta Mathematica, Advances in Mathematics, American Journal of Mathematics, Analysis & PDE, Annali della Scuola Normale Superiore di Pisa, Annali di Matematica Pura ed Applicata, Bulletin de la Société Mathématique de France, 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 Pure and Applied Mathematics, Compositio Mathematica, Duke Mathematical Journal, Geometric and Functional Analysis, International Journal of Mathematics, International Mathematics Research Notices, Journal für die reine und angewandte Mathematik, Journal of the American Mathematical Society, 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, Mathematical Research Letters, Mathematische Annalen, Mathematische Nachrichten, Nonlinear Analysis: Theory, Methods & Applications, Pacific Journal of Mathematics, Proceedings of the American Mathematical Society, Quarterly Journal of Mathematics, Transactions of the American Mathematical Society. Reviewer for Math Reviews and Zentralblatt MATH. Co-organizer of the Emphasis Year in Geometric Analysis at Northwestern University ( ). Co-organizer of the 73 rd Midwest PDE Seminar (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,

9 PhD Thesis defense committees: Xiangwen Zhang (McGill, 2012), Adam Jacob (Columbia, 2012). Grant Proposal Reviewer for NSF (USA), ERC (Europe), FWF (Austria), PRIN (Italy), ANR (France). Mentoring: Xiaokui Yang (2012-present), Northwestern postdoc. References Prof. Simon K. Donaldson, Imperial College London, Prof. S lawomir Ko lodziej, Jagiellonian University, Prof. D.H. Phong, Columbia University, Prof. Shing-Tung Yau (thesis advisor), Harvard University, 9

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