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Valentino Tosatti

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Valentino Tosatti (born ca. 1981 in Trieste) is an Italian mathematician.

Tosatti studied from 2000 at the Scuola Normale Superiore di Pisa and at the University of Pisa, graduating with a laurea in 2004. He then studied at Harvard University, where he graduated with an M.A. in 2005 and a Ph.D. in 2009.[1] His Ph.D. thesis Geometry of complex Monge-Ampère equations was supervised by Shing-Tung Yau.[2][3] Tosatti was from 2009 to 2012 a Joseph Fels Ritt Assistant Professor at Columbia University. At Northwestern University, he was an associate professor from 2012 to 2015 and a full professor from 2015 to 2020. From 2020 to 2022 he taught as a professor at McGill University. In 2022 he became a professor at NYU's Courant Institute of Mathematical Sciences.[1]

Tosatti does research on complex and differential geometry; geometric analysis on complex, Hermitian, and symplectic manifolds; and partial differential equations. He is also interested in the connections of his main research topics with algebraic geometry and dynamical systems.[1]

In 2017, with Gábor Székelyhidi and Ben Weinkove, Valentino Tosatti proved a conjecture published in 1984 by Paul Gauduchon.[4][5] Acta Mathematica published their proof that on n-dimensional compact complex manifolds there is always a Gauduchon metric with prescribed volume form. For this purpose, the behavior of a large class of elliptic nonlinear partial differential equations of second order on Hermitian manifolds had to be investigated.[4]

In 2011 Tosatti received a Blavatnik Award.[6] In 2012 he was awarded a two-year Sloan Research Fellowship.[1] In 2018 he received the Caccioppoli Prize. In 2019 he was elected a Fellow of the American Mathematical Society for "contributions in geometric analysis and complex geometry."[7]

Selected publications

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  • Tosatti, Valentino; Weinkove, Ben; Yau, Shing-Tung (2008). "Taming symplectic forms and the Calabi-Yau equation". Proceedings of the London Mathematical Society. 97 (2): 401–424. arXiv:math/0703773. doi:10.1112/plms/pdn008.
  • Tosatti, Valentino (2010). "Adiabatic limits of Ricci-flat Kähler metrics". Journal of Differential Geometry. 84 (2). arXiv:0905.4718. doi:10.4310/jdg/1274707320.
  • Gross, Mark; Tosatti, Valentino; Zhang, Yuguang (2013). "Collapsing of abelian fibered Calabi–Yau manifolds". Duke Mathematical Journal. 162 (3). arXiv:1108.0967. doi:10.1215/00127094-2019703.
  • Tosatti, Valentino; Weinkove, Ben (2015). "On the evolution of a Hermitian metric by its Chern-Ricci form". Journal of Differential Geometry. 99. arXiv:1201.0312. doi:10.4310/jdg/1418345539.
  • Tosatti, Valentino; Wang, Yu; Weinkove, Ben; Yang, Xiaokui (2015). " estimates for nonlinear elliptic equations in complex and almost complex geometry". Calculus of Variations and Partial Differential Equations. 54: 431–453. doi:10.1007/s00526-014-0791-0.
  • Collins, Tristan C.; Tosatti, Valentino (2015). "Kähler currents and null loci". Inventiones Mathematicae. 202 (3): 1167–1198. arXiv:1304.5216. Bibcode:2015InMat.202.1167C. doi:10.1007/s00222-015-0585-9.
  • Tosatti, Valentino; Weinkove, Ben (2016). "The Monge-Ampère equation for (𝑛-1)-plurisubharmonic functions on a compact Kähler manifold". Journal of the American Mathematical Society. 30 (2): 311–346. arXiv:1305.7511. doi:10.1090/jams/875.
  • Tosatti, Valentino; Yang, Xiaokui (2017). "An extension of a theorem of Wu–Yau". Journal of Differential Geometry. 107 (3). arXiv:1506.01145. doi:10.4310/jdg/1508551226.
  • Tosatti, Valentino; Weinkove, Ben; Yang, Xiaokui (2018). "The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits". American Journal of Mathematics. 140 (3): 653–698. arXiv:1408.0161. doi:10.1353/ajm.2018.0016.
  • Tosatti, Valentino; Weinkove, Ben (2019). "Hermitian metrics, ( n -1, n -1) forms and Monge–Ampère equations". Journal für die Reine und Angewandte Mathematik (Crelles Journal) (755): 67–101. arXiv:1310.6326. doi:10.1515/crelle-2017-0017.

References

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  1. ^ a b c d "Curriculum Vitae: Valentino Tosatti" (PDF). Courant Institute of Mathematical Sciences, New York Univerity. (CV has comprehensive publication list.)
  2. ^ Valentino Tosatti at the Mathematics Genealogy Project
  3. ^ Tosatti, V. (2009). Geometry of Complex Monge-Ampère Equations (PDF).
  4. ^ a b Székelyhidi, Gábor; Tosatti, Valentino; Weinkove, Ben (2017). "Gauduchon metrics with prescribed volume form". Acta Mathematica. 219: 181–211. arXiv:1503.04491. doi:10.4310/ACTA.2017.v219.n1.a6.
  5. ^ Gauduchon, Paul (1984). "La 1-forme de torsion d'une variété hermitienne compacte". Mathematische Annalen. 267: 495–518. doi:10.1007/BF01455968.
  6. ^ "Valentino Tosatti". Blavatnik Awards for Young Scientists (blavatnikawards.org).
  7. ^ "2019 Class of Fellows of the AMS" (PDF). Notices of the American Mathematical Society. 66 (3): 433–436. March 2019.
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