Radu Laza Professor Department of Mathematics Stony Brook University

Office: Math 4-121

E-mail: radu.laza@stonybrook.edu

• Fall 2024 - Calculus B (MAT 126) [OH Tue 3:30-5, Thr 10-11:30], Commutative Algebra (MAT 544) [OH Tue 10-11:30]

• Spring 2024 - Hodge Theory and Singularities (Topics in AG, MAT 691)

Recent Preprints/Publications

• Isotrivial Lagrangian fibrations of compact hyper-Kaehler manifolds (w. YJ Kim and O. Martin), preprint 2023.
• Hodge theory of degenerations, (III): a vanishing-cycle calculus for non-isolated singularities (w. M. Kerr), preprint 2023.
• Deformations of Calabi-Yau varieties with isolated log canonical singularities (w. R. Friedman), preprint 2023.
• Deformations of Calabi-Yau varieties with k-liminal singularities (w. R. Friedman), Forum Math Sigma Vol. 12 (2024), e59, 1-25.
• The Higher Du Bois and higher rational singularities properties for isolated singularities (w. R. Friedman), J. Algebraic Geom. 33 (2024), No. 3, 493-520.
• Higher Du Bois and higher rational singularities (w. R. Friedman, and an Appendix by M. Saito), Duke Math. J. 173 (2024), no. 10, 1839-1881.
• Non-isomorphic smooth compactifications of the moduli space of cubic surfaces (with S. Casalaina-Martin, S. Grushevsky, and K. Hulek), Nagoya Math. J. 254 (2024), 315-365.
• Deformations of some local Calabi-Yau manifolds (w. R. Friedman), EPIGA, special volume in honour of Claire Voisin, Article no. 18 (2024).
• Deformations of singular Fano and Calabi-Yau varieties (w. R. Friedman), to appear in J. Differential Geom.
• Hodge theory of degenerations, (II): Vanishing cohomology and geometric applications, (w. M. Kerr), to appear in "Current developments in Hodge theory", Proceedings of Hodge theory at IMSA, Simons Symposia (Springer).

Selected Publications

• Cohomology of the moduli space of cubic threefolds and its smooth models (with S. Casalaina-Martin, S. Grushevsky, and K. Hulek), Mem. Amer. Math. Soc. 282 (2023), No. 1391.
• Smoothing of rational singularities and Hodge structure (w. M. Kerr and M. Saito), Algebr. Geom. 9 (4) (2022) 476-501.
• The LLV decomposition of hyper-Kaehler cohomology (w. M. Green, YJ Kim, and C. Robles), Math. Ann. 382 (2022), no. 3-4, 1517-1590
• Automorphisms and Periods of Cubic Fourfolds (with Z. Zheng), Math. Z. 300 (2022), no. 2, 1455-1507.
• Hodge theory of degenerations, (I): Consequences of the decomposition theorem , (w. M. Kerr; with an Appendix by M. Saito), Selecta Math. 27 (2021), No. 4, Paper No. 71.
• GIT versus Baily-Borel compactification for K3's which are double covers of P1xP1 (w. K. O'Grady), Adv. Math. 383 (2021), Paper No. 107680.
• Complete moduli of cubic threefolds and their intermediate Jacobians (with S. Casalaina-Martin, S. Grushevsky, and K. Hulek), Proc. Lond. Math. Soc. 122 (2021), no. 2, 259-316.
• Birational geometry of the moduli space of quartic K3 surfaces, (with K. O'Grady), Compositio Math. 155 (2019), no. 9, 1655-1710.
• On the moduli space of pairs consisting of a cubic threefold and a hyperplane, (w. G. Pearlstein and Z. Zhang), Adv. Math. 340 (2018), 684-722.
• Remarks on degenerations of hyper-Kaehler manifolds, (with J. Kollár, G. Saccà and C. Voisin), Ann. Inst. Fourier (Grenoble) 68 (2018), no. 7, 2837-2882.
• GIT versus Baily-Borel compactification for quartic K3 surfaces, (with K. O'Grady), in "Geometry of Moduli" (Abel Symposia), Springer, 2018, 217-283.
• A hyper-Kaehler compactification of the Intermediate Jacobian fibration associated to a cubic fourfold (with G. Saccà and C. Voisin), Acta Math. 218 (2017), no. 1, 55-135.
• Extending the Prym map to toroidal compactifications of the moduli space of abelian varieties (with S. Casalaina-Martin, S. Grushevsky, and K. Hulek), J. Eur. Math. Soc 19 (2017), no. 3, 659-723.
• The KSBA compactification for the moduli space of degree two K3 pairs, J. Eur. Math. Soc. 18 (2016), no. 2, 225-279.
• Log canonical models and variation of GIT for genus four canonical curves (w. S. Casalaina-Martin and D. Jensen), J. Algebraic Geom. 23 (2014), 727-764.
• Semi-algebraic horizontal subvarieties of Calabi-Yau type (w. R. Friedman), Duke Math. J. 162 (2013), no. 12, 2077-2148.
• Simultaneous semi-stable reduction for curves with ADE singularities (w. S. Casalaina-Martin), Trans. Amer. Math. Soc. 365 (2013), no. 5, 2271-2295.
• Moduli space of cubic fourfolds via the period map, Ann. of Math. 172 (2010), no. 1, 673-711.
• Moduli space of cubic fourfolds (the GIT compactification), J. Algebraic Geom. 18 (2009), 511-545.
• The moduli space of cubic threefolds via degenerations of the intermediate Jacobian (w. S. Casalaina-Martin), J. Reine Angew. Math. 633 (2009), 29-65.

Expository:

• Classical Period Domains (with Z. Zhang), in Recent Advances in Hodge Theory (London Mathematical Society Lecture Note Series), Cambridge Univ. Press, 2016.
• Perspectives on the construction and compactification of moduli spaces, in Compactifying Moduli Spaces (Advanced Courses in Mathematics, CRM Barcelona), Birkhauser, 2016, 1-35.
• GIT and moduli with a twist, in "Handbook of Moduli" vol. 2, Adv. Lect. Math. 25 (2013), Int. Press, 259-297.

Books edited:

• Calabi-Yau Varieties: Arithmetic, Geometry and Physics: Lecture Notes on Concentrated Graduate Courses (w. Schuett and N. Yui), lecture notes based on the concentrated graduate courses held during the thematic program on Calabi-Yau varieties at Fields Institute (Fall 2013), Fields Institute Monographs, Springer 2015.
• Arithmetic and Geometry of K3 Surfaces and Calabi-Yau Threefolds (w. M. Schuett and N. Yui), Fields Institute Communications, vol. 67, Springer 2013, (Proceedings of the 2011 Fields workshop on Calabi-Yau's and K3's).

My papers on arXiv. My Scholar profile.

My research is partially supported by NSF (DMS-2101640).

• ANGES (w. S. Grushevsky, C. Schnell, and J. Starr), Stony Brook, October 23-25, 2020.
• Discrete groups and Moduli (w. S. Kondo and S. Mukai), Nagoya, June 17-20, 2019.
• Hodge Theory, Moduli and Representation Theory (final conference for the FRG project), Stony Brook, August 14-18, 2017.
• Positivity in Arithmetic and Geometry (Spring School), Orsay (France), May 29-June 2, 2017.
• Hyper-Kaehler Manifolds, Hodge Theory and Chow Groups (Sanya, China, Dec 18-23, 2016)
• Calabi-Yau varieties: Arithmetic, geometry and physics (Herstmonceux Castle, East Sussex, UK, June 20-25, 2016)
• Algebraic Cycles and Moduli (CRM Montreal, June 2-8, 2016)
• Program on Complex, p-adic, and logarithmic Hodge theory and their applications (SCGP, Mar-Apr, 2016)
• Program on Moduli spaces and singularities in algebraic and Riemannian geometry (SCGP, Aug-Nov, 2015)
• Mini-school on Invariants of Singularities in zero and positive characteristics (December 4, 2015, Stony Brook)
• Collapsing Calabi-Yau Manifolds (SCGP, Aug 31-Sept 4, 2015)
• Topology of algebraic varieties (IAS, 2014-2015)
• Perspectives on complex algebraic geometry (Columbia University, May 22-25, 2015)
• New techniques in birational geometry (Stony Brook, April 6-10, 2015)
• K3, Enriques Surfaces and Related Topics (Nagoya, Nov 10-14, 2014)
• Thematic Program on Calabi-Yau varieties (Fields Institute, Fall 2013).

Former Associates

• Lisa Marquand (graduated 2023; now at NYU)
• Yoonjoo Kim (graduated 2022; now at Columbia)
• Alexandra Viktorova (graduated 2022; not PD at KU Leuven)
• Francois Greer (RTG postdoc) - now at IAS, going to Michigan State
• Adrian Brunyate (NSF postdoc)
• Giulia Sacca (postdoc) - now at Columbia
• Zheng Zhang (geometric and motivic realizations of VHS) - now at Shanghai Tech
• Patricio Gallardo (moduli of surfaces of general type, esp. quintics) - now at UC Riverside
• Ken Ascher (undergraduate, Honors Thesis) - now at Princeton, going to UC Irvine.
• Dave Jensen (postdoc) - now at U. Kentucky.

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