Radu Laza Professor Department of Mathematics Stony Brook University

Office: Math 4-121

E-mail: radu.laza@stonybrook.edu

• Spring 2025 - Singularities in Algebraic Geometry (Topics in AG, MAT 691)
• Fall 2024 - Calculus B (MAT 126), Commutative Algebra (MAT 544)

• Perspectives on Moduli in Algebraic Geometry, Brin Center (U. Maryland), Jan 27-31. 2025.
• Hyperkaehler varieties, Derived Categories, and Moduli Spaces, Columbia, Feb 7-9, 2025.
• Lund University (seminar), March 19, 2025.
• Princeton University (seminar), April 22, 2025.

Recent Publications (partially supported by NSF DMS-2101640)

• Isotrivial Lagrangian fibrations of compact hyper-Kaehler manifolds (w. YJ Kim and O. Martin), preprint 2023, submitted.
• Hodge theory of degenerations, (III): a vanishing-cycle calculus for non-isolated singularities (w. M. Kerr), preprint 2023, submitted.
• 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 honor 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 (my papers are available on arXiv; see also my Scholar profile)

• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• Deformations of singularities and variation of GIT quotients Trans. Amer. Math. Soc. 361 (2009), no. 4, 2109-2161 (published version of my Columbia thesis).

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).

Students

• Dingchang Zhou
• Heather Werth

• AIM workshop on Higher Du Bois and higher rational singularities (w. B. Dirks), Pasadena (CA), Oct 28 - Nov 1, 2024.
• School and Workshop on Moduli, K-trivial Varieties, and Related Topics (w. J.-M. Hwang and Y. Lee), Daejon (Korea), February 21-29, 2024.
• 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 (PhD, graduated May 2023, birational automorphisms of hyper-Kaehler manifolds), now at NYU.
• Olivier Martin (postdoc), now at IMPA.
• Alexandra Viktorova (graduated Aug 2022, singularities of cubic threefolds), now at KU Leuven.
• Yoonjoo Kim (PhD, graduated May 2022, Lagrangian fibrations on hyper-Kaehler manifolds), now at Columbia.
• Francois Greer (RTG postdoc), now at Michigan State
• Adrian Brunyate (NSF postdoc)
• Giulia Sacca (postdoc), now at Columbia
• Zheng Zhang (PhD, geometric and motivic realizations of VHS), now at Shanghai Tech
• Patricio Gallardo (PhD, moduli of surfaces of general type, esp. quintics), now at UC Riverside
• Ken Ascher (undergraduate, Honors Thesis), now at UC Irvine.
• Dave Jensen (postdoc), now at U. Kentucky.

Mailing Address