
Radu Laza
Professor
Department of Mathematics
Stony Brook University

Office: Math 4121
Email: radu.laza@stonybrook.edu
Teaching
Resume
Research Algebraic
Geometry, esp. moduli problems, degenerations, singularities, special
classes of varieties (K3s, CalabiYau, Hyperkahler manifolds).
Recent & Selected Publications:
 Hodge theory of degenerations, (II): Vanishing cohomology and geometric applications, (w. M. Kerr), preprint 2020.
 Period mappings and ampleness of the Hodge bundle, (w. M. Green, P. Griffiths, and C. Robles), preprint 2020.
 Smoothing of rational singularities and Hodge structure (w. M. Kerr and M. Saito), to appear in Algebr. Geom.
 The LLV decomposition of hyperKaehler cohomology (w. M. Green, YJ Kim, and C. Robles), to appear in Math. Ann. (DOI 10.1007/s0020802102238y)
 Automorphisms and Periods of Cubic Fourfolds (with Z. Zheng), to appear in Math. Z. (DOI 10.1007/s0020902102810x)
 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.

Cohomology of the moduli space of cubic threefolds and its smooth models (with S. CasalainaMartin, S. Grushevsky, and K. Hulek), to appear in Mem. Amer. Math. Soc.
 Maximally algebraic potentially irrational cubic fourfolds, Proc. Amer. Math. Soc. 149 (2021), no. 8, 32093220.
 GIT versus BailyBorel compactification for K3's which are double covers of P1xP1 (w. K. O'Grady), Adv. Math. 383 (2021).
 Complete moduli of cubic threefolds and their intermediate Jacobians (with S. CasalainaMartin, S. Grushevsky, and K. Hulek), Proc. Lond. Math. Soc. 122 (2021), no. 2, 259316.
 A conjectural bound on the second Betti number for hyperKaehler manifolds
(w. YJ Kim), Bull. Soc. Math. France 148 (2020), no. 3, 467480.
 The Euler number of hyperKaehler manifolds of OG10 type (w. K. Hulek and G. Sacca), in Proceedings of the ICM 2018 Satellite conference "Moduli Spaces in Algebraic Geometry and Applications", Mat. Contemp. 47 (2020), 152172.
 Birational geometry of the moduli space of quartic K3 surfaces, (with K. O'Grady), Compositio Math. 155 (2019), no. 9, 16551710.
 On the moduli space of pairs consisting of a cubic threefold and a hyperplane, (w. G. Pearlstein and Z. Zhang), Adv. Math. 340 (2018), 684722.
 Remarks on degenerations of hyperKaehler manifolds, (with J. Kollár, G. Saccà and C. Voisin), Ann. Inst. Fourier (Grenoble) 68 (2018), no. 7, 28372882.
 GIT versus BailyBorel compactification for quartic K3 surfaces, (with K. O'Grady), in "Geometry of Moduli" (Abel Symposia), Springer, 2018, 217283.
 A hyperKaehler compactification of the Intermediate Jacobian fibration associated to a cubic fourfold (with G. Saccà and C. Voisin), Acta Math. 218 (2017), no. 1, 55135.
 Extending the Prym map to toroidal compactifications of the moduli space of abelian varieties (with S. CasalainaMartin, S. Grushevsky, and K. Hulek), J. Eur. Math. Soc 19 (2017), no. 3, 659723.
 The KSBA compactification for the moduli space of degree two K3 pairs, J. Eur. Math. Soc. 18 (2016), no. 2, 225279.
 Log canonical models and variation of GIT for genus four canonical curves (w. S. CasalainaMartin and D. Jensen), J. Algebraic Geom. 23 (2014), 727764.
 Semialgebraic horizontal subvarieties of CalabiYau type (w. R. Friedman), Duke Math. J. 162 (2013), no. 12, 20772148.
 Simultaneous semistable reduction for curves with ADE singularities (w. S. CasalainaMartin), Trans. Amer. Math. Soc. 365 (2013), no. 5, 22712295.
 Moduli space of cubic fourfolds via the period map, Ann. of Math. 172 (2010), no. 1, 673711.
 Moduli space of cubic fourfolds (the GIT compactification), J. Algebraic Geom. 18 (2009), 511545.
 The moduli space of cubic threefolds via degenerations of the intermediate Jacobian (w. S. CasalainaMartin), J. Reine Angew. Math. 633 (2009), 2965.
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, 135.
 GIT and moduli with a twist, in "Handbook of Moduli" vol. 2, Adv. Lect. Math. 25 (2013), Int. Press, 259297.
Expository lecture series given at: Luminy (Jan 2017), Guanajuato (CIMPACIMATICTP school, Feb 2016), Angers (June 2014), KAIST (Mar 2014), Fields Institute (Aug and Nov 2013), Vancouver (Jul 2013), Barcelona (May 2013).
Books edited:
My papers on arXiv. My Scholar profile.
My research is partially supported by NSF (DMS1802128, DMS2101640).
Past Activities
 ANGES (w. S. Grushevsky, C. Schnell, and J. Starr), Stony Brook, October 2325, 2020.
 Discrete groups and Moduli (w. S. Kondo and S. Mukai), Nagoya, June 1720, 2019.
 Hodge Theory, Moduli and Representation Theory (final conference for the FRG project), Stony Brook, August 1418, 2017.
 Positivity in Arithmetic and Geometry (Spring School), Orsay (France), May 29June 2, 2017.
 HyperKaehler Manifolds, Hodge Theory and Chow Groups (Sanya, China, Dec 1823, 2016)
 CalabiYau varieties: Arithmetic, geometry and physics (Herstmonceux Castle, East Sussex, UK, June 2025, 2016)
 Algebraic Cycles and Moduli (CRM Montreal, June 28, 2016)
 Program on Complex, padic, and logarithmic Hodge theory and their applications (SCGP, MarApr, 2016)
 Program on
Moduli spaces and singularities in algebraic and Riemannian geometry (SCGP, AugNov, 2015)
 Minischool on Invariants of Singularities in zero and positive characteristics (December 4, 2015, Stony Brook)
 Collapsing CalabiYau Manifolds (SCGP, Aug 31Sept 4, 2015)
 Topology of algebraic varieties (IAS, 20142015)
 Perspectives on complex algebraic geometry (Columbia University, May 2225, 2015)
 New techniques in birational geometry (Stony Brook, April 610, 2015)
 K3, Enriques Surfaces and Related Topics (Nagoya, Nov 1014, 2014)
 Thematic Program on CalabiYau varieties (Fields Institute, Fall 2013).
Students
 Yoonjoo Kim
 Alexandra Viktorova
 Lisa Marquand
Former Associates
 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.
Address
Mathematics Department
Stony Brook University
Stony Brook, NY 117943651
Office Phone: (631) 6324506
Last Modified: Nov 29, 2021