Department of Mathematics
Stony Brook University
Office: Math 4-121
Geometry, esp. moduli problems, degenerations, singularities, special
classes of varieties (K3s, Calabi-Yau, Hyperkahler manifolds).
Recent & Selected Publications:
- Complete moduli of cubic threefolds and their intermediate Jacobians (with S. Casalaina-Martin, S. Grushevsky, and K. Hulek), preprint 2015.
- Extending the Prym map to toroidal compactifications of the moduli space of abelian varieties (with S. Casalaina-Martin, S. Grushevsky, and K. Hulek), to appear in J. Eur. Math. Soc.
- The KSBA compactification for the moduli space of degree two K3 pairs, to appear in J. Eur. Math. Soc.
- On some Hermitian variations of Hodge structure of Calabi-Yau type with real multiplication (w. R. Friedman), Michigan Math. J. 63 (2014), no. 1, 83-99.
- 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.
- The geometry of the ball quotient model of the moduli space of genus four curves (w. S. Casalaina-Martin and D. Jensen), in "Compact Moduli Spaces and Vector Bundles", Contemp. Math. 564 (2012), 107-136.
- 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 lecture series given at: Angers (June 2014), KAIST (Mar 2014), Fields Institute (Aug and Nov 2013), Vancouver (Jul 2013), Barcelona (May 2013).
- Classical Period Domains (with Z. Zhang), based on my 2013 Vancouver lectures, to appear in "Recent Advances in Hodge Theory", Cambridge Univ. Press.
- Perspectives on the construction and compactification of moduli spaces, Lectures for the school on "Compactifying Moduli Spaces" (Barcelona, May 2013), to appear in a volume of CRM Lecture Notes.
- GIT and moduli with a twist, in "Handbook of Moduli" vol. 2, Adv. Lect. Math. 25 (2013), Int. Press, 259-297.
My papers on arXiv. My Scholar profile.
My research is partially supported by NSF (CAREER DMS-125481). I am also part of an FRG group "Hodge theory, Moduli and Representation theory" (DMS-1361143) with P. Brosnan, M. Kerr, G. Pearlstein, and C. Robles.
- 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)
- FRG Workshop (Stony Brook, January 5-8, 2015)
- K3, Enriques Surfaces and Related Topics (Nagoya, Nov 10-14, 2014)
- AGNES (SBU, Apr 25-27, 2014)
- Mini-course on Dynamics and Algebraic Surfaces (SBU, April 9, 2014)
- Mini-course on K-stability (SBU, Dec 6, 2013)
- Thematic Program on Calabi-Yau varieties (Fields Institute, Fall 2013) - esp. Workshop 4 (Hodge Theory), Workshop 2 (Enumerative), Workshop 0 (Intro).
- Adrian Brunyate (NSF postdoc)
- Giulia Sacca (postdoc)
- Letao Zhang (postdoc)
- Zheng Zhang (geometric and motivic realizations of VHS) - now at TAMU
- Patricio Gallardo (moduli of surfaces of general type, esp. quintics) - now at U. Georgia
- Thao Do (undergraduate, Honors Thesis: On Delsarte surfaces with log canonical singularities) - now at MIT
- Ken Ascher (undergraduate, Honors Thesis) - now at Brown.
- Ren Yi (undergraduate) - now at Brown.
- Dave Jensen (postdoc) - now at U. Kentucky.
Personal - Irina & Iuliana
Stony Brook University
Stony Brook, NY 11794-3651
Office Phone: (631) 632-4506
Last Modified: Sept 22, 2015