Research Interests 
I am a member of the algebraic geometry
group , and I study the geometry and topology of complex algebraic
varieties. My research focuses on Hodge theory, and on applications of mixed
Hodge modules in algebraic geometry.
Fall 2025 Teaching 
This semester, I am teaching MAT 534  (Algebra I)
and MAT 132  (Calculus II).  
      
        
Mailing Address 
Department of Mathematics
 
Contact Information 
 Office: Math Tower 4–110 (map )
 
 
 
Graduate students who plan to attend the 2025 Summer Research Institute in
Algebraic Geometry should apply to the Graduate Student Bootcamp as well. The
application deadline for lodging and financial support is January 31,
2025 .
Upcoming Events 
Finiteness, Tameness, and Complexity 
CMSA, Harvard University, November 12 to November 14, 2025AGNES UMass Amherst 2025 
University of Massachusetts, Amherst, November 21 to November 23, 2025Tour de Formosa 
Taiwan, January 12 to January 16, 2026Complex Analysis 
Oberwolfach, April 5 to April 10, 2026 
Past Events 
Mid-Atlantic Geometry and Singularities Conference 
Universidad de La Laguna, May 12 to May 16, 2025Hodge Theory and Algebraic Geometry (Mark 60) 
Stony Brook University, May 27 to May 29, 2025Graduate Student Bootcamp (for Summer Research Institute)) 
Colorado State University, July 8 to July 12, 2025Summer Research Institute in Algebraic Geometry 
Fort Collins, Colorado, July 14 to August 1, 2025 
Click on the title of any paper to download a PDF file.
Preprints 
A Hodge-theoretic proof of Hwang's theorem on base manifolds of Lagrangian fibrations 
[with B. Bakker ]
Higher multiplier ideals 
[with R. Yang ]
Hodge theory and Lagrangian fibrations on holomorphic symplectic manifolds  
Degenerating complex variations of Hodge structure in dimension one 
[with C. Sabbah ]
A log resolution for the theta divisor of a hyperelliptic curve 
[with R. Yang ]
     
 
 Published Papers 
Singular hermitian metrics and the decomposition theorem of Catanese, Fujita, and Kawamata 
Proc. Amer. Math. Soc. 152  (2024), no. 1, 137–146 [with L. Lombardi ]
On the behavior of Kodaira dimension under smooth morphisms 
Algebr. Geom. 10  (2023), no. 5, 607–619 [with M. Popa ]
Singular metrics and a conjecture by Campana and Peternell 
Pure Appl.  Math. Q. 21  (2025), no. 3, 1269–1281
 
Finiteness for self-dual classes in integral variations of Hodge structure 
Épijournal de Géométrie Algébrique, Special volume in honour of C. Voisin, Article no. 1 (2023) [with B. Bakker , Th. Grimm  and J. Tsimerman ]
Correction to "Height bounds and the Siegel property" 
Algebra Number Theory 17  (2023), no. 6, 1231–1237 [with M. Orr ]
Hodge modules and singular hermitian metrics 
Math. Z. 303:28 (2023) [with R. Yang ]
The Fourier-Mukai transform made easy 
Pure Appl. Math. Quart. 18  (2022), no. 4, 1749–1770
 
Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities 
J. Amer. Math. Soc. 34  (2021), no. 2, 315–368 [with S. Kebekus ]
Pushforwards of pluricanonical bundles under morphisms to abelian varieties 
J. Eur. Math. Soc. 22  (2020), 2511–2536 [with L. Lombardi  and M. Popa ]
An overview of Morihiko Saito's theory of mixed Hodge modules 
In: Representation Theory, Automorphic Forms & Complex Geometry, A Tribute to Wilfried Schmid. Intl. Press, 2020, pp.27–80.
 
On a theorem of Campana and Păun 
Épijournal de Géométrie Algébrique, Sep. 1, 2017, Vol. 1
 
Vanishing theorems for perverse sheaves on abelian varieties, revisited 
Selecta Math. (N.S.) 24  (2018), no. 1, 63–84 [with B. Bhatt  and P. Scholze ]
Algebraic fiber spaces over abelian varieties: around a recent theorem by Cao and Păun 
Contemp. Math. 712  (2018), 143–195 [with Ch. Hacon  and M. Popa ]
Viehweg's hyperbolicity conjecture for families with maximal variation 
Invent. Math. 208  (2017), no. 3, 677–713 [with M. Popa ]
Hodge modules on complex tori and generic vanishing for compact Kähler manifolds 
Geometry & Topology 21  (2017), 2419–2460 [with G. Pareschi  and M. Popa ]
Fields of definition of Hodge loci 
London Math. Soc. Lecture Note Ser. 427  (2016), 275–291 [with M. Saito ]
On Saito's vanishing theorem 
Math. Res. Lett. 23 , No. 2 (2016), pp. 499–527
 
On direct images of pluricanonical bundles 
Algebra Number Theory 8  (2014), no. 9, 2273–2295 [with M. Popa ]
The Cremmer-Scherk Mechanism in F-theory Compactifications on K3 Manifolds 
J. High Energ. Phys. 1405 , 135 (2014) [with M. Douglas  and D. Park ]
Holonomic D-modules on abelian varieties [Erratum ] 
Inst. Hautes Études Sci. Publ. Math. 121  (2015), no. 1, 1–55
 
Kodaira dimension and zeros of holomorphic one-forms 
Ann. of Math. 179  (2014), no. 3, 1109–1120 [with M. Popa ]
Torsion points on cohomology support loci: from D-modules to Simpson's theorem 
London Math. Soc. Lecture Note Ser. 417  (2015), 405–421
 
Weak positivity via mixed Hodge modules 
Contemp. Math. 647  (2015), 129–137
 
Absolute Hodge classes 
In: Hodge theory. Vol. 49. Mathematical Notes. Princeton Univ. Press, 2014, pp.469–530 [with F. Charles ]
Generic vanishing theory via mixed Hodge modules 
Forum Math. Sigma 1  (2013), e1, 60pp. [with M. Popa ]
Moduli of products of stable varieties 
Compositio Math. 149  (2013), no. 12, 2036–2070 [with B. Bhatt , Z. Patakfalvi  and W. Ho ]
The zero locus of the infinitesimal invariant 
Fields Inst. Commun. 67  (2013), 589–602 [with G. Pearlstein ]
Residues and filtered D-modules 
Math. Annalen 354  (2012), no. 2, 727–763
 
Complex-analytic Néron models for arbitrary families of intermediate Jacobians 
Invent. Math. 188  (2012), no. 1, 1–81
 
The fundamental group is not a derived invariant 
EMS Ser. Congr. Rep. 8  (2011), 279–285
 
Canonical cohomology as an exterior module 
Pure Appl. Math. Quart. 7  (2011), no. 4, 1529–1542 [with R. Lazarsfeld  and M. Popa ]
Derived invariance of the number of holomorphic 1-forms and vector fields 
Ann. Sci. Éc. Norm. Supér (4) 44  (2011), no. 3, 527–536 [with M. Popa ]
A variant of Néron models over curves 
Manuscripta Math. 134  (2011), no. 34, 359–375 [with M. Saito ]
Local duality and polarized Hodge modules 
Publ. Math. Res. Inst. Sci. 47  (2011), no. 3, 705–725
 
Primitive cohomology and the tube mapping 
Math. Z. 268  (2011), no. 3–4, 1069–1089
 
Two lectures about Mumford-Tate groups 
Rend. Semin. Mat. Univ. Politec. Torino 69  (2011), no. 2, 199–216
 
The locus of Hodge classes in an admissible variation of mixed Hodge structure 
C. R. Acad. Sci. Paris, Ser. I 348  (2010), 657–660 [with P. Brosnan  and G. Pearlstein ]
Two observations about normal functions 
Clay Math. Proc. 9  (2010), 75–79
 
                        
 
 Unpublished Papers 
Graded duality for filtered D-modules 
[with M. Saito ]
On the locus of limit Hodge classes  
Surfaces with big anticanonical class 
[with D. Chen ]
Canonical extensions of local systems  
Idempotent ultrafilters and polynomial recurrence  
   
 
 
Ph.D. Thesis 
      
        
          
            
              The boundary behavior of cohomology classes and singularities of normal functions 
	      [Ohio State University, 2008]
             
           
         
       
Mixed Hodge modules 
Claude Sabbah and I are adapting Saito's theory of mixed Hodge modules to the case of complex coefficients. A collection of notes (in progress) can be found on Claude's website .
Notes from courses and talks 
A graduate course on Abelian varieties  (Stony Brook, 2025) 
Four lectures on Degenerating variations of Hodge structure in dimension one  (Aussois, 2023) 
A graduate course on Algebraic D-modules  
(Stony Brook, 2019) 
A graduate course on Basic topology  (Stony Brook, 2014 and 2022) 
A talk on Zeros of holomorphic one-forms  (Paris, 2014) 
A graduate course on the Generic vanishing theorem  
(Stony Brook and Bonn, 2013 and 2024) 
A graduate course on Complex manifolds  
(Chicago, 2010 and Stony Brook, 2024) 
A seminar on Deformations of complex structure 
(Columbus, 2005) 
A seminar about Picard-Fuchs equations 
(Columbus, 2004) 
A talk on the Gauss-Bonnet theorem 
(Columbus, 2004) 
A lecture on the De Giorgi-Nash-Moser estimates 
(Columbus, 2002)  
 
Miscellaneous notes