Benjamin Bakker

• Deformations of fibered Calabi--Yau varieties
  with K. DeVleming, S. Filipazzi, R. Laza, J. Li, R. Svaldi, C. Wang, and J. Zhao
  submitted (pdf, arXiv)
• p-adic hyperbolicity for Shimura varieties and period images
  with A. Oswal, A. Shankar, and Z. Yao
  submitted (pdf, arXiv)
• Finiteness of function field-valued points on exceptional Shimura varieties
  with A. N. Shankar and J. Tsimerman
  submitted (pdf, arXiv)
• Baily--Borel compactifications of period images and the b-semiampleness conjecture
  with S. Filipazzi, M. Mauri, and J. Tsimerman
  submitted (pdf, arXiv)
• CM points have everywhere good reduction
  with J. Tsimerman
  submitted (pdf, arXiv)
• The linear Shafarevich conjecture for quasiprojective varieties and algebraicity of Shafarevich morphisms
  with Y. Brunebarbe and J. Tsimerman
  submitted (pdf, arXiv)
• Integral canonical models of exceptional Shimura varieties
  with A. N. Shankar and J. Tsimerman
  submitted (pdf, arXiv)
• Periods in families and derivatives of period maps
  with J. Pila and J. Tsimerman
  J. Inst. Math. Jussieu, to appear (pdf, arXiv, journal)
• A Hodge theoretic proof of Hwang's theorem on base manifolds of Lagrangian fibrations
  with C. Schnell
  Ann. Inst. Fourier (Grenoble), to appear (pdf, arXiv, journal)
• A short proof of a conjecture of Matsushita
  Adv. Math., Volume 482, Part A, Paper No. 110560 (2025) (pdf, arXiv, journal)
• Functional transcendence of periods and the geometric André–Grothendieck period conjecture
  with J. Tsimerman
  Forum Math. Sigma, Volume 13, Paper No. e97 (2025) (pdf, arXiv, journal)
• Appendix to "Teichmüller curves in hyperelliptic components of meromorphic strata", by M. Möller and S. Mullane
  with S. Mullane
  J. Inst. Math. Jussieu, Volume 24, Issue 4 (2025) (arXiv, journal)
• Definability of mixed period maps
  with Y. Brunebarbe, B. Klingler, and J. Tsimerman
  J. Eur. Math. Soc., Volume 26, No. 6 (2024) (pdf, arXiv, journal)
• Quasiprojectivity of images of mixed period maps
  with Y. Brunebarbe and J. Tsimerman
  J. Reine Angew. Math., Volume 2023, No. 804 (2023) (pdf, arXiv, journal)
• Definable structures on flat bundles
  with S. Mullane
  Bull. Lond. Math. Soc., Volume 55, Issue 5 (2023) (pdf, arXiv, journal)
• Finiteness for self-dual classes in integral variations of Hodge structure
  with T. W. Grimm, C. Schnell, and J. Tsimerman
  Épijournal Géom. Algébrique, Special volume in honour of Claire Voisin (2023) (pdf, arXiv, journal)
• o-minimal GAGA and a conjecture of Griffiths
  with Y. Brunebarbe and J. Tsimerman
  Invent. Math., Volume 232, Issue 1 (2023) (pdf, arXiv, journal)
• The global moduli theory of symplectic varieties
  with C. Lehn
  J. Reine Angew. Math., Volume 2022, No. 790 (2022) (pdf, arXiv, journal)
• Algebraic approximation and the decomposition theorem for Kahler Calabi–Yau varieties
  with H. Guenancia and C. Lehn
  Invent. Math., Volume 228, Issue 3 (2022) (pdf, arXiv, journal)
• A global Torelli theorem for singular symplectic varieties
  with C. Lehn
  J. Eur. Math. Soc., Volume 23, Issue 3 (2021) (pdf, arXiv, journal)
• Tame topology of arithmetic quotients and algebraicity of Hodge loci
  with B. Klingler and J. Tsimerman
  J. Amer. Math. Soc., Volume 33, No. 4 (2020) (pdf, arXiv, journal)
  (Erratum, J. Amer. Math. Soc., Volume 36, No. 4 (2023) (pdf, journal))
• The Ax-Schanuel conjecture for variations of Hodge structures
  with J. Tsimerman
  Invent. Math., Volume 217, Issue 1 (2019) (pdf, arXiv, journal)
• The Mercat conjecture for stable rank 2 vector bundles on generic curves
  with G. Farkas
  Amer. J. Math., Volume 140, No. 5 (2018) (pdf, arXiv, journal)
• The geometric torsion conjecture for abelian varieties with real multiplication
  with J. Tsimerman
  J. Differential Geom., Volume 109, No. 3 (2018) (pdf, arXiv, journal)
• The Kodaira dimension of complex hyperbolic manifolds with cusps
  with J. Tsimerman
  Compos. Math., Volume 154, Issue 3 (2018) (pdf, arXiv, journal)
• A classification of Lagrangian planes in holomorphic symplectic varieties
  J. Inst. Math. Jussieu, Volume 16, Issue 4 (2017) (pdf, arXiv, journal)
• p-torsion monodromy representations of elliptic curves over geometric function fields
  with J. Tsimerman
  Ann. of Math. 184, No. 3 (2016) (pdf, arXiv, journal)
  (Erratum (pdf))
• Lagrangian 4-planes in holomorphic symplectic varieties of K3^[4] type
  with A. Jorza
  Cent. Eur. J. Math., Volume 12, Issue 7 (2014) (pdf, arXiv, journal)
  Computational appendix and Code
• On the Frey-Mazur conjecture over low genus curves
  with J. Tsimerman
  arXiv preprint (2013) (pdf, arXiv)
• Higher rank stable pairs on K3 surfaces
  with A. Jorza
  Commun. Number Theory Phys., Volume 6, Number 4 (2012) (pdf, arXiv, journal)
• Hodge polynomials of moduli spaces of stable pairs on K3 surfaces
  My thesis from Princeton University, under Rahul Pandharipande
  June 2010 (pdf)

• Mixed non-abelian Hodge theory and the linear Shafarevich conjecture
  To appear in Proceedings of the ICM 2026, (pdf, arXiv)
• Hodge theory and o-minimality
  Notes from the Felix Klein lecture series in Bonn, May 2019 (pdf)
• Lectures on the Ax-Schanuel Conjecture
  with J. Tsimerman
  Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces, CRM Short Courses, Springer (2020) (pdf, book)

• p-adic Borel extension for Shimura varieties and period images
  CIRM, September 2026.
  Abstract.
  In 1972, Borel proved that every holomorphic map from a product of punctured unit disks to a complex Shimura variety extends to a map from a product of disks to its Baily--Borel compactification. Recently, Oswal--Shankar--Zhu and Patel proved the corresponding p-adic statement over discretely valued fields in the abelian-type case using Rapoport--Zink uniformizations. I will discuss joint work with Oswal, Shankar, and Yao extending this result to all Shimura varieties for large primes p by instead relying on techniques from p-adic Hodge theory. I will also describe how the same proof works in the context of geometric period images, at least under a good reduction hypothesis.
• o-minimal GAGA, Hodge theory, and compact moduli of algebraic varieties
  ICBS, August 2026.
  Abstract.
  For any complex algebraic variety X, the singular cohomology of X is an important topological invariant. This invariant can be enhanced to a Hodge structure, which additionally records the integrals of algebraic differential forms along topological cycles, and therefore also sees the algebraic structure. Hodge structures turn out to be extremely powerful tools in many areas of mathematics, for example in moduli theory: any family of algebraic varieties yields a family (or "variation") of Hodge structures, which can often be used to build a moduli space of those varieties. The downside is that since Hodge structures are by their very nature highly transcendental, it is more difficult to realize these moduli spaces as algebraic varieties themselves.
  
  Famously, this story plays out very elegantly for the moduli space A_g of (principally polarized) g-dimensional abelian varieties where this perspective gives an exact moduli space, and the work of Baily--Borel provides a beautiful projective compactification of this space which connects the Hodge theory to the classical theory of automorphic forms. I will explain joint work with S. Filipazzi, M. Mauri, and J. Tsimerman which generalizes this picture to any family by constructing Baily--Borel compactifications for arbitrary variations of Hodge structures using o-minimal GAGA. This settles a question of Griffiths first raised in his 1970 ICM address. Our result has especially nice applications to the moduli of Calabi--Yau varieties, and in particular implies the b-semiampleness conjecture of Prokhorov--Shokurov.
• Mixed non-abelian Hodge theory and the linear Shafarevich conjecture
  ICM, July 2026.
  Abstract.
  For a complex algebraic variety X, classical Hodge theory imposes extra structure on the singular cohomology H^k(X,C) of X using the theory of harmonic forms. Non-abelian Hodge theory similarly enriches the geometry of the algebraic variety of representations of the fundamental group (which is thought of as H¹(X,GL_r(C))) by using harmonic metrics on local systems. The theory in the "pure" case of smooth projective X was largely worked out in the 1990s beginning with the seminal work of Simpson and has seen many applications, for example the proof of Eyssidieux--Katzarkov--Pantev--Ramachandran of the linear Shafarevich conjecture for such X. In this talk, I will survey recent advances in the "mixed" case of arbitrary complex algebraic varieties X, and show how these tools can be used to prove a number of important results about the topology of algebraic varieties, as well as a general version of the linear Shafarevich conjecture. This is based on joint work with Y. Brunebarbe and J. Tsimerman.
• Deformations of fibered Calabi--Yau manifolds
  Princeton, December 2025.
  Abstract.
  A number of years ago, Kollár proved that any small deformation of an elliptically fibered Calabi--Yau variety X is also elliptically fibered, provided H²(X,O_X)=0. We show the same is true for any fibration of a Calabi--Yau manifold. More generally, without any assumption on H²(X,O_X), any small deformation of a semiample bundle remains semiample up to numerical equivalence. I will describe the proof using some Hodge theory and the T1 lifting criterion of Kawamata--Ran, as well as discuss some related questions. This is joint work in progress with Kristin DeVleming, Stefano Filipazzi, Radu Laza, Jennifer Li, Roberto Svaldi, Chengxi Wang, and Junyan Zhao.

My course websites are maintained here.

I'm not teaching Autumn 2026.

• UIC Spring 2026: Introduction to advanced mathematics (Math 215) -- (10am, 12pm).
• UIC Spring 2025: Non-abelian Hodge theory (Math 571).
• UIC Spring 2025: Abstract algebra I (Math 330).
• UIC Fall 2024: Complex manifolds II (Math 555).
• UIC Fall 2023: Introduction to advanced mathematics (Math 215) -- (11am, 1pm).
• UIC Fall 2022: Calculus III (Math 210) -- (4pm, 5pm).
• UIC Spring 2022: Hyperkähler manifolds (Math 571).
• UIC Fall 2021: Second course in abstract algebra I (Math 516).
• UIC Fall 2021: Definable complex analytic geometry (Math 571).
• UIC Spring 2021: Linear algebra (Math 320) -- (10am, 1pm).
• UGA Spring 2020: Moduli spaces (Math 8330).
• UGA Fall 2019: Calculus II for science and engineering (Math 2260)
• UGA Fall 2018: Differential equations (Math 2700).
• UGA Fall 2018: (Counter)examples in char. p geometry (Math 8330).
• UGA Spring 2018: Commutative algebra (Math 8020).
• UGA 2017-2018: Topics in Hodge theory (VRG) (Math 8850).
• UGA Fall 2017: Differential equations (Math 2700).
• UGA Spring 2017: Modern algebra and geometry I (Math 4000/6000).
• UGA Spring 2017: Abelian varieties (Math 8330).
• HU Summer 2016: Berkovich spaces.
• HU Winter 2015: Literature seminar.
• HU Summer 2015: Faltings theorem.
• HU Winter 2014: Abelian varieties and Fourier-Mukai transforms.
• NYU Spring 2013: Number theory (MATH-GA 2210.001).
• NYU Fall 2012: Theory of numbers (MATH-UA 248.001).
• NYU Fall 2011: Algebra I (MATH-GA 2130.001).
• NYU Spring 2011: Topology II (MATH-GA 2320.001).
• NYU Fall 2010: Calculus I (V63.0121.026.FA10).

• Ben Tighe
• Zhehao Li
• Hank Morris
• Anh Tran
• Edward Varvak