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BENJAMIN BAKKER

University of Illinois at Chicago
Department of Mathematics, Statistics, and Computer Science
851 S. Morgan St.
Chicago, IL 60607


Email: last name dot uic at gmail dot com

CV: pdf


I am an associate professor of Mathematics at UIC.

Research Interests: Algebraic geometry, hodge theory, moduli of abelian,
symplectic, and calabi-yau varieties, relations to arithmetic geometry and model
theory, derived categories.

UIC Algebraic Geometry Seminar

Midwest Algebraic Geometry Graduate Conference (MAGGC), UIC, August 10-11 2022.



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Publications and Preprints
   
 * CM points have everywhere good reduction
   with J. Tsimerman
   preprint (pdf, arXiv)
 * Periods in families and derivatives of period maps
   with J. Pila and J. Tsimerman
   preprint (pdf, arXiv)
 * The linear Shafarevich conjecture for quasiprojective varieties and
   algebraicity of Shafarevich morphisms
   with Y. Brunebarbe and J. Tsimerman
   preprint (pdf, arXiv)
 * Integral canonical models of exceptional Shimura varieties
   with A. N. Shankar and J. Tsimerman
   preprint (pdf, arXiv)
 * A Hodge theoretic proof of Hwang's theorem on base manifolds of Lagrangian
   fibrations
   with C. Schnell
   preprint (pdf, arXiv)
 * Appendix to "Teichmüller curves in hyperelliptic components of meromorphic
   strata", by M. Möller and S. Mullane
   with S. Mullane
   preprint (arXiv)
 * A short proof of a conjecture of Matsushita
   submitted (pdf, arXiv)
 * Functional transcendence of periods and the geometric André–Grothendieck
   period conjecture
   with J. Tsimerman
   submitted (pdf, arXiv)
 * 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)
 * Definability of mixed period maps
   with Y. Brunebarbe, B. Klingler, and J. Tsimerman
   J. Eur. Math. Soc., to appear (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 to “Tame topology of arithmetic quotients and algebraicity of Hodge
   loci”
   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)
 * 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)


Lecture Notes
 * 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)
 * Slides

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Recent Talks
   
   
 * Hwang's theorem on the base of a Lagrangian fibration revisited
   Geometry of Hyperkähler varieties, Hangzhou, September 2022.
   Abstract.
   Irreducible hyperkahler manifolds are higher dimensional analogs of K3
   surfaces; their geometry is tightly controlled by the existence of a nowhere
   degenerate holomorphic 2-form. The only nontrivial fibration structure f:X ->
   B a hyperkahler manifold X admits is a fibration by Lagrangian tori, and for
   such Lagrangian fibrations the base B is conjectured to always be isomorphic
   to projective space. In 2008 Hwang proved that this is the case if B is
   assumed to be smooth by using the theory of varieties of minimal rational
   tangents on Fano manifolds. In this talk I will present a simpler proof of
   this result which leans more heavily on Hodge theory. Specifically, the main
   input is a basic functoriality result coming from Hodge modules. This is
   joint work with C. Schnell.
 * The geometric André--Grothendieck period conjecture
   Midrasha Mathematicae, December 2023.
   Abstract.
   A period integral of a complex algebraic variety is the integral of an
   algebraic differential form along a topological cycle. These numbers are at
   the heart of Hodge theory. In this talk I will explain how to prove a version
   of the Ax--Schanuel conjecture for these period integrals in families, and
   how it provides a capstone to the advances in the transcendence theory of
   period maps made over the past decade. I will also discuss the relationship
   with the functional version of the Andre--Grothendieck period conjecture,
   which predicts that all algebraic relations between such periods integrals
   arise from geometry. This is joint work with J. Tsimerman.
 * The Matsushita alternative
   Hyperkähler varieties and related topics, September 2022.
   Abstract.
   Matsushita conjectured that a Lagrangian fibration of an irreducible
   hyperkähler manifold is either isotrivial or of maximal variation. In this
   talk I will show how to prove this conjecture by adapting previous work of
   Voisin and van Geemen. I will also deduce some applications to the density of
   torsion points of sections of Lagrangian fibrations.
   
   
   

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Teaching

My course websites are maintained here.

Current Teaching
 * UIC Fall 2024: Complex manifolds II (Math 555).

Past Teaching
 * 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).

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Students
 * Ben Tighe
 * Zhehao Li
 * Hank Morris
 * Anh Tran
 * Edward Varvak