For Fall Semester 2022, I am at the Hausdorff Research Institute Trimester on Tensor-Triangular Geometry. NYU Fall 2010: Calculus I (10).I am a third year PhD student and Teaching Assistant in the Department of Mathematics, Statistics, and Computer Science at the University of Illinois at Chicago.HU Winter 2014: Abelian varieties and Fourier-Mukai transforms.UGA Spring 2017: Abelian varieties (Math 8330).UGA Spring 2017: Modern algebra and geometry I (Math 4000/6000).UGA Fall 2017: Differential equations (Math 2700).UGA Spring 2018: Commutative algebra (Math 8020).UGA Fall 2018: (Counter)examples in char.UGA Fall 2018: Differential equations (Math 2700).UGA Fall 2019: Calculus II for Science and Engineering (Math 2260).UGA Spring 2020: Moduli spaces (Math 8330).UIC Spring 2021: Linear Algebra (Math 320) - ( 10am, 1pm).UIC Fall 2021: Definable Complex Analytic Geometry (Math 571).UIC Fall 2021: Second Course in Abstract Algebra I (Math 516).UIC Spring 2022: Hyperkähler manifolds (Math 571).A crucial step in the proof is the resolution of the K-trivial case of a conjecture of Peternell asserting that any minimal Kähler variety can be approximated by algebraic varieties. Lehn extending the decomposition theorem to nonprojective varieties via deformation theory. In this talk I will describe joint work with H. Work of Druel–Guenancia–Greb–Horing–Kebekus–Peternell over the last decade has culminated in a generalization of this result to projective Calabi–Yau varieties with the kinds of singularities that arise in the MMP, and the proofs critically use algebraic methods. Abstract.Ĭalabi–Yau manifolds are built out of simple pieces by the Beauville–Bogomolov decomposition theorem: any Calabi–Yau Kähler manifold up to an etale cover is a product of complex tori, irreducible holomorphic symplectic manifolds, and strict Calabi–Yau manifolds (which have no holomorphic forms except a holomorphic volume form). Hyperkähler varieties and related topics, September 2022. Notes from the Felix Klein lecture series in Bonn, May 2019 ( pdf)Īrithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces, CRM Short Courses, Springer (2020) ( pdf, book) My thesis from Princeton University, under Rahul Pandharipande Hodge polynomials of moduli spaces of stable pairs on K3 surfaces.Number Theory Phys., Volume 6, Number 4 (2012) ( pdf, arXiv, journal) Higher rank stable pairs on K3 surfacesĬommun.On the Frey-Mazur conjecture over low genus curves.Math., Volume 12, Issue 7 (2014) ( pdf, arXiv, journal) Lagrangian 4-planes in holomorphic symplectic varieties of K3^ typeĬent.p-torsion monodromy representations of elliptic curves over geometric function fieldsĪnn.Jussieu, Volume 16, Issue 4 (2017) ( pdf, arXiv, journal) A classification of Lagrangian planes in holomorphic symplectic varieties.Math., Volume 154, Issue 3 (2018) ( pdf, arXiv, journal) The Kodaira dimension of complex hyperbolic manifolds with cuspsĬompos.The geometric torsion conjecture for abelian varieties with real multiplication.The Mercat conjecture for stable rank 2 vector bundles on generic curvesĪmer.The Ax-Schanuel conjecture for variations of Hodge structures.Tame topology of arithmetic quotients and algebraicity of Hodge loci.Soc., Volume 23, Issue 3 (2021) ( pdf, arXiv, journal) A global Torelli theorem for singular symplectic varieties.Math., Volume 228, Issue 3 (2022) ( pdf, arXiv, journal) Algebraic approximation and the decomposition theorem for Kahler Calabi–Yau varieties.The global moduli theory of symplectic varieties.o-minimal GAGA and a conjecture of Griffiths.Quasiprojectivity of images of mixed period maps.Finiteness for self-dual classes in integral variations of Hodge structure.Functional transcendence of periods and the geometric André–Grothendieck period conjecture.A short proof of a conjecture of Matsushita.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |