The Algebraic Geometry Seminar takes place on Wednesdays 3:30–4:30PM. Pre-talks (which graduate students are particularly encouraged to attend) take place Wednesdays 3:00–3:25PM.
The in-person talks will take place in STON 215. Some talks will be presented online via Zoom.
Please see below for the most up to date information. Here is the Zoom link for the online talks:
https://purdue-edu.zoom.us/j/99467898661?pwd=FOMrspNCAywfyh5VFOKDS80aWZLZuX.1
October 21: Ze Yun (Stony Brook University)
Location: STON 215
Title: Generic vanishing of Dolbeault cohomology of mixed Hodge modules on abelian varieties
Abstract: Laumon and Rothstein showed there is a Fourier-Mukai transform for D-modules on abelian varieties. Schnell studied the transform from the point of view of generic vanishing theory. Motivated by studying D-modules on abelian varieties via their Fourier transforms, we study generic vanishing for the Dolbeault cohomology of mixed Hodge modules, where the differentials in the graded de Rham complex are modified by a one-form. We prove that, under the nonabelian Hodge correspondence, the Dolbeault cohomology support loci on Higgs moduli space of mixed Hodge modules twisted by Higgs line bundles agree with the images of the cohomology support loci of their underlying D-modules on the de Rham moduli space. Time permitting, I'll also talk about how this gives an extension of Fourier transform to a compactification of the de Rham moduli space.
September 2: Laurentiu Maxim (University of Wisconsin, Madison)
Location: STON 215
Title: A conjectural characteristic-class version of the Hodge index theorem for singular complex algebraic varieties
Abstract: In this talk, I will discuss a conjectural characteristic-class version of the Hodge index theorem for singular complex algebraic varieties. This was formulated by Brasselet, Schuermann, and Yokura, expressing the Goresky-MacPherson topological L-classes in terms of suitable Hodge-theoretic L-classes. I will survey recent developments and results on spaces for which the conjecture has been proved. Based on joint work with M. Aligholi and J. Schuermann.
September 9: Hyunsuk Kim (Imperial College London)
Location: Zoom (https://purdue-edu.zoom.us/j/99467898661?pwd=FOMrspNCAywfyh5VFOKDS80aWZLZuX.1)
Title: Hodge theory of toric singularities
Abstract: Toric variety is a normal variety containing an algebraic torus as an open dense subset whose action on itself extends to the whole space. They provide a fruitful interplay between algebraic geometry and convex geometry since properties on one side (e.g. smoothness, compactness) can be translated into properties involving discrete objects (e.g. cones, fans, polytopes). I will talk about singularities of these varieties from a Hodge theoretic point of view, with applications towards local cohomology and singular cohomology, based on joint works with Sridhar Venkatesh.
September 16: Daniil Serebrennikov (Johns Hopkins University)
Location: STON 215
Title: Finiteness, Boundedness, and Constructibility for Calabi-Yau Varieties
Abstract: Grothendieck’s foundational work shows that many geometric properties of fibers in a projective family, for example smoothness, define constructible subsets of the base. However, one natural property is absent from this list: given a fiber, is the locus of points whose fibers are isomorphic to it constructible? Surprisingly, this question is closely related to the Minimal Model Program and the Kawamata-Morrison cone conjecture, a longstanding central problem in birational geometry. In this talk, I will explain the relationship between the cone conjecture and this constructibility problem and show how it yields a partial answer to the Kawamata-Matsuki conjecture on the finiteness of isomorphism classes of Calabi-Yau varieties within a fixed birational class.
September 23: Deepam Patel (Purdue University)
Location: STON 215
Title: Positivity of Euler Charactersitics of Perverse Sheaves.
Abstract: Perverse sheaves on abelian varieties, and more generally on varieties with nef cotangent bundle, have non-negative Euler characteristic. I will survey the results of this type in the literature, from Franecki–Kapranov to recent work of Debarre–Moonen and Arapura–Mese–Patel, and explain how the theory of characteristic cycles makes them available in positive characteristic and for torsion coefficients, with applications to semi-abelian varieties, to Bézout-type theorems, and to decomposition numbers of modular perverse sheaves.
September 30 (Rescheduled for March 3, 2027): Nao Moriyama (Kyoto University)
Location: STON 215
Title: Some results on the MMP for surfaces
Abstract: The Minimal Model Program (MMP) is a central framework in birational geometry that aims to simplify a given algebraic variety into a desirable model. For normal projective surfaces, the MMP works in various settings, including surfaces with log canonical, $\mathbb{Q}$-factorial, or Gorenstein singularities. In this talk, we discuss recent results on the MMP for surfaces and look at several related topics. This talk is based in part on joint work with Osamu Fujino and Hiroshi Sato.
October 7: Christopher Hacon (University of Utah)
Location: Zoom (https://purdue-edu.zoom.us/j/99467898661?pwd=FOMrspNCAywfyh5VFOKDS80aWZLZuX.1)
Title: Algebraic geometry vs Kahler geometry
Abstract: The minimal model program is the cornestone of our understanding of the birational geometry of projective varieties. A large portion of this program was completed by Birkar-Cascini-Hacon-McKernan and Siu around 2010. In this talk I will discuss recent progress in the study of compact Kahler varieties up to bimeromorphic equivalence. In particular I will describe recent work of Hacon and Xie leading do a Kahler analog of [BCHM2010] and to a resolution of Tosatti's transcendental base point free conjecture.
October 14: Mert Akdenizli (Purdue University)
Location: STON 215
Title: Perverse Euler characteristics of locally Hermitian symmetric varieties
Abstract: A complex algebraic variety has the perverse Euler characteristic property if every perverse sheaf on it has nonnegative Euler characteristic. In joint work with Quoc-Anh Tran, we prove this property for finite-volume locally Hermitian symmetric varieties of noncompact type. Examples include ball quotients and finite-level Shimura varieties. For this, I will show nefness of the logarithmic cotangent bundle on suitable toroidal compactifications, using the adjoint variation of Hodge structure and semipositivity of Hodge bundles. If time permits, I will also talk about what to expect for the strict positivity.
October 21: Ze Yun (Stony Brook University)
Location: STON 215
Title: Generic vanishing of Dolbeault cohomology of mixed Hodge modules on abelian varieties
Abstract: Laumon and Rothstein showed there is a Fourier-Mukai transform for D-modules on abelian varieties. Schnell studied the transform from the point of view of generic vanishing theory. Motivated by studying D-modules on abelian varieties via their Fourier transforms, we study generic vanishing for the Dolbeault cohomology of mixed Hodge modules, where the differentials in the graded de Rham complex are modified by a one-form. We prove that, under the nonabelian Hodge correspondence, the Dolbeault cohomology support loci on Higgs moduli space of mixed Hodge modules twisted by Higgs line bundles agree with the images of the cohomology support loci of their underlying D-modules on the de Rham moduli space. Time permitting, I'll also talk about how this gives an extension of Fourier transform to a compactification of the de Rham moduli space.
October 28: Scott Hiatt (University of Wisconsin, Madison)
Location: STON 215
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November 4: Shubhankar Sahai (University of California, San Diego)
Location: STON 215
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November 11:
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November 18:
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December 2: Elden Elmanto (University of Toronto)
Location: STON 215
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December 9: Ritvik Ramkumar (University of Notre Dame)
Location: STON 215
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If you are interested in giving a talk, please contact one of the organizers:
Donu Arapura