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 7: Christopher Hacon (University of Utah)
Location: Zoom (https://purdue-edu.zoom.us/j/99467898661?pwd=FOMrspNCAywfyh5VFOKDS80aWZLZuX.1)
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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)
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October 14: Mert Akdenizli (Purdue University)
Location: STON 215
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October 21: Ze Yun (Stony Brook University)
Location: STON 215
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October 28: Scott Hiatt (University of Wisconsin, Madison)
Location: STON 215
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November 4:
Location: STON 215
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November 11:
Location: STON 215
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November 18:
Location: STON 215
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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