This will be a seminar style course where we take turns presenting on recent influential papers in the algebraic geometry literature. Each speaker will pick a single "recent hit" to cover.
The style and content of the presentation is entirely up to you. You could present a single result from the paper and give an overview of the proof. Or you could simply provide background material necessary to state and appreciate a given result. Alternatively, you could focus the lecture on the significance and applications of the paper.
The classroom will be a friendly and welcoming space. There is no expectation whatsoever that you've mastered the material of the paper. Just do your best job in presenting what you understand and other audience members may be able to add to the discussion.
Examples: We will be flexible on what it means for a paper to be "recent" or a "hit," or even whether it lies in "algebraic geometry." You are really free to choose any paper to present on.
Here are some examples of recent influential papers. There are of course many, many others and I have made no effort whatsoever to create a definitive or exhaustive list.
- Abramovich, Temkin, and Włodarczyk: Functorial embedded resolution via weighted blowings up
- Araujo, Druel, Kovács: Cohomological characterizations of projective spaces and hyperquadrics.
- Bayer, Lahoz, Macrì, Nuer, Perry, and Stellari: Stability conditions in families
- Bhatt: On the direct summand conjecture and its derived variant
- Birkar, Cascini, Hacon, McKernan: Existence of minimal models for varieties of log general type
- Blanc and Cantat: Dynamical degrees of birational transformations of projective surfaces.
- Blekherman, Smith, Velasco: Sums of squares and varieties of minimal degree.
- Bondal and Orlov, Reconstruction of a variety from the derived category and groups of autoequivalences
- Bridgeland: Stability conditions on triangulated categories
- Cesnavicius and Scholze: Purity for flat cohomology
- Eisenbud and Schreyer: Betti numbers of graded modules and cohomology of vector bundles.
- Esnault and Mehta: Simply connected projective manifolds in characteristic p>0 have no nontrivial stratified bundles
- Hassett, Pirutka, and Tschinkel: Stable rationality of quadric surface bundles over surfaces
- Huh: Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs.
- Kuznetsov, Homological projective duality
- Laza, Saccà, Voisin: A hyper-Kähler compactification of the intermediate Jacobian fibration associated with a cubic 4-fold.
- Maulik, Nekrasov, Okounkov, and Pandharipande: Gromov-Witten theory and Donaldson-Thomas theory. I & II
- Nicaise and Shinder: The motivic nearby fiber and degeneration of stable rationality
- Popa and Schnell: Kodaira dimension and zeros of holomorphic one-forms
- Totaro: Hodge theory of classifying stacks.
- Voisin: Unirational threefolds with no universal codimension 2 cycle