![]() Polynomials are introduced at a very early stage in our studies. Thus begins a poem composed by Shreeram S. March 2 8 (Colloquium, Special Date) : Neena Gupta (Indian Statistical Institute) ![]() This is a joint work with Federico Scavia. As an application, we show the vanishing of the third unramified cohomology for a large class of rationally chain connected threefolds over finite fields, confirming a conjecture of Colliot-Thelene and Kahn. I would like to discuss some consequences of the equality of the two filtrations for algebraic equivalence for codimension 2 cycles over finite fields. The two filtrations differ in general as recently shown by Benoist and Ottem, and this result may be exnteded to the l-adic setting over any algebraically closed field of characteristic not 2. Title: Two coniveau filtrations and algebraic equivalence over finite fieldsĪbstract: Over the complex numbers, the integral cohomology of a smooth projective variety is endowed with the coniveau and strong coniveau filtrations. March 22: Fumiaki Suzuki (University of California, Los Angeles) As a consequence of this characterization, we can show that a log Fano cone singularity is K-polystable with respect to a larger class of test configurations if it admits a Ricci-flat Kähler cone metric, strengthening earlier results of Collins-Székelyhidi and Li. In this talk, we aim to give a characterization for local K-stability from a non-Archimedean point of view. Title: A non-Archimedean characterization of local K-stabilityĪbstract: Log Fano cone singularities are generalizations of cones over log Fano varieties, and have a local K-stability theory extending the one for log Fano varieties. March 1: Yueqiao Wu (University of Michigan) This is partially based on joint work with M. If there is time, I'll discuss some analogous results in the setting of formal schemes (where previously even the existence of a MHS was unknown). ![]() ![]() I will discuss an enrichment of the category of mixed Hodge structures and some results on the existence of natural objects in this category which allow for the possibility of understanding cycles on complex analytic links. On the other hand, mixed hodge theory is often insufficient for the study of cycles/K-theory in the open or singular settings. This is joint work with Brian Lehmann and Sho Tanimoto.įebruary 22: Deepam Patel (Purdue University)Ībstract: An important application of the theory of mixed Hodge structures is in the study of algebraic cycles or K-theory (for example via the Hodge or Bloch-Beilinson conjectures) of smooth projective varieties. This proves the first of Batyrev's heuristics that make up Geometric Manin's Conjecture for Fano fibrations over arbitrary base curves. In the more general setting of a Fano fibration, we show that these curves come from a-covers of X, and we show that the set of such a-covers up to equivalence form a bounded family. In this talk, we provide a geometric classification of the ways that a family of curves can be nonfree. ![]() The components of the space of maps that consist entirely of nonfree curves are particularly difficult to understand. Nonfree curves, on the other hand, can be much more difficult to understand. They are smooth points of the space of morphisms, and lie on a unique component of the expected dimension. Title: Non-free curves and Geometric Manin's ConjectureĪbstract: When studying the space of maps from a smooth curve B to X, the free curves, that is, those whose restricted tangent bundle has vanishing higher cohomology, are particularly nice. We shall see the historical background of this conjecture, followed by the techniques that go into the proof of the quasi-split case in the analogous situation when X is a smooth scheme over a valuation ring of rank one.įebruary 8: Eric Riedl (University of Notre Dame) Recently, this conjecture has seen progress through the work of Fedorov, Panin and Česnavičius. Location: Zoom (Special Time: 11:30 AM EST)Ībstract: A conjecture of Grothendieck and Serre states that a torsor under a reductive group over a Noetherian regular scheme X is Zariski locally trivial if it is generically trivial. January 25: Arnab Kundu (Université Paris-Saclay) ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |