BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Harold Blum (Utah) DTSTART:20200508T220000Z DTEND:20200508T225000Z DTSTAMP:20260404T094752Z UID:UCLA_algebra/1 DESCRIPTION:Title: Openness of K-semistability for Fano varieties\nby Harold Blum (Utah) as part of UCLA Algebra Seminar\n\n\nAbstract\nUntil recently\ , it was unclear if there was a natural way to construct (compactified) mo duli spaces of Fano varieties. One approach to solving this problem is the K-moduli Conjecture\, which predicts that K-polystable Fano varieties of fixed dimension and volume are parametrized by a projective good moduli sp ace. In this talk\, I will survey recent progress on this conjecture and d iscuss a result with Yuchen Liu and Chenyang Xu proving the openness of K- semistability in families of Fano varieties (a step in constructing K-modu li spaces).\n LOCATION:https://stable.researchseminars.org/talk/UCLA_algebra/1/ END:VEVENT BEGIN:VEVENT SUMMARY:David Hemminger (UCLA) DTSTART:20200522T231000Z DTEND:20200523T000000Z DTSTAMP:20260404T094752Z UID:UCLA_algebra/2 DESCRIPTION:Title: Lannes's T-functor and Chow rings of classifying spaces\nb y David Hemminger (UCLA) as part of UCLA Algebra Seminar\n\n\nAbstract\nEq uivariant Chow rings\, including Chow rings of classifying spaces of algeb raic groups\, appear often in nature but are difficult to compute. Like si ngular cohomology in topology\, these Chow rings modulo a prime p carry th e additional structure of unstable modules over the Steenrod algebra. We u tilize this extra structure to refine estimates of equivariant Chow rings mod p. As a special case\, we prove an analog of Quillen's stratification theorem\, generalizing and recovering prior results of Yagita and Totaro.\ n LOCATION:https://stable.researchseminars.org/talk/UCLA_algebra/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefano Filipazzi (UCLA) DTSTART:20210506T180000Z DTEND:20210506T185000Z DTSTAMP:20260404T094752Z UID:UCLA_algebra/3 DESCRIPTION:Title: On the boundedness of elliptically fibered varieties\nby S tefano Filipazzi (UCLA) as part of UCLA Algebra Seminar\n\n\nAbstract\nIn this talk\, we will survey some ideas to address the boundedness of variet ies admitting an elliptic fibration. After introducing general ideas\, we will discuss how they apply concretely to special classes of varieties: n- folds of Kodaira dimension n-1\, and elliptic Calabi-Yau varieties. Part of this talk is based on current work in progress joint with C.D. Hacon an d R. Svaldi.\n LOCATION:https://stable.researchseminars.org/talk/UCLA_algebra/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Fumiaki Suzuki (UCLA) DTSTART:20210513T180000Z DTEND:20210513T185000Z DTSTAMP:20260404T094752Z UID:UCLA_algebra/4 DESCRIPTION:Title: An O-acyclic variety of even index\nby Fumiaki Suzuki (UCL A) as part of UCLA Algebra Seminar\n\n\nAbstract\nI will construct a famil y of Enriques surfaces parametrized by ${\\bf P}^1$ such that any multi-se ction has even degree over the base ${\\bf P}^1$. Over the function field of a complex curve\, this gives the first example of an $O$-acyclic variet y ($H^i(X\,O)=0$ for $i>0$) whose index is not equal to one\, and an affir mative answer to a question of Colliot-Thé\;lè\;ne and Voisin. I will also discuss applications to related problems\, including the inte gral Hodge conjecture and Murre's question on universality of the Abel-Jac obi maps. This is joint work with John Christian Ottem.\n LOCATION:https://stable.researchseminars.org/talk/UCLA_algebra/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Chengxi Wang (UCLA) DTSTART:20210520T180000Z DTEND:20210520T185000Z DTSTAMP:20260404T094752Z UID:UCLA_algebra/5 DESCRIPTION:Title: Varieties of general type with small volume\nby Chengxi Wa ng (UCLA) as part of UCLA Algebra Seminar\n\n\nAbstract\nBy Hacon-McKernan \, Takayama\, and Tsuji\, there is a constant r_n such that for every r at least r_n\, the r-canonical map of every n-dimensional variety of general type is birational. In this talk\, we show that r_n must grow faster than any polynomial in n by giving examples of general type with small volume in high dimensions. In particular\, we construct a klt n-fold with ample c anonical class whose volume is less than 1/2^(2^n). The klt examples shoul d be close to optimal. This is joint work with Burt Totaro.\n LOCATION:https://stable.researchseminars.org/talk/UCLA_algebra/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Charles Vial (Bielefeld) DTSTART:20210601T180000Z DTEND:20210601T185000Z DTSTAMP:20260404T094752Z UID:UCLA_algebra/6 DESCRIPTION:Title: The co-radical filtration on the Chow group of zero-cycles \nby Charles Vial (Bielefeld) as part of UCLA Algebra Seminar\n\n\nAbstrac t\nI will discuss a filtration of the Chow group of zero-cycles on a smoot h projective variety\, obtained roughly by considering the kernels of iter ates of a modified diagonal embedding of the variety. This filtration is p articularly relevant for abelian varieties and hyperkä\;hler varieties \, where it is expected to be opposite to the conjectural Bloch-Beilinson filtration. In the case of abelian varieties\, it can in fact be described explicitly in terms of the Beauville decomposition. In the case of hyperk ä\;hler varieties\, I conjecture (and prove in some cases) that the fi ltration coincides with one introduced earlier by Claire Voisin.\n LOCATION:https://stable.researchseminars.org/talk/UCLA_algebra/6/ END:VEVENT END:VCALENDAR