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SUMMARY:Harold Blum (Utah)
DTSTART;VALUE=DATE-TIME:20200508T220000Z
DTEND;VALUE=DATE-TIME:20200508T225000Z
DTSTAMP;VALUE=DATE-TIME:20230925T224726Z
UID:UCLA_algebra/1
DESCRIPTION:Title: Openness of K-semistability for Fano varieties\nby Harold Blum (U
tah) as part of UCLA Algebra Seminar\n\n\nAbstract\nUntil recently\, it wa
s unclear if there was a natural way to construct (compactified) moduli sp
aces of Fano varieties. One approach to solving this problem is the K-modu
li Conjecture\, which predicts that K-polystable Fano varieties of fixed d
imension and volume are parametrized by a projective good moduli space. In
this talk\, I will survey recent progress on this conjecture and discuss
a result with Yuchen Liu and Chenyang Xu proving the openness of K-semista
bility in families of Fano varieties (a step in constructing K-moduli spac
es).\n
LOCATION:https://researchseminars.org/talk/UCLA_algebra/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Hemminger (UCLA)
DTSTART;VALUE=DATE-TIME:20200522T231000Z
DTEND;VALUE=DATE-TIME:20200523T000000Z
DTSTAMP;VALUE=DATE-TIME:20230925T224726Z
UID:UCLA_algebra/2
DESCRIPTION:Title: Lannes's T-functor and Chow rings of classifying spaces\nby David
Hemminger (UCLA) as part of UCLA Algebra Seminar\n\n\nAbstract\nEquivaria
nt Chow rings\, including Chow rings of classifying spaces of algebraic gr
oups\, appear often in nature but are difficult to compute. Like singular
cohomology in topology\, these Chow rings modulo a prime p carry the addit
ional structure of unstable modules over the Steenrod algebra. We utilize
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://researchseminars.org/talk/UCLA_algebra/2/
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BEGIN:VEVENT
SUMMARY:Stefano Filipazzi (UCLA)
DTSTART;VALUE=DATE-TIME:20210506T180000Z
DTEND;VALUE=DATE-TIME:20210506T185000Z
DTSTAMP;VALUE=DATE-TIME:20230925T224726Z
UID:UCLA_algebra/3
DESCRIPTION:Title: On the boundedness of elliptically fibered varieties\nby Stefano
Filipazzi (UCLA) as part of UCLA Algebra Seminar\n\n\nAbstract\nIn this ta
lk\, we will survey some ideas to address the boundedness of varieties adm
itting an elliptic fibration. After introducing general ideas\, we will di
scuss how they apply concretely to special classes of varieties: n-folds o
f 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 and R. Sv
aldi.\n
LOCATION:https://researchseminars.org/talk/UCLA_algebra/3/
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SUMMARY:Fumiaki Suzuki (UCLA)
DTSTART;VALUE=DATE-TIME:20210513T180000Z
DTEND;VALUE=DATE-TIME:20210513T185000Z
DTSTAMP;VALUE=DATE-TIME:20230925T224726Z
UID:UCLA_algebra/4
DESCRIPTION:Title: An O-acyclic variety of even index\nby Fumiaki Suzuki (UCLA) as p
art of UCLA Algebra Seminar\n\n\nAbstract\nI will construct a family of En
riques surfaces parametrized by ${\\bf P}^1$ such that any multi-section h
as even degree over the base ${\\bf P}^1$. Over the function field of a co
mplex curve\, this gives the first example of an $O$-acyclic variety ($H^i
(X\,O)=0$ for $i>0$) whose index is not equal to one\, and an affirmative
answer to a question of Colliot-Thé\;lè\;ne and Voisin. I will
also discuss applications to related problems\, including the integral Ho
dge conjecture and Murre's question on universality of the Abel-Jacobi map
s. This is joint work with John Christian Ottem.\n
LOCATION:https://researchseminars.org/talk/UCLA_algebra/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chengxi Wang (UCLA)
DTSTART;VALUE=DATE-TIME:20210520T180000Z
DTEND;VALUE=DATE-TIME:20210520T185000Z
DTSTAMP;VALUE=DATE-TIME:20230925T224726Z
UID:UCLA_algebra/5
DESCRIPTION:Title: Varieties of general type with small volume\nby Chengxi Wang (UCL
A) as part of UCLA Algebra Seminar\n\n\nAbstract\nBy Hacon-McKernan\, Taka
yama\, 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 i
s birational. In this talk\, we show that r_n must grow faster than any po
lynomial in n by giving examples of general type with small volume in high
dimensions. In particular\, we construct a klt n-fold with ample canonica
l class whose volume is less than 1/2^(2^n). The klt examples should be cl
ose to optimal. This is joint work with Burt Totaro.\n
LOCATION:https://researchseminars.org/talk/UCLA_algebra/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Vial (Bielefeld)
DTSTART;VALUE=DATE-TIME:20210601T180000Z
DTEND;VALUE=DATE-TIME:20210601T185000Z
DTSTAMP;VALUE=DATE-TIME:20230925T224726Z
UID:UCLA_algebra/6
DESCRIPTION:Title: The co-radical filtration on the Chow group of zero-cycles\nby Ch
arles Vial (Bielefeld) as part of UCLA Algebra Seminar\n\n\nAbstract\nI wi
ll discuss a filtration of the Chow group of zero-cycles on a smooth proje
ctive variety\, obtained roughly by considering the kernels of iterates of
a modified diagonal embedding of the variety. This filtration is particul
arly relevant for abelian varieties and hyperkä\;hler varieties\, wher
e it is expected to be opposite to the conjectural Bloch-Beilinson filtrat
ion. In the case of abelian varieties\, it can in fact be described explic
itly in terms of the Beauville decomposition. In the case of hyperkä\;
hler varieties\, I conjecture (and prove in some cases) that the filtratio
n coincides with one introduced earlier by Claire Voisin.\n
LOCATION:https://researchseminars.org/talk/UCLA_algebra/6/
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