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BEGIN:VEVENT
SUMMARY:Gavril Farkas (Humboldt University of Berlin)
DTSTART;VALUE=DATE-TIME:20200417T180000Z
DTEND;VALUE=DATE-TIME:20200417T193000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/1
DESCRIPTION:Title: Green’s conjecture via Koszul modules\nby Gavril Farkas (Humboldt
University of Berlin) as part of Stanford algebraic geometry seminar\n\n\
nAbstract\nUsing ideas from geometric group theory we provide a novel\napp
roach to Green’s Conjecture on syzygies of canonical curves. Via a\nstro
ng vanishing result for Koszul modules we deduce that a general\ncanonical
curve of genus g satisfies Green’s Conjecture when the\ncharacteristic
is zero or at least $(g+2)/2$. Our results are new in\npositive characteri
stic (and answer positively a conjecture of Eisenbud\nand Schreyer)\, wher
eas in characteristic zero they provide a different\nproof for theorems fi
rst obtained in two landmark papers by Voisin.\nJoint work with Aprodu\, P
apadima\, Raicu and Weyman.\n
LOCATION:https://researchseminars.org/talk/agstanford/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirsten Wickelgren (Duke)
DTSTART;VALUE=DATE-TIME:20200424T180000Z
DTEND;VALUE=DATE-TIME:20200424T193000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/2
DESCRIPTION:Title: There are $160\,839 \\langle 1 \\rangle + 160\,650 \\langle -1\\rangle$
3-planes in a 7-dimensional cubic hypersurface\nby Kirsten Wickelgren
(Duke) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nIt i
s a result of Debarre--Manivel that the variety of $d$-planes on a generic
complete intersection has the expected dimension. When this dimension is
0\, the number of such $d$-planes is given by the Euler number of a vector
bundle on a Grassmannian. There are several Euler numbers from $A^1$-homo
topy theory which take a vector bundle to a bilinear form. We equate some
of these\, including those of Barge-Morel\, Kass-W.\, Déglise-Jin-Khan\,
and one suggested by M.J. Hopkins\, A. Raksit\, and J.-P. Serre using dual
ity of coherent sheaves. We establish integrality results for this Euler c
lass\, and use this to compute the Euler classes associated to arithmetic
counts of d-planes on complete intersections in projective space in terms
of topological Euler numbers over the real and complex numbers. The exampl
e in the title uses work of Finashin-Kharlamov. This is joint work with To
m Bachmann.\n
LOCATION:https://researchseminars.org/talk/agstanford/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Burt Totaro (UCLA)
DTSTART;VALUE=DATE-TIME:20200501T190000Z
DTEND;VALUE=DATE-TIME:20200501T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/3
DESCRIPTION:Title: The Hilbert scheme of infinite affine space\nby Burt Totaro (UCLA)
as part of Stanford algebraic geometry seminar\n\n\nAbstract\nI will discu
ss the Hilbert scheme of $d$ points in affine $n$-space\, with some exampl
es. This space has many irreducible components for $n$ at least 3 and is p
oorly understood. Nonetheless\, in the limit where $n$ goes to infinity\,
we show that the Hilbert scheme of $d$ points in infinite affine space ha
s a very simple homotopy type. In fact\, it has the $A^1$-homotopy type of
the infinite Grassmannian $BGL(d-1)$. Many questions remain. (Joint with
Marc Hoyois\, Joachim Jelisiejew\, Denis Nardin\, Maria Yakerson.)\n
LOCATION:https://researchseminars.org/talk/agstanford/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Borys Kadets (MIT)
DTSTART;VALUE=DATE-TIME:20200501T174500Z
DTEND;VALUE=DATE-TIME:20200501T184500Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/4
DESCRIPTION:Title: 38406501359372282063949 & all that: Monodromy of Fano problems\nby
Borys Kadets (MIT) as part of Stanford algebraic geometry seminar\n\n\nAbs
tract\nA Fano problem is an enumerative problem of counting linear subspac
es on complete intersections. Some familiar examples are finding the numbe
r of lines on a cubic surface\, and finding the number of lines on the int
ersection of $2$ quadrics in $\\mathbb{P}^4$. Suppose a general complete i
ntersection of type $[d]=(d_1\, ...\, d_s)$ in $\\mathbb{P}^n$ contains fi
nitely many $r$-planes. To this Fano problem\, described by the triple $([
d]\,n\,r)$\, one can associate a group $G_{[d]\,n\,r}$\, the monodromy gro
up of the Fano problem\; it describes the permutations of $r$-planes on a
complete intersection of type $[d]$\, as the complete intersection varies.
I will show that $G_{[d]\,n\,r}$ is either a symmetric or an alternating
group for almost all Fano problems with an explicit list of exceptions\, a
nd describe the monodromy groups of the exceptional problems. An interesti
ng feature of this computation is that it avoids any local calculations\,
which seems necessary to get the result in full generality. This is joint
work with Sachi Hashimoto.\n\nDiscussion during the talk will be at https:
//tinyurl.com/2020-05-01-a\n(and this will be deleted in 3 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julie Desjardins (Toronto)
DTSTART;VALUE=DATE-TIME:20200508T174500Z
DTEND;VALUE=DATE-TIME:20200508T184500Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/5
DESCRIPTION:Title: Density of rational points on a family of del Pezzo surface of degree 1
\nby Julie Desjardins (Toronto) as part of Stanford algebraic geometry
seminar\n\n\nAbstract\nLet $k$ be a number field and $X$ an algebraic var
iety over $k$. We want to study the set of $k$-rational points $X(k)$. For
example\, is $X(k)$ empty? If not\, is it dense with respect to the Zaris
ki topology? Del Pezzo surfaces are classified by their degrees $d$ (an in
teger between 1 and 9). Manin and various authors proved that for all del
Pezzo surfaces of degree $>1$ is dense provided that the surface has a $k$
-rational point (that lies outside a specific subset of the surface for $d
=2$). For $d=1$\, the del Pezzo surface always has a rational point. Howev
er\, we don't know it the set of rational points is Zariski-dense. In this
talk\, I present a result that is joint with Rosa Winter in which we prov
e the density of rational points for a specific family of del Pezzo surfac
es of degree 1 over $k$.\n\nThe discussion for Julie Desjardins’s talk i
s taking place not in zoom-chat\, but at https://tinyurl.com/stagMay08a (a
nd will be deleted after 3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bjorn Poonen (MIT)
DTSTART;VALUE=DATE-TIME:20200508T190000Z
DTEND;VALUE=DATE-TIME:20200508T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/6
DESCRIPTION:Title: Bertini irreducibility theorems via statistics\nby Bjorn Poonen (MI
T) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nLet $X \\
subset \\mathbb{P}^n$ be a geometrically irreducible subvariety\nwith $\\d
im X \\ge 2$\, over any field.\nLet $\\check{\\mathbb{P}}^n$ be the moduli
space\nparametrizing hyperplanes $H \\subset \\mathbb{P}^n$.\nLet $L \\su
bset \\check{\\mathbb{P}}^n$ be the locus parametrizing $H$\nfor which $H
\\cap X$ is geometrically irreducible.\nThe classical Bertini irreducibili
ty theorem states that\n$L$ contains a dense open subset of $\\check{\\mat
hbb{P}}^n$\,\nso the bad locus $L' := \\mathbb{P}^n - L$ satisfies $\\dim
L' \\le n-1$.\nBenoist improved this to $\\dim L' \\le \\operatorname{codi
m} X + 1$.\n\nWe describe a new way to prove and generalize such theorems\
,\nby reducing to the case of a finite field\nand studying the mean and va
riance\nof the number of points of a random hyperplane section.\nThis is j
oint work with Kaloyan Slavov.\n\nThe discussion for Bjorn Poonen’s talk
is taking place not in the zoom-chat\, but at https://tinyurl.com/stagMay
08b (and will be deleted after 3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rohini Ramadas (Brown)
DTSTART;VALUE=DATE-TIME:20200515T174500Z
DTEND;VALUE=DATE-TIME:20200515T184500Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/7
DESCRIPTION:Title: The locus of post-critically finite maps in the moduli space of self-ma
ps of $\\mathbb{P}^n$\nby Rohini Ramadas (Brown) as part of Stanford a
lgebraic geometry seminar\n\n\nAbstract\nA degree $d>1$ self-map $f$ of $\
\mathbb{P}^n$ is called post critically finite (PCF) if its critical hyper
surface $C_f$ is pre-periodic for $f$\, that is\, if there exist integers
$r \\geq 0$ and $k>0$ such that $f^{r+k}(C_f)$ is contained in $f^{r}(C_f)
$. \n\nI will discuss the question: what does the locus of PCF maps look l
ike as a subset of the moduli space of degree $d$ maps on $\\mathbb{P}^n$?
I’ll give a survey of many known results and some conjectures in dimens
ion $1$. I’ll then present a result\, joint with Patrick Ingram and Jose
ph Silverman\, that suggests that in dimensions two or greater\, PCF maps
are comparatively scarce in the moduli space of all self-maps.\n\nThe disc
ussion for Rohini Ramadas’s talk is taking place not in zoom-chat\, but
at https://tinyurl.com/2020-05-15-rr (and will be deleted after 3-7 days)
.\n
LOCATION:https://researchseminars.org/talk/agstanford/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Silversmith (Northeastern)
DTSTART;VALUE=DATE-TIME:20200515T190000Z
DTEND;VALUE=DATE-TIME:20200515T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/8
DESCRIPTION:Title: Studying subschemes of affine/projective space via matroids\nby Rob
Silversmith (Northeastern) as part of Stanford algebraic geometry seminar
\n\n\nAbstract\nGiven a homogeneous ideal $I$ in a polynomial ring\, one m
ay apply the following combinatorial operation: for each degree $d$\, make
a list of all subsets $S$ of the set of degree-$d$ monomials such that $S
$ is the set of nonzero coefficients of an element of $I$. For each $d$\,
this set of subsets is a combinatorial object called a matroid. As $d$ var
ies\, the resulting sequence of matroids is called the tropicalization of
$I$.\n\nI will discuss some of the many questions one can ask about tropic
alizations of ideals\, and how they are related to some classical question
s in combinatorial algebraic geometry\, such as the classification of toru
s orbits on Hilbert schemes of points in $\\mathbb{C}^2$. Some unexpected
combinatorial objects appear: e.g. when studying tropicalizations of subsc
hemes of $\\mathbb{P}^1$\, one is led to Schur polynomials and binary neck
laces.\n
LOCATION:https://researchseminars.org/talk/agstanford/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenyang Xu (MIT)
DTSTART;VALUE=DATE-TIME:20200522T180000Z
DTEND;VALUE=DATE-TIME:20200522T193000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/9
DESCRIPTION:Title: K-moduli of Fano varieties\nby Chenyang Xu (MIT) as part of Stanfor
d algebraic geometry seminar\n\n\nAbstract\nOne main theme of the algebrai
c K-stability theory of Fano varieties is to use it to construct moduli sp
aces of Fano varieties. This has once been beyond algebraic geometers’ i
magination\, but K-stability is proven to give the right framework. By no
w except the properness\, all other main ingredients have essentially been
established\, based on the recent development of our understanding of K-s
tability theory and other inputs. In this talk\, we will give an outline o
f the construction\, with the focus on the essential role that the new cha
racterisation of K-stability plays\, and its connection to minimal model p
rogram theory.\n
LOCATION:https://researchseminars.org/talk/agstanford/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bhargav Bhatt (University of Michigan)
DTSTART;VALUE=DATE-TIME:20200605T190000Z
DTEND;VALUE=DATE-TIME:20200605T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/11
DESCRIPTION:Title: A p-adic Riemann-Hilbert functor and vanishing theorems\nby Bharga
v Bhatt (University of Michigan) as part of Stanford algebraic geometry se
minar\n\n\nAbstract\nI will discuss an ongoing project (joint with Jacob L
urie) aiming to construct a $p$-adic Riemann-Hilbert functor\, attaching c
oherent complexes to constructible sheaves (with coefficients in $\\mathbb
{F}_p$\, $\\mathbb{Z}_p$ or $\\mathbb{Q}_p$) on a compact algebraic variet
y over a $p$-adic field. When combined with results on constructible sheav
es\, these yields vanishing theorems (old and new) on the coherent side.\n
\nThe discussion for Bhargav Bhatt’s talk is taking place not in zoom-ch
at\, but at https://tinyurl.com/2020-06-05-bb (and will be deleted after
3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wei Ho (University of Michigan)
DTSTART;VALUE=DATE-TIME:20200612T190000Z
DTEND;VALUE=DATE-TIME:20200612T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/12
DESCRIPTION:Title: Splitting Brauer classes\nby Wei Ho (University of Michigan) as pa
rt of Stanford algebraic geometry seminar\n\n\nAbstract\nGiven a Brauer cl
ass over a field\, what types of varieties split it? Or more geometrically
\, can we say anything about the varieties that map to a given Brauer-Seve
ri variety? In this talk\, we will discuss some open questions related to
splitting Brauer classes. For example\, we will review some classical alge
bro-geometric constructions that produce genus one curves splitting low in
dex Brauer classes ((old) joint work with A.J. de Jong)\, and we will expl
ain why a Brauer class of any index is split by a torsor under an abelian
variety (joint work with M. Lieblich).\n\nThe discussion for Wei Ho’s ta
lk is taking place not in zoom-chat\, but at https://tinyurl.com/2020-06-1
2-wh (and will be deleted after 3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuchen Liu (Yale)
DTSTART;VALUE=DATE-TIME:20200529T174500Z
DTEND;VALUE=DATE-TIME:20200529T184500Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/13
DESCRIPTION:Title: Moduli spaces of quartic hyperelliptic K3 surfaces via K-stability
\nby Yuchen Liu (Yale) as part of Stanford algebraic geometry seminar\n\n\
nAbstract\nA general polarized hyperelliptic K3 surfaces of degree 4 is a
double cover of $\\mathbf{P\n}^ 1 \\times \\mathbf{P}^1$ branched along a
bidegree $(4\,4)$ curve. Classically there are two compactifications of th
eir moduli spaces: one is the GIT quotient of $(4\,4)$ curves\, the other
is the Baily-Borel compactification of their periods. We show that K-stabi
lity provides a natural modular interpolation between these two compactifi
cations. This provides a new aspect toward a recent result of Laza-O'Grady
. Based on joint work in progress with K. Ascher and K. DeVleming.\n\nThe
discussion for Yuchen Liu’s talk is taking place not in zoom-chat\, but
at https://tinyurl.com/2020-05-29-yl (and will be deleted after 3-7 days).
\n
LOCATION:https://researchseminars.org/talk/agstanford/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margaret Bilu (NYU)
DTSTART;VALUE=DATE-TIME:20200612T174500Z
DTEND;VALUE=DATE-TIME:20200612T184500Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/14
DESCRIPTION:Title: Arithmetic and motivic statistics via zeta functions\nby Margaret
Bilu (NYU) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nT
he Grothendieck group of varieties over a field $k$ is the quotient of the
free abelian group on isomorphism classes of algebraic varieties over k b
y the so-called cut-and-paste relations. Many results in number theory hav
e a natural motivic analogue which can be formulated in the Grothendieck r
ing of varieties. For example\, Poonen's finite field Bertini theorem has
a motivic counterpart due to Vakil and Wood\, though none of the two state
ments can be deduced from the other. We describe a conjectural way to unif
y the number-theoretic and motivic statements (when the base field is fini
te) in this and other examples\, and will provide some evidence towards it
. A key step is to reformulate everything in terms of convergence of zeta
functions of varieties in several different topologies. This is joint work
with Ronno Das and Sean Howe.\n
LOCATION:https://researchseminars.org/talk/agstanford/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Christian Ottem (University of Oslo)
DTSTART;VALUE=DATE-TIME:20200710T190000Z
DTEND;VALUE=DATE-TIME:20200710T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/15
DESCRIPTION:Title: On (2\,3)-fourfolds\nby John Christian Ottem (University of Oslo)
as part of Stanford algebraic geometry seminar\n\n\nAbstract\nI will expla
in how tropical degenerations and birational specialization techniques can
be used in rationality problems. In particular\, I will apply these techn
iques to study quartic fivefolds and complete intersections of a quadric a
nd a cubic in $\\mathbb{P}^6$. This is joint work with Johannes Nicaise.\n
LOCATION:https://researchseminars.org/talk/agstanford/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Escobar (Washington University St. Louis)
DTSTART;VALUE=DATE-TIME:20200717T190000Z
DTEND;VALUE=DATE-TIME:20200717T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/16
DESCRIPTION:Title: Wall-crossing phenomena for Newton-Okounkov bodies\nby Laura Escob
ar (Washington University St. Louis) as part of Stanford algebraic geometr
y seminar\n\n\nAbstract\nA Newton-Okounkov body is a convex set associated
to a projective variety\, equipped with a valuation. These bodies general
ize the theory of Newton polytopes. Work of Kaveh-Manon gives an explicit
link between tropical geometry and Newton-Okounkov bodies. We use this lin
k to describe a wall-crossing phenomenon for Newton-Okounkov bodies. This
is joint work with Megumi Harada.\n\nThe discussion for Laura Escobar Vega
’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/20
20-07-17-lev (and will be deleted after 3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brendan Hassett (Brown University / ICERM)
DTSTART;VALUE=DATE-TIME:20200724T190000Z
DTEND;VALUE=DATE-TIME:20200724T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/17
DESCRIPTION:Title: Symbols\, birational geometry\, and computations\nby Brendan Hasse
tt (Brown University / ICERM) as part of Stanford algebraic geometry semin
ar\n\n\nAbstract\nWe are interested in G-birational equivalence of varieti
es where G is a finite group. Kontsevich-Tschinkel and Kresch-Tschinkel ha
ve developed symbol formalism to construct invariants that show rich inter
nal structure. We present examples of computations of these invariants for
varieties in small dimensions\, illustrating how they compare to existing
classification techniques.\n
LOCATION:https://researchseminars.org/talk/agstanford/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Abramovich (Brown University)
DTSTART;VALUE=DATE-TIME:20200731T193000Z
DTEND;VALUE=DATE-TIME:20200731T203000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/18
DESCRIPTION:Title: Resolution and logarithmic resolution via weighted blowings up\nby
Dan Abramovich (Brown University) as part of Stanford algebraic geometry
seminar\n\n\nAbstract\nThis lecture combines resolution of singularities\,
logarithmic geometry and algebraic stacks. I will not assume familiarity
neither with resolution of singularities nor with logarithmic geometry. I
report on work with Temkin and Wlodarczyk and work of Quek. Resolving sing
ularities in families requires logarithmic geometry. Surprisingly\, trying
to do this canonically forces us to use stack-theoretic modifications. Su
rprisingly\, stack-theoretic modifications provides an efficient iterative
resolution method in which the worst singularities are blown up without r
egard to the history. Not so surprisingly\, to make exceptional divisors c
ooperate we need logarithmic geometry again.\n
LOCATION:https://researchseminars.org/talk/agstanford/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Larson (Stanford University)
DTSTART;VALUE=DATE-TIME:20200821T190000Z
DTEND;VALUE=DATE-TIME:20200821T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/19
DESCRIPTION:Title: Brill--Noether theory over the Hurwitz space\nby Hannah Larson (St
anford University) as part of Stanford algebraic geometry seminar\n\n\nAbs
tract\nLet $C$ be a curve of genus $g$. A fundamental problem in the theor
y of algebraic curves is to understand maps of $C$ to projective space of
dimension r of degree d. When the curve $C$ is general\, the moduli space
of such maps is well-understood by the main theorems of Brill-Noether theo
ry. However\, in nature\, curves $C$ are often encountered already equipp
ed with a map to some projective space\, which may force them to be specia
l in moduli. The simplest case is when $C$ is general among curves of fix
ed gonality. Despite much study over the past three decades\, a similarly
complete picture has proved elusive in this case. In this talk\, I will d
iscuss recent joint work with Eric Larson and Isabel Vogt that completes s
uch a picture\, by proving analogs of all of the main theorems of Brill--N
oether theory in this setting.\n\nThe discussion for Hannah Larson’s tal
k is taking place not in zoom-chat\, but at https://tinyurl.com/2020-08-21
-hl (and will be deleted after 3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Olsson (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20200828T190000Z
DTEND;VALUE=DATE-TIME:20200828T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/20
DESCRIPTION:Title: Determinants and deformation theory of perfect complexes\nby Marti
n Olsson (UC Berkeley) as part of Stanford algebraic geometry seminar\n\n\
nAbstract\nIn this talk I will discuss the interplay between the deformati
on theory of perfect complexes\, determinants\, and traces. I will discuss
\, in particular\, the verification of an expected compatibility among the
se that has been used in various places in the literature. For the speake
r this project also provided an entry-point to the world of $\\infty$-cate
gories\, and I will try to motivate why such a perspective is useful. Thi
s is joint work with Max Lieblich.\n
LOCATION:https://researchseminars.org/talk/agstanford/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Webb (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20200918T190000Z
DTEND;VALUE=DATE-TIME:20200918T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/21
DESCRIPTION:Title: Virtual cycle on the moduli space of maps to a complete intersection\nby Rachel Webb (UC Berkeley) as part of Stanford algebraic geometry se
minar\n\n\nAbstract\nA driving question in Gromov-Witten theory is to rela
te the invariants of a complete intersection to the invariants of the ambi
ent variety. In genus-zero this can often be done with a ``twisted theory\
,'' but this fails in higher genus. Several years ago\, Chang-Li presented
the moduli space of p-fields as a piece of the solution to the higher-gen
us problem\, constructing the virtual cycle on the space of maps to the qu
intic 3-fold as a cosection localized virtual cycle on a larger moduli spa
ce (the space of p-fields). Their result is analogous to the classical sta
tement that the Euler class of a vector bundle is the class of the zero lo
cus of a generic section. I will discuss work joint with Qile Chen and Fel
ix Janda where we extend Chang-Li's result to a more general setting\, a s
etting that includes standard Gromov-Witten theory of smooth orbifold targ
ets and quasimap theory of GIT targets.\n
LOCATION:https://researchseminars.org/talk/agstanford/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Eur (Stanford)
DTSTART;VALUE=DATE-TIME:20200904T190000Z
DTEND;VALUE=DATE-TIME:20200904T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/22
DESCRIPTION:Title: Simplicial generation of Chow rings of matroids\nby Chris Eur (Sta
nford) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nWe pr
esent a new set of generators for the Chow ring of a matroid. We show tha
t these generators behave like base-point-free divisors by establishing th
at (i) they correspond to matroid operations that combinatorially mirror h
yperplane pullbacks\, and (ii) the volume polynomial with respect to these
generators satisfies Hodge-type inequalities. We thereby generalize Post
nikov's results on generalized permutohedra\, and also give a simplified p
roof of the combinatorially relevant portion of the Hodge theory of matroi
ds developed by Adiprasito-Huh-Katz. No knowledge of matroids will be ass
umed. This is joint work with Spencer Backman and Connor Simpson.\n\nThe
discussion for Christopher Eur’s talk is taking place not in zoom-chat\,
but at https://tinyurl.com/2020-09-04-ce (and will be deleted after 3-7
days).\n
LOCATION:https://researchseminars.org/talk/agstanford/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Kobin (UC Santa Cruz)
DTSTART;VALUE=DATE-TIME:20200911T190000Z
DTEND;VALUE=DATE-TIME:20200911T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/23
DESCRIPTION:Title: Zeta functions and decomposition spaces\nby Andrew Kobin (UC Santa
Cruz) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nZeta
functions show up everywhere in math these days. While some recent work ha
s brought homotopical methods into the theory of zeta functions\, there is
in fact a lesser-known zeta function that is native to homotopy theory. N
amely\, every suitably finite decomposition space (aka 2-Segal space) admi
ts an abstract zeta function as an element of its incidence algebra. In th
is talk\, I will show how many 'classical' zeta functions from number theo
ry and algebraic geometry can be realized in this homotopical framework\,
and outline some preliminary work in progress with Julie Bergner and Matt
Feller towards a motivic version of the above story.\n\nThe discussion for
Andrew Kobin’s talk is taking place not in zoom-chat\, but at https://t
inyurl.com/2020-09-11-ak (and will be deleted after 3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Thomas (Imperial College London)
DTSTART;VALUE=DATE-TIME:20200925T190000Z
DTEND;VALUE=DATE-TIME:20200925T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/24
DESCRIPTION:Title: Square root Euler classes and counting sheaves on Calabi-Yau 4-folds\nby Richard Thomas (Imperial College London) as part of Stanford algebr
aic geometry seminar\n\n\nAbstract\nI will explain a nice characteristic c
lass of $SO(2n\,\\mathbf{C})$ bundles in both Chow cohomology and K-theory
\, and how to localise it to the zeros of an isotropic section. This build
s on work of Edidin-Graham\, Polishchuk-Vaintrob\, Anderson and many other
s.\n\nThis can be used to construct an algebraic virtual cycle (and virtua
l structure sheaf) on moduli spaces of stable sheaves on Calabi-Yau 4-fold
s.\nIt recovers the real derived differential geometry virtual cycle of Bo
risov-Joyce but has nicer properties\, like a torus localisation formula.
Joint work with Jeongseok Oh (KIAS).\n\nThe discussion for Richard Thomas
’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/20
20-09-25-rt (and will be deleted after 3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jarod Alper (University of Washington)
DTSTART;VALUE=DATE-TIME:20201023T190000Z
DTEND;VALUE=DATE-TIME:20201023T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/25
DESCRIPTION:Title: Coherent completeness and the local structure of algebraic stacks\
nby Jarod Alper (University of Washington) as part of Stanford algebraic g
eometry seminar\n\n\nAbstract\nFormal GAGA is an important theorem in form
al geometry which categorizes coherent sheaves on a scheme proper over a c
omplete local noetherian ring in terms of compatible families of coherent
sheaves on the thickenings of its central fiber. We will discuss generali
zations of this result to algebraic stacks and explain how such results ca
n be used to prove local structure theorems for algebraic stacks. After r
eviewing joint work with Hall and Rydh which establishes a satisfactory re
sult in characteristic 0\, we will discuss partial progress in joint work
with Hall and Lim on extending this result to positive characteristic.\n
LOCATION:https://researchseminars.org/talk/agstanford/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Landesman (Stanford)
DTSTART;VALUE=DATE-TIME:20201030T190000Z
DTEND;VALUE=DATE-TIME:20201030T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/26
DESCRIPTION:Title: The Torelli map restricted to the hyperelliptic locus\nby Aaron La
ndesman (Stanford) as part of Stanford algebraic geometry seminar\n\n\nAbs
tract\nThe classical Torelli theorem states that the Torelli map\, sending
a curve to\nits Jacobian\, is injective on points. However\, the Torelli
map is not injective \non tangent spaces at points corresponding to hypere
lliptic curves. This leads to\nthe natural question: If one restricts the
Torelli map to the locus of\nhyperelliptic curves\, is it then an immersio
n?\n\nWe give a complete answer to this question\, starting out by describ
ing the\nclassical history and several surprising foundational gaps in the
\nliterature. Along the way\, we will learn about Shinichi Mochizuki's val
uative\ncriterion for locally closed immersions and its relation to Brian
Conrad's\nlibrary app idea.\n\nThe discussion for Aaron Landesman’s talk
is taking place not in zoom-chat\, but at https://tinyurl.com/2020-10-3
0-al (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juliette Bruce (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20201002T190000Z
DTEND;VALUE=DATE-TIME:20201002T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/27
DESCRIPTION:Title: The top weight cohomology of $A_g$\nby Juliette Bruce (UC Berkeley
) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nI will dis
cuss recent work calculating the top weight cohomology of the moduli space
$A_g$ of principally polarized abelian varieties of dimension $g$ for sma
ll values of $g$. The key idea is that this piece of cohomology is encoded
combinatorially via the relationship between the boundary complex of a co
mpactification of $A_g$ and the moduli space of tropical abelian varieties
. This is joint work with Madeline Brandt\, Melody Chan\, Margarida Melo\,
Gwyneth Moreland\, and Corey Wolfe.\n
LOCATION:https://researchseminars.org/talk/agstanford/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Antieau (Northwestern)
DTSTART;VALUE=DATE-TIME:20210115T200000Z
DTEND;VALUE=DATE-TIME:20210115T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/28
DESCRIPTION:Title: Genus 1 curves in twisted projective spaces\nby Ben Antieau (North
western) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nDoe
s every Severi—Brauer variety contain a (possibly singular) genus 1 curv
e? This basic question was asked by David Saltman and Pete Clark and answe
red in low dimensions by Johan de Jong and Wei Ho. I will explain somethin
g of the history of the problem as well as recent joint work with Asher Au
el where we show\, with the help of a nice observation of David Saltman\,
that the answer is `yes’ for twisted forms of $\\mathbb{P}^r$ for $r=6$
over global fields.\n\nThe discussion for Ben Antieau’s talk is taking p
lace not in zoom-chat\, but at https://tinyurl.com/2021-01-15-ba (and wi
ll be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karen Smith (University of Michigan)
DTSTART;VALUE=DATE-TIME:20201009T190000Z
DTEND;VALUE=DATE-TIME:20201009T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/29
DESCRIPTION:Title: Extremal Singularities in Prime Characteristic\nby Karen Smith (Un
iversity of Michigan) as part of Stanford algebraic geometry seminar\n\n\n
Abstract\nWhat is the most singular possible singularity? What can we say
about its geometric and algebraic properties? This seemingly naive questio
n has a sensible answer in characteristic $p$.\nThe "F-pure threshold\," w
hich is an analog of the log canonical threshold\, can be used to "measur
e" how bad a singularity is. The F-pure threshold is a numerical invariant
of a point on (say) a hypersurface---a positive rational number that is
1 at any smooth point (or more generally\, any F-pure point) but less tha
n one in general\, with "more singular" points having smaller F-pure thres
holds. We explain a recently proved lower bound on the F-pure threshold i
n terms of the multiplicity of the singularity. We also show that there is
a nice class of hypersurfaces---which we call "Extremal hypersurfaces"---
for which this bound is achieved. These have very nice (extreme!) geometri
c properties. For example\, the affine cone over a non Frobenius split cub
ic surface of characteristic two is one example of an "extremal singularit
y". Geometrically\, these are the only cubic surfaces with the property th
at *every* triple of coplanar lines on the surface meets in a single point
(rather than a "triangle" as expected)---a very extreme property indeed.\
n\nThe discussion for Karen Smith’s talk is taking place not in zoom-cha
t\, but at https://tinyurl.com/2020-10-09-ks (and will be deleted after ~
3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Fantechi (SISSA)
DTSTART;VALUE=DATE-TIME:20201016T190000Z
DTEND;VALUE=DATE-TIME:20201016T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/30
DESCRIPTION:Title: Infinitesimal deformations of semi-smooth varieties\nby Barbara Fa
ntechi (SISSA) as part of Stanford algebraic geometry seminar\n\n\nAbstrac
t\nThis is a report on joint work with Marco Franciosi and Rita Pardini. G
eneralizing the standard definition for surfaces\, we call a variety $X$ (
over an alg closed field of char not 2) {\\em semi-smooth} if its singular
ities are \\'etale locally either $uv=0$ or $u^2=v^2w$ (pinch point)\; equ
ivalently\, if $X$ can be obtained by gluing a smooth variety (the normali
zation of $X$) along an involution (with smooth quotient) on a smooth divi
sor. They are the simplest singularities for non normal\, KSBA-stable surf
aces.\nFor a semi-smooth variety $X$\, we calculate the tangent sheaf $T_X
$ and the infinitesimal deformations sheaf ${\\mathcal T}^1_X:={\\mathcal
E}xt^1(\\Omega_X\,\\mathcal O_X)$ which determine the infinitesimal deform
ations and smoothability of $X$.\nAs an application\, we use Tziolas' form
al smoothability criterion to show that every stable semi-smooth Godeaux s
urface (classified by Franciosi\, Pardini and S\\"onke) corresponds to a s
mooth point of the KSBA moduli space\, in the closure of the open locus of
smooth surfaces.\n\nThe discussion for Barbara Fantechi’s talk is takin
g place not in zoom-chat\, but at https://tinyurl.com/2020-10-16-bf (and
will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akhil Mathew (University of Chicago)
DTSTART;VALUE=DATE-TIME:20201106T200000Z
DTEND;VALUE=DATE-TIME:20201106T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/31
DESCRIPTION:Title: \\'Etale K-theory and motivic cohomology\nby Akhil Mathew (Univers
ity of Chicago) as part of Stanford algebraic geometry seminar\n\n\nAbstra
ct\nTwo key features of algebraic K-theory are its failure to\nsatisfy \\'
etale descent\, and its motivic filtration in terms of higher\nChow groups
in the case of smooth schemes over a field (but expected\nmore generally)
. I will explain a description of \\'etale K-theory\,\nwhich is the univer
sal approximation to K-theory that satisfies\n\\'etale descent\; this is j
oint work with Dustin Clausen. Moreover\,\nfollowing the recent work of Bh
att--Morrow--Scholze on topological\ncyclic homology\, I will also explain
a construction of (an analog of)\nthe motivic filtration on \\'etale K-th
eory (and \\'etale motivic\ncohomology) for arbitrary schemes (work in pro
gress with Bhargav Bhatt\nand Dustin Clausen).\n
LOCATION:https://researchseminars.org/talk/agstanford/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taylor Dupuy (University of Vermont)
DTSTART;VALUE=DATE-TIME:20201113T200000Z
DTEND;VALUE=DATE-TIME:20201113T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/32
DESCRIPTION:Title: Abelian Varieties Over Finite Fields in the LMFDB\nby Taylor Dupuy
(University of Vermont) as part of Stanford algebraic geometry seminar\n\
n\nAbstract\nI will talk about things around the LMFDB database of isogeny
classes of abelian varieties over finite fields (and maybe even about iso
morphism classes). \n\nThese could include: \n--"Sato-Ain't" distributions
\, \n--weird Tate classes\, \n--Bizzaro Hodge co-levels (and very strange
Ax-Katz/Chevalley-Warning type congruences with fractional exponent!)\, \n
--the counter-example to the conjecture of Ahmadi-Shparlinski\,\n--what we
know about angle ranks vs galois groups vs Newton polygons\,\n--new conje
ctures \n\nThe database and "census" is joint work with Kiran Kedlaya\, Da
vid Roe\, and Christelle Vincent (currently available on the arxiv). The w
ork on Tate classes is ongoing with Kiran Kedlaya and David Zureick-Brown.
\n
LOCATION:https://researchseminars.org/talk/agstanford/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rahul Pandharipande (ETH Zurich)
DTSTART;VALUE=DATE-TIME:20201204T200000Z
DTEND;VALUE=DATE-TIME:20201204T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/33
DESCRIPTION:Title: The top Chern class of the Hodge bundle and the log Chow ring of the m
oduli space of curves\nby Rahul Pandharipande (ETH Zurich) as part of
Stanford algebraic geometry seminar\n\n\nAbstract\nI will first explain ho
w the top Chern class of the Hodge bundle is very complicated and then\nI
will explain how it is very simple. Joint work with S. Molcho and J. Schmi
tt.\n
LOCATION:https://researchseminars.org/talk/agstanford/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takumi Murayama (Princeton University)
DTSTART;VALUE=DATE-TIME:20210122T200000Z
DTEND;VALUE=DATE-TIME:20210122T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/34
DESCRIPTION:Title: Grothendieck's localization problem\nby Takumi Murayama (Princeton
University) as part of Stanford algebraic geometry seminar\n\n\nAbstract\
nLet $f\\colon Y \\rightarrow X$ be a proper flat morphism of algebraic v
arieties. Grothendieck and Dieudonné showed that the smoothness of $f$ ca
n be detected at closed points of $X$. Using André–Quillen homology\, A
ndré showed that when $X$ is excellent\, the same conclusion holds when $
f$ is a closed flat morphism between locally noetherian schemes. We give a
new proof of André's result using a version of resolutions of singularit
ies due to Gabber. Our method gives a uniform treatment of Grothendieck's
localization problem and resolves various new cases of this problem\, whic
h asks whether similar statements hold for other local properties of morph
isms.\n
LOCATION:https://researchseminars.org/talk/agstanford/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soumya Sankar (The Ohio State University)
DTSTART;VALUE=DATE-TIME:20210129T200000Z
DTEND;VALUE=DATE-TIME:20210129T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/35
DESCRIPTION:Title: Derived equivalences of gerbey curves\nby Soumya Sankar (The Ohio
State University) as part of Stanford algebraic geometry seminar\n\n\nAbst
ract\nThe question of whether derived equivalences determine a variety has
been studied widely. Antieau\, Krashen and Ward (AKW) studied the questio
n of when two genus 1 curves are derived equivalent. A gerbey curve is a G
_m gerbe over a usual curve. In joint work with Libby Taylor\, we explore
the question of when two gerbey genus 1 curves are derived equivalent. In
this talk\, I will give some background on derived equivalences of varieti
es\, how they relate to derived equivalences of stacks and then talk about
some extensions of the results of AKW.\n\nThe discussion for Soumya Sanka
r’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/2
021-01-29-ss (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Keel (UT Austin)
DTSTART;VALUE=DATE-TIME:20210205T200000Z
DTEND;VALUE=DATE-TIME:20210205T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/36
DESCRIPTION:Title: Berkovich geometry and mirror symmetry\nby Sean Keel (UT Austin) a
s part of Stanford algebraic geometry seminar\n\n\nAbstract\nI will explai
n my Berkovich geometric construction\, joint with Tony Yu\, of the mirror
to an affine log CY variety\, with the aim of convincing you of its simpl
icity\, both in concept\, and technical detail.\n
LOCATION:https://researchseminars.org/talk/agstanford/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laure Flapan (Michigan State)
DTSTART;VALUE=DATE-TIME:20210212T200000Z
DTEND;VALUE=DATE-TIME:20210212T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/37
DESCRIPTION:Title: Fano manifolds associated to hyperkähler manifolds\nby Laure Flap
an (Michigan State) as part of Stanford algebraic geometry seminar\n\n\nAb
stract\nMany of the known examples of hyperkähler manifolds arise from ge
ometric constructions that begin with a Fano manifold whose cohomology loo
ks like that of a K3 surface. In this talk\, I will focus on a program who
se goal is to reverse this process\, namely to begin with a hyperkähler m
anifold and from it produce geometrically a Fano manifold. This is joint w
ork in progress with K. O’Grady\, E. Macrì\, and G. Saccà.\n\nThe disc
ussion for Laure Flapan’s talk is taking place not in zoom-chat\, but at
https://tinyurl.com/2021-02-12-lf (and will be deleted after ~3-7 days)
.\n
LOCATION:https://researchseminars.org/talk/agstanford/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Izzet Coskun (University of Illinois at Chicago)
DTSTART;VALUE=DATE-TIME:20210219T200000Z
DTEND;VALUE=DATE-TIME:20210219T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/38
DESCRIPTION:Title: Algebraic Hyperbolicity and Lang-type loci in hypersurfaces\nby Iz
zet Coskun (University of Illinois at Chicago) as part of Stanford algebra
ic geometry seminar\n\n\nAbstract\nIn this talk\, I will discuss joint wor
k with Eric Riedl on algebraic hyperbolicity and Lang-type loci. I will de
scribe an improvement of G. Xu's genus bounds which allow us to prove the
algebraic hyperbolicity of very general quintic surfaces. The same techniq
ue allows us to obtain the classification of algebraically hyperbolic sur
faces in certain toric threefolds. Finally\, I will discuss Lang-type loci
for algebraic hyperbolicity in very general hypersurfaces.\n\nThe discuss
ion for Izzet Coskun’s talk is taking place not in zoom-chat\, but at h
ttps://tinyurl.com/2021-02-19-ic (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Baker (Georgia Tech)
DTSTART;VALUE=DATE-TIME:20210402T190000Z
DTEND;VALUE=DATE-TIME:20210402T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/39
DESCRIPTION:Title: Pastures\, Polynomials\, and Matroids\nby Matt Baker (Georgia Tech
) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nA pasture
is\, roughly speaking\, a field in which addition is allowed to be both mu
ltivalued and partially undefined. Pastures are natural objects from the p
oint of view of $\\mathbf{F}_1$ geometry and Lorscheid’s theory of order
ed blueprints. I will describe a theorem about univariate polynomials over
pastures which simultaneously generalizes Descartes’ Rule of Signs and
the theory of Newton polygons. Conjecturally\, there should be a similar p
icture for several polynomials in several variables generalizing tropical
intersection theory. I will also describe a novel approach to the theory o
f matroid representations which revolves around a canonical universal past
ure\, called the “foundation”\, that one can attach to any matroid. Th
is is joint work with Oliver Lorscheid.\n\nThe discussion for Matt Baker
’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/2
021-04-02-mb (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jihao Liu (University of Utah)
DTSTART;VALUE=DATE-TIME:20210226T200000Z
DTEND;VALUE=DATE-TIME:20210226T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/40
DESCRIPTION:Title: Complements and local singularities in birational geometry\nby Jih
ao Liu (University of Utah) as part of Stanford algebraic geometry seminar
\n\n\nAbstract\nThe theory of complements was introduced by Shokurov when
he investigated log flips of threefolds\, and plays an important role in m
any areas in birational geometry\, e.g. boundedness of Fano varieties\, lo
g Calabi-Yau fibrations\, K-stability theory\, etc. In a recent work\, we
prove a complements conjecture of Shokurov\, and we apply this result to t
he study of local singularities in birational geometry. Part of this talk
is joint work with J. Han and V.V. Shokurov.\n
LOCATION:https://researchseminars.org/talk/agstanford/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arend Bayer (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20210305T200000Z
DTEND;VALUE=DATE-TIME:20210305T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/41
DESCRIPTION:Title: Fano varieties: from derived categories to geometry via stability\
nby Arend Bayer (University of Edinburgh) as part of Stanford algebraic ge
ometry seminar\n\n\nAbstract\nA Fano variety $X$ can be reconstructed from
its bounded derived category $D^b(X)$. How to use this fact to extract\nc
oncrete geometric information from $D^b(X)$? \nIn this talk\, I will surve
y one such approach\, via certain subcategories of $D^b(X)$ called Kuznets
ov components\, and stability conditions. Via moduli spaces of stable obje
cts inside Kuznetsov components\, this naturally leads to the reconstructi
on of many natural moduli spaces classically associated to $X$. \nIn addit
ion to results by a number of authors for Fano threefolds\, I will also di
scuss work in progress (joint with Bertram\, Macri\, Perry) for cubic four
folds. Combined with studying Brill-Noether loci\, this leads to the const
ruction of special surfaces on an infinite sequence of Hassett-special cub
ic fourfolds. In some cases\, this leads to a natural reinterpretation of
recent proofs of rationality of such cubic fourfolds via wall-crossing.\n
LOCATION:https://researchseminars.org/talk/agstanford/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuuji Tanaka (Kyoto University)
DTSTART;VALUE=DATE-TIME:20210313T000000Z
DTEND;VALUE=DATE-TIME:20210313T010000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/42
DESCRIPTION:Title: On the virtual Euler characteristics of the moduli spaces of semistab
le sheaves on a complex projective surface\nby Yuuji Tanaka (Kyoto Uni
versity) as part of Stanford algebraic geometry seminar\n\n\nAbstract\n(wa
rning: notice unusual time)\n\nI'll deliver an overview of studies on the
virtual Euler \ncharacteristics of the moduli spaces of semistable sheave
s on a complex \nprojective surface. The virtual Euler characteristic is a
refinement of \nthe topological Euler characteristic for a proper scheme
with a perfect \nobstruction theory，which was introduced by Fantechi and
Goettsche\, and \nby Ciocan-Fontanine and Kapranov. Motivated by the work
of Vafa and \nWitten in the early 90's on the S-duality conjecture in N=4
super \nYang-Mills theory in physics\, Goettsche and Kool conjectured tha
t the \ngenerating function of the virtual Euler characteristics\, or othe
r \nvariants\, of the moduli space of semistable sheaves on a complex \npr
ojective surfaces could be written in terms of modular forms (and the \nSe
iberg-Witten invariants)\, and they verified it in examples. I'll \ndescri
be the recent progress around this topic\, starting by mentioning \nmore b
ackground materials such as the studies on the topological Euler \ncharact
eristics of the moduli spaces.\n
LOCATION:https://researchseminars.org/talk/agstanford/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geoff Smith (UIC)
DTSTART;VALUE=DATE-TIME:20210507T190000Z
DTEND;VALUE=DATE-TIME:20210507T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/43
DESCRIPTION:Title: Normal bundles of rational curves and separably rationally connected v
arieties\nby Geoff Smith (UIC) as part of Stanford algebraic geometry
seminar\n\n\nAbstract\nIn positive characteristic\, there are two differen
t notions of rational connectedness: a variety can be rationally connected
or separably rationally connected (SRC). SRC varieties share many of the
nice properties that rationally connected varieties have in characteristic
0. But\, while it is conjectured that smooth Fano varieties are SRC\, it
is only known that they are rationally connected. In the last decade\, sev
eral mathematicians have come up with different ways to show that general
Fano complete intersections are SRC. In this talk\, I'll explain this stor
y\, and then discuss an approach Izzet Coskun and I are using to show that
other sorts of varieties are SRC by comparing the normal bundle of a rati
onal curve on a variety and its normal bundle to some subvariety containin
g it. For instance\, I'll show that a Fano complete intersection of hypers
urfaces each of degree at least 3 on a Grassmannian is SRC.\n\nThe discuss
ion for Geoff Smith’s talk is taking place not in zoom-chat\, but at htt
ps://tinyurl.com/2021-05-07-gs (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolas Kuhn (Stanford University)
DTSTART;VALUE=DATE-TIME:20210326T190000Z
DTEND;VALUE=DATE-TIME:20210326T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/44
DESCRIPTION:Title: A blowup formula for virtual Donaldson invariants\nby Nikolas Kuhn
(Stanford University) as part of Stanford algebraic geometry seminar\n\n\
nAbstract\nDonaldson invariants were a breakthrough in the study of smooth
four-manifolds when they were introduced in the 1980s and even found appl
ications to the classification of compact complex surfaces. With the adven
t of the virtual fundamental class\, it has become possible to give an ele
gant purely algebraic definition when working on a complex projective surf
ace X\, which was done by T. Mochizuki. The two definitions agree in most
cases\, and whether they agree in general comes down to knowing a blowup f
ormula for Mochizuki's invariants. We present a direct proof of such a blo
wup formula that generalizes earlier results by Göttsche-Nakajima-Yoshiok
a and has applications to other types of enumerative invariants of X. This
is joint work with Yuuji Tanaka.\n\nThe discussion for Nikolas Kuhn’s t
alk is taking place not in zoom-chat\, but at https://tinyurl.com/2021-03-
26-nk (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joachim Jelisiejew (University of Warsaw)
DTSTART;VALUE=DATE-TIME:20210514T190000Z
DTEND;VALUE=DATE-TIME:20210514T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/45
DESCRIPTION:Title: Pathologies on the Hilbert scheme of points\nby Joachim Jelisiejew
(University of Warsaw) as part of Stanford algebraic geometry seminar\n\n
\nAbstract\nIn the talk I will discuss recent advances in our understandin
g of singularities and components of the Hilbert scheme of points on a hig
her-dimensional smooth variety. The key underlying tool\, interesting on i
ts own\, is the Bialynicki-Birula decomposition in the singular setting. I
will mention some open questions.\n
LOCATION:https://researchseminars.org/talk/agstanford/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Molcho (ETH)
DTSTART;VALUE=DATE-TIME:20210409T190000Z
DTEND;VALUE=DATE-TIME:20210409T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/46
DESCRIPTION:Title: The strict transform in logarithmic geometry\nby Sam Molcho (ETH)
as part of Stanford algebraic geometry seminar\n\n\nAbstract\nLet $(X\,D)$
be a pair of a smooth variety and a normal crossings divisor. The loci of
curves that admit a map to X with prescribed tangency along D exhibit som
e pathological behavior: for instance\, the locus of maps to a product $(X
\\times Y\, D \\times E)$ does not coincide with the intersection of the
loci of maps to $(X\,D)$ and $(Y\,E)$. In this talk I want to explain how
the root of such pathologies arises from the difference between taking the
strict and total of a cycle under a very special kind of birational map\,
called a logarithmic modification. I will discuss how for a logarithmic m
odification\, the strict transform of a cycle has a modular interpretation
\, and how its difference with the total transform can be explicitly compu
ted\, in terms of certain piecewise polynomial functions on a combinatoria
l shadow of the original spaces\, the tropicalization. Time permitting\, I
will discuss some applications -- for instance\, how these calculations i
mply that loci of curves with a map to a toric variety lie in the tautolog
ical ring.\n
LOCATION:https://researchseminars.org/talk/agstanford/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samir Canning (UC San Diego)
DTSTART;VALUE=DATE-TIME:20210416T190000Z
DTEND;VALUE=DATE-TIME:20210416T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/47
DESCRIPTION:Title: The Chow rings of $M_7$\, $M_8$\, and $M_9$\nby Samir Canning (UC
San Diego) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nT
he rational Chow ring of the moduli space of smooth curves is known when t
he genus is at most $6$ by work of Mumford ($g=2$)\, Faber ($g=3$\, $4$)\,
Izadi ($g=5$)\, and Penev-Vakil ($g=6$). In each case\, it is generated b
y the tautological classes. On the other hand\, van Zelm has shown that th
e bielliptic locus is not tautological when $g=12$. In recent joint work w
ith Hannah Larson\, we show that the Chow rings of $M_7$\, $M_8$\, and $M_
9$ are generated by tautological classes\, which determines the Chow ring
by work of Faber. I will explain an overview of the proof with an emphasis
on the special geometry of curves of low genus and low gonality.\n\nThe s
ynchronous discussion for Sam Canning’s talk is taking place not in zoom
-chat\, but at https://tinyurl.com/2021-04-16-sc (and will be deleted afte
r ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Temkin (HUJI)
DTSTART;VALUE=DATE-TIME:20210423T190000Z
DTEND;VALUE=DATE-TIME:20210423T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/48
DESCRIPTION:Title: Logarithmic resolution of singularities\nby Michael Temkin (HUJI)
as part of Stanford algebraic geometry seminar\n\n\nAbstract\nI will talk
about a recent series of works with Abramovich and Wlodarczyk\, where a lo
garithmic analogue of the classical resolution of singularities of schemes
in characteristic zero is constructed. Already for usual schemes\, the lo
garithmic algorithm is faster and more functorial\, though as a price one
has to work with log smooth ambient orbifolds rather than smooth ambient m
anifolds. But the main achievement is that essentially the same algorithm
resolves log schemes and even morphisms of log schemes\, yielding a major
generalization of various semistable reduction theorems.\n\nThe synchronou
s discussion for Michael Temkin’s talk is taking place not in zoom-chat\
, but at https://tinyurl.com/2021-04-23-mt (and will be deleted after ~3-
7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Remy van Dobben de Bruyn (Princeton and IAS)
DTSTART;VALUE=DATE-TIME:20210430T190000Z
DTEND;VALUE=DATE-TIME:20210430T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/49
DESCRIPTION:Title: Constructing varieties with prescribed Hodge numbers modulo m in posit
ive characteristic\nby Remy van Dobben de Bruyn (Princeton and IAS) as
part of Stanford algebraic geometry seminar\n\n\nAbstract\nThe inverse Ho
dge problem asks which possible Hodge diamonds can occur for smooth projec
tive varieties. While this is a very hard problem in general\, Paulsen and
Schreieder recently showed that in characteristic 0 there are no restrict
ions on the modulo $m$ Hodge numbers\, besides the usual symmetries. In jo
int work with Matthias Paulsen\, we extend this to positive characteristic
\, where the story is more intricate.\n\nThe synchronous discussion for Re
my van Dobben de Bruyn’s talk is taking place not in zoom-chat\, but at
https://tinyurl.com/2021-04-30-rvddb (and will be deleted after ~3-7 day
s).\n
LOCATION:https://researchseminars.org/talk/agstanford/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Katz (Ohio State)
DTSTART;VALUE=DATE-TIME:20210521T190000Z
DTEND;VALUE=DATE-TIME:20210521T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/50
DESCRIPTION:Title: Iterated p-adic integration on semistable curves\nby Eric Katz (Oh
io State) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nHo
w do you integrate a 1-form on an algebraic curve over the p-adic numbers?
One can integrate locally\, but because the topology is totally disconnec
ted\, it's not possible to perform analytic continuation. For good reducti
on curves\, this question was answered by Coleman who introduced analytic
continuation by Frobenius. For bad reduction curves\, there are two notion
s of integration: a local theory that is easy to compute\; and a global si
ngle-valued theory that is useful for number theoretic applications. We di
scuss the relationship between these integration theories\, concentrating
on the p-adic analogue of Chen's iterated integration which is important f
or the non-Abelian Chabauty method. We explain how to use combinatorial id
eas\, informed by tropical geometry and Hodge theory\, to compare the two
integration theories and outline an explicit approach to computing these i
ntegrals. This talk will start from the beginning of the story and require
s no background besides some fluency in algebraic geometry and topology. T
his is joint work with Daniel Litt.\n\nThe synchronous discussion for Eric
Katz’s talk is taking place not in zoom-chat\, but at https://tinyurl.c
om/2021-05-21-ek (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Ulirsch (Goethe-Universität Frankfurt)
DTSTART;VALUE=DATE-TIME:20210604T190000Z
DTEND;VALUE=DATE-TIME:20210604T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/51
DESCRIPTION:Title: Tropical geometry and logarithmic compactifications of reductive algeb
raic groups\nby Martin Ulirsch (Goethe-Universität Frankfurt) as part
of Stanford algebraic geometry seminar\n\n\nAbstract\nIn this talk I will
present two approaches towards the tropicalization of a reductive algebra
ic group $G$\, one via Mumford’s toroidal compactification\, the other v
ia de Concini and Procesi’s wonderful compacitification. The Bruhat-Tits
building of G and its root system will play a crucial role in both approa
ches. Using these insights I will propose two corresponding logarithmic co
mpactifications of $G$. The first approach will provide us with a new loga
rithmic perspective on toric (and more generally parabolic) vector bundles
\, the other will allow us to study the geometry of the free group charact
er variety at infinity\, thereby providing evidence for the geometric $P=W
$ conjecture. Depending on the preferences of the audience I might also en
gage in some wild speculations concerning a yet-to-be-discovered logarithm
ic incarnation of Simpson’s non-abelian Hodge correspondence. Parts of t
his talk are based on ongoing joint work with Lorenzo Fantini and Alex Kur
onya.\n\nThe synchronous discussion for Martin Ulirsch’s talk is taking
place not in zoom-chat\, but at https://tinyurl.com/2021-06-04-mu (and wi
ll be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dhruv Ranganathan (Cambridge)
DTSTART;VALUE=DATE-TIME:20210528T190000Z
DTEND;VALUE=DATE-TIME:20210528T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/52
DESCRIPTION:Title: Constructing logarithmic moduli\nby Dhruv Ranganathan (Cambridge)
as part of Stanford algebraic geometry seminar\n\n\nAbstract\nIn recent wo
rk\, Davesh Maulik and I built a theory “logarithmic” Donaldson-Thomas
invariants\, and in the process we constructed a new version of the Hilbe
rt scheme of curves: one that is sensitive to the manner in which subschem
es interact with a chosen simple normal crossings divisor. There are two i
nputs. The first is a piece of geometry\, which comes from study torus orb
it closures in Hilbert schemes\, following ideas of Kapranov and Tevelev.
The second is an exceedingly useful piece of formalism\, in the shape of t
ropical moduli spaces and an associated collection of Artin stacks. I’ll
try to explain how to combine these ingredients to get what we get\, and
also share some general lessons that we learned while working this stuff o
ut.\n\nThe synchronous discussion for Dhruv Ranganathan’s talk is taking
place not in zoom-chat\, but at https://tinyurl.com/2021-05-28-dr (and
will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lena Ji (Princeton/Michigan)
DTSTART;VALUE=DATE-TIME:20210611T190000Z
DTEND;VALUE=DATE-TIME:20210611T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/53
DESCRIPTION:Title: The Noether–Lefschetz theorem\nby Lena Ji (Princeton/Michigan) a
s part of Stanford algebraic geometry seminar\n\n\nAbstract\nThe classical
Noether–Lefschetz theorem says that for a very general surface $S$ of d
egree $ \\geq 4$ in $\\mathbf{P}^3$ over the complex numbers\, the restric
tion map from the divisor class group on $\\mathbf{P}^3$ to $S$ is an isom
orphism. In this talk\, we give an elementary proof of Noether–Lefschetz
. We do not use any Hodge theory\, cohomology\, or monodromy. This argumen
t has the additional advantage that it works over fields of arbitrary char
acteristic and for singular varieties (for Weil divisors).\n\nThe synchron
ous discussion for Lena Ji’s talk is taking place not in zoom-chat\, but
at https://tinyurl.com/2021-06-11-lj (and will be deleted after ~3-7 day
s).\n
LOCATION:https://researchseminars.org/talk/agstanford/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Scavia (UBC)
DTSTART;VALUE=DATE-TIME:20210730T190000Z
DTEND;VALUE=DATE-TIME:20210730T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/54
DESCRIPTION:Title: The Grothendieck ring of stacks\nby Federico Scavia (UBC) as part
of Stanford algebraic geometry seminar\n\n\nAbstract\nThe Grothendieck rin
g of algebraic stacks was introduced by T. Ekedahl in \n2009\, following u
p on work of other authors. It is a generalization of the \nGrothendieck r
ing of varieties. For every linear algebraic group $G$\, we may \nconsider
the class of its classifying stack $BG$ in this ring. Computing the \ncla
ss of $BG$ is related to the famous rationality problem for fields of \n$G
$-invariants (Noether's problem). I will give a brief introduction to the
\nGrothendieck ring of stacks\, and then talk about some of my results in
this \narea.\n\nThe synchronous discussion for Federico Scavia’s talk is
taking place not in zoom-chat\, but at https://tinyurl.com/2021-07-30-fs
(and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raymond Cheng (Columbia)
DTSTART;VALUE=DATE-TIME:20210716T190000Z
DTEND;VALUE=DATE-TIME:20210716T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/55
DESCRIPTION:Title: $q$-bic Hypersurfaces\nby Raymond Cheng (Columbia) as part of Stan
ford algebraic geometry seminar\n\n\nAbstract\nLet’s count: 1\, $q$\, $q
+1$\; here\, $q$ is a power of a prime $p$. In this talk\, I will sketch a
n analogy between the geometry of a class of hypersurfaces over a field of
positive characteristic $p$\, which I call $q$-bic hypersurfaces\, and th
e geometry of low degree hypersurfaces\, such as quadrics and cubics\, ove
r the complex numbers. For instance\, a smooth $q$-bic threefold has a smo
oth Fano surface of lines\, and the intermediate Jacobian of the threefold
is isogenous to the Albanese of the Fano surface.\n
LOCATION:https://researchseminars.org/talk/agstanford/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ritvik Ramkumar (Berkeley)
DTSTART;VALUE=DATE-TIME:20210806T190000Z
DTEND;VALUE=DATE-TIME:20210806T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/56
DESCRIPTION:Title: On the tangent space to the Hilbert scheme of points in $\\mathbf{P}^3
$\nby Ritvik Ramkumar (Berkeley) as part of Stanford algebraic geometr
y seminar\n\n\nAbstract\nThe Hilbert scheme of $n$ points in $\\mathbf{P}^
2$ is smooth of dimension $2n$ and the tangent space to any monomial subsc
heme admits a pleasant combinatorial description. On the other hand\, the
Hilbert scheme of $n$ points in $\\mathbf{P}^3$ is almost always singular
and there is a conjecture by Briançon and Iarrobino describing the monomi
al subscheme with the largest tangent space dimension. In this talk we wil
l generalize the combinatorial description to the Hilbert scheme of points
in $\\mathbf{P}^3$\, revealing new symmetries in the tangent space to any
monomial subscheme. We will use these symmetries to prove many cases of t
he conjecture and strengthen previous bounds on the dimension of the Hilbe
rt scheme. In addition\, we will also characterize smooth monomial points
on the Hilbert scheme. This is joint work with Alessio Sammartano.\n
LOCATION:https://researchseminars.org/talk/agstanford/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elden Elmanto (Harvard)
DTSTART;VALUE=DATE-TIME:20210813T190000Z
DTEND;VALUE=DATE-TIME:20210813T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/57
DESCRIPTION:Title: The completely decomposed arc topology and motivic applications\nb
y Elden Elmanto (Harvard) as part of Stanford algebraic geometry seminar\n
\n\nAbstract\nI will introduce a Grothendieck topology\, the cdarc topolog
y\, discovered in joint work with Marc Hoyois\, Ryomei Iwasa and Shane Kel
ly which is a completely decomposed counterpart to Bhatt and Mathew's arc
topology. It is a non-noetherian analog of Suslin-Voevodsky's cdh topology
and is thus useful in the study of K-theory and algebraic cycles. I will
focus on two applications to algebraic cycles and K-theory:\n\n1) an excis
ion result for algebraic cycles (joint with Hoyois\, Iwasa and Kelly) and\
n\n2) a motivic refinement of the equivalence $L_{cdh}K = KH$ (joint with
Tom Bachmann and Matthew Morrow).\n\nThe synchronous discussion for Elden
Elmanto’s talk is taking place not in zoom-chat\, but at https://tinyurl
.com/2021-08-13-ee (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ming Hao Quek (Brown University)
DTSTART;VALUE=DATE-TIME:20210924T190000Z
DTEND;VALUE=DATE-TIME:20210924T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/58
DESCRIPTION:Title: Logarithmic resolution of singularities via multi-weighted blow-ups\nby Ming Hao Quek (Brown University) as part of Stanford algebraic geome
try seminar\n\n\nAbstract\nWe revisit the theorem of Hironaka that one can
resolve the singularities of a singular\, reduced closed subscheme X of a
smooth scheme Y over a field of characteristic zero\, such that the singu
lar locus of X is transformed to a simple normal crossings divisor. We pro
pose a computable yet efficient algorithm\, which accomplishes this by tak
ing successive proper transforms along a sequence of multi-weighted blow-u
ps\, where at each step\, the worst singular locus is blown up\, and one w
itnesses an immediate improvement in singularities. Here\, multi-weighted
blow-ups are necessary to ensure that the ambient space remains smooth (in
fact\, also logarithmically smooth with respect to the logarithmic struct
ure associated to the exceptional divisors)\, although one has to work mor
e broadly with Artin stacks. This is joint work with Dan Abramovich.\n
LOCATION:https://researchseminars.org/talk/agstanford/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Yakerson (ETH)
DTSTART;VALUE=DATE-TIME:20210910T190000Z
DTEND;VALUE=DATE-TIME:20210910T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/59
DESCRIPTION:Title: Twisted K-theory in motivic homotopy theory\nby Maria Yakerson (ET
H) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nIn this t
alk\, we will speak about algebraic K-theory of vector bundles twisted by
a Brauer class\, and its place in motivic homotopy theory. In particular\,
we will discuss a new approach to the motivic spectral sequence for twist
ed K-theory\, constructed earlier by Bruno Kahn and Marc Levine. The talk
is based on joint work in progress\, with Elden Elmanto and Denis Nardin.\
n
LOCATION:https://researchseminars.org/talk/agstanford/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Graber (Caltech)
DTSTART;VALUE=DATE-TIME:20210723T190000Z
DTEND;VALUE=DATE-TIME:20210723T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/60
DESCRIPTION:Title: Virtual localization for relative obstruction theories and stable log
maps\nby Tom Graber (Caltech) as part of Stanford algebraic geometry s
eminar\n\n\nAbstract\nI will discuss how to formulate and prove a localiza
tion theorem for the virtual fundamental class of a moduli space with a re
lative perfect obstruction theory over a singular base. In the motivating
example of the moduli space of stable log maps\, I will explain how this
leads to sums over types of tropical curves and cycle classes on moduli sp
aces of curves related to the double ramification cycle that have been of
recent interest in other contexts.\n
LOCATION:https://researchseminars.org/talk/agstanford/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Denis Nardin (Regensburg)
DTSTART;VALUE=DATE-TIME:20210709T190000Z
DTEND;VALUE=DATE-TIME:20210709T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/61
DESCRIPTION:Title: Quadratic forms on rings and the homotopy limit problem\nby Denis
Nardin (Regensburg) as part of Stanford algebraic geometry seminar\n\n\nAb
stract\nHermitian K-theory is an invariant of rings (or\, more generally\,
schemes) constructed using the behaviour of quadratic forms. In recent ye
ars significant progress has been made in the study of it for rings where
2 is not invertible. In this talk I will give an introduction to the subje
ct from a modern perspective\, using as a guide work in progress on the ho
motopy limit problem\, which essentially is asking how much information we
can recover from just knowing the algebraic K-theory of the ring.\n
LOCATION:https://researchseminars.org/talk/agstanford/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joaquín Moraga (Princeton University)
DTSTART;VALUE=DATE-TIME:20211008T190000Z
DTEND;VALUE=DATE-TIME:20211008T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/62
DESCRIPTION:Title: Toroidalization principles for klt singularities\nby Joaquí
n Moraga (Princeton University) as part of Stanford algebraic geometry sem
inar\n\n\nAbstract\nIn this talk\, I will discuss some recent progress on
toroidalization principles for klt singularities. These toroidalizations
allow us to prove theorems about the topology of klt singularities and abo
ut their minimal log discrepancies. If time permits\, I will also explain
the relationship between these toroidalization principles and the termina
tion of flips.\n
LOCATION:https://researchseminars.org/talk/agstanford/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maddie Weinstein (Stanford University)
DTSTART;VALUE=DATE-TIME:20211015T190000Z
DTEND;VALUE=DATE-TIME:20211015T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/64
DESCRIPTION:Title: Algebraic Geometry of Curvature and Matrices with Partitioned Eigenval
ues\nby Maddie Weinstein (Stanford University) as part of Stanford alg
ebraic geometry seminar\n\n\nAbstract\nThis talk is a combined discussion
of an upcoming paper with Paul Breiding and Kristian Ranestad on the enume
rative geometry of the curvature of algebraic varieties and a past paper c
alled Real Symmetric Matrices with Partitioned Eigenvalues. Curvature is a
n important concept in differential geometry. We approach curvature from t
he perspective of algebraic geometry\, studying the critical curvature loc
us of an algebraic variety. A curvature feature known as an umbilical poin
t occurs when the eigenvalues of the second fundamental form coincide. Thi
s leads us to a discussion of the real algebraic variety of matrices with
eigenvalue multiplicities determined by a partition.\n
LOCATION:https://researchseminars.org/talk/agstanford/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Han-Bom Moon (Fordham/Stanford)
DTSTART;VALUE=DATE-TIME:20210917T190000Z
DTEND;VALUE=DATE-TIME:20210917T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/65
DESCRIPTION:Title: Derived category of moduli of vector bundles\nby Han-Bom Moon (For
dham/Stanford) as part of Stanford algebraic geometry seminar\n\n\nAbstrac
t\nI will present recent progress on the structure of the derived category
of the moduli space of stable vector bundles on a curve. This talk is bas
ed on ongoing joint work with Kyoung-Seog Lee.\n
LOCATION:https://researchseminars.org/talk/agstanford/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arnav Tripathy (Stanford University)
DTSTART;VALUE=DATE-TIME:20211001T190000Z
DTEND;VALUE=DATE-TIME:20211001T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/66
DESCRIPTION:Title: Line bundles in equivariant elliptic cohomology\nby Arnav Tripathy
(Stanford University) as part of Stanford algebraic geometry seminar\n\n\
nAbstract\nGiven a compact Lie group G acting on a space X\, the G-equivar
iant elliptic cohomology of X is naturally a scheme Ell_G(X) (with a map d
own to the moduli space of G-bundles on elliptic curves). Given a G-equiva
riant vector bundle V on X\, one obtains an interesting line bundle Thom(V
) on Ell_G(X). Both topologists and string theorists have predicted that g
iven two vector bundles V_1\, V_2 whose first Chern classes both vanish an
d whose second Chern classes agree\, the resulting line bundles Thom(V_1)
and Thom(V_2) should agree in Pic(Ell_G(X)). I'll describe how the theory
of pushforwards in topology gives rise to this subtle question in algebrai
c geometry\, and I hope to indicate in broad strokes the proof of this con
jecture. This is joint work with D. Berwick-Evans.\n
LOCATION:https://researchseminars.org/talk/agstanford/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohammed Abouzaid (Columbia University)
DTSTART;VALUE=DATE-TIME:20211105T190000Z
DTEND;VALUE=DATE-TIME:20211105T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/67
DESCRIPTION:Title: What can symplectic topology tell us about algebraic varieties?\nb
y Mohammed Abouzaid (Columbia University) as part of Stanford algebraic ge
ometry seminar\n\nLecture held in 383-N.\n\nAbstract\nI will begin by brie
fly recalling the relationship between\ncomplex projective algebraic geome
try and symplectic topology\, which\ngoes through Kaehler manifolds. I wil
l then survey results from the\nend of the last century\, largely due to S
eidel and McDuff\, about the\nsymplectic topology of Hamiltonian fibration
s over the 2-sphere\, and\ntheir consequences for smooth projective maps o
ver the projective\nline. Finally\, I will indicate some recent advances i
n this area\,\nincluding the use of methods of Floer homotopy theory to\nr
efine our knowledge about the topology of these spaces.\n
LOCATION:https://researchseminars.org/talk/agstanford/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kai Behrend (UBC)
DTSTART;VALUE=DATE-TIME:20211112T200000Z
DTEND;VALUE=DATE-TIME:20211112T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/68
DESCRIPTION:Title: Donaldson-Thomas theory of the quantum Fermat quintic\nby Kai Behr
end (UBC) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nWe
study non-commutative projective varieties in the sense of Artin-Zhang\,
which are given by non-commutative homogeneous coordinate rings\, which ar
e finite over their centre. We construct moduli spaces of stable modules
for these\, and construct a symmetric obstruction theory in the CY3-case.
This gives deformation invariants of Donaldson-Thomas type. The simplest
example is the Fermat quintic in quantum projective space\, where the coor
dinates commute up to carefully chosen 5th roots of unity. We explore the
moduli theory of finite length modules\, which mixes features of the Hilbe
rt scheme of commutative 3-folds\, and the representation theory of quiver
s with potential. This is mostly work of Yu-Hsiang Liu\, with contributio
ns by myself and Atsushi Kanazawa.\n
LOCATION:https://researchseminars.org/talk/agstanford/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renzo Cavalieri (Colorado State University)
DTSTART;VALUE=DATE-TIME:20211119T200000Z
DTEND;VALUE=DATE-TIME:20211119T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/69
DESCRIPTION:Title: The integral Chow ring of $M_{0}(\\mathbb{P}^r\,d)$\nby Renzo Cava
lieri (Colorado State University) as part of Stanford algebraic geometry s
eminar\n\n\nAbstract\nWe give an efficient presentation of the Chow ring w
ith integral coefficients of the open part of the moduli space of rational
maps of odd degree to projective space. A less fancy description of this
space has its closed points correspond to equivalence classes of $(r+1)$-t
uples of degree $d$ polynomials in one variable with no common positive de
gree factor. We identify this space as a $GL(2\,\\mathbb{C})$ quotient of
an open set in a projective space\, and then obtain a (highly redundant) p
resentation by considering an envelope of the complement. A combinatorial
analysis then leads us to eliminating a large number of relations\, and to
express the remaining ones in generating function form for all dimensions
. The upshot of this work is to observe the rich combinatorial structure c
ontained in the Chow rings of these moduli spaces as the degree and the ta
rget dimension vary. This is joint work with Damiano Fulghesu.\n\nThe sync
hronous discussion for Renzo Cavalieri’s talk is taking place not in zoo
m-chat\, but at https://tinyurl.com/2021-11-19-rc (and will be deleted aft
er ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Olander (Columbia University)
DTSTART;VALUE=DATE-TIME:20211210T200000Z
DTEND;VALUE=DATE-TIME:20211210T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/70
DESCRIPTION:Title: Semiorthogonal decompositions and dimension\nby Noah Olander (Colu
mbia University) as part of Stanford algebraic geometry seminar\n\n\nAbstr
act\nA conjecture of Orlov predicts that we can recover the dimension of a
smooth quasi-projective variety from its derived category via the Rouquie
r dimension. We explain the meaning of the conjecture and some things we k
now about it\, then we explain the proof of a weakened version. We use thi
s to prove a fact predicted by Orlov’s conjecture: If the derived catego
ry of X appears as a component of a semiorthogonal decomposition of the d
erived category of Y (X\,Y smooth proper varieties) then the dimension of
X is at most the dimension of Y.\n\nThe synchronous discussion for Noah Ol
ander’s talk is taking place not in zoom-chat\, but at https://tinyurl.c
om/2021-12-10-no (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Esser (UCLA)
DTSTART;VALUE=DATE-TIME:20211203T200000Z
DTEND;VALUE=DATE-TIME:20211203T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/71
DESCRIPTION:Title: Varieties of general type with doubly exponential asymptotics\nby
Louis Esser (UCLA) as part of Stanford algebraic geometry seminar\n\n\nAbs
tract\nBy a theorem of Hacon–McKernan\, Takayama\, and Tsuji\, for every
$n$ there is a constant $r_n$ for which every smooth variety $X$ of dimen
sion $n$ of general type has birational pluricanonical maps $|mK_X|$ for $
m \\geq r_n$. In joint work with Burt Totaro and Chengxi Wang (see https:
//arxiv.org/abs/2109.13383)\, we show that the constants $r_n$ grow at lea
st doubly exponentially. Conjecturally\, it's expected that the optimal b
ound is in fact doubly exponential. We do this by finding weighted projec
tive hypersurfaces of general type with extreme behavior: this includes ex
amples of very small volume and many vanishing plurigenera. We also consi
der the analogous questions for other classes of varieties and provide som
e conjecturally optimal examples. For instance\, we conjecture the termin
al Fano variety of minimal volume and the canonical Calabi-Yau variety of
minimal volume in each dimension.\n\nThe synchronous discussion for Louis
Esser’s talk is taking place not in zoom-chat\, but at https://tinyurl.c
om/2021-12-03-le (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ziquan Zhuang (MIT)
DTSTART;VALUE=DATE-TIME:20211217T200000Z
DTEND;VALUE=DATE-TIME:20211217T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/72
DESCRIPTION:Title: Properness of the K-moduli space\nby Ziquan Zhuang (MIT) as part o
f Stanford algebraic geometry seminar\n\n\nAbstract\nK-stability is an alg
ebraic condition that characterizes the existence of Kahler-Einstein metri
cs on Fano varieties. Recently there has been a lot of work on the constru
ction of the K-moduli space\, i.e. a good moduli space parametrizing K-pol
ystable Fano varieties. Motivated by results in differential geometry\, it
is conjectured that this K-moduli space is proper and projective. In this
talk\, I'll discuss some recent progress in birational geometry that lead
s to a full solution of this conjecture. Based on joint work with Yuchen L
iu and Chenyang Xu.\n\nThe synchronous discussion for Ziquan Zhuang’s ta
lk is taking place not in zoom-chat\, but at https://tinyurl.com/2021-12-1
7-zz (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chelsea Walton (Rice)
DTSTART;VALUE=DATE-TIME:20220121T200000Z
DTEND;VALUE=DATE-TIME:20220121T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/73
DESCRIPTION:Title: Representation theory of elliptic algebras\nby Chelsea Walton (Ric
e) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nIn this t
alk\, I will discuss how to use algebro-geometric and Poisson geometric me
thods to study the representation theory of noncommutative algebras that a
re ‘close’ to being commutative. Such algebras will include the 3- and
the 4-dimensional Sklyanin algebras\, which are noncommutative analogues
of polynomial algebras whose behavior is governed by a certain elliptic cu
rve. This will be based on joint work with Xingting Wang and Milen Yakimov
available in PLMS (2019) and Selecta Math (2021). I also aim to keep the
presentation as down-to-earth as possible so that everybody will have fun.
\n\nThe synchronous discussion for Chelsea Walton’s talk is taking place
not in zoom-chat\, but at https://tinyurl.com/2022-01-21-cw (and will be
deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Clader (SFSU)
DTSTART;VALUE=DATE-TIME:20220114T200000Z
DTEND;VALUE=DATE-TIME:20220114T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/74
DESCRIPTION:Title: Permutohedral complexes and rational curves with cyclic action\nby
Emily Clader (SFSU) as part of Stanford algebraic geometry seminar\n\n\nA
bstract\nAlthough the moduli space of genus-zero curves is not toric\, it
shares an intriguing amount of the combinatorial structure that a toric va
riety would enjoy. In fact\, by adjusting the moduli problem slightly\, o
ne finds a moduli space that is indeed toric\, known as Losev-Manin space.
The associated polytope is the permutohedron\, which also encodes the gr
oup-theoretic structure of the symmetric group. Batyrev and Blume general
ized this story by constructing a type-B version of Losev-Manin space\, wh
ose associated polytope is a signed permutohedron that relates to the grou
p of signed permutations. In joint work with C. Damiolini\, D. Huang\, S.
Li\, and R. Ramadas\, we carry out the next stage of generalization\, def
ining a family of moduli spaces of rational curves with Z_r action encoded
by an associated "permutohedral complex" for a more general complex refle
ction group\, which specializes when r=2 to Batyrev and Blume's moduli spa
ce.\n\nThe synchronous discussion for Emily Clader’s talk is taking plac
e not in zoom-chat\, but at https://tinyurl.com/2022-01-14-ec (and will be
deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Madeline Brandt (Brown)
DTSTART;VALUE=DATE-TIME:20220204T200000Z
DTEND;VALUE=DATE-TIME:20220204T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/75
DESCRIPTION:Title: Top Weight Cohomology of $A_g$\nby Madeline Brandt (Brown) as part
of Stanford algebraic geometry seminar\n\n\nAbstract\nI will discuss a re
cent project in computing the top weight cohomology of the moduli space $A
_g$ of principally polarized abelian varieties of dimension $g$ for small
values of $g$. This piece of the cohomology is controlled by the combinato
rics of the boundary strata of a compactification of $A_g$. Thus\, it can
be computed combinatorially. This is joint work with Juliette Bruce\, Melo
dy Chan\, Margarida Melo\, Gwyneth Moreland\, and Corey Wolfe.\n\nThe sync
hronous discussion for Madeline Brandt’s talk is taking place not in zoo
m-chat\, but at https://tinyurl.com/2022-02-04-mb (and will be deleted aft
er ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allen Knutson (Cornell)
DTSTART;VALUE=DATE-TIME:20220128T200000Z
DTEND;VALUE=DATE-TIME:20220128T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/76
DESCRIPTION:Title: Resolutions of Richardson varieties\, stable curves\, and dual simplic
ial spheres\nby Allen Knutson (Cornell) as part of Stanford algebraic
geometry seminar\n\n\nAbstract\nThe combinatorics of a simple normal cross
ings divisor determines a "dual" simplicial complex. Kollár and Xu showed
that when this divisor is anticanonical\, the simplicial complex has the
rational homology of a sphere. I'll construct two resolutions-of-singulari
ties of Richardson varieties (a slight generalization of Schubert varietie
s)\, one using Bott-Samelson manifolds\, the other (requiring no choices!)
using circle-equivariant stable curves. In each case the dual simplicial
complex is actually **homeomorphic** to a sphere.\n
LOCATION:https://researchseminars.org/talk/agstanford/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrica Mazzon (University of Michigan)
DTSTART;VALUE=DATE-TIME:20220218T200000Z
DTEND;VALUE=DATE-TIME:20220218T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/77
DESCRIPTION:Title: Higher Fano manifolds\nby Enrica Mazzon (University of Michigan) a
s part of Stanford algebraic geometry seminar\n\n\nAbstract\nFano manifold
s are complex projective manifolds having positive first Chern class. The
positivity condition on the first Chern class has far-reaching geometric a
nd arithmetic implications. For instance\, Fano manifolds are covered by r
ational curves\, and families of Fano manifolds over one-dimensional bases
always admit holomorphic sections. In recent years\, there has been a gre
at effort towards defining suitable higher analogues of the Fano condition
. Higher Fano manifolds are expected to enjoy stronger versions of several
of the nice properties of Fano manifolds. For instance\, they should be c
overed by higher dimensional rational varieties\, and families of higher F
ano manifolds over higher-dimensional bases should admit meromorphic secti
ons (modulo Brauer obstruction). In this talk\, I will discuss a possible
notion of higher Fano manifolds in terms of positivity of higher Chern cha
racters\, and discuss special geometric features of these manifolds.\n\nTh
e synchronous discussion for Enrica Mazzon’s talk is taking place not in
zoom-chat\, but at https://tinyurl.com/2022-02-18-em (and will be deleted
after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi Hu (University of Arizona)
DTSTART;VALUE=DATE-TIME:20220225T200000Z
DTEND;VALUE=DATE-TIME:20220225T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/78
DESCRIPTION:Title: Resolution of Singularities in Arbitrary Characteristics\nby Yi Hu
(University of Arizona) as part of Stanford algebraic geometry seminar\n\
n\nAbstract\nLet X be an integral affine or projective scheme over a perfe
ct field of an arbitrary characteristic. Then\, X admits a resolution. Tha
t is\, there exists a smooth scheme Y and a projective birational morphism
from Y onto X.\n\nThe synchronous discussion for Yi Hu’s talk is taking
place not in zoom-chat\, but at https://tinyurl.com/2022-02-25-yh (and wi
ll be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Balibanu (Harvard)
DTSTART;VALUE=DATE-TIME:20220304T200000Z
DTEND;VALUE=DATE-TIME:20220304T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/79
DESCRIPTION:Title: Regular centralizers and the wonderful compactification\nby Ana Ba
libanu (Harvard) as part of Stanford algebraic geometry seminar\n\n\nAbstr
act\nThe universal centralizer of a complex semisimple adjoint group G is
the family of regular centralizers in G\, parametrized by the regular conj
ugacy classes. It has a natural symplectic structure which is inherited fr
om the cotangent bundle of G. I will construct a smooth\, log-symplectic r
elative compactification of this family using the wonderful compactificati
on of G. Its compactified centralizer fibers are isomorphic to Hessenberg
varieties\, and its symplectic leaves are indexed by root system combinato
rics. I will also explain how to produce a multiplicative analogue of this
construction\, by moving from the Poisson to the quasi-Poisson setting.\n
\nThe synchronous discussion for Ana Balibanu’s talk is taking place not
in zoom-chat\, but at https://tinyurl.com/2022-03-04-ab (and will be dele
ted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omid Amini (École Polytechnique)
DTSTART;VALUE=DATE-TIME:20220311T200000Z
DTEND;VALUE=DATE-TIME:20220311T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/80
DESCRIPTION:Title: Geometry of hybrid curves and their moduli spaces\, with a view toward
applications\nby Omid Amini (École Polytechnique) as part of Stanfor
d algebraic geometry seminar\n\n\nAbstract\nThe talk will be an introducti
on to the mathematics of geometric objects called hybrid curves and their
moduli spaces\, which mix features from higher rank non-Archimedean\, trop
ical and complex geometries. Some applications to questions around the asy
mptotic geometry of Riemann surfaces close to the boundary of their moduli
spaces will be discussed.\n\nBased on joint works with Noema Nicolussi.\n
\nThe synchronous discussion for Omid Amini’s talk is taking place not i
n zoom-chat\, but at https://tinyurl.com/2022-03-11-oa (and will be delete
d after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Yue Yu (Caltech)
DTSTART;VALUE=DATE-TIME:20220318T190000Z
DTEND;VALUE=DATE-TIME:20220318T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/81
DESCRIPTION:Title: Non-archimedean Quantum K-theory and Gromov-Witten invariants\nby
Tony Yue Yu (Caltech) as part of Stanford algebraic geometry seminar\n\n\n
Abstract\nMotivated by mirror symmetry and the enumeration of curves with
boundaries\, it is desirable to develop a theory of Gromov-Witten invarian
ts in the setting of non-archimedean geometry. I will explain our recent w
orks in this direction. Our approach differs from the classical one in alg
ebraic geometry via perfect obstruction theory. Instead\, we build on our
previous works on the foundation of derived non-archimedean geometry\, the
representability theorem and Gromov compactness. We obtain numerical inva
riants by passing to K-theory or motivic cohomology. We prove a list of na
tural geometric relations between the stacks of stable maps\, directly at
the derived level\, with respect to elementary operations on graphs\, name
ly\, products\, cutting edges\, forgetting tails and contracting edges. Th
ey imply the corresponding properties of numerical invariants. The derived
approach produces highly intuitive statements and functorial proofs. Furt
hermore\, its flexibility allows us to impose not only simple incidence co
nditions for marked points\, but also incidence conditions with multiplici
ties. Joint work with M Porta.\n\nThe synchronous discussion for Tony Yue
Yu’s talk is taking place not in zoom-chat\, but at https://tinyurl.com
/2022-03-18-ty (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Spink (Stanford)
DTSTART;VALUE=DATE-TIME:20220325T190000Z
DTEND;VALUE=DATE-TIME:20220325T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/82
DESCRIPTION:Title: A new Chern character for "classical Lie type" combinatorics\nby H
unter Spink (Stanford) as part of Stanford algebraic geometry seminar\n\n\
nAbstract\nFor X of “classical Lie type” (formally such that X has a G
KM torus action where all characters are of the form t_i\, t_i+t_j\, and t
_i-t_j for various i\,j)\, we adapt for combinatorial applications the (eq
uivariant) Hirzebruch-Riemann-Roch framework which computes Euler characte
ristics of vector bundles via cohomological computations\, extending previ
ous joint work in type A with Andrew Berget\, Chris Eur\, and Dennis Tseng
.\n\nThis framework directly relates the structure sheaf of Schubert varie
ties to Grothendieck polynomials\, produces formulas (some of them new) re
lating the number of lattice points and volumes for type A and B generaliz
ed permutahedrons\, and when applied to ample equivariant vector bundles o
n toric varieties is a key component in recent progress on establishing an
d unifying results on the log-concavity of sequences associated to matroid
s and delta-matroids.\n\n[This is joint work with Chris Eur\, Alex Fink\,
and Matthew Larson.]\n\nThe synchronous discussion for Hunter Spink’s ta
lk is taking place not in zoom-chat\, but at https://tinyurl.com/2022-03-2
5-hs (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kiran Kedlaya (UC San Diego)
DTSTART;VALUE=DATE-TIME:20220415T190000Z
DTEND;VALUE=DATE-TIME:20220415T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/84
DESCRIPTION:Title: Angle ranks of abelian varieties\nby Kiran Kedlaya (UC San Diego)
as part of Stanford algebraic geometry seminar\n\n\nAbstract\nThe angle ra
nk of an abelian variety over a finite field (or a CM abelian variety over
C) quantifies the extent to which the Tate conjecture (or the Hodge conje
cture) holds "for trivial reasons"\; cases where this does not happen tend
to be rare in practice. Picking up a thread from some old (1980s and 1990
s) results of Tankeev and Lenstra-Zarhin\, we show that in many cases\, th
e Tate conjecture is forced to hold by the Newton polygon of the abelian v
ariety or the Galois group of the Frobenius eigenvalues. Joint work with T
aylor Dupuy and David Zureick-Brown.\n\nThe synchronous discussion for Kir
an Kedlaya’s talk is taking place not in zoom-chat\, but at https://tiny
url.com/2022-04-15-kk (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michail Savvas (UT Austin)
DTSTART;VALUE=DATE-TIME:20220408T190000Z
DTEND;VALUE=DATE-TIME:20220408T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/85
DESCRIPTION:Title: Reduction of stabilizers and generalized Donaldson-Thomas invariants\nby Michail Savvas (UT Austin) as part of Stanford algebraic geometry s
eminar\n\n\nAbstract\nStarting with a sufficiently nice Artin stack\, we e
xplain a canonical blowup procedure that produces a Deligne-Mumford stack\
, resolving the locus of points with infinite automorphism group. This con
struction can be applied to moduli stacks parametrizing semistable sheaves
or complexes on Calabi-Yau threefolds. We show that their stabilizer redu
ctions admit natural virtual fundamental cycles\, allowing us to define ge
neralized Donaldson-Thomas invariants which act as counts of these objects
. Everything in this talk is (maybe not so) secretly expected to be the sh
adow of a corresponding phenomenon in derived algebraic geometry\, giving
a new\, derived perspective on Donaldson-Thomas invariants.\n\nBased on jo
int work with Young-Hoon Kiem and Jun Li and joint work in progress with J
eroen Hekking and David Rydh.\n\nThe synchronous discussion for Michail Sa
vvas’ talk is taking place not in zoom-chat\, but at https://tinyurl.com
/2022-04-08-ms (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Agostini (Max Planck Institute (Leipzig))
DTSTART;VALUE=DATE-TIME:20220513T190000Z
DTEND;VALUE=DATE-TIME:20220513T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/86
DESCRIPTION:Title: Singular curves\, degenerate theta functions and KP solutions\nby
Daniele Agostini (Max Planck Institute (Leipzig)) as part of Stanford alge
braic geometry seminar\n\n\nAbstract\nSmooth algebraic curves give rise to
solutions to the KP equation\, which models waves in shallow water\, via
Riemann's theta function. Singular curves produce solutions as well\, but
the theta function in this case becomes degenerate. I will present some
results and questions in this direction\, focusing on soliton and rationa
l solutions.\n\nThe synchronous discussion for Daniele Agostini’s talk i
s taking place not in zoom-chat\, but at https://tinyurl.com/2022-05-13-da
(and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soheyla Feyzbakhsh (Imperial College London)
DTSTART;VALUE=DATE-TIME:20220527T190000Z
DTEND;VALUE=DATE-TIME:20220527T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/87
DESCRIPTION:Title: Hyperkahler varieties as Brill-Noether loci on curves\nby Soheyla
Feyzbakhsh (Imperial College London) as part of Stanford algebraic geometr
y seminar\n\n\nAbstract\nConsider the moduli space $M_C(r\; K_C)$ of stabl
e rank r vector bundles on a curve $C$ with canonical determinant\, and le
t $h$ be the maximum number of linearly independent global sections of the
se bundles. If $C$ embeds in a K3 surface $X$ as a generator of $Pic(X)$ a
nd the genus of $C$ is sufficiently high\, I will show the Brill-Noether l
ocus $BN_C \\subset M_C(r\; K_C)$ of bundles with $h$ global sections is a
smooth projective Hyperkahler manifold\, isomorphic to a moduli space of
stable vector bundles on $X$. The main technique is to apply wall-crossing
with respect to Bridgeland stability conditions on K3 surfaces.\n\nThe sy
nchronous discussion for Soheyla Feyzbakhsh’s talk is taking place not i
n zoom-chat\, but at https://tinyurl.com/2022-05-27-sf (and will be delete
d after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniil Rudenko (University of Chicago)
DTSTART;VALUE=DATE-TIME:20220506T190000Z
DTEND;VALUE=DATE-TIME:20220506T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/89
DESCRIPTION:Title: Rational Elliptic Surfaces and Trigonometry of Non-Euclidean Tetrahedr
a\nby Daniil Rudenko (University of Chicago) as part of Stanford algeb
raic geometry seminar\n\n\nAbstract\nI will explain how to construct a rat
ional elliptic\nsurface out of every non-Euclidean tetrahedra. This surfac
e\n"remembers" the trigonometry of the tetrahedron: the length of edges\,\
ndihedral angles and the volume can be naturally computed in terms of\nthe
surface. The main property of this construction is self-duality:\nthe sur
faces obtained from the tetrahedron and its dual coincide. This\nleads to
some unexpected relations between angles and edges of the tetrahedron. For
instance\, the cross-ratio of the exponents of the spherical angles coin
cides with the cross-ratio of the exponents of the perimeters of its faces
. The construction is based on relating mixed Hodge structures\, associate
d to the tetrahedron and the corresponding surface.\n\nThe synchronous dis
cussion for Daniil Rudenko’s talk is taking place not in zoom-chat\, but
at https://tinyurl.com/2022-05-06-dr (and will be deleted after ~3-7 days
).\n
LOCATION:https://researchseminars.org/talk/agstanford/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Feng (MIT)
DTSTART;VALUE=DATE-TIME:20220520T190000Z
DTEND;VALUE=DATE-TIME:20220520T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/90
DESCRIPTION:Title: Enumerative arithmetic geometry and automorphic forms\nby Tony Fen
g (MIT) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nThe
problem of counting vectors with given length in a lattice turns out to ha
ve much more structure than initially expected\, and is connected with the
theory of so-called automorphic forms. A geometric analogue of this probl
em is to count global sections of vector bundles on a curve over a finite
field. The generating functions for such counts are special automorphic fo
rms called theta series. In joint work with Zhiwei Yun and Wei Zhang\, we
find a family of generalizations of such counting problems in the enumerat
ive geometry of arithmetic moduli spaces\, which lead to generating functi
ons that we call higher theta series. I will explain theorems and conjectu
res around these higher theta series.\n\nThe synchronous discussion for To
ny Feng’s talk is taking place not in zoom-chat\, but at https://tinyurl
.com/2022-05-20-tf (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siddarth Kannan (Brown University)
DTSTART;VALUE=DATE-TIME:20220401T190000Z
DTEND;VALUE=DATE-TIME:20220401T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/91
DESCRIPTION:Title: Moduli of relative stable maps to $\\mathbf{P}^1$: cut-and-paste invar
iants\nby Siddarth Kannan (Brown University) as part of Stanford algeb
raic geometry seminar\n\n\nAbstract\nI will give an introduction to the mo
duli space of genus zero rubber stable maps to $\\mathbf{P}^1$\, relative
to 0 and infinity\, with fixed ramification profiles. Then I will discuss
two recent results on the topology of these moduli spaces. The first conce
rns a chamber structure for the classes of these moduli spaces in the Grot
hendieck ring of varieties. The second gives a recursive algorithm for the
calculation of the Euler characteristic\, in the case where the maps are
fully ramified over zero\, and unramified over infinity. If time permits\,
I will also discuss some potential future directions.\n\nThe synchronous
discussion for Siddarth Kannan’s talk is taking place not in zoom-chat\,
but at https://tinyurl.com/2022-04-01-sk (and will be deleted after ~3-7
days).\n
LOCATION:https://researchseminars.org/talk/agstanford/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Anderson (Ohio State)
DTSTART;VALUE=DATE-TIME:20220429T190000Z
DTEND;VALUE=DATE-TIME:20220429T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/92
DESCRIPTION:Title: The direct sum morphism in (equivariant) Schubert calculus\nby Dav
id Anderson (Ohio State) as part of Stanford algebraic geometry seminar\n\
n\nAbstract\nDirect sum of subspaces defines a map on Grassmannians\, whic
h\, after taking an appropriate limit\, leads to a product-like structure
on the infinite Grassmannian. The corresponding cohomology pullback coinc
ides with a famous co-product on the ring of symmetric functions. I’ll
describe torus-equivariant extensions of this setup\, along with positivit
y results for structure constants\, and some open questions. This story p
artially extends work by Thomas-Yong\, Knutson-Lederer\, and Lam-Lee-Shimo
zono\, and connects to joint work with W. Fulton. (No special knowledge o
f Schubert calculus -- equivariant or not -- will be assumed.)\n
LOCATION:https://researchseminars.org/talk/agstanford/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Spink (Stanford)
DTSTART;VALUE=DATE-TIME:20220902T190000Z
DTEND;VALUE=DATE-TIME:20220902T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/93
DESCRIPTION:Title: Examples of o-minimality in algebraic geometry\nby Hunter Spink (S
tanford) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nIn
this introductory talk\, we will define o-minimality (a way of augmenting
algebraic geometry with functions like $e^x$\, $\\sin$\, $\\cos$\, etc.)\,
and show:\n\n(1) The number of solutions to a system of polynomials equat
ions is bounded by a function of the sizes of the supports of the equation
s\, independent of the sizes of the exponents.\n\n(2) For an irreducible p
olynomial $f(x\,y)$ not of the form $ax^iy^j+bx^ky^l$ there are only finit
ely many solutions to $f(x\,y)=0$ with $x$\, $y$ roots of unity.\n
LOCATION:https://researchseminars.org/talk/agstanford/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adeel Khan (Academia Sinica)
DTSTART;VALUE=DATE-TIME:20220909T190000Z
DTEND;VALUE=DATE-TIME:20220909T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/94
DESCRIPTION:Title: An invitation to motivic sheaves (part 1)\nby Adeel Khan (Academia
Sinica) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nThe
se lectures will be an introduction to Voevodsky's theory of motivic sheav
es. In the first lecture we will try to understand what the theory is sup
posed to look like\, according to Beilinson's 1985 conjectures. To better
appreciate these we will briefly review some of the ideas that influenced
him\, such as Grothendieck's theory of pure motives and Deligne's theory
of mixed Hodge structures (i.e.\, why motives?)\, and the six functor form
alism on l-adic sheaves (i.e.\, why sheaves?). In the second lecture\, we
will begin looking into Voevodsky's work on actually constructing categor
ies of motivic sheaves\, as well as the connection with invariants like Ch
ow groups and algebraic K-theory.\n\nDespite the seemingly forbidding natu
re of the topic\, these lectures are intended for an audience with familia
rity with basic algebraic geometry\, but no familiarity with any of the ad
vanced topics being addressed.\n\nThe synchronous discussion for Adeel Kha
n’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/2
022-09-09-ak (and will be deleted after ~2 weeks).\n
LOCATION:https://researchseminars.org/talk/agstanford/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adeel Khan (Academia Sinica)
DTSTART;VALUE=DATE-TIME:20220916T190000Z
DTEND;VALUE=DATE-TIME:20220916T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/95
DESCRIPTION:Title: An invitation to motivic sheaves (part 2)\nby Adeel Khan (Academia
Sinica) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nThe
se lectures will be an introduction to Voevodsky's theory of motivic sheav
es. In the first lecture we will try to understand what the theory is sup
posed to look like\, according to Beilinson's 1985 conjectures. To better
appreciate these we will briefly review some of the ideas that influenced
him\, such as Grothendieck's theory of pure motives and Deligne's theory
of mixed Hodge structures (i.e.\, why motives?)\, and the six functor form
alism on l-adic sheaves (i.e.\, why sheaves?). In the second lecture\, we
will begin looking into Voevodsky's work on actually constructing categor
ies of motivic sheaves\, as well as the connection with invariants like Ch
ow groups and algebraic K-theory.\n\nDespite the seemingly forbidding natu
re of the topic\, these lectures are intended for an audience with familia
rity with basic algebraic geometry\, but no familiarity with any of the ad
vanced topics being addressed.\n\nThe synchronous discussion for Adeel Kha
n’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/2
022-09-16-ak (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Emerton (University of Chicago)
DTSTART;VALUE=DATE-TIME:20221028T190000Z
DTEND;VALUE=DATE-TIME:20221028T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/96
DESCRIPTION:Title: Stacks in the arithmetic Langlands program\nby Matthew Emerton (Un
iversity of Chicago) as part of Stanford algebraic geometry seminar\n\nLec
ture held in Room 383-N.\n\nAbstract\nRecent years have seen the introduct
ion of geometric ideas\, formerly the sole province of the geometric Langl
ands program\, into the arithmetic Langlands program as well. In particula
r\, stacks of Langlands parameters have taken a central place in the arith
metic theory.\n\nIn this talk I will discuss some aspects of these stacks\
, with an emphasis on their interesting geometric features. Much of the w
ork I’ll report on will be joint with Toby Gee. Some will also be joint
with Xinwen Zhu.\n
LOCATION:https://researchseminars.org/talk/agstanford/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Tsimerman (University of Toronto)
DTSTART;VALUE=DATE-TIME:20221111T200000Z
DTEND;VALUE=DATE-TIME:20221111T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/97
DESCRIPTION:Title: Abelian Varieties not Isogenous to Jacobians\nby Jacob Tsimerman (
University of Toronto) as part of Stanford algebraic geometry seminar\n\nL
ecture held in Room 383-N.\n\nAbstract\nKatz and Oort raised the following
question: Given an algebraically closed field k\, and a positive integer
g>3\, does there exist an abelian variety over k not isogenous to a Jacobi
an over k? There has been much progress on this question\, with several pr
oofs now existing over $\\overline{\\mathbb{Q}}$. We discuss recent work w
ith Ananth Shankar\, answering this question in the affirmative over $\\ov
erline{\\mathbb{F}_q(T)}$. Our method introduces new types of local obstru
ctions\, and can be used to give another proof over $\\overline{\\mathbb{Q
}}$.\n
LOCATION:https://researchseminars.org/talk/agstanford/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau (University of Georgia)
DTSTART;VALUE=DATE-TIME:20221118T200000Z
DTEND;VALUE=DATE-TIME:20221118T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/98
DESCRIPTION:Title: Fock–Goncharov Dual Cluster Varieties and Gross–Siebert Mirrors\nby Pierrick Bousseau (University of Georgia) as part of Stanford algebr
aic geometry seminar\n\n\nAbstract\nCluster varieties are algebraic variet
ies obtained by gluing together complex tori using explicit birational tra
nsformations. They play an important role in algebra and geometric represe
ntation theory\, and have the peculiarity to come in pairs (A\,X). On the
other hand\, in the context of mirror symmetry\, associated with any log C
alabi–Yau variety is its mirror dual\, which can be constructed using th
e enumerative geometry of rational curves in the framework of the Gross–
Siebert program. I will explain how to bridge the theory of cluster variet
ies with the algebro-geometric framework of Gross–Siebert mirror symmetr
y and show that the mirror to the X-cluster variety is a degeneration of t
he Fock–Goncharov dual A-cluster variety and vice versa. To do this\, we
investigate how the cluster scattering diagram of Gross–Hacking–Keel
–Kontsevich compares with the canonical scattering diagram defined by Gr
oss–Siebert to construct mirror duals in arbitrary dimensions. This is j
oint work with Hulya Arguz.\n\nThe synchronous discussion for Pierrick Bou
sseau’s talk is taking place not in zoom-chat\, but at https://tinyurl.c
om/2022-11-18-pb (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Larson (Stanford)
DTSTART;VALUE=DATE-TIME:20221021T190000Z
DTEND;VALUE=DATE-TIME:20221021T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/99
DESCRIPTION:Title: The local motivic monodromy conjecture for simplicial nondegenerate si
ngularities\nby Matt Larson (Stanford) as part of Stanford algebraic g
eometry seminar\n\nLecture held in 383-N.\n\nAbstract\nThe monodromy conje
cture predicts a relationship between the motivic zeta function of a hyper
surface V(f)\, which governs the number of solutions to f = 0 (mod p^n) if
f has integer coefficients and p is a sufficiently large prime\, and the
eigenvalues of the monodromy action on the cohomology of the Milnor fiber\
, which is a topological invariant of the complex hypersurface. When f is
nondegenerate with respect to its Newton polyhedron\, which is true for "g
eneric" polynomials\, there are combinatorial formulas for both the motivi
c zeta function and the eigenvalue of monodromy. I will describe recent re
sults (joint with S. Payne and A. Stapledon) which prove a version of the
monodromy conjecture for nondegenerate polynomials which have a simplicial
Newton polyhedron.\n
LOCATION:https://researchseminars.org/talk/agstanford/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chengxi Wang (UCLA)
DTSTART;VALUE=DATE-TIME:20221202T200000Z
DTEND;VALUE=DATE-TIME:20221202T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/100
DESCRIPTION:Title: Calabi-Yau varieties of large index\nby Chengxi Wang (UCLA) as pa
rt of Stanford algebraic geometry seminar\n\n\nAbstract\nA projective vari
ety $X$ is called Calabi-Yau if its canonical divisor is $\\mathbb{Q}$-lin
early equivalent to zero. The smallest positive integer $m$ with $mK_X$ li
nearly equivalent to zero is called the index of $X$. Using ideas from mir
ror symmetry\, we construct Calabi-Yau varieties with index growing doubly
exponentially with dimension. We conjecture they are the largest index in
each dimension based on evidence in low dimensions. We also give Calabi-Y
au varieties with large orbifold Betti numbers or small minimal log discre
pancy. Joint work with Louis Esser and Burt Totaro.\n\nThe synchronous dis
cussion for Chengxi Wang’s talk is taking place not in zoom-chat\, but a
t https://tinyurl.com/2022-12-02-cw (and will be deleted after ~3-7 days).
\n
LOCATION:https://researchseminars.org/talk/agstanford/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patricio Gallardo Candela (UC Riverside)
DTSTART;VALUE=DATE-TIME:20230224T200000Z
DTEND;VALUE=DATE-TIME:20230224T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/101
DESCRIPTION:Title: A perspective on explicit compactifications of the moduli space of su
rfaces and pairs\nby Patricio Gallardo Candela (UC Riverside) as part
of Stanford algebraic geometry seminar\n\nLecture held in Room 383-N.\n\nA
bstract\nIn this talk\, we will discuss techniques for explicitly describi
ng the degenerations parametrized by the KSBA moduli space of surfaces and
log pairs of general type. We will focus on specific examples\, such as c
ertain Horikawa surfaces and cubic surfaces\, and how our techniques have
been applied to them. These results were obtained in joint work with L. Sc
haffler\, G. Pearlstein\, Z. Zhang\, and M. Kerr.\n
LOCATION:https://researchseminars.org/talk/agstanford/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Will Sawin (Columbia)
DTSTART;VALUE=DATE-TIME:20230120T200000Z
DTEND;VALUE=DATE-TIME:20230120T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/102
DESCRIPTION:Title: Quantitative $\\ell$-adic sheaf theory\nby Will Sawin (Columbia)
as part of Stanford algebraic geometry seminar\n\nLecture held in Room 383
-N.\n\nAbstract\nSheaf cohomology is a powerful tool both in algebraic \ng
eometry and its applications to other fields. Often\, one wants to \nprove
bounds for the dimension of sheaf cohomology groups. Katz gave \nbounds f
or the dimension of the étale cohomology groups of a variety \nin terms o
f its defining equations (degree\, number of equations\, \nnumber of varia
bles). But the utility of sheaf cohomology arises less \nfrom the ability
to compute the cohomology of varieties and more from \nthe toolbox of func
tors that let us construct new sheaves from old\, \nwhich we often apply i
n quite complicated sequences. In joint work \nwith Arthur Forey\, Javier
Fresán\, and Emmanuel Kowalski\, we prove \nbounds for the dimensions of
étale cohomology groups which are \ncompatible with the six functors form
alism (and other functors \nbesides) in the sense that we define the “co
mplexity” of a sheaf and \ncontrol how much the complexity can grow when
we apply one of these \noperations.\n
LOCATION:https://researchseminars.org/talk/agstanford/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiji Lyu (Princeton)
DTSTART;VALUE=DATE-TIME:20230310T200000Z
DTEND;VALUE=DATE-TIME:20230310T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/103
DESCRIPTION:Title: Behavior of some invariants in characteristic $p$\nby Shiji Lyu (
Princeton) as part of Stanford algebraic geometry seminar\n\nLecture held
in Room 383-N.\n\nAbstract\nThere are many numerical invariants of a ring
in characteristic $p$ measuring its singularity. In this talk\, we will di
scuss two classical ones\, Hilbert-Kunz multiplicity and the $F$-signature
\, and a rather recent one\, the $F$-rational signature. We will discuss s
everal properties of these invariants\, including semi-continuity and beha
vior under smooth extensions.\n
LOCATION:https://researchseminars.org/talk/agstanford/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ming Hao Quek (Brown University)
DTSTART;VALUE=DATE-TIME:20230519T190000Z
DTEND;VALUE=DATE-TIME:20230519T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/105
DESCRIPTION:Title: Around the motivic monodromy conjecture for non-degenerate hypersurfa
ces\nby Ming Hao Quek (Brown University) as part of Stanford algebraic
geometry seminar\n\nLecture held in Room 383-N.\n\nAbstract\nI will discu
ss my ongoing effort to comprehend\, from a geometric viewpoint\, the moti
vic monodromy conjecture for a "generic" complex multivariate polynomial $
f$\, namely any polynomial $f$ that is non-degenerate with respect to its
Newton polyhedron. This conjecture\, due to Igusa and Denef--Loeser\, stat
es that for every pole $s$ of the motivic zeta function associated to $f$\
, $\\exp(2\\pi is)$ is a "monodromy eigenvalue" associated to $f$. On the
other hand\, the non-degeneracy condition on $f$ ensures that the singular
ity theory of $f$ is governed\, up to a certain extent\, by faces of the N
ewton polyhedron of $f$. The extent to which the former is governed by the
latter is one key aspect of the conjecture\, and will be the main focus o
f my talk.\n
LOCATION:https://researchseminars.org/talk/agstanford/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dusty Ross (San Francisco State)
DTSTART;VALUE=DATE-TIME:20230127T200000Z
DTEND;VALUE=DATE-TIME:20230127T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/106
DESCRIPTION:Title: Putting the “volume” back in “volume polynomials”\nby Dus
ty Ross (San Francisco State) as part of Stanford algebraic geometry semin
ar\n\nLecture held in Room 383-N.\n\nAbstract\nRecent developments in trop
ical geometry and matroid theory have led to the study of “volume polyno
mials” associated to tropical varieties\, the coefficients of which reco
rd all possible degrees of top powers of tropical divisors. In this talk\,
I’ll discuss a volume-theoretic interpretation of volume polynomials of
tropical fans\; namely\, they measure volumes of polyhedral complexes obt
ained by truncating the tropical fan with normal hyperplanes. I’ll also
discuss how this volume-theoretic interpretation inspires a general framew
ork for studying an analogue of the Alexandrov-Fenchel inequalities for de
grees of divisors on tropical fans. Parts of this work are joint with Anas
tasia Nathanson\, Lauren Nowak\, and Patrick O’Melveny.\n
LOCATION:https://researchseminars.org/talk/agstanford/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hernan Iriarte (UT Austin)
DTSTART;VALUE=DATE-TIME:20230203T200000Z
DTEND;VALUE=DATE-TIME:20230203T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/107
DESCRIPTION:Title: Weak continuity on the variation of Newton Okounkov bodies\nby He
rnan Iriarte (UT Austin) as part of Stanford algebraic geometry seminar\n\
nLecture held in Room 383-N.\n\nAbstract\nWe start by presenting new tools
and results suitable for\nthe study of valuations of higher rank on funct
ion fields of algebraic\nvarieties. This will be based on a study of highe
r rank quasi-monomial\nvaluations taking values in the lexicographically o
rdered group R^k.\nThis gives us a space of higher rank valuations that we
endow with a\nweak "tropical" topology. In this setting\, we show that th
e Newton\nOkounkov bodies of a given line bundle vary continuously with re
spect\nto the valuation. We explain how this result fits in the literature
\nand how it gives us a restriction in the existence of mutations of\nNewt
on Okounkov bodies. Joint work with Omid Amini.\n
LOCATION:https://researchseminars.org/talk/agstanford/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Landesman (MIT)
DTSTART;VALUE=DATE-TIME:20230210T200000Z
DTEND;VALUE=DATE-TIME:20230210T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/108
DESCRIPTION:Title: Splitting types of finite monodromy vector bundles\nby Aaron Land
esman (MIT) as part of Stanford algebraic geometry seminar\n\nLecture held
in Room 383-N.\n\nAbstract\nGiven a finite degree $d$ cover of curves $f:
X \\to \\mathbb P^1$\, we study $f_* \\mathscr O_X$\, which is a rank $d$
vector bundle on $\\mathbb P^1$\, hence\ncan be written as a direct sum o
f line bundles \n$f_* \\mathscr O_X \\simeq \\oplus_{i=1}^d \\mathscr O(a_
i)$.\nNaively\, one might expect that if the cover above is general\, this
vector bundle is balanced\, meaning that the $a_i$'s are as close to each
other as possible.\nWhile this is not quite true\, we explain what can be
said about these splitting types\, by studying how they change as we defo
rm the cover. This is based on joint work with Daniel Litt.\n\nThe ideas c
ropping up here were also instrumental in resolving\nconjectures of Esnaul
t-Kerz and Budur-Wang regarding the density of geometric local\nsystems in
the moduli space of local systems.\n
LOCATION:https://researchseminars.org/talk/agstanford/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Larson (Brown University)
DTSTART;VALUE=DATE-TIME:20230421T190000Z
DTEND;VALUE=DATE-TIME:20230421T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/109
DESCRIPTION:Title: Interpolation for Brill--Noether Curves\nby Eric Larson (Brown Un
iversity) as part of Stanford algebraic geometry seminar\n\nLecture held i
n Room 383-N.\n\nAbstract\nIn this talk\, we determine when there is a Bri
ll--Noether curve of given degree and given genus that passes through a gi
ven number of general points in any projective space.\n
LOCATION:https://researchseminars.org/talk/agstanford/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Larson (Harvard/Berkeley)
DTSTART;VALUE=DATE-TIME:20230505T190000Z
DTEND;VALUE=DATE-TIME:20230505T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/110
DESCRIPTION:Title: The embedding theorem in Hurwitz--Brill--Noether theory\nby Hanna
h Larson (Harvard/Berkeley) as part of Stanford algebraic geometry seminar
\n\nLecture held in Room 383-N.\n\nAbstract\nBrill--Noether theory studies
the maps of general curves to projective spaces. The embedding theorem of
Eisenbud and Harris states that a general degree $d$ map $C \\rightarrow
\\mathbb{P}^r$ is an embedding when $r \\geq 3$. Hurwitz--Brill--Noether t
heory starts with a curve $C$ already equipped with a fixed map $C \\right
arrow \\mathbb{P}^1$ (which often forces $C$ to be special) and studies th
e maps of $C$ to other projective spaces. In this setting\, the appropriat
e analogue of the invariants $d$ and $r$ is a finer invariant called the s
plitting type. Our embedding theorem determines the splitting types $\\vec
{e}$ such that a general map of splitting type $\\vec{e}$ is an embedding.
This is joint work with Kaelin Cook--Powel\, Dave Jensen\, Eric Larson\,
and Isabel Vogt.\n
LOCATION:https://researchseminars.org/talk/agstanford/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allen Knutson (Cornell)
DTSTART;VALUE=DATE-TIME:20230120T214500Z
DTEND;VALUE=DATE-TIME:20230120T224500Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/111
DESCRIPTION:Title: Generic pipe dreams and the commuting scheme\nby Allen Knutson (C
ornell) as part of Stanford algebraic geometry seminar\n\nLecture held in
Room 383-N.\n\nAbstract\nConsider the equations XY=YX on a pair of matrice
s. Do these generate a prime ideal\, or\, are there secret equations that
pairs of commuting matrices satisfy? Mel Hochster asked this in '84 and no
one has answered it (past small matrix size). I'll degenerate this scheme
into pieces indexed by "generic pipe dreams"\, thereby giving a formula fo
r its degree as a sum of powers of 2\, and use an associated formula to de
rive both the ordinary and bumpless pipe dream formulae for Schubert polyn
omials. This work is joint with Paul Zinn-Justin.\n\nThis is the second al
gebraic geometry seminar of the day. We will zip out to buy lunch in betw
een\, and enjoy lunchtime theater with this talk.\n
LOCATION:https://researchseminars.org/talk/agstanford/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chih-Wei Chang (UT Austin)
DTSTART;VALUE=DATE-TIME:20230217T200000Z
DTEND;VALUE=DATE-TIME:20230217T210000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/112
DESCRIPTION:Title: The Iitaka dimensions of toric vector bundles\nby Chih-Wei Chang
(UT Austin) as part of Stanford algebraic geometry seminar\n\nLecture held
in Room 383-N.\n\nAbstract\nIn this talk\, we will start by briefly revie
wing the notion of the Iitaka dimension for vector bundles\, introduced by
E. C. Mistretta and S. Urbinati. Then we will discuss how to compute it i
n the toric geometry setting by studying the map defined by the global sec
tions of a toric vector bundle. We then demonstrate how to use this to con
struct some interesting examples.\n
LOCATION:https://researchseminars.org/talk/agstanford/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabel Vogt (Brown University)
DTSTART;VALUE=DATE-TIME:20230414T190000Z
DTEND;VALUE=DATE-TIME:20230414T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/113
DESCRIPTION:Title: Curve classes on conic bundles threefolds and applications to rationa
lity\nby Isabel Vogt (Brown University) as part of Stanford algebraic
geometry seminar\n\n\nAbstract\nIn this talk I'll discuss joint work with
Sarah Frei\, Lena Ji\, Soumya Sankar and Bianca Viray on the problem of de
termining when a geometrically rational variety is birational to projectiv
e space over its field of definition. Hassett--Tschinkel and Benoist--Wit
tenberg recently refined the classical intermediate Jacobian obstruction o
f Clemens--Griffiths by considering torsors under the intermediate Jacobia
n of a geometrically rational threefold. By work of Hassett--Tschinkel\,
Benoist--Wittenberg and Kuznetsov--Prokhorov\, this obstruction is strong
enough to characterize rationality of geometrically rational Fano threefol
ds of geometric Picard rank 1. Moving into higher Picard rank\, we comput
e this obstruction for conic bundles over $\\mathbf{P}^2$. As a consequenc
e of our work\, when the ground field is the real numbers\, we show that n
either the topological obstruction nor the refined intermediate Jacobian o
bstruction is sufficient to determine rationality.\n
LOCATION:https://researchseminars.org/talk/agstanford/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helene Esnault (Freie Universität Berlin)
DTSTART;VALUE=DATE-TIME:20230428T190000Z
DTEND;VALUE=DATE-TIME:20230428T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/114
DESCRIPTION:Title: Crystallinity properties of complex rigid local systems [not online]<
/a>\nby Helene Esnault (Freie Universität Berlin) as part of Stanford alg
ebraic geometry seminar\n\nLecture held in 383-N.\n\nAbstract\nJoint work
in progress with Michael Groechenig\n\n We prove in all generality that on
a smooth complex quasi-projective variety $X$\, Rigid connections yiel
d $F$-isocrystals on almost all good reductions $X_{\\mathbb F_q}$ and tha
t rigid local systems yield crystalline local systems on $X_K$ for $K$ th
e field of fractions of the Witt vectors of a finite field $\\mathbb F_q$\
, for almost all $X_{\\mathbb F_q}$. This improves our earlier work where\
, if $X$ was not projective\, we assumed a strong cohomological condition
(which is fulfilled for Shimura varieties of real rank $\\geq 2$)\,\n and
we obtained only infinitely many $\\mathbb F_q$ of growing characteristic
. While the earlier proof was via characteristic $p$\, the new one is pure
ly $p$-adic and uses $p$-adic topology.\n\n We shall discuss the projectiv
e case during the lecture.\n
LOCATION:https://researchseminars.org/talk/agstanford/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Chen (Columbia University)
DTSTART;VALUE=DATE-TIME:20230310T220000Z
DTEND;VALUE=DATE-TIME:20230310T230000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/115
DESCRIPTION:Title: Fano hypersurfaces and differential forms via positive characteristic
\nby Nathan Chen (Columbia University) as part of Stanford algebraic g
eometry seminar\n\nLecture held in 383-N.\n\nAbstract\nHolomorphic forms a
re an important birational invariant for studying the geometry of a variet
y. In characteristic 0\, Fano varieties do not have any holomorphic forms.
Surprisingly\, Kollár showed that in positive characteristic certain (si
ngular) Fano varieties admit many global (n-1)-forms\, and he combined thi
s with a specialization method to prove nonrationality of many complex Fan
o hypersurfaces. In this talk\, we will revisit this construction and use
it to address several related questions for Fano hypersurfaces in certain
ranges: (1) how can one further measure their nonrationality\, (2) what ar
e their possible rational endomorphisms\, and (3) is their birational auto
morphism group infinite or finite? Parts of this will be joint with David
Stapleton as well as with Lena Ji-Stapleton.\n
LOCATION:https://researchseminars.org/talk/agstanford/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melody Chan (Brown University)
DTSTART;VALUE=DATE-TIME:20230602T190000Z
DTEND;VALUE=DATE-TIME:20230602T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/117
DESCRIPTION:Title: The weight 0 compactly supported Euler characteristic of moduli space
s of marked hyperelliptic curves\nby Melody Chan (Brown University) as
part of Stanford algebraic geometry seminar\n\nLecture held in 383-N.\n\n
Abstract\nJoint work with Madeline Brandt and Siddarth Kannan. We use mod
uli spaces of $G$-admissible covers and tropical geometry to give a sum-ov
er-graphs formula for the weight-0 compactly supported Euler characteristi
c of the moduli spaces $H_{g\,n}$ of $n$-marked hyperelliptic curves of ge
nus $g$\, as a virtual representation of $S_n$. Computer calculations the
n enable fully explicit formulas for the above in small genus. My aim is
to make this talk accessible to anyone with passing familiarity with $M_g$
and its Deligne-Mumford compactification.\n
LOCATION:https://researchseminars.org/talk/agstanford/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Church (Stanford University)
DTSTART;VALUE=DATE-TIME:20230609T190000Z
DTEND;VALUE=DATE-TIME:20230609T200000Z
DTSTAMP;VALUE=DATE-TIME:20230529T045226Z
UID:agstanford/118
DESCRIPTION:by Ben Church (Stanford University) as part of Stanford algebr
aic geometry seminar\n\nLecture held in 383-N.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/agstanford/118/
END:VEVENT
END:VCALENDAR