BEGIN:VCALENDAR
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PRODID:researchseminars.org
CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Dustin Clausen (Bonn/Copenhagen)
DTSTART:20200601T150000Z
DTEND:20200601T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/1
DESCRIPTION:Title: Th
e K-theory of adic spaces\nby Dustin Clausen (Bonn/Copenhagen) as part
of electronic Algebraic K-theory Seminar\n\n\nAbstract\nMorrow and Kerz-S
aito-Tamme have each proposed a definition\nfor the K-theory of rigid anal
ytic varieties. They start with a\nconstruction on affinoids\, then use p
ro-cdh descent of usual algebraic\nK-theory (a theorem of Kerz-Strunk-Tamm
e) to see that their\nconstruction satisfies descent for rigid coverings\,
which lets one\nextend it to the global case. We propose a definition wh
ich is\ninherently global in nature\, and for which descent can be proven
in a\nsimilar manner to the Zariski descent of usual algebraic K-theory.
We\nrely on the theory of "solid modules"\, a convenient replacement for\n
the usual notion of linearly topologized modules\, plus Efimov's\nbeautifu
l observation that K-theory naturally makes sense for certain\nlarge (dual
izable presentable) categories. Namely\, we take the Efimov\nK-theory of
a full subcategory of solid modules called "nuclear".\nThis is joint work
with Peter Scholze.\n
LOCATION:https://researchseminars.org/talk/eAKTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Moritz Kerz (Regensburg)
DTSTART:20200615T150000Z
DTEND:20200615T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/2
DESCRIPTION:Title: So
me remarks on Vorst's conjecture\nby Moritz Kerz (Regensburg) as part
of electronic Algebraic K-theory Seminar\n\nAbstract: TBA\n\nAbstract: Vor
st conjectured that an affine algebra over a field is regular\nif and only
if its K-theory is $\\mathbb{A}^1$-homotopy invariant.\nIn the talk I wil
l explain how to approach this conjecture and\nI will discuss the role of
resolution of singularity in the proof.\n
LOCATION:https://researchseminars.org/talk/eAKTS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lennart Meier (Utrecht)
DTSTART:20200629T150000Z
DTEND:20200629T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/3
DESCRIPTION:Title: Th
e chromatic behavior of algebraic K-theory\nby Lennart Meier (Utrecht)
as part of electronic Algebraic K-theory Seminar\n\n\nAbstract\nThere is
a classic theorem of Waldhausen stating that algebraic K-theory preserves
under certain hypotheses rational equivalences of ring spectra. From the v
iewpoint of chromatic homotopy theory\, rationalization is just the zeroth
step in an infinite ladder of localizations. I will report on joint work
with Land and Tamme\, where we extend Waldhausen's theorem to higher chrom
atic localizations. This has a number of consequences\, in particular abou
t the K(1)-local K-theory of rings and red shift phenomena.\n
LOCATION:https://researchseminars.org/talk/eAKTS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wiesława Nizioł (Sorbonne)
DTSTART:20200727T150000Z
DTEND:20200727T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/4
DESCRIPTION:Title: p-
adic comparison theorem for analytic spaces\nby Wiesława Nizioł (Sor
bonne) as part of electronic Algebraic K-theory Seminar\n\n\nAbstract\nI w
ill discuss a comparison theorem between p-adic pro-etale cohomology and d
e Rham cohomology for smooth overconvergent analytic spaces. This generali
zes the known de Rham-to-pro-etale comparison theorems for proper and Ste
in rigid analytic spaces. The key ingredient is the theory of Banach-Colme
z spaces and almost Cp-representations. This is a joint work with Pierre C
olmez.\n
LOCATION:https://researchseminars.org/talk/eAKTS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sander Kupers (Harvard)
DTSTART:20200810T150000Z
DTEND:20200810T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/5
DESCRIPTION:Title: Al
gebraic K-theory and the unstable homology of general linear groups\nb
y Sander Kupers (Harvard) as part of electronic Algebraic K-theory Seminar
\n\n\nAbstract\nThe stable homology of general linear groups over a field
is\nwell-known to be closely related to its algebraic K-theory. I will\ndi
scuss joint work with Soren Galatius and Oscar Randal-Williams which\ninve
stigates the unstable homology of general linear groups. We will\nfind it
is closely related to the Milnor K-theory\, by constructing a\npresentatio
n of the disjoint union of $BGL_n(F)$ as an $\\mathbb{E}_{\\infty}$-algebr
a.\n
LOCATION:https://researchseminars.org/talk/eAKTS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guillermo Cortiñas (Buenos Aires)
DTSTART:20200713T150000Z
DTEND:20200713T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/6
DESCRIPTION:Title: Bi
variant (hermitian) K-theory and applications\nby Guillermo Cortiñas
(Buenos Aires) as part of electronic Algebraic K-theory Seminar\n\nLecture
held in 914-5033-3867.\n\nAbstract\nAbstract: Bivariant algebraic K-theor
y is a functor from a category of associative algebras over a commutative
ring to a certain triangulated category\; this functor is homotopy invaria
nt\, matricially stable and excisive and is universal with those propertie
s. Weibel's homotopy algebraic $K$-theory is recovered as a $\\hom$ in the
above triangulated category.\n\nIn the talk we shall explain how this biv
ariant theory --and its newly hatched hermitian version-- is used to tackl
e a long standing problem in the theory of graph algebras\, which asserts
that for a certain family of these algebras\, $K_0$ is a complete invarian
t of its isomorphism class.\n
LOCATION:https://researchseminars.org/talk/eAKTS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Groechenig (Toronto)
DTSTART:20200831T150000Z
DTEND:20200831T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/7
DESCRIPTION:Title: Th
e epsilon-connection and algebraic K-theory\nby Michael Groechenig (To
ronto) as part of electronic Algebraic K-theory Seminar\n\nLecture held in
914-5033-3867.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/eAKTS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Burt Totaro (UCLA)
DTSTART:20200915T160000Z
DTEND:20200915T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/8
DESCRIPTION:Title: To
rus actions\, Morse homology\, and the Hilbert scheme of points on affine
space\nby Burt Totaro (UCLA) as part of electronic Algebraic K-theory
Seminar\n\nLecture held in 915 7106 9041.\n\nAbstract\nWe formulate a conj
ecture on actions of the multiplicative\n group. In short\, if the m
ultiplicative group $\\mathbb{G}_m$\n acts on a quasi-projective sch
eme $U$ such that\n $U$ is attracted as $t$ approaches $0$ in $\\mat
hbb{G}_m$\n to a closed subset $Y$ in $U$\, then the inclusion from
$Y$ to $U$ should be\n an $\\mathbb{A}^1$-homotopy equivalence. This
would be useful if true\,\n since actions of the multiplicative gro
up occur everywhere\n in algebraic geometry. We prove several partia
l results.\n The proofs use an analog of Morse theory\n for si
ngular varieties.\n We give an application to the Hilbert scheme of
points\n on affine space $\\mathbb{A}^n$.\n
LOCATION:https://researchseminars.org/talk/eAKTS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arpon Raksit (Stanford)
DTSTART:20201110T170000Z
DTEND:20201110T180000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/9
DESCRIPTION:Title: Ho
chschild homology and the derived de Rham complex revisited\nby Arpon
Raksit (Stanford) as part of electronic Algebraic K-theory Seminar\n\nLect
ure held in 915 7106 9041.\n\nAbstract\nI will discuss "filtered circle ac
tions" and "homotopy-coherent cochain complexes"\,\nand how these notions
provide a conceptual perspective on the relationship between\n(HKR-filtere
d) Hochschild homology and (Hodge-filtered) derived de Rham cohomology.\n
LOCATION:https://researchseminars.org/talk/eAKTS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raman Parimala (Emory)
DTSTART:20201124T170000Z
DTEND:20201124T180000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/10
DESCRIPTION:by Raman Parimala (Emory) as part of electronic Algebraic K-th
eory Seminar\n\nLecture held in 915 7106 9041.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/eAKTS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Morrow (Jussieu)
DTSTART:20201201T170000Z
DTEND:20201201T180000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/11
DESCRIPTION:Title: p
-adic Milnor K-theory of p-adic rings\nby Matthew Morrow (Jussieu) as
part of electronic Algebraic K-theory Seminar\n\nLecture held in 915 7106
9041.\n\nAbstract\nJoint with Morten L\\"uders. The Milnor K-theory of a l
ocal ring may initially appear to be an ad-hoc invariant\, but turns out t
o be motivic in nature. In particular\, Nesterenko and Suslin showed that
the Milnor K-groups of a field were isomorphic to its motivic cohomology i
n the range where degree equals weight\; by then proving the Beilinson----
Lichtenbaum conjectures\, Voevodsky connected motivic cohomology to l-adic
\\'etale cohomology and so established the Bloch---Kato conjecture. We wi
ll present p-adic analogues of these results by describing the p-adic Miln
or K-theory of p-complete local rings in terms of the syntomic cohomology
introduced by Bhatt---M.---Scholze.\n
LOCATION:https://researchseminars.org/talk/eAKTS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph Ayoub (UZH)
DTSTART:20201215T170000Z
DTEND:20201215T180000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/12
DESCRIPTION:Title: R
igid analytic motivic sheaves\nby Joseph Ayoub (UZH) as part of electr
onic Algebraic K-theory Seminar\n\nLecture held in 915 7106 9041.\nAbstrac
t: TBA\n\nI will report on recent work concerning motives in rigid analyti
c geometry.\nIn particular\, I would like to discuss a vast generalisation
of an old theorem of\nmine describing the category of rigid analytic moti
ves over a non Archimedean field\nof equi-characteristic zero in terms of
algebraic motives over its residue field.\nThe generalisation is to an arb
itrary rigid analytic base. This is joint work with\nM. Gallauer and A. Ve
zzani.\n
LOCATION:https://researchseminars.org/talk/eAKTS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marc Hoyois (Regensburg)
DTSTART:20200929T160000Z
DTEND:20200929T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/13
DESCRIPTION:Title: M
ilnor excision for motivic spectra\nby Marc Hoyois (Regensburg) as par
t of electronic Algebraic K-theory Seminar\n\nLecture held in 915 7106 904
1.\n\nAbstract\nIt is a classical result of Weibel that homotopy invariant
algebraic K-theory satisfies excision\, in the sense that for any ring $A
$ and ideal $I \\subset A$\, the fiber of $KH(A) \\rightarrow KH(A/I)$ de
pends only on $I$ as a nonunital ring. In joint work with Elden Elmanto\,
Ryomei Iwasa\, and Shane Kelly\, we show that this is true more generally
for any cohomology theory represented by a motivic spectrum.\n
LOCATION:https://researchseminars.org/talk/eAKTS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Nikolaus (Münster)
DTSTART:20201013T160000Z
DTEND:20201013T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/14
DESCRIPTION:Title: O
n Grothendieck--Witt theory of the integers\nby Thomas Nikolaus (Müns
ter) as part of electronic Algebraic K-theory Seminar\n\nLecture held in 9
15 7106 9041.\n\nAbstract\nWe introduce the Grothendieck--Witt groups of t
he integers and\nthe Grothendieck--Witt spectrum of the integers. Then we
explain how to\ncompute these groups and the homotopy type of the spectru
m using recent\nwork on K-theory and L-theory. If time permits we also exp
lain how to\nresolve the homotopy limit problem for rings of integers in n
umber\nfields and prove Karoubi's periodicity conjecure for arbitrary ring
s.\n
LOCATION:https://researchseminars.org/talk/eAKTS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikala Jansen (Copenhagen)
DTSTART:20201027T160000Z
DTEND:20201027T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/15
DESCRIPTION:Title: T
he reductive Borel--Serre compactification as a model for the K-theory spa
ce\nby Mikala Jansen (Copenhagen) as part of electronic Algebraic K-th
eory Seminar\n\nLecture held in 915 7106 9041.\n\nAbstract\nThe reductive
Borel--Serre compactification\, introduced by Zucker in 1982\, is a strati
fied space which is well suited for the study of $L^2$-cohomology of arith
metic groups and has come to play a central role in the theory of compacti
fications. We determine its stratified homotopy type (the exit path $\\inf
ty$-category) to be a $1$-category defined purely in terms of parabolic su
bgroups. This category makes sense in a much more general setting\, in fac
t for any exact category\, but in this talk we restrict ourselves to well-
behaved rings. With direct sum\, these naturally give rise to a monoidal c
ategory\, and we show that (the loop space of the classifying space of) th
is monoidal category is a model for the K-theory space. For finite fields\
, we encounter much better homological stability properties than for the g
eneral linear groups.\n
LOCATION:https://researchseminars.org/talk/eAKTS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Wilson
DTSTART:20210316T160000Z
DTEND:20210316T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/16
DESCRIPTION:Title: L
ichtenbaum-Quillen phenomena in chromatic homotopy theory\nby Dylan Wi
lson as part of electronic Algebraic K-theory Seminar\n\nLecture held in 9
79 0634 7355.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/eAKTS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Bachmann (LMU)
DTSTART:20210330T160000Z
DTEND:20210330T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/17
DESCRIPTION:Title: C
ellular motivic invariants of Z[1/2]\nby Tom Bachmann (LMU) as part of
electronic Algebraic K-theory Seminar\n\nLecture held in 979 0634 7355.\n
\nAbstract\nA cellular motivic invariant is a special type of functor from
the category of commutative rings (or the opposite of schemes\, say) to s
pectra. Examples include algebraic K-theory\, motivic cohomology\, etale c
ohomology and algebraic cobordism. Dwyer-Friedlander observed that for 2-a
dic etale K-theory and certain related invariants\, the value on $\\mathbb
{Z}[1/2]$ can be described in terms of a fiber square involving the values
on the real numbers\, the complex numbers\, and the field with three elem
ents.\nI will explain a generalization of this result to arbitrary 2-adic
cellular motivic invariants.\n\nThis is joint work with Paul Arne Østvær
\n
LOCATION:https://researchseminars.org/talk/eAKTS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allen Yuan
DTSTART:20210413T160000Z
DTEND:20210413T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/18
DESCRIPTION:Title: E
xamples of chromatic redshift\nby Allen Yuan as part of electronic Alg
ebraic K-theory Seminar\n\nLecture held in 979 0634 7355.\n\nAbstract\nOne
form of the Ausoni-Rognes chromatic redshift philosophy\nis that algebrai
c K-theory raises the chromatic complexity of a ring\nby one. Work of Cla
usen-Mathew-Naumann-Noel shows\, in particular\,\nthat K-theory raises hei
ght by at most one\; on the other hand\, recent\nwork of Hahn-Wilson gives
an example at each height (a form of $BP\\langle n\\rangle$)\nwhere this
height shifting does occur. In this talk\, I will discuss a\nsimple non-c
omputational proof of this height shifting in a range of\nexamples\, inclu
ding Lubin-Tate theories and the iterated K-theory of\nfields.\n
LOCATION:https://researchseminars.org/talk/eAKTS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Feng
DTSTART:20210427T160000Z
DTEND:20210427T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/19
DESCRIPTION:Title: T
he Galois action on symplectic K-theory\nby Tony Feng as part of elect
ronic Algebraic K-theory Seminar\n\nLecture held in 979 0634 7355.\n\nAbst
ract\nThe algebraic K-theory of the integers has fascinating\nconnections
with number theory\; for example\, the values of the Riemann\nzeta functio
n at negative integers turn out to be related to the sizes\nof K-groups (b
y work of Rost-Voevodsky and Mazur-Wiles). Such\nconnections come from une
xpected structure on the classifying spaces\nof arithmetic groups\, and ca
n be explained in terms of the philosophy\nof the so-called Langlands prog
ram. Motivated by this picture\, Akshay\nVenkatesh and Soren Galatius and
I considered a symplectic variant of\nalgebraic K-theory of the integers\,
constructed a natural Galois\naction on it\, and computed that Galois act
ion. I will explain this\nstory with a K-theory audience in mind.\n
LOCATION:https://researchseminars.org/talk/eAKTS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Thomas
DTSTART:20210511T160000Z
DTEND:20210511T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/20
DESCRIPTION:Title: S
quare root Euler classes and counting sheaves on Calabi-Yau 4-folds\nb
y Richard Thomas as part of electronic Algebraic K-theory Seminar\n\nLectu
re held in 979 0634 7355.\n\nAbstract\nI will explain a nice characteristi
c class of SO(2n\,C) bundles in both Chow cohomology and K-theory\, and ho
w to localise it to the zeros of an isotropic section. This builds on work
of Edidin-Graham\, Polishchuk-Vaintrob\, Anderson and others. This can be
used to construct an algebraic virtual cycle (and virtual structure sheaf
) on moduli spaces of stable sheaves on Calabi-Yau 4-folds. It recovers th
e real derived differential geometry virtual cycle of Borisov-Joyce but ha
s nicer properties\, like a torus localisation formula. Joint work with Je
ongseok Oh (KIAS).\n
LOCATION:https://researchseminars.org/talk/eAKTS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Binda
DTSTART:20210525T160000Z
DTEND:20210525T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/21
DESCRIPTION:Title: G
AGA type conjecture for the Brauer group via derived geometry\nby Fede
rico Binda as part of electronic Algebraic K-theory Seminar\n\nLecture hel
d in 979 0634 7355.\n\nAbstract\nIn Brauer III\, Grothendieck considered t
he problem of comparing the cohomological Brauer group $Br(X) = H^2_{et}(X
\,G_m)$ of a scheme $X$\, proper and flat over a henselian DVR $R$\, and t
he inverse limit of the Brauer groups $\\lim_nBr(X_n)$\, where $X_n = X\\o
times_R R/m^n$. He proved that the canonical map $Br(X) \\to \\lim_n Br(X_
n)$ is injective under a number of restrictions\, and left as an open prob
lem the question on whether the formal injectivity holds in a fairly gener
al setting.\nThanks to the machinery of derived algebraic geometry and the
results of To\\"en on derived Azumaya algebras and derived Morita theory\
, we are able to rephrase Grothendieck’s question in terms of a formal G
AGA-type problem for smooth and proper categories\, enriched over the $\\i
nfty$-category $QCoh(X)$ of quasi-coherent $O_X$-modules. In this framewor
k we can show that Grothendieck’s injectivity conjecture always holds fo
r a proper derived scheme $X \\to S$ where S is the spectrum of any comple
te Noetherian local ring\, if we are willing to replace the inverse limit
$\\lim_n Br(X_n)$ with the Brauer group $Br(X)$ of the formal scheme $\\ma
thfrak{X}$ given by the colimit of the thickenings $X_n$. The obstruction
involving the inverse system $Pic(X_n)$ considered by Grothendieck appears
naturally in the Milnor sequence for a certain tower of spaces. This is a
joint work in progress with Mauro Porta (IRMA\, Strasbourg).\n
LOCATION:https://researchseminars.org/talk/eAKTS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Dyckerhoff (Hamburg)
DTSTART:20210608T160000Z
DTEND:20210608T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/22
DESCRIPTION:Title: S
-constructions\, Auslander algebras\, and wrapped Floer theory\nby Tob
ias Dyckerhoff (Hamburg) as part of electronic Algebraic K-theory Seminar\
n\nLecture held in https://bbbvl.physnet.uni-hamburg.de/b/tob-ten-ytm-x9v.
\n\nAbstract\nWe will explain that\, beyond their purpose for defining alg
ebraic\nK-theory\, Waldhausen's S-construction and higher variants have in
teresting\nstructural interpretations in the representation theory of fini
te-dimensional\nalgebras and in wrapped Floer theory. This opens up the op
portunity to apply\ntechniques from either of the involved subjects to the
benefit of the others. We\nwill demonstrate this by giving a symplectic p
roof of a certain "binomial\nduality" among the cells of the higher S-cons
truction discovered by Beckert.\nFinally\, we discuss further applications
to gluing formalisms for Fukaya\ncategories of symmetric products.\n
LOCATION:https://researchseminars.org/talk/eAKTS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amalendu Krishna (TIFR)
DTSTART:20210622T160000Z
DTEND:20210622T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/23
DESCRIPTION:Title: C
how groups and Euler class groups of affine varieties\nby Amalendu Kri
shna (TIFR) as part of electronic Algebraic K-theory Seminar\n\nLecture he
ld in 979 0634 7355.\n\nAbstract\nIn this talk\, I shall present two resul
ts on the Chow group of 0-cycles on affine schemes over algebraically clos
ed fields and give\nseveral consequences of these results. In particular\,
I shall discuss proofs of an old conjecture of Murthy\, a conjecture of M
ohan Kumar-Murthy-Roy and also the Euler class groups of such schemes.\n
LOCATION:https://researchseminars.org/talk/eAKTS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirsten Wickelgren (Duke)
DTSTART:20210706T160000Z
DTEND:20210706T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/24
DESCRIPTION:Title: C
ounts of rational curves on Del Pezzo surfaces enriched in bilinear forms<
/a>\nby Kirsten Wickelgren (Duke) as part of electronic Algebraic K-theory
Seminar\n\nLecture held in 979 0634 7355.\n\nAbstract\nDel Pezzo surfaces
here are smooth projective surfaces with\nample anticanonical bundle\, in
cluding $\\mathbb{P}^2\, \\mathbb{P}^1 \\times \\mathbb{P}^1$\, and cubic\
nsurfaces. By imposing the condition that a rational curve of fixed\ndegre
e passes through an appropriate number of points\, the number of\nsuch cur
ves is finite. Over the complex numbers\, these counts are\nindependent of
the generic choice of points. This invariance of number\nfails over the r
eals\, but there is a beautiful method of Welschinger\nto correct this. It
is a feature of $\\mathbb{A}^1$-homotopy theory that analogous\nreal and
complex results can indicate the presence of a common\ngeneralization\, va
lid over a general field. For $\\mathbbA^1$-connected Del Pezzo\nsurfaces
under appropriate hypotheses\, we give counts of rational\ncurves valued i
n the group completion GW(k) of symmetric\,\nnon-degenerate\, bilinear for
ms over k\, which are again independent of\nthe generic choice of points.
By replacing the positive integer count\nwith such a bilinear form\, one r
ecords information about the field of\ndefinition of the rational curve an
d the tangent directions at its\nnodes. We compute some low degree example
s\, including on the Del Pezzo\nsurfaces listed above. This is joint work
with Jesse Kass\, Marc\nLevine\, and Jake Solomon.\n
LOCATION:https://researchseminars.org/talk/eAKTS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anand Sawant (TIFR)
DTSTART:20210720T160000Z
DTEND:20210720T170000Z
DTSTAMP:20260422T225718Z
UID:eAKTS/25
DESCRIPTION:Title: C
entral extensions of algebraic groups via cellular $\\mathbb{A}^1$-homolog
y\nby Anand Sawant (TIFR) as part of electronic Algebraic K-theory Sem
inar\n\nLecture held in 979 0634 7355.\n\nAbstract\nI will outline the com
putation of the cellular $\\mathbb{A}^1$-homology of a split\, semisimple\
, simply connected algebraic group in low degrees and use it to describe t
he group of central extensions of such a group by a suitable strictly $\\m
athbb{A}^1$-invariant sheaf. These results in particular yield a motivic
proof of the result of Brylinski and Deligne classifying central extension
s of such algebraic groups by $K_2$. The talk is based on joint work with
Fabien Morel.\n
LOCATION:https://researchseminars.org/talk/eAKTS/25/
END:VEVENT
END:VCALENDAR