BEGIN:VCALENDAR
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CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Dustin Clausen (Bonn/Copenhagen)
DTSTART:20200601T150000Z
DTEND:20200601T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/1
DESCRIPTION:Title: The K-theory of adic spaces\nby Dustin Clausen (Bonn/Copenhagen)
as part of electronic Algebraic K-theory Seminar\n\n\nAbstract\nMorrow and
Kerz-Saito-Tamme have each proposed a definition\nfor the K-theory of rig
id analytic varieties. They start with a\nconstruction on affinoids\, the
n use pro-cdh descent of usual algebraic\nK-theory (a theorem of Kerz-Stru
nk-Tamme) to see that their\nconstruction satisfies descent for rigid cove
rings\, which lets one\nextend it to the global case. We propose a defini
tion which is\ninherently global in nature\, and for which descent can be
proven in a\nsimilar manner to the Zariski descent of usual algebraic K-th
eory. We\nrely on the theory of "solid modules"\, a convenient replacemen
t for\nthe usual notion of linearly topologized modules\, plus Efimov's\nb
eautiful observation that K-theory naturally makes sense for certain\nlarg
e (dualizable presentable) categories. Namely\, we take the Efimov\nK-the
ory of a full subcategory of solid modules called "nuclear".\nThis is join
t work with Peter Scholze.\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Moritz Kerz (Regensburg)
DTSTART:20200615T150000Z
DTEND:20200615T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/2
DESCRIPTION:Title: Some remarks on Vorst's conjecture\nby Moritz Kerz (Regensburg) a
s part of electronic Algebraic K-theory Seminar\n\nAbstract: TBA\n\nAbstra
ct: Vorst conjectured that an affine algebra over a field is regular\nif a
nd only if its K-theory is $\\mathbb{A}^1$-homotopy invariant.\nIn the tal
k I will explain how to approach this conjecture and\nI will discuss the r
ole of resolution of singularity in the proof.\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lennart Meier (Utrecht)
DTSTART:20200629T150000Z
DTEND:20200629T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/3
DESCRIPTION:Title: The chromatic behavior of algebraic K-theory\nby Lennart Meier (U
trecht) as part of electronic Algebraic K-theory Seminar\n\n\nAbstract\nTh
ere is a classic theorem of Waldhausen stating that algebraic K-theory pre
serves under certain hypotheses rational equivalences of ring spectra. Fro
m the viewpoint of chromatic homotopy theory\, rationalization is just the
zeroth step in an infinite ladder of localizations. I will report on join
t work with Land and Tamme\, where we extend Waldhausen's theorem to highe
r chromatic localizations. This has a number of consequences\, in particul
ar about the K(1)-local K-theory of rings and red shift phenomena.\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wiesława Nizioł (Sorbonne)
DTSTART:20200727T150000Z
DTEND:20200727T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/4
DESCRIPTION:Title: p-adic comparison theorem for analytic spaces\nby Wiesława Nizio
ł (Sorbonne) as part of electronic Algebraic K-theory Seminar\n\n\nAbstra
ct\nI will discuss a comparison theorem between p-adic pro-etale cohomolog
y and de Rham cohomology for smooth overconvergent analytic spaces. This g
eneralizes the known de Rham-to-pro-etale comparison theorems for proper
and Stein rigid analytic spaces. The key ingredient is the theory of Banac
h-Colmez spaces and almost Cp-representations. This is a joint work with P
ierre Colmez.\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sander Kupers (Harvard)
DTSTART:20200810T150000Z
DTEND:20200810T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/5
DESCRIPTION:Title: Algebraic K-theory and the unstable homology of general linear groups
\nby 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 w
ill\ndiscuss joint work with Soren Galatius and Oscar Randal-Williams whic
h\ninvestigates the unstable homology of general linear groups. We will\nf
ind it is closely related to the Milnor K-theory\, by constructing a\npres
entation of the disjoint union of $BGL_n(F)$ as an $\\mathbb{E}_{\\infty}$
-algebra.\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guillermo Cortiñas (Buenos Aires)
DTSTART:20200713T150000Z
DTEND:20200713T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/6
DESCRIPTION:Title: Bivariant (hermitian) K-theory and applications\nby Guillermo Cor
tiñas (Buenos Aires) as part of electronic Algebraic K-theory Seminar\n\n
Lecture held in 914-5033-3867.\n\nAbstract\nAbstract: Bivariant algebraic
K-theory is a functor from a category of associative algebras over a commu
tative ring to a certain triangulated category\; this functor is homotopy
invariant\, matricially stable and excisive and is universal with those pr
operties. Weibel's homotopy algebraic $K$-theory is recovered as a $\\hom$
in the above triangulated category.\n\nIn the talk we shall explain how t
his bivariant theory --and its newly hatched hermitian version-- is used t
o tackle a long standing problem in the theory of graph algebras\, which a
sserts that for a certain family of these algebras\, $K_0$ is a complete i
nvariant of its isomorphism class.\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Groechenig (Toronto)
DTSTART:20200831T150000Z
DTEND:20200831T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/7
DESCRIPTION:Title: The epsilon-connection and algebraic K-theory\nby Michael Groeche
nig (Toronto) as part of electronic Algebraic K-theory Seminar\n\nLecture
held in 914-5033-3867.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Burt Totaro (UCLA)
DTSTART:20200915T160000Z
DTEND:20200915T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/8
DESCRIPTION:Title: Torus 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 conjecture on actions of the multiplicative\n group. In short\, i
f the multiplicative group $\\mathbb{G}_m$\n acts on a quasi-project
ive scheme $U$ such that\n $U$ is attracted as $t$ approaches $0$ in
$\\mathbb{G}_m$\n to a closed subset $Y$ in $U$\, then the inclusio
n from $Y$ to $U$ should be\n an $\\mathbb{A}^1$-homotopy equivalenc
e. This would be useful if true\,\n since actions of the multiplicat
ive group occur everywhere\n in algebraic geometry. We prove several
partial results.\n The proofs use an analog of Morse theory\n
for singular varieties.\n We give an application to the Hilbert sch
eme of points\n on affine space $\\mathbb{A}^n$.\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arpon Raksit (Stanford)
DTSTART:20201110T170000Z
DTEND:20201110T180000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/9
DESCRIPTION:Title: Hochschild homology and the derived de Rham complex revisited\nby
Arpon Raksit (Stanford) as part of electronic Algebraic K-theory Seminar\
n\nLecture held in 915 7106 9041.\n\nAbstract\nI will discuss "filtered ci
rcle actions" and "homotopy-coherent cochain complexes"\,\nand how these n
otions provide a conceptual perspective on the relationship between\n(HKR-
filtered) Hochschild homology and (Hodge-filtered) derived de Rham cohomol
ogy.\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raman Parimala (Emory)
DTSTART:20201124T170000Z
DTEND:20201124T180000Z
DTSTAMP:20260404T111136Z
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://stable.researchseminars.org/talk/eAKTS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Morrow (Jussieu)
DTSTART:20201201T170000Z
DTEND:20201201T180000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/11
DESCRIPTION:Title: p-adic Milnor K-theory of p-adic rings\nby Matthew Morrow (Jussi
eu) as part of electronic Algebraic K-theory Seminar\n\nLecture held in 91
5 7106 9041.\n\nAbstract\nJoint with Morten L\\"uders. The Milnor K-theory
of a local ring may initially appear to be an ad-hoc invariant\, but turn
s out to be motivic in nature. In particular\, Nesterenko and Suslin showe
d that the Milnor K-groups of a field were isomorphic to its motivic cohom
ology in the range where degree equals weight\; by then proving the Beilin
son----Lichtenbaum conjectures\, Voevodsky connected motivic cohomology to
l-adic \\'etale cohomology and so established the Bloch---Kato conjecture
. We will present p-adic analogues of these results by describing the p-ad
ic Milnor K-theory of p-complete local rings in terms of the syntomic coho
mology introduced by Bhatt---M.---Scholze.\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph Ayoub (UZH)
DTSTART:20201215T170000Z
DTEND:20201215T180000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/12
DESCRIPTION:Title: Rigid analytic motivic sheaves\nby Joseph Ayoub (UZH) as part of
electronic Algebraic K-theory Seminar\n\nLecture held in 915 7106 9041.\n
Abstract: TBA\n\nI will report on recent work concerning motives in rigid
analytic geometry.\nIn particular\, I would like to discuss a vast general
isation of an old theorem of\nmine describing the category of rigid analyt
ic motives over a non Archimedean field\nof equi-characteristic zero in te
rms of algebraic motives over its residue field.\nThe generalisation is to
an arbitrary rigid analytic base. This is joint work with\nM. Gallauer an
d A. Vezzani.\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marc Hoyois (Regensburg)
DTSTART:20200929T160000Z
DTEND:20200929T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/13
DESCRIPTION:Title: Milnor excision for motivic spectra\nby Marc Hoyois (Regensburg)
as part of electronic Algebraic K-theory Seminar\n\nLecture held in 915 7
106 9041.\n\nAbstract\nIt is a classical result of Weibel that homotopy in
variant algebraic K-theory satisfies excision\, in the sense that for any
ring $A$ and ideal $I \\subset A$\, the fiber of $KH(A) \\rightarrow KH(A
/I)$ depends only on $I$ as a nonunital ring. In joint work with Elden Elm
anto\, Ryomei Iwasa\, and Shane Kelly\, we show that this is true more gen
erally for any cohomology theory represented by a motivic spectrum.\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Nikolaus (Münster)
DTSTART:20201013T160000Z
DTEND:20201013T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/14
DESCRIPTION:Title: On Grothendieck--Witt theory of the integers\nby Thomas Nikolaus
(Münster) as part of electronic Algebraic K-theory Seminar\n\nLecture he
ld in 915 7106 9041.\n\nAbstract\nWe introduce the Grothendieck--Witt grou
ps of the integers and\nthe Grothendieck--Witt spectrum of the integers.
Then we explain how to\ncompute these groups and the homotopy type of the
spectrum using recent\nwork on K-theory and L-theory. If time permits we a
lso explain how to\nresolve the homotopy limit problem for rings of intege
rs in number\nfields and prove Karoubi's periodicity conjecure for arbitra
ry rings.\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikala Jansen (Copenhagen)
DTSTART:20201027T160000Z
DTEND:20201027T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/15
DESCRIPTION:Title: The reductive Borel--Serre compactification as a model for the K-the
ory space\nby Mikala Jansen (Copenhagen) as part of electronic Algebra
ic K-theory Seminar\n\nLecture held in 915 7106 9041.\n\nAbstract\nThe red
uctive Borel--Serre compactification\, introduced by Zucker in 1982\, is a
stratified space which is well suited for the study of $L^2$-cohomology o
f arithmetic groups and has come to play a central role in the theory of c
ompactifications. We determine its stratified homotopy type (the exit path
$\\infty$-category) to be a $1$-category defined purely in terms of parab
olic subgroups. This category makes sense in a much more general setting\,
in fact for any exact category\, but in this talk we restrict ourselves t
o well-behaved rings. With direct sum\, these naturally give rise to a mon
oidal category\, and we show that (the loop space of the classifying space
of) this monoidal category is a model for the K-theory space. For finite
fields\, we encounter much better homological stability properties than fo
r the general linear groups.\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Wilson
DTSTART:20210316T160000Z
DTEND:20210316T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/16
DESCRIPTION:Title: Lichtenbaum-Quillen phenomena in chromatic homotopy theory\nby D
ylan Wilson as part of electronic Algebraic K-theory Seminar\n\nLecture he
ld in 979 0634 7355.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Bachmann (LMU)
DTSTART:20210330T160000Z
DTEND:20210330T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/17
DESCRIPTION:Title: Cellular 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 funct
or from the category of commutative rings (or the opposite of schemes\, sa
y) to spectra. Examples include algebraic K-theory\, motivic cohomology\,
etale cohomology and algebraic cobordism. Dwyer-Friedlander observed that
for 2-adic 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 thr
ee elements.\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://stable.researchseminars.org/talk/eAKTS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allen Yuan
DTSTART:20210413T160000Z
DTEND:20210413T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/18
DESCRIPTION:Title: Examples of chromatic redshift\nby Allen Yuan as part of electro
nic Algebraic K-theory Seminar\n\nLecture held in 979 0634 7355.\n\nAbstra
ct\nOne form of the Ausoni-Rognes chromatic redshift philosophy\nis that a
lgebraic K-theory raises the chromatic complexity of a ring\nby one. Work
of Clausen-Mathew-Naumann-Noel shows\, in particular\,\nthat K-theory rai
ses height by at most one\; on the other hand\, recent\nwork of Hahn-Wilso
n gives an example at each height (a form of $BP\\langle n\\rangle$)\nwher
e this height shifting does occur. In this talk\, I will discuss a\nsimpl
e non-computational proof of this height shifting in a range of\nexamples\
, including Lubin-Tate theories and the iterated K-theory of\nfields.\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Feng
DTSTART:20210427T160000Z
DTEND:20210427T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/19
DESCRIPTION:Title: The Galois action on symplectic K-theory\nby Tony Feng as part o
f electronic Algebraic K-theory Seminar\n\nLecture held in 979 0634 7355.\
n\nAbstract\nThe algebraic K-theory of the integers has fascinating\nconne
ctions with number theory\; for example\, the values of the Riemann\nzeta
function at negative integers turn out to be related to the sizes\nof K-gr
oups (by work of Rost-Voevodsky and Mazur-Wiles). Such\nconnections come f
rom unexpected structure on the classifying spaces\nof arithmetic groups\,
and can be explained in terms of the philosophy\nof the so-called Langlan
ds program. Motivated by this picture\, Akshay\nVenkatesh and Soren Galati
us and I considered a symplectic variant of\nalgebraic K-theory of the int
egers\, constructed a natural Galois\naction on it\, and computed that Gal
ois action. I will explain this\nstory with a K-theory audience in mind.\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Thomas
DTSTART:20210511T160000Z
DTEND:20210511T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/20
DESCRIPTION:Title: Square root Euler classes and counting sheaves on Calabi-Yau 4-folds
\nby Richard Thomas as part of electronic Algebraic K-theory Seminar\n
\nLecture held in 979 0634 7355.\n\nAbstract\nI will explain a nice charac
teristic class of SO(2n\,C) bundles in both Chow cohomology and K-theory\,
and how 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 structur
e sheaf) on moduli spaces of stable sheaves on Calabi-Yau 4-folds. It reco
vers the real derived differential geometry virtual cycle of Borisov-Joyce
but has nicer properties\, like a torus localisation formula. Joint work
with Jeongseok Oh (KIAS).\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Binda
DTSTART:20210525T160000Z
DTEND:20210525T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/21
DESCRIPTION:Title: GAGA type conjecture for the Brauer group via derived geometry\n
by Federico Binda as part of electronic Algebraic K-theory Seminar\n\nLect
ure held in 979 0634 7355.\n\nAbstract\nIn Brauer III\, Grothendieck consi
dered the 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 the inverse limit of the Brauer groups $\\lim_nBr(X_n)$\, where $X_n
= X\\otimes_R R/m^n$. 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 op
en problem the question on whether the formal injectivity holds in a fairl
y general 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 f
ormal GAGA-type problem for smooth and proper categories\, enriched over t
he $\\infty$-category $QCoh(X)$ of quasi-coherent $O_X$-modules. In this f
ramework we can show that Grothendieck’s injectivity conjecture always h
olds for a proper derived scheme $X \\to S$ where S is the spectrum of any
complete 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 schem
e $\\mathfrak{X}$ given by the colimit of the thickenings $X_n$. The obstr
uction involving the inverse system $Pic(X_n)$ considered by Grothendieck
appears naturally in the Milnor sequence for a certain tower of spaces. Th
is is a joint work in progress with Mauro Porta (IRMA\, Strasbourg).\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Dyckerhoff (Hamburg)
DTSTART:20210608T160000Z
DTEND:20210608T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/22
DESCRIPTION:Title: S-constructions\, Auslander algebras\, and wrapped Floer theory\
nby Tobias Dyckerhoff (Hamburg) as part of electronic Algebraic K-theory S
eminar\n\nLecture held in https://bbbvl.physnet.uni-hamburg.de/b/tob-ten-y
tm-x9v.\n\nAbstract\nWe will explain that\, beyond their purpose for defin
ing algebraic\nK-theory\, Waldhausen's S-construction and higher variants
have interesting\nstructural interpretations in the representation theory
of finite-dimensional\nalgebras and in wrapped Floer theory. This opens up
the opportunity to apply\ntechniques from either of the involved subjects
to the benefit of the others. We\nwill demonstrate this by giving a sympl
ectic proof of a certain "binomial\nduality" among the cells of the higher
S-construction discovered by Beckert.\nFinally\, we discuss further appli
cations to gluing formalisms for Fukaya\ncategories of symmetric products.
\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amalendu Krishna (TIFR)
DTSTART:20210622T160000Z
DTEND:20210622T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/23
DESCRIPTION:Title: Chow groups and Euler class groups of affine varieties\nby Amale
ndu Krishna (TIFR) as part of electronic Algebraic K-theory Seminar\n\nLec
ture held in 979 0634 7355.\n\nAbstract\nIn this talk\, I shall present tw
o results on the Chow group of 0-cycles on affine schemes over algebraical
ly closed fields and give\nseveral consequences of these results. In parti
cular\, I shall discuss proofs of an old conjecture of Murthy\, a conjectu
re of Mohan Kumar-Murthy-Roy and also the Euler class groups of such schem
es.\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirsten Wickelgren (Duke)
DTSTART:20210706T160000Z
DTEND:20210706T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/24
DESCRIPTION:Title: Counts of rational curves on Del Pezzo surfaces enriched in bilinear
forms\nby Kirsten Wickelgren (Duke) as part of electronic Algebraic K
-theory Seminar\n\nLecture held in 979 0634 7355.\n\nAbstract\nDel Pezzo s
urfaces here are smooth projective surfaces with\nample anticanonical bund
le\, including $\\mathbb{P}^2\, \\mathbb{P}^1 \\times \\mathbb{P}^1$\, and
cubic\nsurfaces. By imposing the condition that a rational curve of fixed
\ndegree passes through an appropriate number of points\, the number of\ns
uch curves is finite. Over the complex numbers\, these counts are\nindepen
dent of the generic choice of points. This invariance of number\nfails ove
r the reals\, but there is a beautiful method of Welschinger\nto correct t
his. It is a feature of $\\mathbb{A}^1$-homotopy theory that analogous\nre
al and complex results can indicate the presence of a common\ngeneralizati
on\, valid over a general field. For $\\mathbbA^1$-connected Del Pezzo\nsu
rfaces under appropriate hypotheses\, we give counts of rational\ncurves v
alued in the group completion GW(k) of symmetric\,\nnon-degenerate\, bilin
ear forms over k\, which are again independent of\nthe generic choice of p
oints. By replacing the positive integer count\nwith such a bilinear form\
, one records information about the field of\ndefinition of the rational c
urve and the tangent directions at its\nnodes. We compute some low degree
examples\, including on the Del Pezzo\nsurfaces listed above. This is join
t work with Jesse Kass\, Marc\nLevine\, and Jake Solomon.\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anand Sawant (TIFR)
DTSTART:20210720T160000Z
DTEND:20210720T170000Z
DTSTAMP:20260404T111136Z
UID:eAKTS/25
DESCRIPTION:Title: Central extensions of algebraic groups via cellular $\\mathbb{A}^1$-
homology\nby Anand Sawant (TIFR) as part of electronic Algebraic K-the
ory Seminar\n\nLecture held in 979 0634 7355.\n\nAbstract\nI will outline
the computation of the cellular $\\mathbb{A}^1$-homology of a split\, semi
simple\, simply connected algebraic group in low degrees and use it to des
cribe the group of central extensions of such a group by a suitable strict
ly $\\mathbb{A}^1$-invariant sheaf. These results in particular yield a m
otivic proof of the result of Brylinski and Deligne classifying central ex
tensions of such algebraic groups by $K_2$. The talk is based on joint wo
rk with Fabien Morel.\n
LOCATION:https://stable.researchseminars.org/talk/eAKTS/25/
END:VEVENT
END:VCALENDAR