BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200714T143000Z
DTEND;VALUE=DATE-TIME:20200714T160000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4668@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4668/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4668/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A Local Construction of Stable Motivic Homotopy Theory (2/3)
DTSTART;VALUE=DATE-TIME:20200715T110000Z
DTEND;VALUE=DATE-TIME:20200715T120000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4670@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ivan PANIN (St. Petersburg Department of Steklov Ins
titute of Mathematics)\nV. Voevodsky [6] invented the category of framed c
orrespondences with the hope to give a new construction of stable motivic
homotopy theory SH(k) which will be more friendly for computational purpos
es. Joint with G. Garkusha we used framed correspondences to develop the t
heory of framed motives in [4]. This theory led us in [5] to a genuinely l
ocal construction of SH(k). In particular\, we get rid of motivic equivale
nces completely.\nIn my lectures I will recall the definition of framed co
rrespondences and describe the genuinely local model for SH(k) (assuming t
hat the base field k is infinite and perfect). I will also discuss several
applications. Let Fr(Y\,X) be the pointed set of stable framed correspond
ences between smooth algebraic varieties Y and X. For the first two applic
ations I choose k = ℂ for simplicity. For further two applications k is
any infinite and perfect field.\n(1) The simplicial space Fr(𝚫alg\,S^1)
has the homotopy type of the topological space Ω∞Σ∞(S^1_top). So th
e topological space Ω^∞_S1Σ^∞_S1(S^1_top) is recovered as the simpli
cial set Fr(𝚫alg\,S^1)\, which is described in terms of algebraic varie
ties only. This is one of the computational miracles of framed corresponde
nces.\n(2) The assignment X ↦ π_*(Fr(𝚫alg\,X⨂S^1)) is a homology t
heory on complex algebraic varieties. Moreover\, this homology theory rega
rded with ℤ/n-coefficients coincides with the stable homotopies X ↦ π
^S_*(X+^S^1_top\;ℤ/n) with ℤ/n-coefficients.\nThe latter result is an
extension of the celebrated Suslin–Voevodsky theorem on motivic homolog
y of weight zero to the stable motivic homotopy context.\n(3) Another appl
ication of the theory is as follows. It turns out that π^s_0\,0(X+) = H0(
ℤF(𝚫\,X))\, where (ℤF(𝚫\,X)) is the chain complex of stable line
ar framed correspondences introduced in [4]. For X = G_m^^n this homology
group was computed by A. Neshitov as the nth Milnor–Witt group K_n^MW (k
) of the base field k recovering the celebrated theorem of Morel.\n(4) As
a consequence of the theory of framed motives\, the canonical morphism of
motivic spaces can : C_*Fr(X) → Ω^∞_ℙ^1 Σ^∞_ℙ^1 (X+) is Nisnic
h locally a group completion for any smooth simplicial scheme X. In partic
ular\, if C_*Fr(X) is Nisnevich locally connected\, then the morphism can
is a Nisnevich local weak equivalence. Thus in this case C_*Fr(X) is an in
finite motivic loop space and π_n(C_*FR(X)(K)) = π^A1_n\,0 (Σ^∞_ℙ^1
(X+))(K).\n\nIn my lectures I will adhere to the following references:\n[
1] A. Ananyevskiy\, G. Garkusha\, I. Panin\, Cancellation theorem for fram
ed motives of algebraic varieties\, arXiv:1601.06642\n[2] G. Garkusha\, A.
Neshitov\, I. Panin\, Framed motives of relative motivic spheres\, arXiv:
1604.02732v3.\n[3] G. Garkusha\, I. Panin\, Homotopy invariant presheaves
with framed transfers\, Cambridge J. Math. 8(1) (2020)\, 1-94.\n[4] G. Gar
kusha\, I. Panin\, Framed motives of algebraic varieties (after V. Voevods
ky)\, J. Amer. Math. Soc.\, to appear.\n[5] G. Garkusha\, I. Panin\, The t
riangulated categories of framed bispectra and framed motives\, arXiv:1809
.08006.\n[6] V. Voevodsky\, Notes on framed correspondences\, unpublished\
, 2001\, www.math.ias.edu/vladimir/publications\n\nhttps://indico.math.cnr
s.fr/event/5160/contributions/4670/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4670/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enumerative Geometry and Quadratic Forms (3/3)
DTSTART;VALUE=DATE-TIME:20200710T110000Z
DTEND;VALUE=DATE-TIME:20200710T120000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4655@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marc LEVINE (Universität Duisburg-Essen)\nMotivic W
elschinger invariants\n\nhttps://indico.math.cnrs.fr/event/5160/contributi
ons/4655/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4655/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200706T120000Z
DTEND;VALUE=DATE-TIME:20200706T133000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4638@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4638/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4638/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200709T143000Z
DTEND;VALUE=DATE-TIME:20200709T160000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4653@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4653/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4653/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A Local Construction of Stable Motivic Homotopy Theory (1/3)
DTSTART;VALUE=DATE-TIME:20200714T110000Z
DTEND;VALUE=DATE-TIME:20200714T120000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4660@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ivan PANIN (St. Petersburg Department of Steklov Ins
titute of Mathematics)\nV. Voevodsky [6] invented the category of framed c
orrespondences with the hope to give a new construction of stable motivic
homotopy theory SH(k) which will be more friendly for computational purpos
es. Joint with G. Garkusha we used framed correspondences to develop the t
heory of framed motives in [4]. This theory led us in [5] to a genuinely l
ocal construction of SH(k). In particular\, we get rid of motivic equivale
nces completely.\nIn my lectures I will recall the definition of framed co
rrespondences and describe the genuinely local model for SH(k) (assuming t
hat the base field k is infinite and perfect). I will also discuss several
applications. Let Fr(Y\,X) be the pointed set of stable framed correspond
ences between smooth algebraic varieties Y and X. For the first two applic
ations I choose k = ℂ for simplicity. For further two applications k is
any infinite and perfect field.\n(1) The simplicial space Fr(𝚫alg\,S^1)
has the homotopy type of the topological space Ω∞Σ∞(S^1_top). So th
e topological space Ω^∞_S1Σ^∞_S1(S^1_top) is recovered as the simpli
cial set Fr(𝚫alg\,S^1)\, which is described in terms of algebraic varie
ties only. This is one of the computational miracles of framed corresponde
nces.\n(2) The assignment X ↦ π_*(Fr(𝚫alg\,X⨂S^1)) is a homology t
heory on complex algebraic varieties. Moreover\, this homology theory rega
rded with ℤ/n-coefficients coincides with the stable homotopies X ↦ π
^S_*(X+^S^1_top\;ℤ/n) with ℤ/n-coefficients.\nThe latter result is an
extension of the celebrated Suslin–Voevodsky theorem on motivic homolog
y of weight zero to the stable motivic homotopy context.\n(3) Another appl
ication of the theory is as follows. It turns out that π^s_0\,0(X+) = H0(
ℤF(𝚫\,X))\, where (ℤF(𝚫\,X)) is the chain complex of stable line
ar framed correspondences introduced in [4]. For X = G_m^^n this homology
group was computed by A. Neshitov as the nth Milnor–Witt group K_n^MW (k
) of the base field k recovering the celebrated theorem of Morel.\n(4) As
a consequence of the theory of framed motives\, the canonical morphism of
motivic spaces can : C_*Fr(X) → Ω^∞_ℙ^1 Σ^∞_ℙ^1 (X+) is Nisnic
h locally a group completion for any smooth simplicial scheme X. In partic
ular\, if C_*Fr(X) is Nisnevich locally connected\, then the morphism can
is a Nisnevich local weak equivalence. Thus in this case C_*Fr(X) is an in
finite motivic loop space and π_n(C_*FR(X)(K)) = π^A1_n\,0 (Σ^∞_ℙ^1
(X+))(K).\n\nIn my lectures I will adhere to the following references:\n[
1] A. Ananyevskiy\, G. Garkusha\, I. Panin\, Cancellation theorem for fram
ed motives of algebraic varieties\, arXiv:1601.06642\n[2] G. Garkusha\, A.
Neshitov\, I. Panin\, Framed motives of relative motivic spheres\, arXiv:
1604.02732v3.\n[3] G. Garkusha\, I. Panin\, Homotopy invariant presheaves
with framed transfers\, Cambridge J. Math. 8(1) (2020)\, 1-94.\n[4] G. Gar
kusha\, I. Panin\, Framed motives of algebraic varieties (after V. Voevods
ky)\, J. Amer. Math. Soc.\, to appear.\n[5] G. Garkusha\, I. Panin\, The t
riangulated categories of framed bispectra and framed motives\, arXiv:1809
.08006.\n[6] V. Voevodsky\, Notes on framed correspondences\, unpublished\
, 2001\, www.math.ias.edu/vladimir/publications\n\nhttps://indico.math.cnr
s.fr/event/5160/contributions/4660/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4660/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200706T143000Z
DTEND;VALUE=DATE-TIME:20200706T160000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4640@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4640/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4640/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200707T120000Z
DTEND;VALUE=DATE-TIME:20200707T133000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4643@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4643/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4643/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200707T143000Z
DTEND;VALUE=DATE-TIME:20200707T160000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4645@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4645/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4645/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200708T153000Z
DTEND;VALUE=DATE-TIME:20200708T160000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4648@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4648/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4648/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200709T120000Z
DTEND;VALUE=DATE-TIME:20200709T133000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4651@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4651/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4651/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200710T120000Z
DTEND;VALUE=DATE-TIME:20200710T133000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4656@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4656/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4656/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200710T143000Z
DTEND;VALUE=DATE-TIME:20200710T160000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4658@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4658/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4658/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200713T120000Z
DTEND;VALUE=DATE-TIME:20200713T133000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4661@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4661/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4661/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200713T143000Z
DTEND;VALUE=DATE-TIME:20200713T160000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4663@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4663/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4663/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200714T120000Z
DTEND;VALUE=DATE-TIME:20200714T133000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4666@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4666/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4666/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Real and Hyperreal Equivariant and Motivic Computations
DTSTART;VALUE=DATE-TIME:20200717T160000Z
DTEND;VALUE=DATE-TIME:20200717T170000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4664@indico.math.cnrs.fr
DESCRIPTION:Speakers: Mike HILL (UCLA)\nFoundational work of Hu—Kriz and
Dugger showed that for Real spectra\, we can often compute as easily as n
on-equivariantly. The general equivariant slice filtration was developed t
o show how this philosophy extends from $C_2$-equivariant homotopy to larg
er cyclic $2$-groups\, and this has some fantastic applications to chromat
ic homotopy. This talk will showcase how one can carry out computations\,
and some of the tools that make these computations easier.\n\nThe natural
source for Real spectra is the complex points of motivic spectra over $\\m
athbb R$\, and there is a more initial\, parallel story here. I will discu
ss some of how the equivariant shadow can show us structure in the motivic
case as well.\n\nhttps://indico.math.cnrs.fr/event/5160/contributions/466
4/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4664/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A Local Construction of Stable Motivic Homotopy Theory (3/3)
DTSTART;VALUE=DATE-TIME:20200717T110000Z
DTEND;VALUE=DATE-TIME:20200717T120000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4678@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ivan PANIN (St. Petersburg Department of Steklov Ins
titute of Mathematics)\nV. Voevodsky [6] invented the category of framed c
orrespondences with the hope to give a new construction of stable motivic
homotopy theory SH(k) which will be more friendly for computational purpos
es. Joint with G. Garkusha we used framed correspondences to develop the t
heory of framed motives in [4]. This theory led us in [5] to a genuinely l
ocal construction of SH(k). In particular\, we get rid of motivic equivale
nces completely.\nIn my lectures I will recall the definition of framed co
rrespondences and describe the genuinely local model for SH(k) (assuming t
hat the base field k is infinite and perfect). I will also discuss several
applications. Let Fr(Y\,X) be the pointed set of stable framed correspond
ences between smooth algebraic varieties Y and X. For the first two applic
ations I choose k = ℂ for simplicity. For further two applications k is
any infinite and perfect field.\n(1) The simplicial space Fr(𝚫alg\,S^1)
has the homotopy type of the topological space Ω∞Σ∞(S^1_top). So th
e topological space Ω^∞S1Σ^∞_S1(S^1_top) is recovered as the simplic
ial set Fr(𝚫alg\,S^1)\, which is described in terms of algebraic variet
ies only. This is one of the computational miracles of framed corresponden
ces.\n(2) The assignment X ↦ π(Fr(𝚫alg\,X⨂S^1)) is a homology theo
ry on complex algebraic varieties. Moreover\, this homology theory regarde
d with ℤ/n-coefficients coincides with the stable homotopies X ↦ π ^S
_(X+^S^1_top\;ℤ/n) with ℤ/n-coefficients.\nThe latter result is an ext
ension of the celebrated Suslin–Voevodsky theorem on motivic homology of
weight zero to the stable motivic homotopy context.\n(3) Another applicat
ion of the theory is as follows. It turns out that π^s_0\,0(X+) = H0(ℤF
(𝚫\,X))\, where (ℤF(𝚫\,X)) is the chain complex of stable linear f
ramed correspondences introduced in [4]. For X = G_m^^n this homology grou
p was computed by A. Neshitov as the nth Milnor–Witt group K_n^MW (k) of
the base field k recovering the celebrated theorem of Morel.\n(4) As a co
nsequence of the theory of framed motives\, the canonical morphism of moti
vic spaces can : C_Fr(X) → Ω^∞ℙ^1 Σ^∞_ℙ^1 (X+) is Nisnich loca
lly a group completion for any smooth simplicial scheme X. In particular\,
if CFr(X) is Nisnevich locally connected\, then the morphism can is a Nis
nevich local weak equivalence. Thus in this case C_Fr(X) is an infinite mo
tivic loop space and π_n(C_FR(X)(K)) = π^A1_n\,0 (Σ^∞_ℙ^1 (X+))(K).
\n\nIn my lectures I will adhere to the following references:\n[1] A. Anan
yevskiy\, G. Garkusha\, I. Panin\, Cancellation theorem for framed motives
of algebraic varieties\, arXiv:1601.06642\n[2] G. Garkusha\, A. Neshitov\
, I. Panin\, Framed motives of relative motivic spheres\, arXiv:1604.02732
v3.\n[3] G. Garkusha\, I. Panin\, Homotopy invariant presheaves with frame
d transfers\, Cambridge J. Math. 8(1) (2020)\, 1-94.\n[4] G. Garkusha\, I.
Panin\, Framed motives of algebraic varieties (after V. Voevodsky)\, J. A
mer. Math. Soc.\, to appear.\n[5] G. Garkusha\, I. Panin\, The triangulate
d categories of framed bispectra and framed motives\, arXiv:1809.08006.\n[
6] V. Voevodsky\, Notes on framed correspondences\, unpublished\, 2001\, w
ww.math.ias.edu/vladimir/publications\n\nhttps://indico.math.cnrs.fr/event
/5160/contributions/4678/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4678/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Equivariant Infinite Loop Space Machines
DTSTART;VALUE=DATE-TIME:20200715T160000Z
DTEND;VALUE=DATE-TIME:20200715T170000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4672@indico.math.cnrs.fr
DESCRIPTION:Speakers: Angélica M. Osorno (Reed College)\nAn equivariant i
nfinite loop space machine is a functor that constructs genuine equivarian
t spectra out of simpler categorical or space level data. In the late 80
’s Lewis–May–Steinberger and Shimakawa developed generalizations of
the operadic approach and the G-space approach respectively. In this talk
I will report on joint work with Bert Guillou\, Peter May and Mona Merling
on adapting these machines to work multiplicatively and on understanding
their categorical input\n\nhttps://indico.math.cnrs.fr/event/5160/contribu
tions/4672/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4672/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Exodromy for ℓ-adic Sheaves (1/3)
DTSTART;VALUE=DATE-TIME:20200706T160000Z
DTEND;VALUE=DATE-TIME:20200706T170000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4641@indico.math.cnrs.fr
DESCRIPTION:Speakers: Clark BARWICK (University of Edinburgh)\nIn joint wo
rk with Saul Glasman and Peter Haine\, we proved that the derived ∞-cate
gory of constructible ℓ-adic sheaves ’is’ the ∞-category of contin
uous functors from an explicitly defined 1-category to the ∞-category of
perfect complexes over ℚℓ. In this series of talks\, I want to offer
some historical context for these ideas and to explain some of the techolo
gies that go into both the statement and the proof. If time permits\, I wi
ll also discuss newer work that aims to expand the scope of these results\
n\nhttps://indico.math.cnrs.fr/event/5160/contributions/4641/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4641/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fibrant Resolutions of Motivic Thom Spectra
DTSTART;VALUE=DATE-TIME:20200714T160000Z
DTEND;VALUE=DATE-TIME:20200714T170000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4669@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alexander NESHITOV (Western University)\nThis is a j
oint work with G. Garkusha. In the talk I will discuss the construction of
fibrant replacements for spectra consisting of Thom spaces (suspension sp
ectra of varieties and algebraic cobordism 𝑀𝐺𝐿 being the motivati
ng examples) that uses the theory of framed correspondences. As a conseque
nce we get a description of the infinite loop space of 𝑀𝐺𝐿 in ter
ms of Hilbert schemes\n\nhttps://indico.math.cnrs.fr/event/5160/contributi
ons/4669/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4669/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200715T120000Z
DTEND;VALUE=DATE-TIME:20200715T133000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4695@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4695/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4695/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Algebraic K-theory and Trace Methods (2/3)
DTSTART;VALUE=DATE-TIME:20200707T160000Z
DTEND;VALUE=DATE-TIME:20200707T170000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4646@indico.math.cnrs.fr
DESCRIPTION:Speakers: Teena GERHARDT (Michigan State University)\nAlgebrai
c K-theory is an invariant of rings and ring spectra which illustrates a f
ascinating interplay between algebra and topology. Defined using topologic
al tools\, this invariant has important applications to algebraic geometry
\, number theory\, and geometric topology. One fruitful approach to studyi
ng algebraic K-theory is via trace maps\, relating algebraic K-theory to (
topological) Hochschild homology\, and (topological) cyclic homology. In t
his mini-course I will introduce algebraic K-theory and related Hochschild
invariants\, and discuss recent advances in this area. Topics will includ
e cyclotomic spectra\, computations of the algebraic K-theory of rings\, a
nd equivariant analogues of Hochschild invariants.\n\nhttps://indico.math.
cnrs.fr/event/5160/contributions/4646/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4646/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200716T120000Z
DTEND;VALUE=DATE-TIME:20200716T133000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4674@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4674/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4674/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enumerative Geometry and Quadratic Forms (2/3)
DTSTART;VALUE=DATE-TIME:20200708T160000Z
DTEND;VALUE=DATE-TIME:20200708T170000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4647@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marc LEVINE (Universität Duisburg-Essen)\nComputati
ons of Euler Characteristics and Euler Classes\n\nhttps://indico.math.cnrs
.fr/event/5160/contributions/4647/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4647/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Exodromy for ℓ-adic Sheaves (3/3)
DTSTART;VALUE=DATE-TIME:20200710T160000Z
DTEND;VALUE=DATE-TIME:20200710T170000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4659@indico.math.cnrs.fr
DESCRIPTION:Speakers: Clark BARWICK (University of Edinburgh)\nIn joint wo
rk with Saul Glasman and Peter Haine\, we proved that the derived ∞-cate
gory of constructible ℓ-adic sheaves ’is’ the ∞-category of contin
uous functors from an explicitly defined 1-category to the ∞-category of
perfect complexes over ℚℓ. In this series of talks\, I want to offer
some historical context for these ideas and to explain some of the techolo
gies that go into both the statement and the proof. If time permits\, I wi
ll also discuss newer work that aims to expand the scope of these results.
\n\nhttps://indico.math.cnrs.fr/event/5160/contributions/4659/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4659/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200715T143000Z
DTEND;VALUE=DATE-TIME:20200715T160000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4671@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4671/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4671/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200716T143000Z
DTEND;VALUE=DATE-TIME:20200716T160000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4676@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4676/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4676/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200717T120000Z
DTEND;VALUE=DATE-TIME:20200717T133000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4679@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4679/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4679/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussions / Coffee Break
DTSTART;VALUE=DATE-TIME:20200717T143000Z
DTEND;VALUE=DATE-TIME:20200717T160000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4681@indico.math.cnrs.fr
DESCRIPTION:https://indico.math.cnrs.fr/event/5160/contributions/4681/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4681/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enumerative Geometry and Quadratic Forms (1/3)
DTSTART;VALUE=DATE-TIME:20200706T110000Z
DTEND;VALUE=DATE-TIME:20200706T120000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4637@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marc LEVINE (Universität Duisburg-Essen)\nEnumerati
ve Geometry and Quadratic Forms: Euler characteristics and Euler classes\n
\nhttps://indico.math.cnrs.fr/event/5160/contributions/4637/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4637/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Motivic Realizations of Singularity Categories
DTSTART;VALUE=DATE-TIME:20200713T160000Z
DTEND;VALUE=DATE-TIME:20200713T170000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4696@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marco Robalo (IMJ-PRG)\nIn this lecture\, we will ex
plain the connection between the (motivic) theory of vanishing cycles and
the construction of motivic realizations of singularity categories. We rev
iew the results obtained in collaboration with Blanc-Toen-Vezzosi and disc
uss some of the recent progresses in the field.\n\nhttps://indico.math.cnr
s.fr/event/5160/contributions/4696/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4696/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Motivic and Equivariant Stable Homotopy Groups (1/3)
DTSTART;VALUE=DATE-TIME:20200707T133000Z
DTEND;VALUE=DATE-TIME:20200707T143000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4644@indico.math.cnrs.fr
DESCRIPTION:Speakers: Daniel ISAKSEN (Wayne State University)\nI will disc
uss a program for computing C2-equivariant\, ℝ-motivic\, ℂ-motivic\, a
nd classical stable homotopy groups\, emphasizing the connections and rela
tionships between the four homotopical contexts.\nThe Adams spectral seque
nce and the effective spectral sequence are the key tools. The analysis of
these spectral sequences break into three main steps: (1) algebraically c
ompute the E2-page\; (2) analyze differentials\; (3) resolve hidden extens
ions. I will demonstrate a variety of techniques for each of these steps.\
nI will make precise the idea that ℂ-motivic stable homotopy theory is a
deformation of classical stable homotopy theory. I will discuss some futu
re prospects for homotopical deformation theory in general.\n\nhttps://ind
ico.math.cnrs.fr/event/5160/contributions/4644/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4644/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Algebraic K-theory and Trace Methods (3/3)
DTSTART;VALUE=DATE-TIME:20200709T133000Z
DTEND;VALUE=DATE-TIME:20200709T143000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4652@indico.math.cnrs.fr
DESCRIPTION:Speakers: Teena GERHARDT (Michigan State University)\nAlgebra
ic K-theory is an invariant of rings and ring spectra which illustrates a
fascinating interplay between algebra and topology. Defined using topologi
cal tools\, this invariant has important applications to algebraic geometr
y\, number theory\, and geometric topology. One fruitful approach to study
ing algebraic K-theory is via trace maps\, relating algebraic K-theory to
(topological) Hochschild homology\, and (topological) cyclic homology. In
this mini-course I will introduce algebraic K-theory and related Hochschil
d invariants\, and discuss recent advances in this area. Topics will inclu
de cyclotomic spectra\, computations of the algebraic K-theory of rings\,
and equivariant analogues of Hochschild invariants.\n\nhttps://indico.math
.cnrs.fr/event/5160/contributions/4652/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4652/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noncommutative Counterparts of Celebrated Conjectures (1/3)
DTSTART;VALUE=DATE-TIME:20200713T133000Z
DTEND;VALUE=DATE-TIME:20200713T143000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4662@indico.math.cnrs.fr
DESCRIPTION:Speakers: Gonçalo TABUADA (MIT Department of Mathematics)\nSo
me celebrated conjectures of Beilinson\, Grothendieck\, Kimura\, Tate\, Vo
evodsky\, Weil\, and others\, play a key central role in algebraic geometr
y. Notwithstanding the effort of several generations of mathematicians\, t
he proof of (the majority of) these conjectures remains illusive. The aim
of this course\, prepared for a broad audience\, is to give an overview of
a recent noncommutative approach which has led to the proof of the aforem
entioned important conjectures in some new cases.\n\nhttps://indico.math.c
nrs.fr/event/5160/contributions/4662/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4662/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Exodromy for ℓ-adic Sheaves (2/3)
DTSTART;VALUE=DATE-TIME:20200708T143000Z
DTEND;VALUE=DATE-TIME:20200708T153000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4649@indico.math.cnrs.fr
DESCRIPTION:Speakers: Clark BARWICK (University of Edinburgh)\nIn joint wo
rk with Saul Glasman and Peter Haine\, we proved that the derived ∞-cate
gory of constructible ℓ-adic sheaves ’is’ the ∞-category of contin
uous functors from an explicitly defined 1-category to the ∞-category of
perfect complexes over ℚℓ. In this series of talks\, I want to offer
some historical context for these ideas and to explain some of the techolo
gies that go into both the statement and the proof. If time permits\, I wi
ll also discuss newer work that aims to expand the scope of these results.
\n\nhttps://indico.math.cnrs.fr/event/5160/contributions/4649/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4649/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Motivic and Equivariant Stable Homotopy Groups (2/3)
DTSTART;VALUE=DATE-TIME:20200709T160000Z
DTEND;VALUE=DATE-TIME:20200709T170000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4654@indico.math.cnrs.fr
DESCRIPTION:Speakers: Daniel ISAKSEN (Wayne State University)\nI will disc
uss a program for computing C2-equivariant\, ℝ-motivic\, ℂ-motivic\, a
nd classical stable homotopy groups\, emphasizing the connections and rela
tionships between the four homotopical contexts.\nThe Adams spectral seque
nce and the effective spectral sequence are the key tools. The analysis of
these spectral sequences break into three main steps: (1) algebraically c
ompute the E2-page\; (2) analyze differentials\; (3) resolve hidden extens
ions. I will demonstrate a variety of techniques for each of these steps.\
nI will make precise the idea that ℂ-motivic stable homotopy theory is a
deformation of classical stable homotopy theory. I will discuss some futu
re prospects for homotopical deformation theory in general.\n\nhttps://ind
ico.math.cnrs.fr/event/5160/contributions/4654/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4654/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Motives from the Non-commutative Point of View (3/3)
DTSTART;VALUE=DATE-TIME:20200713T110000Z
DTEND;VALUE=DATE-TIME:20200713T120000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4665@indico.math.cnrs.fr
DESCRIPTION:Speakers: Dmitry KALEDIN (Steklov Mathematical Inst. & Nationa
l Research Univ. Higher School of Economics)\nMotives were initially conce
ived as a way to unify various cohomology theories that appear in algebrai
c geometry\, and these can be roughly divided into two groups: theories of
etale type\, and theories of cristalline/de Rham type. The obvious unifyi
ng feature of all the theories is that they carry some version of a Chern
character map from the algebraic K-theory\, and there is a bunch of “mot
ivic” conjectures claiming that in various contexts\, this map can be re
fined to some “regulator map” that is not far from an isomorphism. Alm
ost all of these conjectures are still wide open.\nOne observation whose i
mportance was not obvious at first is that K-theory is actually defined in
a much larger generality: it makes sense for an associative but not neces
sarily commutative ring. From the modern of of view\, the same should be t
rue for all the theories of de Rham type\, with differential forms replace
d by Hochschild homology classes\, and all the motivic conjectures should
also generalize. One prominent example of this is the cyclotomic trace map
of B¨okstedt–Hsiang–Madsen that serves as a non-commutative analog o
f the regulator in the p-adic setting.\nWhile the non-commutative conjectu
res are just as open as the commutative ones\, one can still hope that the
y might be more tractable: after all\, if something holds in a bigger gene
rality\, its potential proof by necessity should use much less\, so it oug
ht to be simpler. In addition to this\, non-commutative setting allows for
completely new methods. One such is the observation that Hochschild Homol
ogy is a two-variable theory: one can define homology groups of an algebra
with coefficients in a bimodule. These groups come equipped with certain
natural trace-like isomorphisms\, and this already allowed one to prove se
veral general comparison results.\n\nhttps://indico.math.cnrs.fr/event/516
0/contributions/4665/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4665/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pullbacks for the Rost-Schmid Complex
DTSTART;VALUE=DATE-TIME:20200714T133000Z
DTEND;VALUE=DATE-TIME:20200714T143000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4667@indico.math.cnrs.fr
DESCRIPTION:Speakers: Tom BACHMANN (MIT)\nLet 𝑘 be a perfect field and
𝑀 a strictly homotopy invariant sheaf of abelian groups on Sm_𝑘. The
cousin complex can be used to compute the cohomology of a smooth variety
𝑋 over 𝑘 with coefficients in 𝑀. However\, if 𝑋 → 𝑌 is a
morphism of smooth varieties\, there is not in general an induced map on c
ousin complexes\, so computing pullbacks of cohomology classes is difficul
t. In this talk I will explain how such pullbacks may nonetheless be compu
ted\, at least up to choosing a good enough cycle representing the cohomol
ogy class (which is always possible in principle\, but may be difficult in
practice). Time permitting\, I will mention applications to the 𝔾_𝑚
-stabilization conjecture (which was formulated jointly with Maria Yakerso
n)\n\nhttps://indico.math.cnrs.fr/event/5160/contributions/4667/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4667/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noncommutative Counterparts of Celebrated Conjectures (2/3)
DTSTART;VALUE=DATE-TIME:20200715T133000Z
DTEND;VALUE=DATE-TIME:20200715T143000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4694@indico.math.cnrs.fr
DESCRIPTION:Speakers: Gonçalo Tabuada (MIT Department of Mathematics)\nSo
me celebrated conjectures of Beilinson\, Grothendieck\, Kimura\, Tate\, Vo
evodsky\, Weil\, and others\, play a key central role in algebraic geometr
y. Notwithstanding the effort of several generations of mathematicians\, t
he proof of (the majority of) these conjectures remains illusive. The aim
of this course\, prepared for a broad audience\, is to give an overview of
a recent noncommutative approach which has led to the proof of the aforem
entioned important conjectures in some new cases.\n\nhttps://indico.math.c
nrs.fr/event/5160/contributions/4694/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4694/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noncommutative Counterparts of Celebrated Conjectures (3/3)
DTSTART;VALUE=DATE-TIME:20200716T133000Z
DTEND;VALUE=DATE-TIME:20200716T143000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4673@indico.math.cnrs.fr
DESCRIPTION:Speakers: Gonçalo TABUADA (MIT Department of Mathematics)\nSo
me celebrated conjectures of Beilinson\, Grothendieck\, Kimura\, Tate\, Vo
evodsky\, Weil\, and others\, play a key central role in algebraic geometr
y. Notwithstanding the effort of several generations of mathematicians\, t
he proof of (the majority of) these conjectures remains illusive. The aim
of this course\, prepared for a broad audience\, is to give an overview of
a recent noncommutative approach which has led to the proof of the aforem
entioned important conjectures in some new cases.\n\nhttps://indico.math.c
nrs.fr/event/5160/contributions/4673/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4673/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Knots and Motives
DTSTART;VALUE=DATE-TIME:20200716T110000Z
DTEND;VALUE=DATE-TIME:20200716T120000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4675@indico.math.cnrs.fr
DESCRIPTION:Speakers: Geoffroy HOREL (University Paris 13)\nThe pure braid
group is the fundamental group of the space of configurations of points i
n the complex plane. This topological space is the Betti realization of a
scheme defined over the integers. It follows\, by work initiated by Delign
e and Goncharov\, that the pronilpotent completion of the pure braid group
is a motive over the integers (what this means precisely is that the Hopf
algebra of functions on that group can be promoted to a Hopf algebra in a
n abelian category of motives over the integers). I will explain a partly
conjectural extension of that story from braids to knots. The replacement
of the lower central series of the pure braid group is the so-called Vassi
liev filtration on knots. The proposed strategy to construct the desired m
otivic structure relies on the technology of manifold calculus of Goodwill
ie and Weiss.\n\nhttps://indico.math.cnrs.fr/event/5160/contributions/4675
/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4675/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Integrality Results for 𝔸^1-Euler Numbers and Arithmetic Counts
of Linear Subspaces of Complete Intersections
DTSTART;VALUE=DATE-TIME:20200716T160000Z
DTEND;VALUE=DATE-TIME:20200716T170000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4677@indico.math.cnrs.fr
DESCRIPTION:Speakers: Kirsten WICKELGREN (Duke University)\n𝔸^1-Euler n
umbers can be constructed with Hochschild homology\, self-duality of Koszu
l complexes\, pushforwards in 𝑆𝐿_𝑐 oriented cohomology theories\,
and sums of local degrees. We show an integrality result for 𝔸^1-Euler
numbers and apply this to the enumeration of 𝑑-planes in complete inte
rsections. Classically such counts are valid over the complex numbers and
sometimes extended to the real numbers. 𝔸^1-homotopy theory allows one
to perform counts over arbitrary fields\, and records information about th
e arithmetic and geometry of the solutions with bilinear forms. For exampl
e\, it then follows from work of Finashin–Kharlamov that there are 160\;
839⟨1⟩+160\;650⟨-1⟩ 3-planes in any 7-dimensional cubic hypersurfa
ce when these 3-planes are counted with an appropriate weight. This is joi
nt work with Tom Bachmann.\n\nhttps://indico.math.cnrs.fr/event/5160/contr
ibutions/4677/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4677/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Triangulated Categories of Log Motives over a Field
DTSTART;VALUE=DATE-TIME:20200717T133000Z
DTEND;VALUE=DATE-TIME:20200717T143000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4680@indico.math.cnrs.fr
DESCRIPTION:Speakers: Federico BINDA (University of Milan)\nIn this talk I
will sketch the construction and highlight the main properties of a new m
otivic category for logarithmic schemes\, log smooth over a ground field k
(without log structure). This construction is based on a new Grothendieck
topology (called the “dividing topology”) and on the principle that h
omotopies should be parametrised by the affine line with compactifying log
structure. The resulting category logDM shares many of the fundamental pr
operties of Voevodsky’s DM\, that can be faithfully embedded inside it\,
and can be used to represent cohomology theories that are not A^1-homotop
y invariant (like Hodge cohomology or Hodge-Witt cohomology). If time perm
its\, we will discuss some conjectures relating the étale version of our
category with integral coefficients with the Milne-Ramachandran category o
f integral étale motivic complexes. This is a joint work with D. Park (Zu
rich) and P.-A.Østvær (Oslo).\n\nhttps://indico.math.cnrs.fr/event/5160/
contributions/4680/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4680/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Algebraic K-theory and Trace Methods (1/3)
DTSTART;VALUE=DATE-TIME:20200706T133000Z
DTEND;VALUE=DATE-TIME:20200706T143000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4639@indico.math.cnrs.fr
DESCRIPTION:Speakers: Teena GERHARDT (Michigan State University)\nAlgebrai
c K-theory is an invariant of rings and ring spectra which illustrates a f
ascinating interplay between algebra and topology. Defined using topologic
al tools\, this invariant has important applications to algebraic geometry
\, number theory\, and geometric topology. One fruitful approach to studyi
ng algebraic K-theory is via trace maps\, relating algebraic K-theory to (
topological) Hochschild homology\, and (topological) cyclic homology. In t
his mini-course I will introduce algebraic K-theory and related Hochschild
invariants\, and discuss recent advances in this area. Topics will includ
e cyclotomic spectra\, computations of the algebraic K-theory of rings\, a
nd equivariant analogues of Hochschild invariants.\n\nhttps://indico.math.
cnrs.fr/event/5160/contributions/4639/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4639/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Motives from the Non-commutative Point of View (1/3)
DTSTART;VALUE=DATE-TIME:20200707T110000Z
DTEND;VALUE=DATE-TIME:20200707T120000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4642@indico.math.cnrs.fr
DESCRIPTION:Speakers: Dmitry KALEDIN (Steklov Mathematical Inst. & Nationa
l Research Univ. Higher School of Economics)\nMotives were initially conce
ived as a way to unify various cohomology theories that appear in algebrai
c geometry\, and these can be roughly divided into two groups: theories of
etale type\, and theories of cristalline/de Rham type. The obvious unifyi
ng feature of all the theories is that they carry some version of a Chern
character map from the algebraic K-theory\, and there is a bunch of “mot
ivic” conjectures claiming that in various contexts\, this map can be re
fined to some “regulator map” that is not far from an isomorphism. Alm
ost all of these conjectures are still wide open.\nOne observation whose i
mportance was not obvious at first is that K-theory is actually defined in
a much larger generality: it makes sense for an associative but not neces
sarily commutative ring. From the modern of of view\, the same should be t
rue for all the theories of de Rham type\, with differential forms replace
d by Hochschild homology classes\, and all the motivic conjectures should
also generalize. One prominent example of this is the cyclotomic trace map
of B¨okstedt–Hsiang–Madsen that serves as a non-commutative analog o
f the regulator in the p-adic setting.\nWhile the non-commutative conjectu
res are just as open as the commutative ones\, one can still hope that the
y might be more tractable: after all\, if something holds in a bigger gene
rality\, its potential proof by necessity should use much less\, so it oug
ht to be simpler. In addition to this\, non-commutative setting allows for
completely new methods. One such is the observation that Hochschild Homol
ogy is a two-variable theory: one can define homology groups of an algebra
with coefficients in a bimodule. These groups come equipped with certain
natural trace-like isomorphisms\, and this already allowed one to prove se
veral general comparison results.\n\nhttps://indico.math.cnrs.fr/event/516
0/contributions/4642/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4642/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Motives from the Non-commutative Point of View (2/3)
DTSTART;VALUE=DATE-TIME:20200709T110000Z
DTEND;VALUE=DATE-TIME:20200709T120000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4650@indico.math.cnrs.fr
DESCRIPTION:Speakers: Dmitry KALEDIN (Steklov Mathematical Inst. & Nationa
l Research Univ. Higher School of Economics)\nMotives were initially conce
ived as a way to unify various cohomology theories that appear in algebrai
c geometry\, and these can be roughly divided into two groups: theories of
etale type\, and theories of cristalline/de Rham type. The obvious unifyi
ng feature of all the theories is that they carry some version of a Chern
character map from the algebraic K-theory\, and there is a bunch of “mot
ivic” conjectures claiming that in various contexts\, this map can be re
fined to some “regulator map” that is not far from an isomorphism. Alm
ost all of these conjectures are still wide open.\nOne observation whose i
mportance was not obvious at first is that K-theory is actually defined in
a much larger generality: it makes sense for an associative but not neces
sarily commutative ring. From the modern of of view\, the same should be t
rue for all the theories of de Rham type\, with differential forms replace
d by Hochschild homology classes\, and all the motivic conjectures should
also generalize. One prominent example of this is the cyclotomic trace map
of B¨okstedt–Hsiang–Madsen that serves as a non-commutative analog o
f the regulator in the p-adic setting.\nWhile the non-commutative conjectu
res are just as open as the commutative ones\, one can still hope that the
y might be more tractable: after all\, if something holds in a bigger gene
rality\, its potential proof by necessity should use much less\, so it oug
ht to be simpler. In addition to this\, non-commutative setting allows for
completely new methods. One such is the observation that Hochschild Homol
ogy is a two-variable theory: one can define homology groups of an algebra
with coefficients in a bimodule. These groups come equipped with certain
natural trace-like isomorphisms\, and this already allowed one to prove se
veral general comparison results.\n\nhttps://indico.math.cnrs.fr/event/516
0/contributions/4650/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4650/
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BEGIN:VEVENT
SUMMARY:Motivic and Equivariant Stable Homotopy Groups (3/3)
DTSTART;VALUE=DATE-TIME:20200710T133000Z
DTEND;VALUE=DATE-TIME:20200710T143000Z
DTSTAMP;VALUE=DATE-TIME:20210518T175957Z
UID:indico-contribution-5160-4657@indico.math.cnrs.fr
DESCRIPTION:Speakers: Daniel ISAKSEN (Wayne State University)\nI will disc
uss a program for computing C2-equivariant\, ℝ-motivic\, ℂ-motivic\, a
nd classical stable homotopy groups\, emphasizing the connections and rela
tionships between the four homotopical contexts.\nThe Adams spectral seque
nce and the effective spectral sequence are the key tools. The analysis of
these spectral sequences break into three main steps: (1) algebraically c
ompute the E2-page\; (2) analyze differentials\; (3) resolve hidden extens
ions. I will demonstrate a variety of techniques for each of these steps.\
nI will make precise the idea that ℂ-motivic stable homotopy theory is a
deformation of classical stable homotopy theory. I will discuss some futu
re prospects for homotopical deformation theory in general.\n\nhttps://ind
ico.math.cnrs.fr/event/5160/contributions/4657/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/5160/contributions/4657/
END:VEVENT
END:VCALENDAR