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BEGIN:VEVENT
SUMMARY:On relative log de Rham-Witt complex
DTSTART;VALUE=DATE-TIME:20180613T140000Z
DTEND;VALUE=DATE-TIME:20180613T150000Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-746@indico.math.cnrs.fr
DESCRIPTION:Speakers: A. Shiho (University of Tokyo)\nThe notion of relati
ve log de Rham-Witt complex\, which is the log version of relative de Rham
-Witt complex of Langer-Zink\, is defined by Matsuue. In this talk\, we gi
ve the comparison theorem between relative log de Rham-Witt cohomology and
relative log crystalline cohomology for log smooth saturated morphism of
fs log schemes satisfying certain condition on which p is nilpotent. Our r
esult generalizes most of the previously known results by Illusie\, Hyodo-
Kato\, Langer-Zink and Matsuue. This is a joint work with Kazuki Hirayama.
\n\nhttps://indico.math.cnrs.fr/event/1771/contributions/746/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/746/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Log Drinfeld modules and moduli spaces
DTSTART;VALUE=DATE-TIME:20180613T123000Z
DTEND;VALUE=DATE-TIME:20180613T133000Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-747@indico.math.cnrs.fr
DESCRIPTION:Speakers: K. Kato (University of Chicago)\nWe construct toroid
al compactifications of the moduli space of Drinfeld modules of rank d wit
h N-level structure. We obtain them as the moduli spaces of log Drinfeld m
odules of rank d with N-level structure. The theory of toroidal compactifi
cations was announced by Pink long ago (using the works of Fujiwara) but t
he details are not yet published. We follow the ideas of Pink adding log s
tudies and considering cone decompositions related to simplices of Bruhat-
Tits buildings. This is a joint work with T. Fukaya and R. Sharifi.\n\nhtt
ps://indico.math.cnrs.fr/event/1771/contributions/747/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/747/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Perverse equivariant sheaves on loop Lie algebras\, and affine Spr
inger theory
DTSTART;VALUE=DATE-TIME:20180614T094500Z
DTEND;VALUE=DATE-TIME:20180614T104500Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-748@indico.math.cnrs.fr
DESCRIPTION:Speakers: Y. Varshavsky (Hebrew University of Jerusalem)\nThis
is a joint work with A. Bouthier and D. Kazhdan.\nLet G be a connected re
ductive group\, and let LG be the corresponding loop group. Our main goal
is to construct a "perverse" t-structure on the derived category of Ad LG-
equivariant sheaves on LG and to show that the affine Grothendieck-Springe
r sheaf belongs to its core.\nMore precisely\, we construct the t-structur
e on the derived category of LG-equivariant sheaves supported on bounded r
egular semi-simple elements of LG\, and we only consider its Lie algebra a
nalog.\n\nhttps://indico.math.cnrs.fr/event/1771/contributions/748/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/748/
END:VEVENT
BEGIN:VEVENT
SUMMARY:"fundamental local equivalence" for quantum geometric Langlands
DTSTART;VALUE=DATE-TIME:20180614T083000Z
DTEND;VALUE=DATE-TIME:20180614T093000Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-749@indico.math.cnrs.fr
DESCRIPTION:Speakers: D. Gaitsgory (Harvard)\nThe key role in the usual ge
ometric Langlands is played by the geometric Satake equivalence\, which sa
ys that the category of spherical perverse sheaves on the affine Grassmann
ian Gr_G of the group G is equivalent to the category Rep(G^L) of algebrai
c representations of the Langlands dual G^L. Despite its importance\, the
above statement is rather fragile\; for example it holds only at the level
of abelian categories\, but fails at the derived level. A more robust ass
ertion can be formulated by replacing the spherical category by the Whitta
ker category. In this talk we will introduce the quantum context\, which a
mounts to replacing sheaves on Gr_G by sheaves twisted by a certain gerbe
(the latter is the quantum parameter q). It turns out that the Whittaker v
ariant of Geometric Satake admits a deformation\, where on the Langlands d
ual side\, the category Rep(G^L) gets deformed to the category of modules
over the quantum group\, whose quantum parameter is the same q. The constr
uction of the equivalence between the two sides relies on the description
of a certain remarkable perverse sheaf on the configuration space of color
ed divisors\, which encodes the combinatorics of the Cartan matrix.\n\nhtt
ps://indico.math.cnrs.fr/event/1771/contributions/749/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/749/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the classification of p-healthy regular schemes
DTSTART;VALUE=DATE-TIME:20180614T140000Z
DTEND;VALUE=DATE-TIME:20180614T150000Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-750@indico.math.cnrs.fr
DESCRIPTION:Speakers: A. Vasiu (Binghamton University)\nA regular local ri
ng R of dimension at least 2 and mixed characteristic (0\,p) is called p-h
ealthy if each p-divisible group over the the punctured spectrum of R exte
nds to a p-divisible group over Spec R. In the book of Faltings and Chai\,
it has been claimed that\, in the current language\, each such R is p-hea
lthy. A counterexample due to Raynaud\, recollected by Ogus\, and worked o
ut by Gabber in 1992 shows that this claim is far from being true. After s
everal erroneous attempts by different specialists\, just in 2010\, Zink a
nd Vasiu were able to generalize Gabber's counterexample\, to show the exi
stence of plenty of p-healthy regular rings of dimension 2 and to provide
a first correct proof of the uniqueness of integral canonical models of Sh
imura varieties. As two joint papers with Gabber\, we report on a complete
classification of p-healthy regular rings of dimension 2 which are hensel
ian and have perfect residue fields and on the very first examples of p-he
althy regular schemes of arbitrary dimension greater than 2. These example
s in dimension greater than 2 correct several errors in the literature and
provide a new (second) proof of the uniqueness of integral canonical mode
ls of Shimura varieties.\n\nhttps://indico.math.cnrs.fr/event/1771/contrib
utions/750/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/750/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spreading-out for families of rigid analytic spaces (joint work wi
th Brian Conrad)
DTSTART;VALUE=DATE-TIME:20180614T123000Z
DTEND;VALUE=DATE-TIME:20180614T133000Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-751@indico.math.cnrs.fr
DESCRIPTION:Speakers: O. Gabber (CNRS & IHES)\nhttps://indico.math.cnrs.fr
/event/1771/contributions/751/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/751/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deligne's geometrical approach to the product formula for l-adic e
psilon factors
DTSTART;VALUE=DATE-TIME:20180615T094500Z
DTEND;VALUE=DATE-TIME:20180615T104500Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-752@indico.math.cnrs.fr
DESCRIPTION:Speakers: F. Orgogozo (CNRS & École polytechnique)\nAround 19
85\, Gérard Laumon gave a proof of the local factorization of the determi
nant of the Frobenius map acting on the cohomology of a curve. Shortly bef
ore Laumon's work\, however\, Deligne had developed a different approach t
o the problem\, which is not well known today. In this talk\, I would like
to introduce Deligne's method to a wider audience\, in the hope that its
full potential has yet to be exploited. Its starting point is Deligne's sy
mmetric Künneth formula and the acyclicity properties of the Abel-Jacobi
morphism\, which led to the first proof of the result in the tame case. (U
nderstanding Deligne's method is one part of an ongoing project with Joël
Riou.)\n\nhttps://indico.math.cnrs.fr/event/1771/contributions/752/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/752/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Characteristic cycle of constructible sheaves and restriction to c
urves
DTSTART;VALUE=DATE-TIME:20180615T083000Z
DTEND;VALUE=DATE-TIME:20180615T093000Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-753@indico.math.cnrs.fr
DESCRIPTION:Speakers: T. Saito (University of Tokyo)\nThe characteristic c
ycle of a constructible sheaf is determined by its rank and the conductor
of the restrictions to curves. We also discuss compatibility with proper p
ush forward.\n\nhttps://indico.math.cnrs.fr/event/1771/contributions/753/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/753/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Compatible systems along the boundary
DTSTART;VALUE=DATE-TIME:20180615T123000Z
DTEND;VALUE=DATE-TIME:20180615T133000Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-755@indico.math.cnrs.fr
DESCRIPTION:Speakers: W. Zheng (Morningside Center of Mathematics)\nA theo
rem of Deligne says that compatible systems of l-adic sheaves on a smooth
curve over a finite field are compatible along the boundary. I will presen
t an extension of Deligne's theorem to schemes of finite type over the rin
g of integers of a local field\, based on Gabber's theorem on compatible s
ystems. This has applications to the equicharacteristic case of some class
ical conjectures on l-independence. I will also discuss the relationship w
ith compatible wild ramification. This is joint work with Qing Lu.\n\nhttp
s://indico.math.cnrs.fr/event/1771/contributions/755/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/755/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Character formulas in the modular representation theory of algebra
ic groups
DTSTART;VALUE=DATE-TIME:20180611T094500Z
DTEND;VALUE=DATE-TIME:20180611T104500Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-756@indico.math.cnrs.fr
DESCRIPTION:Speakers: G. Williamson (University of Sydney)\nI will review
present two formulas for the characters of representations of reductive al
gebraic groups in positive characteristic p. Both formulas involve certain
polynomials ("p-Kazhdan-Lusztig polynomials") which measure the failure o
f the decomposition theorem for resolutions of affine Schubert varieties\,
when the sheaf coefficients are of characteristic p. These formulas are p
roven under mild bounds on p (e.g. p ≥ 2 × Coxeter number) and are expe
cted to hold uniformly. (This is joint work with S. Riche\, with parts als
o joint with P. Achar and S. Makisumi.)\n\nhttps://indico.math.cnrs.fr/eve
nt/1771/contributions/756/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/756/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rigid local systems and (some) finite groups
DTSTART;VALUE=DATE-TIME:20180611T083000Z
DTEND;VALUE=DATE-TIME:20180611T093000Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-757@indico.math.cnrs.fr
DESCRIPTION:Speakers: N. Katz (Princeton)\nWe will discuss rigid local sys
tems on the affine line in positive characteristic whose monodromy groups
are certain finite groups of Lie type.\n\nhttps://indico.math.cnrs.fr/even
t/1771/contributions/757/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/757/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hilbert's thirteenth problem and the moduli space of abelian varie
ties
DTSTART;VALUE=DATE-TIME:20180611T140000Z
DTEND;VALUE=DATE-TIME:20180611T150000Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-758@indico.math.cnrs.fr
DESCRIPTION:Speakers: M. Kisin (Harvard)\nThe (multi-valued) solution of a
general polynomial of degree n is a priori a function of n-1 variables. H
ilbert's thirteenth problem and its variants ask when such functions can b
e written as a composite of functions in a smaller number of variables. I
will explain some progress on this question which uses the geometry of A_g
.\nThis is joint work with Benson Farb and Jesse Wolfson.\n\nhttps://indic
o.math.cnrs.fr/event/1771/contributions/758/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/758/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stratifying reductive groups
DTSTART;VALUE=DATE-TIME:20180611T123000Z
DTEND;VALUE=DATE-TIME:20180611T133000Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-759@indico.math.cnrs.fr
DESCRIPTION:Speakers: G. Lusztig (MIT)\nWe define a decomposition of a red
uctive group into finitely many strata. The largest stratum is the set of
regular elements\, the smallest stratum is the centre.\n\nhttps://indico.m
ath.cnrs.fr/event/1771/contributions/759/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/759/
END:VEVENT
BEGIN:VEVENT
SUMMARY:p-adic K-theory of p-adic rings
DTSTART;VALUE=DATE-TIME:20180612T094500Z
DTEND;VALUE=DATE-TIME:20180612T104500Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-760@indico.math.cnrs.fr
DESCRIPTION:Speakers: P. Scholze (Universität Bonn)\nThe original proof o
f Grothendieck's purity conjecture in étale cohomology (the Thomason-Gabb
er theorem) relies on results on l-adic K-theory and its relation to étal
e cohomology when l is invertible. Using recent advances of Clausen-Mathew
-Morrow and joint work with Bhatt and Morrow\, our understanding in the co
mplementary case of p-adic K-theory of p-adic rings has reached a similar
level. In particular\, we can express p-adic étale K-theory in terms of t
he cohomology theories of integral p-adic Hodge theory\, such as the prism
atic cohomology discussed in Bhatt's talk. Depending on time\, I may indic
ate some possible applications.\n\nhttps://indico.math.cnrs.fr/event/1771/
contributions/760/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/760/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prisms and deformations of de Rham cohomology
DTSTART;VALUE=DATE-TIME:20180612T083000Z
DTEND;VALUE=DATE-TIME:20180612T093000Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-761@indico.math.cnrs.fr
DESCRIPTION:Speakers: B. Bhatt (University of Michigan)\nPrisms are genera
lizations of perfectoid rings to a setting where "Frobenius need not be an
isomorphism". I will explain the definition and use it to construct a pri
smatic site for any scheme. The resulting prismatic cohomology often gives
a one-parameter deformation of de Rham cohomology. For instance\, it reco
vers the recently constructed A_{inf}-cohomology for smooth schemes over p
erfectoid rings (and thus crystalline cohomology when in characteristic p)
. A relative variant yields cohomological Breuil-Kisin modules\, and relat
ed ideas also give a co-ordinate free construction of q-de Rham cohomology
. Joint work with Peter Scholze.\n\nhttps://indico.math.cnrs.fr/event/1771
/contributions/761/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/761/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Perfectoid spaces and log-regular rings
DTSTART;VALUE=DATE-TIME:20180612T140000Z
DTEND;VALUE=DATE-TIME:20180612T150000Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-762@indico.math.cnrs.fr
DESCRIPTION:Speakers: L. Ramero (Université de Lille I)\nI will present a
generalization of Scholze's perfectoid spaces that includes the limits of
certain very ramified towers of log-regular rings. This is part of an on-
going joint work with Ofer Gabber.\n\nhttps://indico.math.cnrs.fr/event/17
71/contributions/762/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/762/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Perfectoid Cohen-Macaulay rings and homological aspects of commuta
tive algebra in mixed characteristic
DTSTART;VALUE=DATE-TIME:20180612T123000Z
DTEND;VALUE=DATE-TIME:20180612T133000Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-763@indico.math.cnrs.fr
DESCRIPTION:Speakers: Y. André (CNRS & IMJ-PRG)\nThe homological turn in
commutative algebra due to Auslander and Serre was pushed forward by Peski
ne and Szpiro with a systematic use of the Frobenius functor\, which led t
o tight closure theory\, a powerful instrument developed by Hochster and H
uneke to study singularities in characteristic p. We shall report on recen
t advances in the mixed characteristic case\, where perfectoid Cohen-Macau
lay algebras play the role of absolute integral closures in characteristic
p\, and lead to a mixed characteristic analog of tight closure theory.\n\
nhttps://indico.math.cnrs.fr/event/1771/contributions/763/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/763/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hochschild and cyclic homology of log schemes
DTSTART;VALUE=DATE-TIME:20180613T094500Z
DTEND;VALUE=DATE-TIME:20180613T104500Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-764@indico.math.cnrs.fr
DESCRIPTION:Speakers: M. Olsson (UC Berkeley)\nI will discuss an approach
to extending the notions of Hochschild and cyclic homology from schemes to
log schemes. The approach is based on a more general theory for morphisms
of algebraic stacks.\n\nhttps://indico.math.cnrs.fr/event/1771/contributi
ons/764/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/764/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arakelov geometry on degenerating curves
DTSTART;VALUE=DATE-TIME:20180613T083000Z
DTEND;VALUE=DATE-TIME:20180613T093000Z
DTSTAMP;VALUE=DATE-TIME:20210510T214150Z
UID:indico-contribution-1771-765@indico.math.cnrs.fr
DESCRIPTION:Speakers: G. Faltings (MPIM)\nWe investigate the asymptotic of
Arakelov Green functions and metrics\, and of the delta-function\, if a s
mooth Riemann surface degenerates to a stable curve.\n\nhttps://indico.mat
h.cnrs.fr/event/1771/contributions/765/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/1771/contributions/765/
END:VEVENT
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