BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Bhargav Bhatt (University of Michigan)
DTSTART;VALUE=DATE-TIME:20200618T160000Z
DTEND;VALUE=DATE-TIME:20200618T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/1
DESCRIPTION:Title: A p-adic Riemann-Hilbert functor and applications\nby B
hargav Bhatt (University of Michigan) as part of Recent Advances in Modern
p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nI will discuss an ongoing projec
t (joint with Jacob Lurie) aiming to construct a p-adic Riemann-Hilbert fu
nctor\, attaching coherent objects to constructible sheaves (with coeffici
ents in F_p\, Z_p or Q_p) on a compact algebraic variety over a p-adic fie
ld. I'll focus on the case of F_p-coefficients\, which leads to a solution
of some old questions in commutative algebra.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Howe (University of Utah)
DTSTART;VALUE=DATE-TIME:20200625T160000Z
DTEND;VALUE=DATE-TIME:20200625T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/2
DESCRIPTION:Title: A p-adic transcendence criterion for CM Galois represen
tations\nby Sean Howe (University of Utah) as part of Recent Advances in M
odern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nWe show that a crystalline
Galois representation with rational de Rham lattice admits a slope filtrat
ion with abelian isoclinic subquotients. As a corollary\, we find that a $
p$-divisible group over $\\mathcal{O}_{\\mathbb{C_p}}$ has complex multipl
ication if and only if it can be defined over a complete discretely valued
subfield and its Hodge-Tate filtration is algebraic -- this is a $p$-adic
analog of classical transcendence results for complex abelian varieties d
ue to Schneider\, Cohen\, and Shiga-Wolfart. More generally\, we character
ize the special points of the diamond moduli of mixed-characteristic local
shtuka with one paw as those with algebraic Hodge-Tate and de Rham period
s. The corresponding archimedean transcendence results for Shimura varieti
es fit into a broader framework of bialgebraicity that plays an important
role in the Andre-Oort conjecture\, and\, time permitting\, we discuss som
e ideas of what this might look like in the $p$-adic setting.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Scholze (University of Bonn / MPIM)
DTSTART;VALUE=DATE-TIME:20200716T160000Z
DTEND;VALUE=DATE-TIME:20200716T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/3
DESCRIPTION:Title: Prismatic crystals and crystalline Galois representatio
ns\nby Peter Scholze (University of Bonn / MPIM) as part of Recent Advance
s in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nLet $K$ be a complete
discrete valuation field of mixed\ncharacteristic with perfect residue fi
eld. We prove that F-crystals on\nthe prismatic site of $\\mathcal{O}_K$ a
re equivalent to lattices in crystalline\n$G_K$-representations. (joint wi
th Bhargav Bhatt)\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wiesława Nizioł (Sorbonne / IMJ)
DTSTART;VALUE=DATE-TIME:20200730T160000Z
DTEND;VALUE=DATE-TIME:20200730T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/4
DESCRIPTION:Title: p-adic étale cohomology of period domains\nby Wiesław
a Nizioł (Sorbonne / IMJ) as part of Recent Advances in Modern p-Adic Geo
metry (RAMpAGe)\n\n\nAbstract\nI will show how to compute $p$-adic étale
cohomology with compact support of period domains over local fields in the
case of a basic isocrystal for quasi-split reductive groups. This follow
the method used by Orlik in his computations of the $\\ell$-adic étale co
homology using as a key new input the computation of Ext groups between mo
d-$p$ generalized Steinberg representations of $p$-adic groups. This is a
joint work with Colmez\, Dospinescu\, and Hauseux.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shizhang Li (University of Michigan)
DTSTART;VALUE=DATE-TIME:20200702T160000Z
DTEND;VALUE=DATE-TIME:20200702T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/5
DESCRIPTION:Title: Some examples and results on integral p-adic Hodge filt
rations\nby Shizhang Li (University of Michigan) as part of Recent Advance
s in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nGiven a smooth proper
scheme over a mixed characteristic DVR\, we try to understand to what ext
ent the special fiber knows the Hodge numbers of the generic fiber. I'll p
rovide some examples as well as a theorem showing that in "good" situation
s some numbers defined purely using the special fiber actually give the Ho
dge numbers of the generic fiber. This naturally leads to consideration of
Breuil-Kisin prismatic cohomology\, and I'll describe an example which il
lustrates certain pathological behavior of Hodge-Tate and Hodge-de Rham sp
ectral sequences in mixed characteristic situations.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdan Zavyalov (Stanford)
DTSTART;VALUE=DATE-TIME:20200723T170000Z
DTEND;VALUE=DATE-TIME:20200723T182000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/6
DESCRIPTION:Title: Mod-p Poincaré duality in p-adic geometry\nby Bogdan Z
avyalov (Stanford) as part of Recent Advances in Modern p-Adic Geometry (R
AMpAGe)\n\n\nAbstract\nÉtale cohomology of $\\mathbf{F}_p$-local systems
does not behave nicely on general smooth p-adic rigid-analytic spaces\; e
.g.\, the $\\mathbf{F}_p$-cohomology of the 1-dimensional closed unit ball
is infinite. However\, it turns out that things are much better for prope
r p-adic rigid-analytic spaces. For example\, Scholze used perfectoid spac
es to show that proper p-adic rigid-analytic spaces have finite cohomology
for any $\\mathbf{F}_p$-local system. Based on Gabber's idea\, I will int
roduce the concept of almost coherent sheaves and use it to “localize”
(in an appropriate sense) some problems in the étale cohomology of rigid
-analytic spaces. For example\, this theory (together with perfectoid spac
es) can be used to give a "new" proof of the finiteness theorem and a proo
f of Poincaré duality for p-torsion coefficients on smooth and proper p-a
dic rigid-analytic spaces.\n\nThis is work in progress.\n\nPlease note tha
t this talk begins one hour later than the usual time.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Caraiani (Imperial)
DTSTART;VALUE=DATE-TIME:20200806T160000Z
DTEND;VALUE=DATE-TIME:20200806T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/7
DESCRIPTION:Title: A comparison theorem for ordinary p-adic modular forms\
nby Ana Caraiani (Imperial) as part of Recent Advances in Modern p-Adic Ge
ometry (RAMpAGe)\n\n\nAbstract\nI will discuss joint work in progress with
Elena Mantovan and James Newton\, whose goal is to compare ordinary compl
eted cohomology with (higher) Hida theory\, in the special case of the mod
ular curve. Both these notions go back to Hida\, though the former can be
reinterpreted using Emerton’s functor of ordinary parts applied to compl
eted cohomology\, and the latter has been redeveloped and expanded recentl
y by Boxer and Pilloni to incorporate higher coherent cohomology. Our work
gives a new proof to a theorem of Ohta\, that is perhaps more amenable to
generalisation. The key ingredients are the Bruhat stratification on the
Hodge-Tate period domain\, and the integral comparison results pioneered b
y Bhatt\, Morrow and Scholze.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Chan (MIT)
DTSTART;VALUE=DATE-TIME:20200709T160000Z
DTEND;VALUE=DATE-TIME:20200709T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/8
DESCRIPTION:Title: L-packets of S-unramified regular supercuspidal represe
ntations\nby Charlotte Chan (MIT) as part of Recent Advances in Modern p-A
dic Geometry (RAMpAGe)\n\n\nAbstract\nIn 2001\, Yu gave an algebraic const
ruction of supercuspidal\nrepresentations of p-adic groups (now known to b
e exhaustive when the\nresidual characteristic is sufficiently large---Kim
\, Fintzen). There\nhas since been a lot of progress towards explicitly co
nstructing the\nlocal Langlands correspondence: Kazhdan-Varshavsky and DeB
acker-Reeder\n(depth zero)\, Reeder and DeBacker-Spice (unramified toral)\
, and\nKaletha (regular supercuspidals). In this talk\, we present recent
and\nongoing work investigating a geometric counterpart to this story. Thi
s\nis based on joint work with Alexander Ivanov and joint work with Masao\
nOi.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Magner (Boston University)
DTSTART;VALUE=DATE-TIME:20200813T160000Z
DTEND;VALUE=DATE-TIME:20200813T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/9
DESCRIPTION:Title: On the Cohomology of Moduli of Mixed Characteristic Sht
ukas\nby Richard Magner (Boston University) as part of Recent Advances in
Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nWe review mixed characteri
stic shtukas and their moduli. These generalize the Lubin-Tate tower and o
ther Rapoport-Zink spaces. Under the Kottwitz conjecture\, the cohomology
of these spaces are expected to realize the local Langlands correspondenc
e. The data defining these spaces involve cocharacters of a Lie group\;
when the cocharacter is minuscule\, we recover classical Rapoport-Zink spa
ces. In the case of $\\mathrm{GL}_n$\, we show that the Kottwitz conjectu
re for general cocharacters can be reduced to the minuscule case. This de
pends on a geometric Satake equivalence for the $B_{\\mathrm{dR}}$-affine
Grassmanian\, due to Fargues and Scholze\, and a formula of Imai on cohomo
logy derived from it.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Cass (Harvard University)
DTSTART;VALUE=DATE-TIME:20200820T160000Z
DTEND;VALUE=DATE-TIME:20200820T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/10
DESCRIPTION:Title: Mod p Hecke algebras and perverse F_p-sheaves\nby Rober
t Cass (Harvard University) as part of Recent Advances in Modern p-Adic Ge
ometry (RAMpAGe)\n\n\nAbstract\nWe explain a mod $p$ version of the geomet
ric Satake isomorphism which gives a sheaf-theoretic description of the sp
herical mod $p$ Hecke algebra. We also construct central elements in the I
wahori mod p Hecke algebra by adapting a method due to Gaitsgory. Our proo
fs rely crucially on the theory of $F$-singularities\, and along the way w
e prove new results about the singularities of affine Schubert varieties.
We expect these results to have applications toward a mod $p$ Langlands co
rrespondence.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miaofen Chen (East China Normal University)
DTSTART;VALUE=DATE-TIME:20200910T150000Z
DTEND;VALUE=DATE-TIME:20200910T162000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/12
DESCRIPTION:Title: Connectedness of Kisin varieties associated to absolut
ely irreducible Galois representations\nby Miaofen Chen (East China Normal
University) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe
)\n\n\nAbstract\nAbstract: Let $K$ be a $p$-adic field. Let $\\rho$ be an
$n$-dimensional continuous absolutely irreducible mod $p$ representation o
f the absolute Galois group of $K$. The Kisin variety is a projective sche
me which parametrizes the finite flat group schemes over the ring of integ
ers of $K$ with generic fiber $\\rho$ satisfying some determinant conditio
n. The connected components of the Kisin variety is in bijection with the
connected components of the generic fiber of the flat deformation ring of
$\\rho$ with given Hodge-Tate weights. Kisin conjectured that the Kisin v
ariety is connected in this case. We show that Kisin's conjecture holds if
$K$ is totally ramified with $n=3$ or the determinant condition is of a
very particular form. We also give counterexamples to show Kisin's conjec
ture does not hold in general. This is a joint work with Sian Nie.\n\nPlea
se note that this talk is one hour earlier than usual.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Gleason (Berkeley)
DTSTART;VALUE=DATE-TIME:20201001T160000Z
DTEND;VALUE=DATE-TIME:20201001T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/13
DESCRIPTION:Title: On the geometric connected components of moduli of mixe
d characteristic shtukas\nby Ian Gleason (Berkeley) as part of Recent Adva
nces in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nBy a theorem of Sc
holze and Weinstein\, moduli spaces of mixed characteristic shtukas genera
lize Rapoport-Zink spaces at infinite level. In this talk\, we describe th
e structure of the set of geometric connected components of those moduli s
paces that are associated to the data $(G\,b\,\\mu)$ with $G$ an unramifie
d reductive group and $(b\,\\mu)$ HN-irreducible. This result generalizes
the work of Chen on the geometric connected components of unramified HN-ir
reducible Rapoport-Zink spaces of EL and PEL type. In the interest of time
\, we only sketch the part of the proof that requires a new geometric ingr
edient: namely\, the specialization map for Scholze's category of diamonds
.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lue Pan (University of Chicago)
DTSTART;VALUE=DATE-TIME:20200827T160000Z
DTEND;VALUE=DATE-TIME:20200827T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/14
DESCRIPTION:Title: On the locally analytic vectors of the completed cohomo
logy of modular curves\nby Lue Pan (University of Chicago) as part of Rece
nt Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nWe study lo
cally analytic vectors of the completed cohomology of\nmodular curves and
determine eigenvectors of a rational Borel subalgebra\nof gl_2(Q_p). As ap
plications\, we are able to prove a classicality result\nfor overconvergen
t eigenform of weight one and give a new proof of\nFontaine-Mazur conjectu
re in the irregular case under some mild\nhypothesis. One technical tool i
s relative Sen theory which allows us to\nrelate infinitesimal group actio
n with Hodge(-Tate) structure.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Wear (Utah)
DTSTART;VALUE=DATE-TIME:20201008T160000Z
DTEND;VALUE=DATE-TIME:20201008T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/15
DESCRIPTION:Title: Perfectoid covers of abelian varieties and the weight-m
onodromy conjecture\nby Peter Wear (Utah) as part of Recent Advances in Mo
dern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nDeligne's weight-monodromy c
onjecture gives control over the zeros of local factors of L-functions of
varieties at places of bad reduction. His proof in characteristic p was a
step in his proof of the generalized Weil conjectures. Scholze developed t
he theory of perfectoid spaces to transfer Deligne's proof to characterist
ic 0\, proving the conjecture for complete intersections in toric varietie
s. Building on Scholze's techniques\, we prove the weight-monodromy conjec
ture for complete intersections in abelian varieties. Part of this talk wi
ll discuss joint work with Blakestad\, Gvirtz\, Heuer\, Shchedrina\, Shimi
zu\, and Yao.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Viehmann (TU Munchen)
DTSTART;VALUE=DATE-TIME:20200917T160000Z
DTEND;VALUE=DATE-TIME:20200917T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/16
DESCRIPTION:Title: Newton strata in the weakly admissible locus\nby Eva Vi
ehmann (TU Munchen) as part of Recent Advances in Modern p-Adic Geometry (
RAMpAGe)\n\n\nAbstract\nGiven a reductive group G over a p-adic local fiel
d and a minuscule\ncocharacter\, Rapoport and Zink constructed an open sub
space inside the\nassociated adic flag variety\, called p-adic period doma
in or weakly\nadmissible locus. These are vast generalizations of Drinfeld
upper half\nspaces. Recently\, Caraiani and Scholze defined a Newton stra
tification\non adic flag varieties. The unique open Newton stratum coincid
es with\nthe so-called admissible locus\, and is contained in the weakly\n
admissible locus. However\, in most cases the two spaces do not coincide.\
nIn my talk\, I describe which of the other Newton strata intersect the\nw
eakly admissible locus.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dustin Clausen (Copenhagen)
DTSTART;VALUE=DATE-TIME:20200924T160000Z
DTEND;VALUE=DATE-TIME:20200924T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/17
DESCRIPTION:Title: Quasicoherent sheaves on rigid analytic spaces\nby Dust
in Clausen (Copenhagen) as part of Recent Advances in Modern p-Adic Geomet
ry (RAMpAGe)\n\n\nAbstract\nI will describe a theory of "solid" quasicoher
ent sheaves on rigid analytic spaces\, and explain how its basic propertie
s give conceptually simple proofs of various foundational results concerni
ng vector bundles and coherent sheaves in rigid geometry. This is joint w
ork with Peter Scholze.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:*No meeting*
DTSTART;VALUE=DATE-TIME:20200903T160000Z
DTEND;VALUE=DATE-TIME:20200903T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/18
DESCRIPTION:by *No meeting* as part of Recent Advances in Modern p-Adic Ge
ometry (RAMpAGe)\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haoyang Guo (Michigan)
DTSTART;VALUE=DATE-TIME:20201015T160000Z
DTEND;VALUE=DATE-TIME:20201015T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/19
DESCRIPTION:Title: Hodge-Tate decomposition for non-smooth rigid spaces\nb
y Haoyang Guo (Michigan) as part of Recent Advances in Modern p-Adic Geome
try (RAMpAGe)\n\n\nAbstract\nGiven a smooth projective variety over a $p$-
adic field\, its $p$-adic étale cohomology admits a natural Galois equiva
riant decomposition\, called Hodge-Tate decomposition. The decomposition b
uilds a connection between the underlying $p$-adic Galois representation a
nd the cohomology of differentials\, relating arithmetic and geometric inf
ormation altogether. In this talk\, we generalize Hodge-Tate decomposition
to non-smooth rigid spaces\, and show how to compute $p$-adic étale coho
mology via cohomology of Deligne-Du Bois complexes.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cong Xue (Cambridge)
DTSTART;VALUE=DATE-TIME:20201105T170000Z
DTEND;VALUE=DATE-TIME:20201105T182000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/20
DESCRIPTION:Title: Smoothness of the cohomology sheaves of stacks of shtuk
as\nby Cong Xue (Cambridge) as part of Recent Advances in Modern p-Adic Ge
ometry (RAMpAGe)\n\n\nAbstract\nLet $X$ be a smooth projective geometrical
ly connected curve\nover a finite field $\\mathbb{F}_q$. Let $G$ be a conn
ected reductive group over the\nfunction field of $X$. For every finite se
t $I$ and every representation of\n$(\\check{G})^I$\, where $\\check{G}$ i
s the Langlands dual group of $G$\, we have\na stack of shtukas over $X^I$
. For every degree\, we have a compact support\nl-adic cohomology sheaf ov
er $X^I$.\n\nIn this talk\, I will recall some properties of these sheaves
. I will\ntalk about a work in progress which proves that these sheaves ar
e\nind-smooth over $X^I$.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Achinger (IMPAN Warsaw)
DTSTART;VALUE=DATE-TIME:20201022T160000Z
DTEND;VALUE=DATE-TIME:20201022T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/21
DESCRIPTION:Title: Hodge theory over $\\mathbf{C}((t))$\nby Piotr Achinger
(IMPAN Warsaw) as part of Recent Advances in Modern p-Adic Geometry (RAMp
AGe)\n\n\nAbstract\nI will describe some ways in which Hodge theory makes
its way into the\ngeometry of rigid-analytic varieties over $\\mathbf{C}((
t))$. Namely\, such spaces\nhave a "Betti realization"\, well-defined up t
o homotopy (joint work\nwith Talpo)\, and their cohomology carries a mixed
Hodge Structure\n(Steenbrink\, Stewart-Vologodsky\, Berkovich). The notio
n of "projective\nreduction" introduced by Li and studied by Hansen-Li is
a good working\nanalog of the Kaehler condition. In this case\, Hodge symm
etry holds\,\neven though it fails in some cases over the $p$-adic numbers
(Petrov).\nMoreover\, there is a Riemann-Hilbert correspondence (work in\
nprogress)\, which should allow us to define variations of mixed Hodge\nst
ructure in this context. All of these analogs rely on corresponding\nstate
ments regarding the logarithmic special fiber of a semistable\nmodel. Open
problems abound.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuel Reinecke (IAS)
DTSTART;VALUE=DATE-TIME:20201119T170000Z
DTEND;VALUE=DATE-TIME:20201119T182000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/22
DESCRIPTION:Title: The cohomology of moduli of curves at infinite level\nb
y Emanuel Reinecke (IAS) as part of Recent Advances in Modern p-Adic Geome
try (RAMpAGe)\n\n\nAbstract\nBy work of Harer\, the Betti cohomology of th
e moduli space of smooth\, complex curves of genus $g > 1$ vanishes in deg
rees above $4g - 5$. In my talk\, I give a new perspective on this result
which uses $p$-adic geometry. The approach also yields statements about mo
duli of stable curves and curves of compact type that are not covered by H
arer's methods.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linus Hamann (Princeton)
DTSTART;VALUE=DATE-TIME:20201029T160000Z
DTEND;VALUE=DATE-TIME:20201029T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/23
DESCRIPTION:Title: Compatibility of the Fargues-Scholze and Gan-Takeda Loc
al Langlands Correspondences\nby Linus Hamann (Princeton) as part of Recen
t Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nIn upcoming
work\, Fargues and Scholze construct a candidate for a general local Langl
ands correspondence\, \nassociating to a smooth irreducible representatio
n of a connected reductive group $G/\\mathbf{Q}_{p}$ a continuous semisimp
le Weil parameter\, using the action of excursion operators\non the moduli
space of $G$-bundles on the Fargues-Fontaine curve. It is a natural quest
ion to ask whether this correspondence is compatible with known instances
of the local Langlands correspondence after semi-simplification. For $G =
\\mathrm{GL}_{n}$\, this compatibility is deduced from the fact that corre
spondence of Harris-Taylor is realized in the cohomology of the Lubin-Tate
tower at infinite level\, via its interpretation as a moduli space of mix
ed characteristic shtukas. For $G = \\mathrm{GSp}_{4}$ or its inner form $
\\mathrm{GU}_{2}(D)$\, there is a local Langlands correspondence construct
ed by Gan-Takeda and Gan-Tantono\, respectively. We will discuss upcoming
work related to proving compatibility in this case. Similar to the case of
$\\mathrm{GL}_{n}$\, this involves realizing this local Langlands corresp
ondence in the cohomology of the local Shimura varieties at infinite level
associated with these groups. We do this by applying basic uniformization
of these local Shimura varieties due to Shen\, as well as results on Galo
is representations in the cohomology of the relevant global Shimura variet
ies due to Sorensen and Kret-Shin. After proving this compatibility\, we e
mploy various new ideas from the geometry of the Fargues Scholze correspon
dence to obtain a complete description of the $\\rho$-isotypic part of the
cohomology of this local Shimura variety at infinite level\, where $\\rho
$ is a representation of $G$ with supercuspidal Gan-Takeda or Gan-Tantono
parameter\, thereby verifying the strongest form of the Kottwitz conjectur
e for these specific representations.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kiran Kedlaya (UCSD)
DTSTART;VALUE=DATE-TIME:20201112T170000Z
DTEND;VALUE=DATE-TIME:20201112T182000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/24
DESCRIPTION:Title: Several forms of Drinfeld's lemma\nby Kiran Kedlaya (UC
SD) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAb
stract\nThe term "Drinfeld's lemma" refers to several related statements a
bout\nthe behavior of etale fundamental groups under formation of products
in\nmixed or positive characteristic. We discuss statements of this form
in\nthe contexts of schemes (after Drinfeld and Lau)\, perfectoid spaces (
after\nScholze-Weinstein\, Carter-Kedlaya-Zabradi\, and Fargues-Scholze)\,
and\nF-isocrystals (work in progress).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Newton (King's College London)
DTSTART;VALUE=DATE-TIME:20201203T170000Z
DTEND;VALUE=DATE-TIME:20201203T182000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/25
DESCRIPTION:Title: Symmetric power functoriality and the geometry of eigen
varieties\nby James Newton (King's College London) as part of Recent Advan
ces in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nI will discuss work
with Jack Thorne on symmetric power functoriality for modular forms\, wit
h a focus on the role of eigenvarieties and their geometry.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Feng (MIT/IAS)
DTSTART;VALUE=DATE-TIME:20201210T170000Z
DTEND;VALUE=DATE-TIME:20201210T182000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/26
DESCRIPTION:Title: Equivariant localization\, parity sheaves\, and cyclic
base change\nby Tony Feng (MIT/IAS) as part of Recent Advances in Modern p
-Adic Geometry (RAMpAGe)\n\n\nAbstract\nLaﬀorgue and Genestier-Laﬀorgu
e have constructed the global and (semisimpliﬁed) local Langlands corres
pondences for arbitrary reductive groups over function ﬁelds. I will exp
lain some recently established properties of these correspondences regardi
ng base change functoriality: existence of transfers for mod $p$ automorph
ic forms through $p$-cyclic base change in the global correspondence\, and
Tate cohomology realizes $p$-cyclic base change in the mod $p$ local corr
espondence. In particular\, the local statement verifies a conjecture\nof
Treumann-Venkatesh. The proofs combine Lafforgue’s theory with equivaria
nt localization arguments for shtukas as well as recent advances in modula
r representation theory\, namely parity sheaves and Smith-Treumann theory.
Compared with previous iterations of the talk\,\nthis time the talk will
emphasize the role of the new representation-theoretic tools\, during the
extra 20 minutes.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lynnelle Ye (Stanford)
DTSTART;VALUE=DATE-TIME:20201217T170000Z
DTEND;VALUE=DATE-TIME:20201217T182000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/27
DESCRIPTION:Title: The valuative criterion for properness for eigenvarieti
es\nby Lynnelle Ye (Stanford) as part of Recent Advances in Modern p-Adic
Geometry (RAMpAGe)\n\n\nAbstract\nThe question of whether the Coleman-Mazu
r eigencurve satisfies the valuative criterion for properness was first as
ked by Coleman and Mazur in 1998 and settled by Diao and Liu in 2016 using
deep\, powerful Galois-theoretic machinery. We will discuss a new proof w
hich is short and explicit and uses no Galois theory. Instead we adapt an
earlier method of Buzzard and Calegari based on elementary properties of o
verconvergent modular forms\, for which we have to extend Pilloni's geomet
ric construction of overconvergent forms of arbitrary weight farther into
the supersingular locus. We will also discuss generalizations in progress.
\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Ivanov (Universitat Bonn)
DTSTART;VALUE=DATE-TIME:20210107T170000Z
DTEND;VALUE=DATE-TIME:20210107T182000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/28
DESCRIPTION:Title: On $p$-adic Deligne--Lusztig spaces\nby Alexander Ivano
v (Universitat Bonn) as part of Recent Advances in Modern p-Adic Geometry
(RAMpAGe)\n\n\nAbstract\nWe discuss a new definition of $p$-adic Deligne--
Lusztig spaces\,\nas arc-sheaves on perfect algebras over the residue fiel
d. We look then\nat some fundamental properties of these sheaves. In parti
cular\, we show\nthat they are ind-representable in many cases. Along the
way we discuss\na general result saying that the (perfect) loop space of a
\nquasi-projective scheme over $\\mathbf{Q}_p$ is an arc-sheaf.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rebecca Bellovin
DTSTART;VALUE=DATE-TIME:20210114T180000Z
DTEND;VALUE=DATE-TIME:20210114T192000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/29
DESCRIPTION:Title: Galois representations over pseudorigid spaces\nby Rebe
cca Bellovin as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe
)\n\n\nAbstract\nIn the past few years\, extended eigenvarieties with\n"bo
undary" in positive characteristic have been constructed as\n"pseudorigid
spaces". I will discuss the construction of\n$(\\varphi\,\\Gamma)$-module
s for $p$-adic Galois representations with\ncoefficients in pseudoaffinoid
algebras and discuss some of their\nproperties. I will conclude by givin
g applications to the extended\neigencurve at the boundary of weight space
.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Dospinescu (ENS Lyon)
DTSTART;VALUE=DATE-TIME:20210121T170000Z
DTEND;VALUE=DATE-TIME:20210121T182000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/30
DESCRIPTION:Title: Cohomology of the Drinfeld tower: a family affair\nby G
abriel Dospinescu (ENS Lyon) as part of Recent Advances in Modern p-Adic G
eometry (RAMpAGe)\n\n\nAbstract\nI will report on joint work with Pierre C
olmez and Wieslawa\nNiziol\, refining our previous results on the cohomolo
gy of the coverings\nof the Drinfeld half-space for GL_2(Q_p). Here we dea
l with integral and\n“family" aspects of the cohomology\, as well as the
realisation of the\np-adic local Langlands correspondence for GL_2(Q_p) f
or all\ntwo-dimensional representations of the absolute Galois group of Q_
p. A\nkey role is played by a re-interpretation of Scholze’s functor.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Heuer (Universitat Bonn)
DTSTART;VALUE=DATE-TIME:20210128T170000Z
DTEND;VALUE=DATE-TIME:20210128T182000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/31
DESCRIPTION:Title: v-vector bundles on rigid spaces\nby Ben Heuer (Univers
itat Bonn) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\
n\nInteractive livestream: https://bostonu.zoom.us/j/99536701681?pwd=TGk2d
nNQVWxyL3oxS1gyOFdOVWdvQT09\nPassword hint: Smallest prime number greater
than 100.\n\nAbstract\nThis talk is about the difference between vector bu
ndles on a\nsmooth rigid space X and v-vector bundles on the associated di
amond. In\nthe case of line bundles\, I will explain how this difference c
an be\nfully described in terms of differentials using a "Hodge-Tate logar
ithm"\nmap. For proper X\, I will explain how one can use the proétale un
iversal\ncover of X to interpret this description as a p-adic Simpson\ncor
respondence of rank 1.\n
URL:https://bostonu.zoom.us/j/99536701681?pwd=TGk2dnNQVWxyL3oxS1gyOFdOVWdv
QT09
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi-Yun Hsu (UCLA)
DTSTART;VALUE=DATE-TIME:20210318T160000Z
DTEND;VALUE=DATE-TIME:20210318T172000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/32
DESCRIPTION:by Chi-Yun Hsu (UCLA) as part of Recent Advances in Modern p-A
dic Geometry (RAMpAGe)\n\nInteractive livestream: https://bostonu.zoom.us/
j/99536701681?pwd=TGk2dnNQVWxyL3oxS1gyOFdOVWdvQT09\nPassword hint: Smalles
t prime number greater than 100.\nAbstract: TBA\n
URL:https://bostonu.zoom.us/j/99536701681?pwd=TGk2dnNQVWxyL3oxS1gyOFdOVWdv
QT09
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Petrov (Harvard)
DTSTART;VALUE=DATE-TIME:20210304T170000Z
DTEND;VALUE=DATE-TIME:20210304T182000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/33
DESCRIPTION:by Alexander Petrov (Harvard) as part of Recent Advances in Mo
dern p-Adic Geometry (RAMpAGe)\n\nInteractive livestream: https://bostonu.
zoom.us/j/99536701681?pwd=TGk2dnNQVWxyL3oxS1gyOFdOVWdvQT09\nPassword hint:
Smallest prime number greater than 100.\nAbstract: TBA\n
URL:https://bostonu.zoom.us/j/99536701681?pwd=TGk2dnNQVWxyL3oxS1gyOFdOVWdv
QT09
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Kramer-Miller (UC Irvine)
DTSTART;VALUE=DATE-TIME:20210211T170000Z
DTEND;VALUE=DATE-TIME:20210211T182000Z
DTSTAMP;VALUE=DATE-TIME:20210124T162251Z
UID:RAMpAGe/34
DESCRIPTION:by Joe Kramer-Miller (UC Irvine) as part of Recent Advances in
Modern p-Adic Geometry (RAMpAGe)\n\nInteractive livestream: https://bosto
nu.zoom.us/j/99536701681?pwd=TGk2dnNQVWxyL3oxS1gyOFdOVWdvQT09\nPassword hi
nt: Smallest prime number greater than 100.\nAbstract: TBA\n
URL:https://bostonu.zoom.us/j/99536701681?pwd=TGk2dnNQVWxyL3oxS1gyOFdOVWdv
QT09
END:VEVENT
END:VCALENDAR