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BEGIN:VEVENT
SUMMARY:Nicolas Bergeron (École normale supérieure\, Paris France)
DTSTART;VALUE=DATE-TIME:20201019T133000Z
DTEND;VALUE=DATE-TIME:20201019T143000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034348Z
UID:Cohomology/1
DESCRIPTION:Title: Sczech cocycles and hyperplane arrangements 1\nby Nicol
as Bergeron (École normale supérieure\, Paris France) as part of CRM wor
kshop: Arithmetic quotients of locally symmetric spaces and their cohomolo
gy\n\nLecture held in Virtual.\n\nAbstract\nMany authors\, among which Nor
i\, Sczech\, Solomon\, Stevens\, or more recently Beilinson—Kings—Levi
n and\nCharollois—Dasgupta—Greenberg\, have constructed different\, bu
t related\, linear groups cocycles that are\nusually referred to as « Eis
enstein cocycles. » In these series of lectures I will explain a topologi
cal\nconstruction that is a common source for all these cocycles. One inte
resting feature of this construction is that\nstarting from a purely topol
ogical class it leads to the algebraic world of meromorphic forms on hyper
plane\ncomplements in n-fold products of either the (complex) additive gro
up\, the multiplicative group or a (family of)\nelliptic curve(s). We will
see that eventually our construction reveals hidden relations between pro
ducts of\nelementary (rational\, trigonometric or elliptic) functions) gov
erned by relations between classes in the\nhomology of linear groups.\nThi
s is based on a work-in-progress with Pierre Charollois\, Luis Garcia and
Akshay Venkatesh\n
LOCATION:Lecture held in Virtual
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Gunnells (University of Massachusetts Amherst)
DTSTART;VALUE=DATE-TIME:20201019T144500Z
DTEND;VALUE=DATE-TIME:20201019T154500Z
DTSTAMP;VALUE=DATE-TIME:20201031T034348Z
UID:Cohomology/2
DESCRIPTION:Title: Modular symbols over function fields\nby Paul Gunnells
(University of Massachusetts Amherst) as part of CRM workshop: Arithmetic
quotients of locally symmetric spaces and their cohomology\n\nLecture held
in Virtual.\n\nAbstract\nModular symbols\, due to Birch and Manin\, provi
de a very\nconcrete way to compute with classical holomorphic modular form
s.\nLater modular symbols were extended to GL(n) by Ash and Rudolph\, and\
nsince then such symbols and variations have played a central role in\ncom
putational investigation of the cohomology of arithmetic groups\nover numb
er fields\, and in particular in explicitly computing the\nHecke action on
cohomology. \n\nA theory of modular symbols for GL(2) over the rational f
unction field\nwas developed by Teitelbaum and later applied by Armana. I
n this talk\nwe extend this construction to GL(n) and show how it can be u
sed to\ncompute Hecke operators on cohomology. This is joint work with Da
n\nYasaki.\n
LOCATION:Lecture held in Virtual
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romyar Sharifi (UCLA)
DTSTART;VALUE=DATE-TIME:20201019T160000Z
DTEND;VALUE=DATE-TIME:20201019T170000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034348Z
UID:Cohomology/3
DESCRIPTION:Title: Eisenstein cocycles in motivic cohomology\nby Romyar Sh
arifi (UCLA) as part of CRM workshop: Arithmetic quotients of locally symm
etric spaces and their cohomology\n\nLecture held in Virtual.\n\nAbstract\
nI will describe joint work with Akshay Venkatesh on the construction and
study of GL_2(Z)-cocycles valued in\nsecond K-groups of the function field
s of squares of the multiplicative group over the rationals and of a\nuniv
ersal elliptic curve over a modular curve. I will also describe the pullba
cks of their restrictions to\ncongruence subgroups under torsion sections\
, relating these specializations to explicit maps on homology\ngroups of m
odular curves\n
LOCATION:Lecture held in Virtual
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Bergeron (École normale supérieure\, Paris France)
DTSTART;VALUE=DATE-TIME:20201020T133000Z
DTEND;VALUE=DATE-TIME:20201020T143000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034348Z
UID:Cohomology/4
DESCRIPTION:Title: Sczech cocycles and hyperplane arrangements 2\nby Nicol
as Bergeron (École normale supérieure\, Paris France) as part of CRM wor
kshop: Arithmetic quotients of locally symmetric spaces and their cohomolo
gy\n\nLecture held in Virtual.\n\nAbstract\nMany authors\, among which Nor
i\, Sczech\, Solomon\, Stevens\, or more recently Beilinson—Kings—Levi
n and\nCharollois—Dasgupta—Greenberg\, have constructed different\, bu
t related\, linear groups cocycles that are\nusually referred to as « Eis
enstein cocycles. » In these series of lectures I will explain a topologi
cal\nconstruction that is a common source for all these cocycles. One inte
resting feature of this construction is that\nstarting from a purely topol
ogical class it leads to the algebraic world of meromorphic forms on hyper
plane\ncomplements in n-fold products of either the (complex) additive gro
up\, the multiplicative group or a (family of)\nelliptic curve(s). We will
see that eventually our construction reveals hidden relations between pro
ducts of\nelementary (rational\, trigonometric or elliptic) functions) gov
erned by relations between classes in the\nhomology of linear groups.\nThi
s is based on a work-in-progress with Pierre Charollois\, Luis Garcia and
Akshay Venkatesh\n
LOCATION:Lecture held in Virtual
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Lecouturier (Yau Mathematical Sciences Center & IAS)
DTSTART;VALUE=DATE-TIME:20201020T150000Z
DTEND;VALUE=DATE-TIME:20201020T160000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034348Z
UID:Cohomology/5
DESCRIPTION:Title: On Sharifi's conjecture and generalizations\nby Emmanue
l Lecouturier (Yau Mathematical Sciences Center & IAS) as part of CRM work
shop: Arithmetic quotients of locally symmetric spaces and their cohomolog
y\n\nLecture held in Virtual.\n\nAbstract\nRomyar Sharifi made beautiful e
xplicit conjectures relating the K-theory of cyclotomic field to modular\n
symbols modulo some Eisenstein ideal.\nWe report on some partial results o
n these conjectures and their implication for Mazur's Eisenstein ideal. We
\nalso discuss some ongoing project exploring the analogue of these conjec
tures for Bianchi manifolds. All this\nis joint work with Jun Wang\n
LOCATION:Lecture held in Virtual
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Bergeron (École normale supérieure\, Paris France)
DTSTART;VALUE=DATE-TIME:20201021T133000Z
DTEND;VALUE=DATE-TIME:20201021T143000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034348Z
UID:Cohomology/6
DESCRIPTION:Title: Sczech cocycles and hyperplane arrangements 3\nby Nicol
as Bergeron (École normale supérieure\, Paris France) as part of CRM wor
kshop: Arithmetic quotients of locally symmetric spaces and their cohomolo
gy\n\nLecture held in Virtual.\nAbstract: TBA\n
LOCATION:Lecture held in Virtual
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Sprang (Universität Regensburg)
DTSTART;VALUE=DATE-TIME:20201021T144500Z
DTEND;VALUE=DATE-TIME:20201021T154500Z
DTSTAMP;VALUE=DATE-TIME:20201031T034348Z
UID:Cohomology/7
DESCRIPTION:Title: The Equivariant Polylogarithm and Eisenstein classes\nb
y Johannes Sprang (Universität Regensburg) as part of CRM workshop: Arith
metic quotients of locally symmetric spaces and their cohomology\n\nLectur
e held in Virtual.\n\nAbstract\nIn this lecture\, I will report on recent
results\, joint with Guido Kings\, on the construction of equivariant\nEis
enstein classes. The equivariant polylogarithm is a very general tool for
constructing motivic cohomology\nclasses of arithmetic groups. A certain r
efinement of the de Rham realization of these classes gives interesting\na
lgebraic Eisenstein classes. As an application of our construction\, we pr
ove algebraicity results for critical\nHecke L-values of totally imaginary
fields. This generalizes previous results of Damerell\, Shimura and Katz
in\nthe CM case. The integrality of our construction allows us to construc
t p-adic L-functions for totally imaginary\nfields at ordinary primes.\n
LOCATION:Lecture held in Virtual
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Garcia Martinez (University College London)
DTSTART;VALUE=DATE-TIME:20201021T160000Z
DTEND;VALUE=DATE-TIME:20201021T170000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034348Z
UID:Cohomology/8
DESCRIPTION:Title: An Eisenstein cocycle for imaginary quadratic fields\nb
y Luis Garcia Martinez (University College London) as part of CRM workshop
: Arithmetic quotients of locally symmetric spaces and their cohomology\n\
nLecture held in Virtual.\n\nAbstract\nI will give details of the general
picture discussed by Nicolas Bergeron in the case of arithmetic subgroups
of\nSL_N(k)\, where k is an imaginary quadratic field. I will introduce a
cocycle for such groups whose values are\npolynomials in classical Kroneck
er—Eisenstein series. We will then see how this cocycle leads to explici
t\nformulas for critical values of Hecke L—functions of degree N extensi
ons of k\, generalising work of Colmez.\nThis is based on a work-in-progre
ss with Pierre Charollois\, Luis Garcia and Akshay Venkatesh.\n
LOCATION:Lecture held in Virtual
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Bergeron (École normale supérieure\, Paris France)
DTSTART;VALUE=DATE-TIME:20201022T133000Z
DTEND;VALUE=DATE-TIME:20201022T143000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034348Z
UID:Cohomology/9
DESCRIPTION:Title: Sczech cocycles and hyperplane arrangements 4\nby Nicol
as Bergeron (École normale supérieure\, Paris France) as part of CRM wor
kshop: Arithmetic quotients of locally symmetric spaces and their cohomolo
gy\n\nLecture held in Virtual.\n\nAbstract\nMany authors\, among which Nor
i\, Sczech\, Solomon\, Stevens\, or more recently Beilinson—Kings—Levi
n and\nCharollois—Dasgupta—Greenberg\, have constructed different\, bu
t related\, linear groups cocycles that are\nusually referred to as « Eis
enstein cocycles. » In these series of lectures I will explain a topologi
cal\nconstruction that is a common source for all these cocycles. One inte
resting feature of this construction is that\nstarting from a purely topol
ogical class it leads to the algebraic world of meromorphic forms on hyper
plane\ncomplements in n-fold products of either the (complex) additive gro
up\, the multiplicative group or a (family of)\nelliptic curve(s). We will
see that eventually our construction reveals hidden relations between pro
ducts of\nelementary (rational\, trigonometric or elliptic) functions) gov
erned by relations between classes in the\nhomology of linear groups.\nThi
s is based on a work-in-progress with Pierre Charollois\, Luis Garcia and
Akshay Venkatesh.\n
LOCATION:Lecture held in Virtual
END:VEVENT
BEGIN:VEVENT
SUMMARY:Preston Wake (Michigan State University)
DTSTART;VALUE=DATE-TIME:20201022T150000Z
DTEND;VALUE=DATE-TIME:20201022T160000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034348Z
UID:Cohomology/10
DESCRIPTION:Title: Torsion in the cohomology of Hilbert modular surfaces\n
by Preston Wake (Michigan State University) as part of CRM workshop: Arith
metic quotients of locally symmetric spaces and their cohomology\n\nLectur
e held in Virtual.\n\nAbstract\nWe investigate the analogue of Mazur's Eis
enstein ideal for Hilbert modular forms over a real quadratic field.\nUnli
ke in the case of modular forms\, we show that\, even in weight two\, ther
e are mod-p modular forms that\ndon't lift to characteristic zero. We expl
ain this by computing the torsion in the cohomology of the Hilbert\nmodula
r surface. This is joint work with Akshay Venkatesh.\n
LOCATION:Lecture held in Virtual
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Bergeron (École normale supérieure\, Paris France)
DTSTART;VALUE=DATE-TIME:20201023T133000Z
DTEND;VALUE=DATE-TIME:20201023T143000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034348Z
UID:Cohomology/11
DESCRIPTION:Title: Sczech cocycles and hyperplane arrangements 5\nby Nicol
as Bergeron (École normale supérieure\, Paris France) as part of CRM wor
kshop: Arithmetic quotients of locally symmetric spaces and their cohomolo
gy\n\nLecture held in Virtual.\n\nAbstract\nMany authors\, among which Nor
i\, Sczech\, Solomon\, Stevens\, or more recently Beilinson—Kings—Levi
n and\nCharollois—Dasgupta—Greenberg\, have constructed different\, bu
t related\, linear groups cocycles that are\nusually referred to as « Eis
enstein cocycles. » In these series of lectures I will explain a topologi
cal\nconstruction that is a common source for all these cocycles. One inte
resting feature of this construction is that\nstarting from a purely topol
ogical class it leads to the algebraic world of meromorphic forms on hyper
plane\ncomplements in n-fold products of either the (complex) additive gro
up\, the multiplicative group or a (family of)\nelliptic curve(s). We will
see that eventually our construction reveals hidden relations between pro
ducts of\nelementary (rational\, trigonometric or elliptic) functions) gov
erned by relations between classes in the\nhomology of linear groups.\nThi
s is based on a work-in-progress with Pierre Charollois\, Luis Garcia and
Akshay Venkatesh.\n
LOCATION:Lecture held in Virtual
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Charollois (Université Paris 6)
DTSTART;VALUE=DATE-TIME:20201023T150000Z
DTEND;VALUE=DATE-TIME:20201023T160000Z
DTSTAMP;VALUE=DATE-TIME:20201031T034348Z
UID:Cohomology/12
DESCRIPTION:Title: Trigonometric and elliptic cocycles overGLN(Z)\nby Pier
re Charollois (Université Paris 6) as part of CRM workshop: Arithmetic qu
otients of locally symmetric spaces and their cohomology\n\nLecture held i
n Virtual.\n\nAbstract\nI will first recall a joint work with Dasgupta and
Greenberg (2016)\, where we elaborate on Shintani's method\nto construct
an Eisenstein cocycle over **GL**_{N}(<**Z**) taking values
in a ring of\nrational generating series that can be expressed in terms of
basic trigonometric functions. We establish that it\nis cohomologous to a
former cocycle of Sczech. After smoothing it enjoys nice integral propert
ies. Combined\nwith evaluation on a tori\, it allows us to recover the bas
ic properties of the Cassou-Noguès p-adic zeta\nfunctions attached to tot
ally real fields.\nThen I'll give an overview of the elliptic generalizati
on I have later obtained\, where trigonometric functions are\nnow replaced
by the Kronecker-Eisenstein function\, which is a generating series for m
odular forms. The action\nof Hecke operators over **GL**_{N} on
that new cocycle has been studied by Hao Zhang in\nhis thesis (2020)\, an
d the end of talk present some of his results too.\n
LOCATION:Lecture held in Virtual
END:VEVENT
END:VCALENDAR