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BEGIN:VEVENT
SUMMARY:Anibal Medina (EPFL)
DTSTART;VALUE=DATE-TIME:20200722T153000Z
DTEND;VALUE=DATE-TIME:20200722T163000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113230Z
UID:PurdueTopology/1
DESCRIPTION:Title: A finitely presented E-infinity prop\nby Anibal Medina
(EPFL) as part of Purdue Topology Seminar\n\n\nAbstract\nThe Comm operad i
n chain complexes admits a presentation in terms of finitely many generato
rs and relations\, but no such presentation can be given for a sigma-free
resolution of it. By passing to the more general setting of props\, we are
able to describe finitely presented E-infinity props in the categories of
chain complexes and of cellular spaces. We relate the operads associated
with these to the E-infinity operad models introduced by McClure-Smith\, B
erger-Fresse and Kaufmann\, and describe novel actions on simplicial and c
ubical sets complementing these authors' work.\n\nPlease email purduetopol
ogyseminar@gmail.com before Wednesday with a request to obtain the link fo
r the Zoom meeting.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Bianchi (University of Bonn)
DTSTART;VALUE=DATE-TIME:20200909T153000Z
DTEND;VALUE=DATE-TIME:20200909T163000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113230Z
UID:PurdueTopology/2
DESCRIPTION:Title: Hurwitz spaces and Moduli spaces of Riemann surfaces\nb
y Andrea Bianchi (University of Bonn) as part of Purdue Topology Seminar\n
\n\nAbstract\nSullivan associates to the dg commutative algebra of Chevall
ey-Eilenberg cochains C*(g) on a nilpotent (or pro-nilpotent) differential
graded Lie algebra g a Kan complex \, using the differential grade
d commutative algebras Ω(Δn) of polynomial-coefficient differential form
s on the simplex. If g is a Lie algebra\, with Lie group G\, this Kan comp
lex is not isomorphic to BG. In 2004\, using Dupont's explicit simplicial
homotopy for the de Rham theorem\, I showed that has a natural sim
plicial subset γ(g) with the following properties:\n\n 1) γ(g) is a Kan
complex (in fact\, the functor takes fibrations to fibrations\, and trivi
al fibrations to trivial fibrations)\;\n 2) if g vanishes in degree -k an
d below\, γ(g) is a k-groupoid in the sense of Duskin\;\n 3) the inclusi
on of γ(g) in is a homotopy equivalence\;\n 4) if g is a nilpote
nt Lie algebra\, γ(g) is naturally isomorphic to BG\;\n 5) if g vanishes
in negative degree\, γ(g) is the nerve of the Deligne groupoid of g.\n \
nIn fact\, γ(g) is really a derived stack\, but I will focus on the under
lying simplicial set\, since it exhibits all of the essential ideas of the
construction.\n\nIn this talk\, I give a new approach to γ(g)\, using di
fferential forms on the cube. The explicit homotopy for the de Rham theore
m is much easier to construct for cubes: the main new result is that this
homotopy is not just cubical in the sense of Serre\, but also in the sense
of Brown and Higgins. This is an important refinement\, since the analogu
e of Moore's theorem that a simplicial group is a Kan complex need the enr
ichment of Brown and Higgins (what they call connections) in order to hold
\, by the work of Tonks.\n\nReplacing the cube by the cubical complex Qn\,
associated with straightening/unstraightening over a point\, we obtain a
new construction of a functor from L-infinity algebras to Kan complexes wi
th the same properties as γ(g).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART;VALUE=DATE-TIME:20200916T153000Z
DTEND;VALUE=DATE-TIME:20200916T163000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113230Z
UID:PurdueTopology/3
DESCRIPTION:by TBA as part of Purdue Topology Seminar\n\nAbstract: TBA\n
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BEGIN:VEVENT
SUMMARY:Pavel Safronov (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20200923T153000Z
DTEND;VALUE=DATE-TIME:20200923T163000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113230Z
UID:PurdueTopology/4
DESCRIPTION:Title: Coproduct in string topology\, Euler structures and top
ological field theories.\nby Pavel Safronov (University of Edinburgh) as p
art of Purdue Topology Seminar\n\n\nAbstract\nChas and Sullivan have intro
duced interesting algebraic operations on the homology of the free loop sp
ace of a manifold which go under the name of the string topology operation
s. Cohen—Gaudin gave a TFT interpretation of the string product. Moreove
r\, Cohen—Klein—Sullivan have shown that the string product is homotop
y-invariant. In this talk I will explain a TFT interpretation of the strin
g coproduct by disassembling it into elementary pieces. In particular\, I
will explain a conjecture that the string coproduct is not homotopy-invari
ant and changes by the Whitehead torsion. This is a report on work in prog
ress joint with Florian Naef.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Holstein (University of Hamburg)
DTSTART;VALUE=DATE-TIME:20200930T153000Z
DTEND;VALUE=DATE-TIME:20200930T163000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113230Z
UID:PurdueTopology/5
DESCRIPTION:Title: Categorical Koszul Duality\nby Julian Holstein (Univers
ity of Hamburg) as part of Purdue Topology Seminar\n\n\nAbstract\nThe alge
braic analogue of the loop space construction of topological spaces is Ada
ms’ cobar construction.\nTogether with the bar construction it induces a
Koszul duality between algebras and coalgebras\,\nproviding an equivalenc
e of suitable homotopy theories of augmented differential graded algebras
and differential graded conilpotent coalgebras.\nInteresting things happen
as one generalises this result\, in particular dropping the augmentation
on the dg algebra side corresponds to introducing a curvature term on the
coalgebra side.\nI will talk about joint work with Andrey Lazarev\, in whi
ch we generalise this to a categorical Koszul duality and find a category
of coalgebras Quillen equivalent to differential graded categories. I will
show that this construction is closely related to the coherent nerve cons
truction from simplicial categories to quasicategories.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Smillie (Caltech)
DTSTART;VALUE=DATE-TIME:20201007T153000Z
DTEND;VALUE=DATE-TIME:20201007T163000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113230Z
UID:PurdueTopology/6
DESCRIPTION:Title: The borders of outer space\nby Peter Smillie (Caltech)
as part of Purdue Topology Seminar\n\n\nAbstract\nThe group Out(F_n) acts
properly on a contractible space known as outer space. Motivated by the Bo
rel-Serre bordification of symmetric spaces\, Bestvina and Feighn gave a b
ordification of outer space and used it to prove that Out(F_n) is a virtua
l duality group. I will define outer space\, and show how to realize the B
estvina-Feighn bordification as a deformation retract instead of an enlarg
ement. This leads to a new proof that Out(F_n) is a virtual duality group
and gives an explicit polyhedral structure on the boundary of outer space.
\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Palmer (Mathematical Institute of the Romanian Academy)
DTSTART;VALUE=DATE-TIME:20201021T153000Z
DTEND;VALUE=DATE-TIME:20201021T163000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113230Z
UID:PurdueTopology/7
DESCRIPTION:by Martin Palmer (Mathematical Institute of the Romanian Acade
my) as part of Purdue Topology Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quoc P Ho (Institute of Science and Technology of Austria)
DTSTART;VALUE=DATE-TIME:20201028T153000Z
DTEND;VALUE=DATE-TIME:20201028T163000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113230Z
UID:PurdueTopology/8
DESCRIPTION:by Quoc P Ho (Institute of Science and Technology of Austria)
as part of Purdue Topology Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Knudsen (Northeastern University)
DTSTART;VALUE=DATE-TIME:20201104T163000Z
DTEND;VALUE=DATE-TIME:20201104T173000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113230Z
UID:PurdueTopology/9
DESCRIPTION:by Ben Knudsen (Northeastern University) as part of Purdue Top
ology Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos De La Cruz Mengual (Weizmann Institute of Science)
DTSTART;VALUE=DATE-TIME:20201111T163000Z
DTEND;VALUE=DATE-TIME:20201111T173000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113230Z
UID:PurdueTopology/10
DESCRIPTION:by Carlos De La Cruz Mengual (Weizmann Institute of Science) a
s part of Purdue Topology Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rita Jiménez Rolland (UNAM Oaxaca)
DTSTART;VALUE=DATE-TIME:20201118T163000Z
DTEND;VALUE=DATE-TIME:20201118T173000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113230Z
UID:PurdueTopology/11
DESCRIPTION:by Rita Jiménez Rolland (UNAM Oaxaca) as part of Purdue Topol
ogy Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Williams (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20201202T163000Z
DTEND;VALUE=DATE-TIME:20201202T173000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113230Z
UID:PurdueTopology/12
DESCRIPTION:by Ben Williams (University of British Columbia) as part of Pu
rdue Topology Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Kapulkin (University of Western Ontario)
DTSTART;VALUE=DATE-TIME:20201014T153000Z
DTEND;VALUE=DATE-TIME:20201014T163000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113230Z
UID:PurdueTopology/13
DESCRIPTION:Title: Cubical models of (∞\,1)-categories\nby Chris Kapulki
n (University of Western Ontario) as part of Purdue Topology Seminar\n\n\n
Abstract\nI will report on the joint work with B. Doherty\, Z. Lindsey\, a
nd C. Sattler\, establishing a family of new models of (∞\,1)-categories
in different categories of (marked) cubical sets.\n
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