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BEGIN:VEVENT
SUMMARY:Ran Levi (University of Aberdeen)
DTSTART;VALUE=DATE-TIME:20200420T140000Z
DTEND;VALUE=DATE-TIME:20200420T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/1
DESCRIPTION:Title: Com
plexes of Tournaments in Directed Networks\nby Ran Levi (University of
Aberdeen) as part of Online algebraic topology seminar\n\n\nAbstract\nCli
que graphs whose edges are oriented are referred to in the combinatorics l
iterature as tournaments. We consider a family of semi-simplicial sets\, t
hat we refer to as “tournaplexes"\, whose simplices are tournaments. In
particular\, given a directed graph G\, we associate with it a “flag tou
rnaplex" which is a tournaplex containing the directed flag complex of G\,
but also the geometric realisation of cliques that are not directed. We d
efine several types of filtration on tournaplexes\, and exploiting persist
ent homology\, we observe that filtered flag tournaplexes provide finer me
ans of distinguishing graph dynamics than the directed flag complex. We th
en demonstrate the power of those ideas by applying them to graph data ari
sing from the Blue Brain Project’s digital reconstruction of a rat’s n
eocortex.\n
LOCATION:https://researchseminars.org/talk/OATS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andy Baker (University of Glasgow)
DTSTART;VALUE=DATE-TIME:20200427T140000Z
DTEND;VALUE=DATE-TIME:20200427T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/2
DESCRIPTION:Title: Fun
and games with the Steenrod algebra\nby Andy Baker (University of Gla
sgow) as part of Online algebraic topology seminar\n\n\nAbstract\nThe mod
2 Steenrod algebra is an important tool in unstable and stable homotopy th
eory but it is also interesting as a purely algebraic gadget. I will brief
ly review its algebraic structure and that of some important finite subHo
pf algebras. Then I will discuss some realisability questions for modules\
, ranging from classical examples to modules over the E-infinity ring spec
tra kO and tmf localised at 2. I hope this talk will be accessible to begi
nners and also have some things to interest experts.\n
LOCATION:https://researchseminars.org/talk/OATS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Constanze Roitzheim (University of Kent)
DTSTART;VALUE=DATE-TIME:20200504T140000Z
DTEND;VALUE=DATE-TIME:20200504T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/3
DESCRIPTION:Title: Equ
ivariant homotopy commutativity\, trees and chicken feet\nby Constanze
Roitzheim (University of Kent) as part of Online algebraic topology semin
ar\n\n\nAbstract\nCommutativity up to homotopy can be daunting\, and it be
comes even more difficult to track when equivariant structures get introdu
ced. In the case of a finite group\, however\, the options for equivariant
homotopy commutativity can be encoded using simple combinatorics\, and we
will show some examples.\n
LOCATION:https://researchseminars.org/talk/OATS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuele Dotto (University of Warwick)
DTSTART;VALUE=DATE-TIME:20200518T140000Z
DTEND;VALUE=DATE-TIME:20200518T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/4
DESCRIPTION:Title: Wit
t vectors with coefficients and characteristic polynomials over non-commut
ative rings\nby Emanuele Dotto (University of Warwick) as part of Onli
ne algebraic topology seminar\n\n\nAbstract\nThe characteristic polynomial
of a matrix with entries in a commutative ring $R$ naturally takes value
in the ring of Witt vectors of $R$. In joint work with Krause\, Nikolaus a
nd Patchkoria\, we extend the classical Witt vectors construction to allow
as input pairs of a ring $R$ and a bimodule $M$. I will explain how this
construction relates to topological Hochschild homology\, the Hill-Hopkins
-Ravenel norm\, and the characteristic polynomial.\n
LOCATION:https://researchseminars.org/talk/OATS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathryn Hess (EPFL)
DTSTART;VALUE=DATE-TIME:20200608T140000Z
DTEND;VALUE=DATE-TIME:20200608T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/5
DESCRIPTION:Title: Cal
culus from comonads\nby Kathryn Hess (EPFL) as part of Online algebrai
c topology seminar\n\n\nAbstract\n(Joint work with Brenda Johnson.) The m
any theories of "calculus" introduced in algebraic topology over the past
couple of decades--e.g.\, Goodwillie's calculus of homotopy functors\, the
Goodwillie-Weiss manifold calculus\, the orthogonal calculus\, and the Jo
hnson-McCarthy cotriple calculus--all have a similar flavor\, though the o
bjects studied and exact methods applied are not the same. We have const
ructed a relatively simple category-theoretic machine for producing towers
of functors from a small category into a simplicial model category\, dete
rmined conditions under which such tower-building machines constitute a ca
lculus\, and showed that this framework encompasses certain well known cal
culi\, as well as providing new classes of examples. The cogs and gears
of our machine are cubical diagrams of reflective subcategories and the co
monads they naturally give rise to.\n\nIn this talk\, I will assume no fam
iliarity with comonads and only basic knowledge of simplicial model catego
ries.\n
LOCATION:https://researchseminars.org/talk/OATS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Adams (Colorado State University)
DTSTART;VALUE=DATE-TIME:20200525T140000Z
DTEND;VALUE=DATE-TIME:20200525T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/6
DESCRIPTION:Title: Vie
toris-Rips complexes and Borsuk-Ulam theorems\nby Henry Adams (Colorad
o State University) as part of Online algebraic topology seminar\n\n\nAbst
ract\nGiven a metric space X and a scale parameter r\, the Vietoris-Rips s
implicial complex VR(X\;r) has X as its vertex set\, and contains a finite
subset as a simplex if its diameter is at most r. Vietoris-Rips complexes
were invented by Vietoris in order to define a (co)homology theory for me
tric spaces\, and by Rips for use in geometric group theory. More recently
\, they have found applications in computational topology for approximatin
g of the shape of a dataset. I will explain how the Vietoris-Rips complexe
s of the circle\, as the scale parameter r increases\, obtain the homotopy
types of the circle\, the 3-sphere\, the 5-sphere\, the 7-sphere\, ...\,
until they are finally contractible. Only very little is understood about
the homotopy types of the Vietoris-Rips complexes of the n-sphere. Knowing
the homotopy connectivities of Vietoris-Rips complexes of spheres allows
one to prove generalizations of the Borsuk-Ulam theorem for maps from the
n-sphere into k-dimensional Euclidean space with k > n. Joint work with Jo
hn Bush and Florian Frick.\n
LOCATION:https://researchseminars.org/talk/OATS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirsten Wickelgren (Duke University)
DTSTART;VALUE=DATE-TIME:20200601T140000Z
DTEND;VALUE=DATE-TIME:20200601T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/7
DESCRIPTION:Title: The
re are 160\,839<1> + 160\,650<-1> 3-planes in a 7-dimensional cubic hypers
urface\nby Kirsten Wickelgren (Duke University) as part of Online alge
braic topology seminar\n\n\nAbstract\nThe expression in the title is a bil
inear form and it comes from an Euler number in A1-algebraic topology. Suc
h Euler numbers can be constructed with Hochschild homology\, self-duality
of Koszul complexes\, pushforwards in SL_c oriented cohomology theories\,
and sums of local degrees. We show an integrality result for A1-Euler num
bers and apply this to the enumeration of d-planes in complete intersectio
ns. Classically such counts are valid over C and sometimes extended to the
real numbers\, but A1-homotopy theory allows one to perform counts over a
large class of fields\, and records information about the solutions in bi
linear form. The example in the title then follows from work of Finashin--
Kharlamov. This is joint work with Tom Bachmann.\n
LOCATION:https://researchseminars.org/talk/OATS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Szymik (NTNU)
DTSTART;VALUE=DATE-TIME:20200615T140000Z
DTEND;VALUE=DATE-TIME:20200615T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/8
DESCRIPTION:Title: Tri
graded spectral sequences for principal fibrations\nby Markus Szymik (
NTNU) as part of Online algebraic topology seminar\n\n\nAbstract\nThe Lera
y--Serre and the Eilenberg--Moore spectral sequence are fundamental tools
for computing the cohomology of a group or\, more generally\, of a space.
In joint work with Frank Neumann (Leicester)\, we describe the relationsh
ip between these two spectral sequences in the situation when both of them
share the same abutment. This talk is an introduction to the topic with
many examples. It should be suitable for an audience from graduate studen
ts in algebraic topology onward\, and I will only assume some casual acqua
intance with spectral sequences.\n
LOCATION:https://researchseminars.org/talk/OATS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrich Pennig (Cardiff University)
DTSTART;VALUE=DATE-TIME:20200511T140000Z
DTEND;VALUE=DATE-TIME:20200511T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/9
DESCRIPTION:Title: Loo
ps\, groups\, and twists - the role of K-theory in mathematical physics\nby Ulrich Pennig (Cardiff University) as part of Online algebraic topol
ogy seminar\n\n\nAbstract\nWhile K-theory has its origins in Grothendieck'
s formulation and proof of his version of the Riemann-Roch theorem\, it no
w plays a significant role in many diverse branches of mathematics: It pro
vides a fundamental example of a cohomology theory\, and it is one of the
most important invariants of C*-algebras. In the first half of the talk\,
I will define the K-groups and discuss some of their applications. In the
second half\, I will concentrate on equivariant twisted K-theory\, which i
s related to the representation theory of loop groups and the geometry of
two-dimensional quantum field theories by a theorem of Freed\, Hopkins\, a
nd Teleman. I will finish with an outline of joint work with D. Evans\, in
which we study generalizations of this work to higher twists.\n
LOCATION:https://researchseminars.org/talk/OATS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Hahn (MIT)
DTSTART;VALUE=DATE-TIME:20200921T130000Z
DTEND;VALUE=DATE-TIME:20200921T140000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/10
DESCRIPTION:Title: Ni
shida Nilpotence\nby Jeremy Hahn (MIT) as part of Online algebraic top
ology seminar\n\n\nAbstract\nIn 1973\, Nishida proved that every positive
degree class in the stable homotopy groups of spheres is nilpotent. We wi
ll discuss some modern perspectives on Nishida's original proof. While th
is will be a mostly expository talk aimed at graduate students\, if time p
ermits we will end with a discussion of some open nilpotence questions in
motivic stable homotopy theory.\n
LOCATION:https://researchseminars.org/talk/OATS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lennart Meier (Utrecht)
DTSTART;VALUE=DATE-TIME:20200928T140000Z
DTEND;VALUE=DATE-TIME:20200928T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/11
DESCRIPTION:Title: El
liptic cohomology of level n\nby Lennart Meier (Utrecht) as part of On
line algebraic topology seminar\n\n\nAbstract\nElliptic genera have played
an important role in algebraic topology and algebraic geometry since the
1980s. To every almost-complex manifold they associate a modular form for
the congruence subgroups $\\Gamma_1(n)$. More recently\, elliptic cohomolo
gy theories have been built that are natural targets of elliptic genera fo
r families. I will give an overview of these theories and report in partic
ular on certain $C_2$-equivariant refinements.\n
LOCATION:https://researchseminars.org/talk/OATS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viktoriya Ozornova (Ruhr-Universität Bochum)
DTSTART;VALUE=DATE-TIME:20201005T140000Z
DTEND;VALUE=DATE-TIME:20201005T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/12
DESCRIPTION:Title: Mo
dels of (infty\,2)-categories\nby Viktoriya Ozornova (Ruhr-Universitä
t Bochum) as part of Online algebraic topology seminar\n\n\nAbstract\nAn $
(\\infty\,2)$-category should be a weak version of a strict $2$-category\,
in which compositions are well-defined\, associative and unital up to som
e higher coherence. There are various models making this precise. In this
talk\, I will describe a direct comparison between two particular models (
which will be introduced)\, namely $\\Theta_2$-spaces and saturated $2$-co
mplicial sets. This is joint work in progress with Julie Bergner and Marti
na Rovelli.\n
LOCATION:https://researchseminars.org/talk/OATS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Birgit Richter (Universität Hamburg)
DTSTART;VALUE=DATE-TIME:20201019T140000Z
DTEND;VALUE=DATE-TIME:20201019T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/13
DESCRIPTION:Title: De
tecting and describing ramification for structured ring spectra\nby Bi
rgit Richter (Universität Hamburg) as part of Online algebraic topology s
eminar\n\n\nAbstract\nThis is a report on joint work in progress with Eva
Höning. \n\nRamification for commutative ring spectra can be detected by
relative topological Hochschild homology and by the spectrum of Kähler di
fferentials. For rings of integers in an extension of number fields\, it i
s important to distinguish between tame and wild ramification. Noether's t
heorem characterizes tame ramification in terms of a normal basis and tame
ramification can also be detected via the surjectivity of the norm map. W
e take the latter fact and use the Tate cohomology spectrum to detect wild
ramification in the context of commutative ring spectra. In the talk\, I
will discuss several examples in the context of topological K-theory and m
odular forms.\n
LOCATION:https://researchseminars.org/talk/OATS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Drew Heard (NTNU)
DTSTART;VALUE=DATE-TIME:20201102T150000Z
DTEND;VALUE=DATE-TIME:20201102T160000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/14
DESCRIPTION:Title: Su
pport theory for triangulated categories in algebra and topology\nby D
rew Heard (NTNU) as part of Online algebraic topology seminar\n\n\nAbstrac
t\nWe will survey the support theory of triangulated categories through th
e machinery of tensor-triangulated geometry. We will discuss the stratific
ation theory of Benson—Iyengar—Krause for triangulated categories\, th
e construction by Balmer of the spectrum of a tensor-triangulated category
\, and the relation between the two. Time permitting\, we will discuss a r
ecent application to the category of derived Mackey functors\, joint with
Beren Sanders.\n
LOCATION:https://researchseminars.org/talk/OATS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julie Bergner (University of Virginia)
DTSTART;VALUE=DATE-TIME:20201130T150000Z
DTEND;VALUE=DATE-TIME:20201130T160000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/15
DESCRIPTION:Title: Va
riants of the Waldhausen S-construction\nby Julie Bergner (University
of Virginia) as part of Online algebraic topology seminar\n\n\nAbstract\nT
he S-construction\, first defined in the setting of cofibration categories
by Waldhausen\, gives a way to define the algebraic K-theory associated t
o certain kinds of categorical input. It was proved by Galvez-Carrillo\,
Kock\, and Tonks that the result of applying this construction to an exact
category is a decomposition space\, also called a 2-Segal space\, and Dyc
kerhoff and Kapranov independently proved the same result for the slightly
more general input of proto-exact categories. In joint work with Osorno\
, Ozornova\, Rovelli\, and Scheimbauer\, we proved that these results can
be maximally generalized to the input of augmented stable double Segal spa
ces\, so that the S-construction defines an equivalence of homotopy theori
es. In this talk\, we'll review the S-construction and the reasoning behi
nd these stages of generalization. Time permitting\, we'll discuss attemp
ts to characterize those augmented stable double Segal spaces that corresp
ond to cyclic spaces\, which is work in progress with Walker Stern.\n
LOCATION:https://researchseminars.org/talk/OATS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Marie Bohmann (Vanderbilt)
DTSTART;VALUE=DATE-TIME:20201110T150000Z
DTEND;VALUE=DATE-TIME:20201110T160000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/16
DESCRIPTION:Title: Al
gebraic K-theory for Lawvere theories: assembly and Morita invariance\
nby Anna Marie Bohmann (Vanderbilt) as part of Online algebraic topology
seminar\n\n\nAbstract\nMuch like operads and monads\, Lawvere theories are
a way of encoding algebraic structures\, such as those of modules over a
ring or sets with a group action. In this talk\, we discuss the algebraic
K-theory of Lawvere theories\, which contains information about automorph
ism groups of these structures. We'll discuss both particular examples an
d general constructions in the K-theory of Lawvere theories\, including ex
amples showing the limits of Morita invariance and the construction of ass
embly-style maps. This is joint work with Markus Szymik.\n
LOCATION:https://researchseminars.org/talk/OATS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angélica Osorno (Reed)
DTSTART;VALUE=DATE-TIME:20201012T150000Z
DTEND;VALUE=DATE-TIME:20201012T160000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/17
DESCRIPTION:Title: Tr
ansfer systems and weak factorization systems\nby Angélica Osorno (Re
ed) as part of Online algebraic topology seminar\n\n\nAbstract\n$N_\\infty
$ operads over a group G encode homotopy commutative operations together w
ith a class of equivariant transfer (or norm) maps. Their homotopy theory
is given by transfer systems\, which are certain discrete objects that hav
e a rich combinatorial structure defined in terms of the subgroup lattice
of G. In this talk\, we will show that when G is finite Abelian\, transfer
systems are in bijection with weak factorization systems on the poset cat
egory of subgroups of G. This leads to an involution on the lattice of tra
nsfer systems\, generalizing the work of Balchin–Bearup–Pech–Roitzhe
im for cyclic groups of squarefree order. We will conclude with an enumera
tion of saturated transfer systems and comments on the Rubin and Blumberg
–Hill saturation conjecture.\n\nThis is joint work with Evan Franchere\,
Usman Hafeez\, Peter Marcus\, Kyle Ormsby\, Weihang Qin\, and Riley Waugh
.\n
LOCATION:https://researchseminars.org/talk/OATS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Rivera (Purdue)
DTSTART;VALUE=DATE-TIME:20201123T150000Z
DTEND;VALUE=DATE-TIME:20201123T160000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/18
DESCRIPTION:Title: Th
e coalgebra of chains and the fundamental group\nby Manuel Rivera (Pur
due) as part of Online algebraic topology seminar\n\n\nAbstract\nRational
homotopy theory tells us that simply connected spaces\, up to rational hom
otopy equivalence\, may be classified algebraically by means of rational c
ocommutative coalgebras (Quillen) or in the finite type case by rational d
g commutative algebras (Sullivan). Goerss and Mandell proved versions of t
hese results for fields of arbitrary characteristic by means of simplicial
cocommutative coalgebras and E-infinity algebras\, respectively. The alge
braic structures in these settings are considered up to quasi-isomorphism.
\nIn this talk\, I will describe how to extend these results to spaces wit
h arbitrary fundamental group.The key new observation is that the homotopy
cocommutative coalgebraic structure of the chains on a space determines t
he fundamental group in complete generality. The corresponding algebraic n
otion of weak equivalence between coalgebras is drawn from Koszul duality.
The end goal of this program is to completely understand homotopy types i
n terms of algebraic “chain level” structure. This is joint work with
M. Zeinalian and F. Wierstra.\n
LOCATION:https://researchseminars.org/talk/OATS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Whitehouse (Sheffield)
DTSTART;VALUE=DATE-TIME:20201116T150000Z
DTEND;VALUE=DATE-TIME:20201116T160000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/19
DESCRIPTION:Title: Mo
del category structures and spectral sequences\nby Sarah Whitehouse (S
heffield) as part of Online algebraic topology seminar\n\n\nAbstract\nI'll
discuss a family of model category structures such that weak equivalences
are morphisms inducing an isomorphism at a fixed stage of a spectral sequ
ence. The talk will focus on joint work with Xin Fu\, Ai Guan and Muriel L
ivernet\, giving such model structures for multicomplexes. A multicomplex
(also known as a twisted chain complex) is an algebraic structure generali
zing the notion of a chain complex and that of a bicomplex. These structur
es have arisen in many different places and play an important role in homo
logical and homotopical algebra.\n
LOCATION:https://researchseminars.org/talk/OATS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigory Garkusha (Swansea)
DTSTART;VALUE=DATE-TIME:20201026T160000Z
DTEND;VALUE=DATE-TIME:20201026T170000Z
DTSTAMP;VALUE=DATE-TIME:20240328T080817Z
UID:OATS/20
DESCRIPTION:Title: Mo
tivic Gamma-spaces\nby Grigory Garkusha (Swansea) as part of Online al
gebraic topology seminar\n\n\nAbstract\nThis is a joint work with Ivan Pan
in and Paul Arne Østvær. We combine several mini miracles to achieve an
elementary understanding of infinite loop spaces and very effective spectr
a in the algebro-geometric setting of motivic homotopy theory. Our approac
h combines Gamma-spaces and framed correspondences into the concept of mot
ivic Gamma-spaces\; these are continuous or enriched functors of two varia
bles that take values in motivic spaces and are equipped with a framing. W
e craft proofs of our main results by imposing further axioms on motivic G
amma-spaces such as a Segal condition for simplicial Nisnevich sheaves\, c
ancellation\, A1- and sigma-invariance\, Nisnevich excision\, Suslin contr
actibility\, and grouplikeness. This adds to the discussion in the literat
ure on coexisting points of view on the A1-homotopy theory of algebraic va
rieties. As prime examples we discuss the motivic sphere spectrum\, algebr
aic cobordism\, motivic cohomology\, and Milnor-Witt motivic cohomology.\n
LOCATION:https://researchseminars.org/talk/OATS/20/
END:VEVENT
END:VCALENDAR