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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:20201031T051417Z
UID:OATS/1
DESCRIPTION:Title: Complexes of Tournaments in Directed Networks\nby Ran L
evi (University of Aberdeen) as part of Online algebraic topology seminar\
n\n\nAbstract\nClique graphs whose edges are oriented are referred to in t
he combinatorics literature as tournaments. We consider a family of semi-s
implicial sets\, that we refer to as “tournaplexes"\, whose simplices ar
e tournaments. In particular\, given a directed graph G\, we associate wit
h it a “flag tournaplex" which is a tournaplex containing the directed f
lag complex of G\, but also the geometric realisation of cliques that are
not directed. We define several types of filtration on tournaplexes\, and
exploiting persistent homology\, we observe that filtered flag tournaplexe
s provide finer means of distinguishing graph dynamics than the directed f
lag complex. We then demonstrate the power of those ideas by applying them
to graph data arising from the Blue Brain Project’s digital reconstruct
ion of a rat’s neocortex.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andy Baker (University of Glasgow)
DTSTART;VALUE=DATE-TIME:20200427T140000Z
DTEND;VALUE=DATE-TIME:20200427T150000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/2
DESCRIPTION:Title: Fun and games with the Steenrod algebra\nby Andy Baker
(University of Glasgow) as part of Online algebraic topology seminar\n\n\n
Abstract\nThe mod 2 Steenrod algebra is an important tool in unstable and
stable homotopy theory but it is also interesting as a purely algebraic ga
dget. I will briefly review its algebraic structure and that of some impo
rtant finite subHopf algebras. Then I will discuss some realisability ques
tions for modules\, ranging from classical examples to modules over the E-
infinity ring spectra kO and tmf localised at 2. I hope this talk will be
accessible to beginners and also have some things to interest experts.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Constanze Roitzheim (University of Kent)
DTSTART;VALUE=DATE-TIME:20200504T140000Z
DTEND;VALUE=DATE-TIME:20200504T150000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/3
DESCRIPTION:Title: Equivariant homotopy commutativity\, trees and chicken
feet\nby Constanze Roitzheim (University of Kent) as part of Online algebr
aic topology seminar\n\n\nAbstract\nCommutativity up to homotopy can be da
unting\, and it becomes even more difficult to track when equivariant stru
ctures get introduced. In the case of a finite group\, however\, the optio
ns for equivariant homotopy commutativity can be encoded using simple comb
inatorics\, and we will show some examples.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuele Dotto (University of Warwick)
DTSTART;VALUE=DATE-TIME:20200518T140000Z
DTEND;VALUE=DATE-TIME:20200518T150000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/4
DESCRIPTION:Title: Witt vectors with coefficients and characteristic polyn
omials over non-commutative rings\nby Emanuele Dotto (University of Warwic
k) as part of Online algebraic topology seminar\n\n\nAbstract\nThe charact
eristic polynomial of a matrix with entries in a commutative ring $R$ natu
rally takes value in the ring of Witt vectors of $R$. In joint work with K
rause\, Nikolaus and Patchkoria\, we extend the classical Witt vectors con
struction 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
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathryn Hess (EPFL)
DTSTART;VALUE=DATE-TIME:20200608T140000Z
DTEND;VALUE=DATE-TIME:20200608T150000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/5
DESCRIPTION:Title: Calculus from comonads\nby Kathryn Hess (EPFL) as part
of Online algebraic topology seminar\n\n\nAbstract\n(Joint work with Brend
a Johnson.) The many theories of "calculus" introduced in algebraic topol
ogy over the past couple of decades--e.g.\, Goodwillie's calculus of homot
opy functors\, the Goodwillie-Weiss manifold calculus\, the orthogonal cal
culus\, and the Johnson-McCarthy cotriple calculus--all have a similar fla
vor\, though the objects studied and exact methods applied are not the sam
e. We have constructed a relatively simple category-theoretic machine fo
r producing towers of functors from a small category into a simplicial mod
el category\, determined conditions under which such tower-building machin
es constitute a calculus\, and showed that this framework encompasses cert
ain well known calculi\, as well as providing new classes of examples. T
he cogs and gears of our machine are cubical diagrams of reflective subcat
egories and the comonads they naturally give rise to.\n\nIn this talk\, I
will assume no familiarity with comonads and only basic knowledge of simpl
icial model categories.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Adams (Colorado State University)
DTSTART;VALUE=DATE-TIME:20200525T140000Z
DTEND;VALUE=DATE-TIME:20200525T150000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/6
DESCRIPTION:Title: Vietoris-Rips complexes and Borsuk-Ulam theorems\nby He
nry Adams (Colorado State University) as part of Online algebraic topology
seminar\n\n\nAbstract\nGiven a metric space X and a scale parameter r\, t
he Vietoris-Rips simplicial 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. Vieto
ris-Rips complexes were invented by Vietoris in order to define a (co)homo
logy theory for metric spaces\, and by Rips for use in geometric group the
ory. More recently\, they have found applications in computational topolog
y for approximating of the shape of a dataset. I will explain how the Viet
oris-Rips complexes of the circle\, as the scale parameter r increases\, o
btain 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 John Bush and Florian Frick.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirsten Wickelgren (Duke University)
DTSTART;VALUE=DATE-TIME:20200601T140000Z
DTEND;VALUE=DATE-TIME:20200601T150000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/7
DESCRIPTION:Title: There are 160\,839<1> + 160\,650<-1> 3-planes in a 7-di
mensional cubic hypersurface\nby Kirsten Wickelgren (Duke University) as p
art of Online algebraic topology seminar\n\n\nAbstract\nThe expression in
the title is a bilinear form and it comes from an Euler number in A1-algeb
raic topology. Such Euler numbers can be constructed with Hochschild homol
ogy\, self-duality of Koszul complexes\, pushforwards in SL_c oriented coh
omology theories\, and sums of local degrees. We show an integrality resul
t for A1-Euler numbers and apply this to the enumeration of d-planes in co
mplete intersections. Classically such counts are valid over C and sometim
es extended to the real numbers\, but A1-homotopy theory allows one to per
form counts over a large class of fields\, and records information about t
he solutions in bilinear form. The example in the title then follows from
work of Finashin--Kharlamov. This is joint work with Tom Bachmann.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Szymik (NTNU)
DTSTART;VALUE=DATE-TIME:20200615T140000Z
DTEND;VALUE=DATE-TIME:20200615T150000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/8
DESCRIPTION:Title: Trigraded spectral sequences for principal fibrations\n
by Markus Szymik (NTNU) as part of Online algebraic topology seminar\n\n\n
Abstract\nThe Leray--Serre and the Eilenberg--Moore spectral sequence are
fundamental tools for computing the cohomology of a group or\, more genera
lly\, of a space. In joint work with Frank Neumann (Leicester)\, we descr
ibe the relationship 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 fr
om graduate students in algebraic topology onward\, and I will only assume
some casual acquaintance with spectral sequences.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrich Pennig (Cardiff University)
DTSTART;VALUE=DATE-TIME:20200511T140000Z
DTEND;VALUE=DATE-TIME:20200511T150000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/9
DESCRIPTION:Title: Loops\, groups\, and twists - the role of K-theory in m
athematical physics\nby Ulrich Pennig (Cardiff University) as part of Onli
ne algebraic topology seminar\n\n\nAbstract\nWhile K-theory has its origin
s in Grothendieck's formulation and proof of his version of the Riemann-Ro
ch theorem\, it now plays a significant role in many diverse branches of m
athematics: It provides a fundamental example of a cohomology theory\, and
it is one of the most important invariants of C*-algebras. In the first h
alf of the talk\, I will define the K-groups and discuss some of their app
lications. In the second half\, I will concentrate on equivariant twisted
K-theory\, which is related to the representation theory of loop groups an
d the geometry of two-dimensional quantum field theories by a theorem of F
reed\, Hopkins\, and Teleman. I will finish with an outline of joint work
with D. Evans\, in which we study generalizations of this work to higher t
wists.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Hahn (MIT)
DTSTART;VALUE=DATE-TIME:20200921T130000Z
DTEND;VALUE=DATE-TIME:20200921T140000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/10
DESCRIPTION:Title: Nishida Nilpotence\nby Jeremy Hahn (MIT) as part of Onl
ine algebraic topology seminar\n\n\nAbstract\nIn 1973\, Nishida proved tha
t every positive degree class in the stable homotopy groups of spheres is
nilpotent. We will discuss some modern perspectives on Nishida's original
proof. While this will be a mostly expository talk aimed at graduate stu
dents\, if time permits we will end with a discussion of some open nilpote
nce questions in motivic stable homotopy theory.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lennart Meier (Utrecht)
DTSTART;VALUE=DATE-TIME:20200928T140000Z
DTEND;VALUE=DATE-TIME:20200928T150000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/11
DESCRIPTION:Title: Elliptic cohomology of level n\nby Lennart Meier (Utrec
ht) as part of Online algebraic topology seminar\n\n\nAbstract\nElliptic g
enera have played an important role in algebraic topology and algebraic ge
ometry since the 1980s. To every almost-complex manifold they associate a
modular form for the congruence subgroups $\\Gamma_1(n)$. More recently\,
elliptic cohomology theories have been built that are natural targets of e
lliptic genera for families. I will give an overview of these theories and
report in particular on certain $C_2$-equivariant refinements.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viktoriya Ozornova (Ruhr-Universität Bochum)
DTSTART;VALUE=DATE-TIME:20201005T140000Z
DTEND;VALUE=DATE-TIME:20201005T150000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/12
DESCRIPTION:Title: Models of (infty\,2)-categories\nby Viktoriya Ozornova
(Ruhr-Universität Bochum) as part of Online algebraic topology seminar\n\
n\nAbstract\nAn $(\\infty\,2)$-category should be a weak version of a stri
ct $2$-category\, in which compositions are well-defined\, associative and
unital up to some higher coherence. There are various models making this
precise. In this talk\, I will describe a direct comparison between two pa
rticular models (which will be introduced)\, namely $\\Theta_2$-spaces and
saturated $2$-complicial sets. This is joint work in progress with Julie
Bergner and Martina Rovelli.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Birgit Richter (Universität Hamburg)
DTSTART;VALUE=DATE-TIME:20201019T140000Z
DTEND;VALUE=DATE-TIME:20201019T150000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/13
DESCRIPTION:Title: Detecting and describing ramification for structured ri
ng spectra\nby Birgit Richter (Universität Hamburg) as part of Online alg
ebraic topology seminar\n\n\nAbstract\nThis is a report on joint work in p
rogress with Eva Höning. \n\nRamification for commutative ring spectra ca
n be detected by relative topological Hochschild homology and by the spect
rum of Kähler differentials. For rings of integers in an extension of num
ber fields\, it is important to distinguish between tame and wild ramifica
tion. Noether's theorem characterizes tame ramification in terms of a norm
al basis and tame ramification can also be detected via the surjectivity o
f the norm map. We take the latter fact and use the Tate cohomology spectr
um to detect wild ramification in the context of commutative ring spectra.
In the talk\, I will discuss several examples in the context of topologic
al K-theory and modular forms.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Drew Heard (NTNU)
DTSTART;VALUE=DATE-TIME:20201102T150000Z
DTEND;VALUE=DATE-TIME:20201102T160000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/14
DESCRIPTION:Title: Support theory for triangulated categories in algebra a
nd topology\nby Drew Heard (NTNU) as part of Online algebraic topology sem
inar\n\n\nAbstract\nWe will survey the support theory of triangulated cate
gories through the machinery of tensor-triangulated geometry. We will disc
uss the stratification theory of Benson—Iyengar—Krause for triangulate
d categories\, the construction by Balmer of the spectrum of a tensor-tria
ngulated category\, and the relation between the two. Time permitting\, we
will discuss a recent application to the category of derived Mackey funct
ors\, joint with Beren Sanders.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julie Bergner (University of Virginia)
DTSTART;VALUE=DATE-TIME:20201130T150000Z
DTEND;VALUE=DATE-TIME:20201130T160000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/15
DESCRIPTION:by Julie Bergner (University of Virginia) as part of Online al
gebraic topology seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Marie Bohmann (Vanderbilt)
DTSTART;VALUE=DATE-TIME:20201110T150000Z
DTEND;VALUE=DATE-TIME:20201110T160000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/16
DESCRIPTION:by Anna Marie Bohmann (Vanderbilt) as part of Online algebrai
c topology seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angélica Osorno (Reed)
DTSTART;VALUE=DATE-TIME:20201012T150000Z
DTEND;VALUE=DATE-TIME:20201012T160000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/17
DESCRIPTION:Title: Transfer systems and weak factorization systems\nby Ang
élica Osorno (Reed) as part of Online algebraic topology seminar\n\n\nAbs
tract\n$N_\\infty$ operads over a group G encode homotopy commutative oper
ations together with a class of equivariant transfer (or norm) maps. Their
homotopy theory is given by transfer systems\, which are certain discrete
objects that have a rich combinatorial structure defined in terms of the
subgroup lattice of G. In this talk\, we will show that when G is finite A
belian\, transfer systems are in bijection with weak factorization systems
on the poset category of subgroups of G. This leads to an involution on t
he lattice of transfer systems\, generalizing the work of Balchin–Bearup
–Pech–Roitzheim for cyclic groups of squarefree order. We will conclud
e with an enumeration of saturated transfer systems and comments on the Ru
bin 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
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Rivera (Purdue)
DTSTART;VALUE=DATE-TIME:20201123T150000Z
DTEND;VALUE=DATE-TIME:20201123T160000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/18
DESCRIPTION:by Manuel Rivera (Purdue) as part of Online algebraic topology
seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Whitehouse (Sheffield)
DTSTART;VALUE=DATE-TIME:20201116T150000Z
DTEND;VALUE=DATE-TIME:20201116T160000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/19
DESCRIPTION:by Sarah Whitehouse (Sheffield) as part of Online algebraic to
pology seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigory Garkusha (Swansea)
DTSTART;VALUE=DATE-TIME:20201026T160000Z
DTEND;VALUE=DATE-TIME:20201026T170000Z
DTSTAMP;VALUE=DATE-TIME:20201031T051417Z
UID:OATS/20
DESCRIPTION:Title: Motivic Gamma-spaces\nby Grigory Garkusha (Swansea) as
part of Online algebraic topology seminar\n\n\nAbstract\nThis is a joint w
ork with Ivan Panin and Paul Arne Østvær. We combine several mini miracl
es to achieve an elementary understanding of infinite loop spaces and very
effective spectra in the algebro-geometric setting of motivic homotopy th
eory. Our approach combines Gamma-spaces and framed correspondences into t
he concept of motivic Gamma-spaces\; these are continuous or enriched func
tors of two variables that take values in motivic spaces and are equipped
with a framing. We craft proofs of our main results by imposing further ax
ioms on motivic Gamma-spaces such as a Segal condition for simplicial Nisn
evich sheaves\, cancellation\, A1- and sigma-invariance\, Nisnevich excisi
on\, Suslin contractibility\, and grouplikeness. This adds to the discussi
on in the literature on coexisting points of view on the A1-homotopy theor
y of algebraic varieties. As prime examples we discuss the motivic sphere
spectrum\, algebraic cobordism\, motivic cohomology\, and Milnor-Witt moti
vic cohomology.\n
END:VEVENT
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