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BEGIN:VEVENT
SUMMARY:Katharine Adamyk (University of Western Ontario)
DTSTART:20201007T173000Z
DTEND:20201007T183000Z
DTSTAMP:20260404T111445Z
UID:ReginaTopology/1
DESCRIPTION:Title: Classifying stable modules over A(1)\nby Katharine Adamy
k (University of Western Ontario) as part of University of Regina topology
seminar\n\n\nAbstract\nThis talk will present a classification theorem fo
r a certain class of modules over A(1)\, a subalgebra of the mod-2 Steenro
d algebra. In order to give the module classification\, there will be some
background on Margolis homology (an invariant of modules over the Steenro
d algebra) and the stable module category. Applications of the classificat
ion theorem to lifting A(1)-modules to modules over the Steenrod algebra a
nd applications to the computation of certain localized Adams spectral seq
uences will also be discussed.\n
LOCATION:https://stable.researchseminars.org/talk/ReginaTopology/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Zhang (Nankai University)
DTSTART:20201104T223000Z
DTEND:20201104T233000Z
DTSTAMP:20260404T111445Z
UID:ReginaTopology/2
DESCRIPTION:Title: Koszul duality and TQ-homological Whitehead theorem of struc
tured ring spectra\nby Yu Zhang (Nankai University) as part of Univers
ity of Regina topology seminar\n\n\nAbstract\nQuillen's work on rational h
omotopy theory illustrates the duality between differential graded Lie alg
ebras and differential graded cocommutative coalgebras. In homotopy theory
\, there is an analogous duality phenomenon\, called Koszul duality\, wher
e the role of differential graded algebras is played by structured ring sp
ectra. In this talk\, I will talk about Koszul duality as well as some of
my related recent work on Topological Quillen (TQ) localization and the ho
mological Whitehead theorem of structured ring spectra. This is joint with
John E. Harper.\n
LOCATION:https://stable.researchseminars.org/talk/ReginaTopology/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duncan Clark (Ohio State University)
DTSTART:20210121T223000Z
DTEND:20210121T233000Z
DTSTAMP:20260404T111445Z
UID:ReginaTopology/3
DESCRIPTION:Title: An intrinsic operad structure for the derivatives of the ide
ntity\nby Duncan Clark (Ohio State University) as part of University o
f Regina topology seminar\n\n\nAbstract\nA long standing slogan in Goodwil
lie's functor calculus is that the derivatives of the identity functor on
a suitable model category should come equipped with a natural operad struc
ture. A result of this type was first shown by Ching for the category of b
ased topological spaces. It has long been expected that in the category of
algebras over a reduced operad $\\mathcal{O}$ of spectra that the derivat
ives of the identity should be equivalent to $\\mathcal{O}$ as operads.\n\
nIn this talk I will discuss my recent work which gives a positive answer
to the above conjecture. My method is to induce a "highly homotopy coheren
t" operad structure on the derivatives of the identity via a pairing of un
derlying cosimplicial objects with respect to the box product. This cosimp
licial object naturally arises by analyzing the derivatives of the Bousfie
ld-Kan cosimplicial resolution of the identity via the stabilization adjun
ction for $\\mathcal{O}$-algebras. Time permitting\, I will describe some
additional applications of these box product pairings including a new desc
ription of an operad structure on the derivatives of the identity in space
s.\n
LOCATION:https://stable.researchseminars.org/talk/ReginaTopology/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niko Schonsheck (Ohio State University)
DTSTART:20210128T223000Z
DTEND:20210128T233000Z
DTSTAMP:20260404T111445Z
UID:ReginaTopology/4
DESCRIPTION:Title: Fibration theorems\, functor calculus\, and chromatic connec
tions in $\\mathcal{O}$-algebras\nby Niko Schonsheck (Ohio State Unive
rsity) as part of University of Regina topology seminar\n\n\nAbstract\nBy
considering algebras over an operad $\\mathcal{O}$ in one's preferred cate
gory of spectra\, we can encode various flavors of algebraic structure (e.
g. commutative ring spectra). Topological Quillen (TQ) homology is a natur
ally occurring notion of homology for these objects\, with analogies to bo
th singular homology and stabilization of spaces. In this talk\, we will b
egin by discussing a fibration theorem for TQ-completion\, showing that TQ
-completion preserves fibration sequences in which the base and total $\\m
athcal{O}$-algebra are connected. We will then describe a few results that
hint towards an intrinsic connection between TQ-completion and the conver
gence of the Taylor tower of the identity functor in the category of $\\ma
thcal{O}$-algebras. Lastly\, time permitting\, we will discuss recent join
t work with Crichton Ogle on the chromatic localization of the homotopy co
mpletion tower of $\\mathcal{O}$-algebras and connections to functor calcu
lus.\n
LOCATION:https://stable.researchseminars.org/talk/ReginaTopology/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20210915T173000Z
DTEND:20210915T183000Z
DTSTAMP:20260404T111445Z
UID:ReginaTopology/5
DESCRIPTION:Title: Higher order Toda brackets\nby Aziz Kharoof (Bilkent Uni
versity) as part of University of Regina topology seminar\n\n\nAbstract\nT
oda brackets are a type of higher homotopy operation. Like Massey products
\, they are not always defined\, and their value is indeterminate. Neverth
eless\, they play an important role in algebraic topology and related fiel
ds. Toda originally constructed them as a tool for computing homotopy grou
ps of spheres. Adams later showed that they can be used to calculate diffe
rentials in spectral sequences.\n\nAfter reviewing the construction and pr
operties of the classical Toda bracket\, we shall describe a higher order
version\, there are two ways to do that. We will provide a diagrammatic de
scription for the system we need to define the higher order Toda brackets\
, then we will use that to give an alternative definition using the homoto
py cofiber.\n
LOCATION:https://stable.researchseminars.org/talk/ReginaTopology/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maximilien Péroux (University of Pennsylvania)
DTSTART:20211102T210000Z
DTEND:20211102T220000Z
DTSTAMP:20260404T111445Z
UID:ReginaTopology/6
DESCRIPTION:Title: Equivariant variations of topological Hochschild homology\nby Maximilien Péroux (University of Pennsylvania) as part of Universit
y of Regina topology seminar\n\n\nAbstract\nTopological Hochschild homolog
y (THH) is an important variant for ring spectra. It is built as a geometr
ic realization of a cyclic bar construction. It is endowed with an action
of circle. This is because it is a geometric realization of a cyclic objec
t. The simplex category factors through Connes’ category $\\Lambda$. Sim
ilarly\, real topological Hochschild homology (THR) for ring spectra with
anti-involution is endowed with a $O(2)$-action. Here instead of the cycli
c category $\\Lambda$\, we use the dihedral category $\\Xi$.\n\nFrom work
in progress with Gabe Angelini-Knoll and Mona Merling\, I present a genera
lization of $\\Lambda$ and $\\Xi$ called crossed simplicial groups\, intro
duced by Fiedorowicz and Loday. To each crossed simplical group $G$\, I de
fine THG\, an equivariant analogue of THH. Its input is a ring spectrum wi
th a twisted group action. THG is an algebraic invariant endowed with diff
erent action and cyclotomic structure\, and generalizes THH and THR.\n
LOCATION:https://stable.researchseminars.org/talk/ReginaTopology/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hana Jia Kong (Institute for Advanced Study)
DTSTART:20220210T190000Z
DTEND:20220210T200000Z
DTSTAMP:20260404T111445Z
UID:ReginaTopology/7
DESCRIPTION:Title: Motivic image-of-J spectrum via the effective slice spectral
sequence\nby Hana Jia Kong (Institute for Advanced Study) as part of
University of Regina topology seminar\n\n\nAbstract\nThe "image-of-J" spec
trum in the classical stable homotopy category has been well-studied\; Bac
hmann–Hopkins defined its motivic analogue. In this talk\, I will start
with the classical story\, and then move to the motivic version. I will ta
lk about the effective slice computation of the motivic "image-of-J" spect
rum over the real numbers. Unlike the classical case\, the map from the mo
tivic sphere is not surjective on homotopy groups. Still\, it captures a r
egular pattern that appears in the $\\mathbb{R}$-motivic stable stems. Thi
s is joint work with Eva Belmont and Dan Isaksen.\n
LOCATION:https://stable.researchseminars.org/talk/ReginaTopology/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Balderrama (University of Virginia)
DTSTART:20220310T190000Z
DTEND:20220310T200000Z
DTSTAMP:20260404T111445Z
UID:ReginaTopology/8
DESCRIPTION:Title: The motivic lambda algebra and Hopf invariant one problem\nby William Balderrama (University of Virginia) as part of University of
Regina topology seminar\n\n\nAbstract\nCurrent best approaches to underst
anding the stable homotopy groups of spheres at the prime $2$ make use of
the Adams spectral sequence\, which computes stable stems starting with in
formation about the cohomology of the Steenrod algebra. The first major su
ccess of the Adams spectral sequence was in Adams' resolution of the Hopf
invariant one problem\, which proceeded via an analysis of secondary cohom
ology operations. Later\, J.S.P. Wang used a certain algebraic device\, th
e lambda algebra\, to give a more thorough computation of the cohomology o
f the Steenrod algebra\, and used this to give a slick almost entirely alg
ebraic derivation of the Hopf invariant one theorem.\n\nIn this talk\, I w
ill go over some of the above history\, and then describe work (joint with
Dominic Culver and J.D. Quigley) on analogues in motivic stable homotopy
theory. In particular\, I will describe a mod $2$ motivic lambda algebra\,
defined over any base field of characteristic not equal to $2$\, as well
as some of what can be said about the $1$-line of the motivic Adams spectr
al sequence for various base fields.\n
LOCATION:https://stable.researchseminars.org/talk/ReginaTopology/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sacha Ikonicoff (University of Calgary)
DTSTART:20220414T190000Z
DTEND:20220414T200000Z
DTSTAMP:20260404T111445Z
UID:ReginaTopology/9
DESCRIPTION:Title: Divided power algebras over an operad\nby Sacha Ikonicof
f (University of Calgary) as part of University of Regina topology seminar
\n\nLecture held in RI 208 (Research and Innovation Centre).\n\nAbstract\n
Divided power algebras were defined by H. Cartan in 1954 to study the homo
logy of Eilenberg-MacLane spaces. They are commutative algebras endowed\,
for each integer $n$\, with an additional monomial operation. Over a field
of characteristic $0$\, this operation corresponds to taking each element
to its $n$-th power divided by factorial of $n$. This definition does not
make sense if the base field is of prime characteristic\, yet Cartan's de
finition of divided power algebra applies in this situation as well. The n
otion of divided power algebra over a field of prime characteristic allows
us to describe algebraic structures that appear in homology and homotopic
al algebra and has found applications in a wide array of mathematical d
omains\, for instance in crystalline cohomology\, and deformation theory.\
n\nIn this talk\, we will introduce the generalised definition of a divide
d power algebra over an operad given by B. Fresse in 2000. We will give a
complete characterisation for generalised divided power algebras in terms
of monomial operations and relations. We will show how to improve this cha
racterisation to particular cases\, including the case of a product of ope
rads with distributive laws.\n
LOCATION:https://stable.researchseminars.org/talk/ReginaTopology/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Martensen (NTNU Trondheim)
DTSTART:20220919T190000Z
DTEND:20220919T200000Z
DTSTAMP:20260404T111445Z
UID:ReginaTopology/10
DESCRIPTION:Title: Triangulated categories and other $n$-angulations\nby S
ebastian Martensen (NTNU Trondheim) as part of University of Regina topolo
gy seminar\n\n\nAbstract\nTriangulated categories were introduced to captu
re some of the extra structure present in the derived category of a ring a
nd the stable homotopy category\, and today they are present wherever homo
logical algebra plays a central role. In the case of derived categories\,
the triangulation captures certain “shadows” of short and long exact s
equences\, and so one may wonder: are there categories that capture only l
ong exact sequences of a certain length? This led to the introduction of $
n$-angulated categories in 2013 by Geiss\, Keller\, and Oppermann. Today\,
they find their use in representation theory\, and it is a hope that they
will one day play a role in topology as well. For this talk we will discu
ss triangulated categories\, stable module categories\, and introduce $n$-
angulated categories along with their main class of examples.\n
LOCATION:https://stable.researchseminars.org/talk/ReginaTopology/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Petersen (MPIM Bonn)
DTSTART:20221114T190000Z
DTEND:20221114T200000Z
DTSTAMP:20260404T111445Z
UID:ReginaTopology/11
DESCRIPTION:Title: The $RO(C_2)$-graded homology of $C_2$-equivariant Eilenber
g-MacLane spaces\nby Sarah Petersen (MPIM Bonn) as part of University
of Regina topology seminar\n\n\nAbstract\nThis talk describes an extension
of Ravenel-Wilson Hopf ring techniques to $C_2$-equivariant homotopy theo
ry. Our main application and motivation for introducing these methods is a
computation of the $RO(C_2)$-graded homology of $C_2$-equivariant Eilenbe
rg-MacLane spaces. The result we obtain for $C_2$-equivariant Eilenberg-Ma
cLane spaces associated to the constant Mackey functor $\\underline{\\math
bb{F}}_2$ gives a $C_2$-equivariant analogue of the classical computation
due to Serre at the prime $2$. We also investigate a twisted bar spectral
sequence computing the homology of these equivariant Eilenberg-MacLane spa
ces.\n
LOCATION:https://stable.researchseminars.org/talk/ReginaTopology/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Sikora (Bilkent University)
DTSTART:20230131T190000Z
DTEND:20230131T200000Z
DTSTAMP:20260404T111445Z
UID:ReginaTopology/12
DESCRIPTION:Title: $RO(C_2)$-graded coefficients of $C_2$-Eilenberg-MacLane sp
ectra\nby Igor Sikora (Bilkent University) as part of University of Re
gina topology seminar\n\n\nAbstract\nIn non-equivariant topology\, the ord
inary homology of a point is described by the dimension axiom and is quite
simple - namely\, it is concentrated in degree zero. The situation in $G$
-equivariant topology is different. This is because Bredon homology - the
equivariant counterpart of ordinary homology - is naturally graded over $R
O(G)$\, the ring of $G$-representations. Whereas the equivariant dimension
axiom describes the part of the Bredon homology of a point graded over tr
ivial representations\, it does not put any requirements on the rest of th
e grading - in which the homology may be quite complicated.\n\nThe $RO(G)$
-graded Bredon homology theories are represented by $G$-Eilenberg-MacLane
spectra\, and thus the Bredon homology of a point is the same as coefficie
nts of these spectra. During the talk\, I will present the method of compu
ting the $RO(C_2)$-graded coefficients of $C_2$-Eilenberg-MacLane spectra
based on the Tate square. As demonstrated by Greenlees\, the Tate square g
ives an algorithmic approach to computing the coefficients of equivariant
spectra. In the talk\, we will discuss how to use this method to obtain th
e $RO(C_2)$-graded coefficients of a $C_2$-Eilenberg-MacLane spectrum as a
$RO(C_2)$-graded abelian group. We will also present the multiplicative s
tructure of the $C_2$-Eilenberg-MacLane spectrum associated to the Burnsid
e Mackey functor. Time permitting\, we will further discuss how to use thi
s knowledge to derive a multiplicative structure for the coefficients for
any ring Mackey functor.\n
LOCATION:https://stable.researchseminars.org/talk/ReginaTopology/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brandon Doherty (Stockholm University)
DTSTART:20230411T190000Z
DTEND:20230411T200000Z
DTSTAMP:20260404T111445Z
UID:ReginaTopology/13
DESCRIPTION:Title: Cubical models of higher categories without connections
\nby Brandon Doherty (Stockholm University) as part of University of Regin
a topology seminar\n\n\nAbstract\nCubical sets with connections model $(\\
infty\,1)$-categories via the cubical Joyal model structure\, constructed
and shown to be equivalent to the Joyal model structure on simplicial sets
by Doherty-Kapulkin-Lindsey-Sattler. In the same work\, an analogous mode
l structure was constructed on the category of cubical sets without connec
tions (i.e.\, having only faces and degeneracies)\, but was not shown to b
e equivalent to any other model of $(\\infty\,1)$-categories.\n\nIn this t
alk\, we will review the cubical Joyal model structure on cubical sets wit
hout connections and discuss the proof that it is Quillen equivalent to th
e Joyal model structure on simplicial sets\, using a construction by which
a fibrant cubical set without connections can be equipped with connection
s via lifting. This talk is based on the paper of the same title.\n
LOCATION:https://stable.researchseminars.org/talk/ReginaTopology/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sacha Ikonicoff (University of Ottawa)
DTSTART:20230822T213000Z
DTEND:20230822T223000Z
DTSTAMP:20260404T111445Z
UID:ReginaTopology/14
DESCRIPTION:Title: Quillen-Barr-Beck cohomology of divided power algebras over
an operad\nby Sacha Ikonicoff (University of Ottawa) as part of Unive
rsity of Regina topology seminar\n\nLecture held in RIC 208.\n\nAbstract\n
Divided power algebras are algebras equipped with additional monomial oper
ations. They are fairly ubiquitous in the positive characteristic setting\
, and appear notably in the study of simplicial algebras\, in crystalline
cohomology\, and in deformation theory. An operad is a device that encodes
operations: there is an operad for associative algebras\, one for commuta
tive algebras\, for Lie algebras\, Poisson algebras\, and so on. Each oper
ad then comes with an associated category of algebras\, and also with a ca
tegory of divided power algebras.\n\nThe aim of this talk is to show how A
ndré-Quillen cohomology generalises to several categories of algebras usi
ng the notion of operad. We will introduce modules and derivations\, but a
lso representing objects for modules - known as the universal enveloping a
lgebra - and for derivations - known as the module of Kähler differential
s - which will allow us to build an analogue of the cotangent complex. We
will see how these notions allow us to recover known cohomology theories o
n many categories of algebras\, while they provide somewhat exotic new not
ions when applied to divided power algebras.\n\nThis is joint work with Ma
rtin Frankland and Ioannis Dokas.\n
LOCATION:https://stable.researchseminars.org/talk/ReginaTopology/14/
END:VEVENT
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