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BEGIN:VEVENT
SUMMARY:Katharine Adamyk (University of Western Ontario)
DTSTART;VALUE=DATE-TIME:20201007T173000Z
DTEND;VALUE=DATE-TIME:20201007T183000Z
DTSTAMP;VALUE=DATE-TIME:20230208T065146Z
UID:ReginaTopology/1
DESCRIPTION:Title: Classifying stable modules over A(1)\nby Katharine Adamyk (Univ
ersity of Western Ontario) as part of University of Regina topology semina
r\n\n\nAbstract\nThis talk will present a classification theorem for a cer
tain class of modules over A(1)\, a subalgebra of the mod-2 Steenrod algeb
ra. In order to give the module classification\, there will be some backgr
ound on Margolis homology (an invariant of modules over the Steenrod algeb
ra) and the stable module category. Applications of the classification the
orem to lifting A(1)-modules to modules over the Steenrod algebra and appl
ications to the computation of certain localized Adams spectral sequences
will also be discussed.\n
LOCATION:https://researchseminars.org/talk/ReginaTopology/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Zhang (Nankai University)
DTSTART;VALUE=DATE-TIME:20201104T223000Z
DTEND;VALUE=DATE-TIME:20201104T233000Z
DTSTAMP;VALUE=DATE-TIME:20230208T065146Z
UID:ReginaTopology/2
DESCRIPTION:Title: Koszul duality and TQ-homological Whitehead theorem of structured r
ing spectra\nby Yu Zhang (Nankai University) as part of University of
Regina topology seminar\n\n\nAbstract\nQuillen's work on rational homotopy
theory illustrates the duality between differential graded Lie algebras a
nd differential graded cocommutative coalgebras. In homotopy theory\, ther
e is an analogous duality phenomenon\, called Koszul duality\, where the r
ole of differential graded algebras is played by structured ring spectra.
In this talk\, I will talk about Koszul duality as well as some of my rela
ted recent work on Topological Quillen (TQ) localization and the homologic
al Whitehead theorem of structured ring spectra. This is joint with John E
. Harper.\n
LOCATION:https://researchseminars.org/talk/ReginaTopology/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duncan Clark (Ohio State University)
DTSTART;VALUE=DATE-TIME:20210121T223000Z
DTEND;VALUE=DATE-TIME:20210121T233000Z
DTSTAMP;VALUE=DATE-TIME:20230208T065146Z
UID:ReginaTopology/3
DESCRIPTION:Title: An intrinsic operad structure for the derivatives of the identity\nby Duncan Clark (Ohio State University) as part of University of Regin
a topology seminar\n\n\nAbstract\nA long standing slogan in Goodwillie's f
unctor calculus is that the derivatives of the identity functor on a suita
ble model category should come equipped with a natural operad structure. A
result of this type was first shown by Ching for the category of based to
pological spaces. It has long been expected that in the category of algebr
as over a reduced operad $\\mathcal{O}$ of spectra that the derivatives of
the identity should be equivalent to $\\mathcal{O}$ as operads.\n\nIn thi
s talk I will discuss my recent work which gives a positive answer to the
above conjecture. My method is to induce a "highly homotopy coherent" oper
ad structure on the derivatives of the identity via a pairing of underlyin
g cosimplicial objects with respect to the box product. This cosimplicial
object naturally arises by analyzing the derivatives of the Bousfield-Kan
cosimplicial resolution of the identity via the stabilization adjunction f
or $\\mathcal{O}$-algebras. Time permitting\, I will describe some additio
nal applications of these box product pairings including a new description
of an operad structure on the derivatives of the identity in spaces.\n
LOCATION:https://researchseminars.org/talk/ReginaTopology/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niko Schonsheck (Ohio State University)
DTSTART;VALUE=DATE-TIME:20210128T223000Z
DTEND;VALUE=DATE-TIME:20210128T233000Z
DTSTAMP;VALUE=DATE-TIME:20230208T065146Z
UID:ReginaTopology/4
DESCRIPTION:Title: Fibration theorems\, functor calculus\, and chromatic connections i
n $\\mathcal{O}$-algebras\nby Niko Schonsheck (Ohio State University)
as part of University of Regina topology seminar\n\n\nAbstract\nBy conside
ring algebras over an operad $\\mathcal{O}$ in one's preferred category of
spectra\, we can encode various flavors of algebraic structure (e.g. comm
utative ring spectra). Topological Quillen (TQ) homology is a naturally oc
curring notion of homology for these objects\, with analogies to both sing
ular homology and stabilization of spaces. In this talk\, we will begin by
discussing a fibration theorem for TQ-completion\, showing that TQ-comple
tion preserves fibration sequences in which the base and total $\\mathcal{
O}$-algebra are connected. We will then describe a few results that hint t
owards an intrinsic connection between TQ-completion and the convergence o
f the Taylor tower of the identity functor in the category of $\\mathcal{O
}$-algebras. Lastly\, time permitting\, we will discuss recent joint work
with Crichton Ogle on the chromatic localization of the homotopy completio
n tower of $\\mathcal{O}$-algebras and connections to functor calculus.\n
LOCATION:https://researchseminars.org/talk/ReginaTopology/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART;VALUE=DATE-TIME:20210915T173000Z
DTEND;VALUE=DATE-TIME:20210915T183000Z
DTSTAMP;VALUE=DATE-TIME:20230208T065146Z
UID:ReginaTopology/5
DESCRIPTION:Title: Higher order Toda brackets\nby Aziz Kharoof (Bilkent University
) as part of University of Regina topology seminar\n\n\nAbstract\nToda bra
ckets are a type of higher homotopy operation. Like Massey products\, they
are not always defined\, and their value is indeterminate. Nevertheless\,
they play an important role in algebraic topology and related fields. Tod
a originally constructed them as a tool for computing homotopy groups of s
pheres. Adams later showed that they can be used to calculate differential
s in spectral sequences.\n\nAfter reviewing the construction and propertie
s of the classical Toda bracket\, we shall describe a higher order version
\, there are two ways to do that. We will provide a diagrammatic descripti
on for the system we need to define the higher order Toda brackets\, then
we will use that to give an alternative definition using the homotopy cofi
ber.\n
LOCATION:https://researchseminars.org/talk/ReginaTopology/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maximilien Péroux (University of Pennsylvania)
DTSTART;VALUE=DATE-TIME:20211102T210000Z
DTEND;VALUE=DATE-TIME:20211102T220000Z
DTSTAMP;VALUE=DATE-TIME:20230208T065146Z
UID:ReginaTopology/6
DESCRIPTION:Title: Equivariant variations of topological Hochschild homology\nby M
aximilien Péroux (University of Pennsylvania) as part of University of Re
gina topology seminar\n\n\nAbstract\nTopological Hochschild homology (THH)
is an important variant for ring spectra. It is built as a geometric real
ization of a cyclic bar construction. It is endowed with an action of circ
le. This is because it is a geometric realization of a cyclic object. The
simplex category factors through Connes’ category $\\Lambda$. Similarly\
, real topological Hochschild homology (THR) for ring spectra with anti-in
volution is endowed with a $O(2)$-action. Here instead of the cyclic categ
ory $\\Lambda$\, we use the dihedral category $\\Xi$.\n\nFrom work in prog
ress with Gabe Angelini-Knoll and Mona Merling\, I present a generalizatio
n of $\\Lambda$ and $\\Xi$ called crossed simplicial groups\, introduced b
y Fiedorowicz and Loday. To each crossed simplical group $G$\, I define TH
G\, an equivariant analogue of THH. Its input is a ring spectrum with a tw
isted group action. THG is an algebraic invariant endowed with different a
ction and cyclotomic structure\, and generalizes THH and THR.\n
LOCATION:https://researchseminars.org/talk/ReginaTopology/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hana Jia Kong (Institute for Advanced Study)
DTSTART;VALUE=DATE-TIME:20220210T190000Z
DTEND;VALUE=DATE-TIME:20220210T200000Z
DTSTAMP;VALUE=DATE-TIME:20230208T065146Z
UID:ReginaTopology/7
DESCRIPTION:Title: Motivic image-of-J spectrum via the effective slice spectral sequen
ce\nby Hana Jia Kong (Institute for Advanced Study) as part of Univers
ity of Regina topology seminar\n\n\nAbstract\nThe "image-of-J" spectrum in
the classical stable homotopy category has been well-studied\; Bachmann
–Hopkins defined its motivic analogue. In this talk\, I will start with
the classical story\, and then move to the motivic version. I will talk ab
out the effective slice computation of the motivic "image-of-J" spectrum o
ver the real numbers. Unlike the classical case\, the map from the motivic
sphere is not surjective on homotopy groups. Still\, it captures a regula
r pattern that appears in the $\\mathbb{R}$-motivic stable stems. This is
joint work with Eva Belmont and Dan Isaksen.\n
LOCATION:https://researchseminars.org/talk/ReginaTopology/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Balderrama (University of Virginia)
DTSTART;VALUE=DATE-TIME:20220310T190000Z
DTEND;VALUE=DATE-TIME:20220310T200000Z
DTSTAMP;VALUE=DATE-TIME:20230208T065146Z
UID:ReginaTopology/8
DESCRIPTION:Title: The motivic lambda algebra and Hopf invariant one problem\nby W
illiam Balderrama (University of Virginia) as part of University of Regina
topology seminar\n\n\nAbstract\nCurrent best approaches to understanding
the stable homotopy groups of spheres at the prime $2$ make use of the Ada
ms spectral sequence\, which computes stable stems starting with informati
on about the cohomology of the Steenrod algebra. The first major success o
f the Adams spectral sequence was in Adams' resolution of the Hopf invaria
nt one problem\, which proceeded via an analysis of secondary cohomology o
perations. Later\, J.S.P. Wang used a certain algebraic device\, the lambd
a algebra\, to give a more thorough computation of the cohomology of the S
teenrod algebra\, and used this to give a slick almost entirely algebraic
derivation of the Hopf invariant one theorem.\n\nIn this talk\, I will go
over some of the above history\, and then describe work (joint with Domini
c Culver and J.D. Quigley) on analogues in motivic stable homotopy theory.
In particular\, I will describe a mod $2$ motivic lambda algebra\, define
d 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 spectral sequ
ence for various base fields.\n
LOCATION:https://researchseminars.org/talk/ReginaTopology/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sacha Ikonicoff (University of Calgary)
DTSTART;VALUE=DATE-TIME:20220414T190000Z
DTEND;VALUE=DATE-TIME:20220414T200000Z
DTSTAMP;VALUE=DATE-TIME:20230208T065146Z
UID:ReginaTopology/9
DESCRIPTION:Title: Divided power algebras over an operad\nby Sacha Ikonicoff (Univ
ersity of Calgary) as part of University of Regina topology seminar\n\nLec
ture held in RI 208 (Research and Innovation Centre).\n\nAbstract\nDivided
power algebras were defined by H. Cartan in 1954 to study the homology of
Eilenberg-MacLane spaces. They are commutative algebras endowed\, for eac
h integer $n$\, with an additional monomial operation. Over a field of cha
racteristic $0$\, this operation corresponds to taking each element to its
$n$-th power divided by factorial of $n$. This definition does not make s
ense if the base field is of prime characteristic\, yet Cartan's definitio
n of divided power algebra applies in this situation as well. The notion o
f divided power algebra over a field of prime characteristic allows us to
describe algebraic structures that appear in homology and homotopical a
lgebra and has found applications in a wide array of mathematical domains\
, for instance in crystalline cohomology\, and deformation theory.\n\nIn t
his talk\, we will introduce the generalised definition of a divided power
algebra over an operad given by B. Fresse in 2000. We will give a complet
e characterisation for generalised divided power algebras in terms of mono
mial operations and relations. We will show how to improve this characteri
sation to particular cases\, including the case of a product of operads wi
th distributive laws.\n
LOCATION:https://researchseminars.org/talk/ReginaTopology/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Martensen (NTNU Trondheim)
DTSTART;VALUE=DATE-TIME:20220919T190000Z
DTEND;VALUE=DATE-TIME:20220919T200000Z
DTSTAMP;VALUE=DATE-TIME:20230208T065146Z
UID:ReginaTopology/10
DESCRIPTION:Title: Triangulated categories and other $n$-angulations\nby Sebastia
n Martensen (NTNU Trondheim) as part of University of Regina topology semi
nar\n\n\nAbstract\nTriangulated categories were introduced to capture some
of the extra structure present in the derived category of a ring and the
stable homotopy category\, and today they are present wherever homological
algebra plays a central role. In the case of derived categories\, the tri
angulation captures certain “shadows” of short and long exact sequence
s\, and so one may wonder: are there categories that capture only long exa
ct sequences of a certain length? This led to the introduction of $n$-angu
lated categories in 2013 by Geiss\, Keller\, and Oppermann. Today\, they f
ind their use in representation theory\, and it is a hope that they will o
ne day play a role in topology as well. For this talk we will discuss tria
ngulated categories\, stable module categories\, and introduce $n$-angulat
ed categories along with their main class of examples.\n
LOCATION:https://researchseminars.org/talk/ReginaTopology/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Petersen (MPIM Bonn)
DTSTART;VALUE=DATE-TIME:20221114T190000Z
DTEND;VALUE=DATE-TIME:20221114T200000Z
DTSTAMP;VALUE=DATE-TIME:20230208T065146Z
UID:ReginaTopology/11
DESCRIPTION:Title: The $RO(C_2)$-graded homology of $C_2$-equivariant Eilenberg-MacLa
ne spaces\nby Sarah Petersen (MPIM Bonn) as part of University of Regi
na topology seminar\n\n\nAbstract\nThis talk describes an extension of Rav
enel-Wilson Hopf ring techniques to $C_2$-equivariant homotopy theory. Our
main application and motivation for introducing these methods is a comput
ation of the $RO(C_2)$-graded homology of $C_2$-equivariant Eilenberg-MacL
ane spaces. The result we obtain for $C_2$-equivariant Eilenberg-MacLane s
paces associated to the constant Mackey functor $\\underline{\\mathbb{F}}_
2$ gives a $C_2$-equivariant analogue of the classical computation due to
Serre at the prime $2$. We also investigate a twisted bar spectral sequenc
e computing the homology of these equivariant Eilenberg-MacLane spaces.\n
LOCATION:https://researchseminars.org/talk/ReginaTopology/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Sikora (Bilkent University)
DTSTART;VALUE=DATE-TIME:20230131T190000Z
DTEND;VALUE=DATE-TIME:20230131T200000Z
DTSTAMP;VALUE=DATE-TIME:20230208T065146Z
UID:ReginaTopology/12
DESCRIPTION:Title: $RO(C_2)$-graded coefficients of $C_2$-Eilenberg-MacLane spectra\nby Igor Sikora (Bilkent University) as part of University of Regina to
pology seminar\n\n\nAbstract\nIn non-equivariant topology\, the ordinary h
omology of a point is described by the dimension axiom and is quite simple
- namely\, it is concentrated in degree zero. The situation in $G$-equiva
riant topology is different. This is because Bredon homology - the equivar
iant counterpart of ordinary homology - is naturally graded over $RO(G)$\,
the ring of $G$-representations. Whereas the equivariant dimension axiom
describes the part of the Bredon homology of a point graded over trivial r
epresentations\, it does not put any requirements on the rest of the gradi
ng - 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 coefficients of
these spectra. During the talk\, I will present the method of computing th
e $RO(C_2)$-graded coefficients of $C_2$-Eilenberg-MacLane spectra based o
n the Tate square. As demonstrated by Greenlees\, the Tate square gives an
algorithmic approach to computing the coefficients of equivariant spectra
. In the talk\, we will discuss how to use this method to obtain the $RO(C
_2)$-graded coefficients of a $C_2$-Eilenberg-MacLane spectrum as a $RO(C_
2)$-graded abelian group. We will also present the multiplicative structur
e of the $C_2$-Eilenberg-MacLane spectrum associated to the Burnside Macke
y functor. Time permitting\, we will further discuss how to use this knowl
edge to derive a multiplicative structure for the coefficients for any rin
g Mackey functor.\n
LOCATION:https://researchseminars.org/talk/ReginaTopology/12/
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