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BEGIN:VEVENT
SUMMARY:John Baez (University of California Riverside)
DTSTART;VALUE=DATE-TIME:20201007T180000Z
DTEND;VALUE=DATE-TIME:20201007T190000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/1
DESCRIPTION:Title: Fock space techniques for stochastic physics\nby John Baez (U
niversity of California Riverside) as part of Categories seminar UNAM\n\n\
nAbstract\nSome ideas from quantum theory are beginning to percolate back
to classical probability theory. For example\, the master equation for a c
hemical reaction network - also known as a stochastic Petri net - describe
s particle interactions in a stochastic rather than quantum way. If we loo
k at this equation from the perspective of quantum theory\, this formalism
turns out to involve creation and annihilation operators\, coherent state
s and other well-known ideas — but with a few big differences.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Moeller (University of California\, Riverside)
DTSTART;VALUE=DATE-TIME:20201014T180000Z
DTEND;VALUE=DATE-TIME:20201014T190000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/2
DESCRIPTION:Title: Network models\nby Joe Moeller (University of California\, Ri
verside) as part of Categories seminar UNAM\n\n\nAbstract\nNetworks can be
combined in various ways\, such as overlaying one on top of another or se
tting two side by side. We introduce `network models' to encode these ways
of combining networks. Different network models describe different kinds
of networks. We show that each network model gives rise to an operad\, who
se operations are ways of assembling a network of the given kind from smal
ler parts. Such operads\, and their algebras\, can serve as tools for desi
gning networks. Technically\, a network model is a lax symmetric monoidal
functor from the free symmetric monoidal category on some set to Cat\, and
the construction of the corresponding operad proceeds via a symmetric mon
oidal version of the Grothendieck construction.\n\nLivestream: https://www
.youtube.com/watch?v=Pa96YVgazQk\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jade Master (University of California Riverside)
DTSTART;VALUE=DATE-TIME:20201021T180000Z
DTEND;VALUE=DATE-TIME:20201021T190000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/3
DESCRIPTION:Title: Open Petri nets and their Categories of Processes\nby Jade Ma
ster (University of California Riverside) as part of Categories seminar UN
AM\n\n\nAbstract\nIn this talk we will discuss Petri nets from a categoric
al perspective. A Petri net freely generates a symmetric monoidal category
whose morphisms represent its executions. We will discuss how to make Pet
ri nets "open" i.e. equip them with input and output boundaries where reso
urces can flow in and out. Open Petri nets freely generate open symmetric
monoidal categories: symmetric monoidal categories which can be glued toge
ther along a shared boundary. The mapping from open Petri nets to their op
en symmetric monoidal categories is functorial and this gives a compositio
nal framework for reasoning about the executions of Petri nets.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Camilo Arias (Universidad de Chile)
DTSTART;VALUE=DATE-TIME:20201028T190000Z
DTEND;VALUE=DATE-TIME:20201028T200000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/4
DESCRIPTION:Title: Grupos cuánticos\, categorías derivadas y anillos de fusión\nby Juan Camilo Arias (Universidad de Chile) as part of Categories semin
ar UNAM\n\n\nAbstract\nSea C una categoría esférica abeliana. Denote por
N_C la subcategoría plena consistente de objetos despreciables\, es deci
r\, objetos tales que la traza de cualquiera de sus endomorfismos se anula
. En esta charla\, propondremos una definición en nivel derivado de categ
oría y anillo de fusión para la categoría C. Como ejemplo\, mostraremos
que esta definición produce los mismos anillos de fusión que se obtiene
n de las categorías de representaciones de los grupos cuánticos grande y
pequeño.\n\nLanguage: Spanish\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrique Becerra (IPN)
DTSTART;VALUE=DATE-TIME:20201104T190000Z
DTEND;VALUE=DATE-TIME:20201104T200000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/5
DESCRIPTION:Title: Algunas ideas sobre la entropia de entrelazamiento\nby Enriqu
e Becerra (IPN) as part of Categories seminar UNAM\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Fritz (University of Innsbruck)
DTSTART;VALUE=DATE-TIME:20201111T190000Z
DTEND;VALUE=DATE-TIME:20201111T200000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/6
DESCRIPTION:Title: Markov categories: Probability and Statistics as a Theory of Info
rmation Flow\nby Tobias Fritz (University of Innsbruck) as part of Cat
egories seminar UNAM\n\n\nAbstract\nMarkov categories have recently gained
prominence as a categorical approach to probability and statistics. In th
is talk\, I will argue that Markov categories provide a very general theor
y of information flow\, and that this theory generalizes probability theor
y in a manner analogous to how topos theory generalizes set theory.\n\nIn
the first part\, I will sketch some theorems of probability and statistics
which have already been developed synthetically in terms of Markov catego
ries\, including a version of the Blackwell-Sherman-Stein theorem which se
ems to be new even when instantiated in the traditional measure-theoretic
framework. In the second part\, I will sketch the vast and largely unexplo
red landscape of Markov categories on which these synthetic results can be
instantiated. Some basic knowledge of monoidal categories and discrete pr
obability should be enough to follow the talk.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alcides Buss (UFSC)
DTSTART;VALUE=DATE-TIME:20201118T190000Z
DTEND;VALUE=DATE-TIME:20201118T200000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/7
DESCRIPTION:Title: Noncommutative Symmetries -a higher category approach-\nby Al
cides Buss (UFSC) as part of Categories seminar UNAM\n\n\nAbstract\nMany o
perator algebras describe "noncommutative spaces" admitting intrinsic symm
etries that cannot be described in a classical way\, through a group actio
n. However\, many of these "noncommutative symmetries" can be understood i
n a broader spectrum via the use of 2-groups or even 2-groupoids. While a
groupoid can be seen as a category where all morphisms are invertible\, a
2-groupoid is nothing but a 2-category (or bicategory) where all morphisms
and 2-morphisms are invertible. A 2-group is just a 2-groupoid with a sin
gle object. To understand how these act on objects of other bicategories\,
like C*-algebras\, we use the theory of bicategories and look at weak fun
ctors from a 2-groupoid to certain bicategories of C*-algebras. This gives
us a good flexibility and allows to understand several sort of new symmet
ries and also rediscover known ones from a different point of view.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophie Libkind (Stanford)
DTSTART;VALUE=DATE-TIME:20201125T190000Z
DTEND;VALUE=DATE-TIME:20201125T200000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/8
DESCRIPTION:by Sophie Libkind (Stanford) as part of Categories seminar UNA
M\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joachim Kock (UAB)
DTSTART;VALUE=DATE-TIME:20201202T190000Z
DTEND;VALUE=DATE-TIME:20201202T200000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/9
DESCRIPTION:Title: Whole-grain Petri nets and processes\nby Joachim Kock (UAB) a
s part of Categories seminar UNAM\n\n\nAbstract\nI will present a new form
alism for Petri nets based on polynomial-style finite-set configurations a
nd etale maps. The processes of a Petri net P are etale maps G -> P from
graphs. The main feature of the formalism is that Petri nets have element
s --- they are the elements you see in the pictures. This makes the defin
ition more representable (in the categorical sense of the word) than previ
ous definitions. The main result I want to arrive at is that P-processes
form a symmetric monoidal Segal space\, which is the free prop-in-groupoid
s on P\, but most of the time will be spent just explaining Petri nets\, t
heir markings and firings\, the token game\, processes\, and the basic ide
a of concurrency and causality --and how these notions look in the new for
malism.\n\n\n\nReference: "Elements of Petri nets and processes" [ArXiv:20
05.05108]\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yasuyuki Kawahigashi (The University of Tokyo)
DTSTART;VALUE=DATE-TIME:20201209T230000Z
DTEND;VALUE=DATE-TIME:20201210T000000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/10
DESCRIPTION:Title: Topological order\, operator algebras and topological quantum fi
eld theory\nby Yasuyuki Kawahigashi (The University of Tokyo) as part
of Categories seminar UNAM\n\n\nAbstract\nWe will explain studies of 2-dim
ensional topological order in terms of tensor networks and subfactors aris
ing from commuting squares. Appearance of braiding strucuture from 3-dime
nsional topological quantum field theory is demonstrated from a viewpoint
of tensor categories. We will give higher relative commutants of a subfac
tor as spaces on which Hamiltonian acts.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Paré (Dalhousie University)
DTSTART;VALUE=DATE-TIME:20210210T230000Z
DTEND;VALUE=DATE-TIME:20210211T000000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/11
DESCRIPTION:Title: A case study in double categories\nby Robert Paré (Dalhousi
e University) as part of Categories seminar UNAM\n\n\nAbstract\nWe give an
elementary introduction to some ideas in double category\ntheory by conce
ntrating on one particular example\, the double category of rings\nwith ho
momorphisms\, and bimodules. Along the way we discover a number of\n“new
” morphisms of rings\, interesting in their own right. We also look at i
nteresting\ndouble adjunctions in this context.\n\nNo previous knowledge o
f double categories is assumed\, just some familiarity\nwith categories\,
rings and modules.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Spivak (Topos Institute)
DTSTART;VALUE=DATE-TIME:20210217T230000Z
DTEND;VALUE=DATE-TIME:20210218T000000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/12
DESCRIPTION:Title: Polynomials and the dynamics of data\nby David Spivak (Topos
Institute) as part of Categories seminar UNAM\n\n\nAbstract\nOne can imag
ine a database schema as a category and an instance or state of that datab
ase as a functor I: C-->Set\; the category of these is denoted C-Set. One
can think of a data-migration functor\, a way of moving data between schem
as C and D\, as a parametric right adjoint C-Set --> D-Set. In database sp
eak\, these are D-indexed "unions of conjunctive queries".\n\nScene change
. The usual semiring of polynomials in one variable with cardinal coeffici
ents\, polynomials such as p = y^3 + 3y + 2\, can be categorified to Poly\
, the category of polynomial functors\, where + and x are the categorical
coproduct and product. Composition of polynomials (p o q) gives a monoidal
operation on this category for which the identity polynomial\, y\, is the
unit. Ahman and Uustalu showed in 2016 that\, up to isomorphism\, the com
onoids in (Poly\, o\, y) are precisely categories (!)\, and Garner sketche
d a proof in a recent video that bimodules between polynomial comonoids ar
e parametric right adjoints between copresheaf categories. Recall that the
se are precisely the data-migration functors described above. In the talk\
, I will describe this circle of ideas.\n\nI propose that in 2021 a great
transition is upon us\; distances that were measured in days are now measu
red in zoom-hiccups. The speed of data migration—if that's indeed a vali
d way to model it—is much faster than ever\, driving dominance into the
hands of those who move data: roughly speaking\, computerized processes. R
esearchers use biomimicry to formalize as many aspects of human intelligen
ce as they can\, much of which is then installed as automated software sys
tems that run constantly. I call the automated speed-up of bio-inspired in
tellectual processes AI\, and I'm not judging it as good or bad\, but I do
consider it immensely important. I propose that we as mathematicians have
the ability to shape the course of AI. Mathematics becomes technology\, a
nd I believe we'll fare better if that technology is based on elegant prin
ciples rather than made ad-hoc. Polynomial functors are my entry point\, a
nd this talk can serve as an invitation to others to join in whatever capa
city appeals to them. To respect the standards of academic talks\, I will
mainly restrict my discussion to mathematics and its applications\, rather
than to speculation.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Perrone (Oxford)
DTSTART;VALUE=DATE-TIME:20210224T230000Z
DTEND;VALUE=DATE-TIME:20210225T000000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/13
DESCRIPTION:Title: Partial evaluations: the results so far\nby Paolo Perrone (O
xford) as part of Categories seminar UNAM\n\n\nAbstract\nPartial evaluatio
ns are a way to encode\, in terms of monads\, operations which have been c
omputed only partially. For example\, the sum "1+2+3+4" can be evaluated t
o "10"\, but also partially evaluated to "3+7"\, or to "6+4".\nSuch struct
ures can be defined for arbitrary algebras over arbitrary monads\, and eve
n 2-monads\, and can be considered the 1-skeleton of a simplicial object c
alled the bar construction. The higher simplices of the bar construction c
an be interpreted as ways to compose partial evaluations. Recent research
has shown that\, while for cartesian monads partial evaluations form a cat
egory\, for weakly cartesian monads the compositional structure is more co
mplex\, and in particular it does not in general form any of the standard
higher-categorical structures.\nMoreover\, partial evaluations return know
n concepts of "partially evaluated operations" in the following contexts:\
n- For the free cocompletion monad\, where the operation is taking the col
imit\, partial evaluations correspond to left Kan extensions\;\n- For prob
ability monads\, where the operation is taking the expected value\, partia
l evaluations correspond to conditional expectations.\n\nThe research pres
ented in this talk has been carried out jointly with Carmen Constantin\, T
obias Fritz\, Brandon Shapiro\, and Walter Tholen.\n\nThe talk will be in
English\, but you are welcome to ask questions in Spanish if anything is n
ot clear.\n\nThe following are references for the topics discussed in the
talk:\n\nhttps://arxiv.org/abs/1810.06037\n\nhttps://arxiv.org/abs/2009.07
302\n\nhttps://arxiv.org/abs/2101.04531\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur Parzygnat (IHÉS)
DTSTART;VALUE=DATE-TIME:20210303T190000Z
DTEND;VALUE=DATE-TIME:20210303T200000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/14
DESCRIPTION:Title: String diagrams for C*-algebras and Bayesian inversion\nby A
rthur Parzygnat (IHÉS) as part of Categories seminar UNAM\n\n\nAbstract\n
Abstract: The foundations of probability\, statistics\, and information th
eory are slowly undergoing a potentially dramatic change of perspective th
rough the language of category theory via string diagrams [3]. This point
of view has been abstracted to finite-dimensional C*-algebras via a stocha
stic variant of the Gelfand—Naimark theorem and quantum Markov categorie
s. Through this abstraction\, one can immediately analyze concepts such as
Bayesian inversion in non-classical settings\, which in fact has recently
been done in finite dimensions [2]. What can be said for more general (po
ssibly infinite dimensional) C*-algebras? In this talk\, I will review som
e background on Markov categories\, provide some motivation for their stud
y\, introduce our main quantum example\, and then I'll provide a small ref
resher on C*-tensor products. Then\, I'll explain why all C*-algebras do n
ot form a quantum Markov category\, and I will provide some suggestions fo
r an alternative framework [1].\n \n\nMain reference:\n\n[1] https://arxiv
.org/abs/2001.08375 (especially Remark 3.12 and Question 3.25).\n\nAdditio
nal references of potential interest:\n\n[2] https://arxiv.org/abs/2005.03
886 (on Bayesian inversion in quantum mechanics)\n\n[3] https://arxiv.org/
abs/1908.07021 (on classical Markov categories)\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Shulman (University of San Diego)
DTSTART;VALUE=DATE-TIME:20210310T190000Z
DTEND;VALUE=DATE-TIME:20210310T200000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/15
DESCRIPTION:Title: Double categories\, multivariable mates\, and Chu constructions<
/a>\nby Michael Shulman (University of San Diego) as part of Categories se
minar UNAM\n\n\nAbstract\nIt is an old observation of Kelly and Street tha
t the\n"calculus of mates" for adjunctions is naturally expressed using a\
ndouble category of functors and adjunctions. This was generalized by\nCh
eng\, Gurski\, and Riehl to mates for multivariable adjunctions\, such\nas
the tensor-hom adjunction of a closed monoidal category or the\ntensor-ho
m-cotensor adjunction of an enriched category\, using a cyclic\nmulti doub
le category. I will explain how the latter is more\nnaturally viewed as a
poly double category (that is\, an internal\ncategory in polycategories)\
, and how it arises as a special case of a\n"double Chu construction".\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brendan Fong (Topos Institute)
DTSTART;VALUE=DATE-TIME:20210331T190000Z
DTEND;VALUE=DATE-TIME:20210331T200000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/16
DESCRIPTION:Title: Cospans as a tool for composition\nby Brendan Fong (Topos In
stitute) as part of Categories seminar UNAM\n\n\nAbstract\nWe often unders
tand our world piece by piece\, weaving local models and perspectives into
a bigger picture. In any category\, amalgamating parts into a single obje
ct can be captured through the notion of colimit. Cospans provide a conven
ient syntax for performing this weaving\, building colimits piece by piece
. Through the use of decorated and structured cospans\, this approach can
extend to categories where colimits may be complicated to compute\, or may
not even exist at all. In this talk\, I'll provide a perspective on both
the power and limits of cospans as a tool for composition\, meditating on
why\, how\, and when cospans can contribute.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martín Szyld (Dalhousie University)
DTSTART;VALUE=DATE-TIME:20210407T180000Z
DTEND;VALUE=DATE-TIME:20210407T190000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/17
DESCRIPTION:Title: The three F's in bicategory theory (joint work with P. Bustillo
and D. Pronk)\nby Martín Szyld (Dalhousie University) as part of Cate
gories seminar UNAM\n\n\nAbstract\nWe consider the notions of Fibration of
categories\, (pseudo)Filtered category\, and the axioms for a category of
Fractions. A basic fact involving them is: given a Fibration\, if the arr
ows of the base category are (pseudo)coFiltered\, then the cartesian arrow
s satisfy Fractions. This is a Proposition in SGA 4 (Exp. VI\, Prop. 6.4)
whose proof is left to the reader as an exercise\, and I want to start thi
s talk by solving this exercise. Let me tell you why.\n\nEach of the three
"F" notions above has been considered for bicategories\, or at least for
2-categories. I will start with what may be the easiest one to understand\
, that of Filtered: in a Filtered bicategory\, in addition to asking for c
ones for two objects and for two parallel arrows\, we add a third axiom as
king for cones for parallel 2-cells. I will present the definitions of Fil
tered and pseudoFiltered bicategory\, a set of axioms for a bicategory of
Fractions\, and some properties of Fibrations of bicategories that all fit
this same pattern. We arrived at these notions when proving a "bicategory
version" of the Proposition in SGA 4\, in fact a small generalization tha
t I will present.\n\nThis result is part of an ongoing collaboration with
P. Bustillo and D. Pronk\, we're working on showing some basic properties
of the bicategorical localization by fractions which are known in dimensio
n 1. If time permits\, I hope to mention how we ended up here within our c
urrent work and how this result can be applied here.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Hernández (Ohio State University)
DTSTART;VALUE=DATE-TIME:20210317T190000Z
DTEND;VALUE=DATE-TIME:20210317T200000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/18
DESCRIPTION:Title: Actions of unitary tensor categories on C*-algebras\nby Robe
rto Hernández (Ohio State University) as part of Categories seminar UNAM\
n\n\nAbstract\nA subfactor is a unital inclusion of simple von Neumann alg
ebras/factors $A\\subset B\,$ and we study it via its standard invariant $
\\cC\,$ which corresponds to a unitary tensor category (UTC). We will revi
ew some subfactor reconstruction techniques by Popa\, and Guionnet-Jones-S
hlyakhtenko (GJS)\, highlighting that subfactors have quantum symmetries w
hich are encoded by UTC-actions. Namely\, we reinterpret the inclusion $A\
\subset B$ as encoding an action of its standard invariant $\\cC$ on $A\,$
and reconstruct the overfactor $B$ as a generalized crossed-product by th
is UTC-action.\n\nLarge scale work of many researchers worldwide has recen
tly culminated in the classification of C*-algebras\, which is now at the
level of Connes' classification of injective factors. Nowadays\, C*-algebr
as is at a similar state to that of von Neumann algebras after Jones intro
duced the index for subfactors in the early 80s. Thereafter\, great intere
st has arisen in constructing and classifying UTC-actions on C*-algebras\,
aiming to understand their structure from the viewpoint of quantum symmet
ries.\n\nWe will see that every UTC $\\cC$ acts on some simple\, unital se
parable and monotracial C*-algebra constructed only from $\\cC$ by adaptin
g diagrammatic and free probabilistic techniques from GJS. Using a 'Hilbe
rtification' technique\, we recover the UTC-action constructed by Brothier
-Harglass-Penneys of $\\cC$ on the free group factor $L\\mathbb{F}_\\infty
.$ This is joint work with Hartglass. Finally\, we will review some recent
developments and obstructions to the existence of UTC actions on (classif
iable) C*-algebras.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nadia Romero (Universidad de Guanajuato)
DTSTART;VALUE=DATE-TIME:20210414T180000Z
DTEND;VALUE=DATE-TIME:20210414T190000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/19
DESCRIPTION:Title: La completación aditiva de la categoría de biconjuntos\nby
Nadia Romero (Universidad de Guanajuato) as part of Categories seminar UN
AM\n\n\nAbstract\nEn los últimos años\, la teoría de funtores en biconj
untos ha\ndemostrado ser una herramienta muy útil para abordar problemas\
nrelacionados con grupos finitos y sus representaciones. En esta\nplática
comenzaré por la definición de funtor en biconjuntos y la\nmotivación
que llevó a esta definición. Después\, presentaré la\ncompletación ad
itiva de la categoría de biconjuntos\, veremos que los\nobjetos en esta c
ategoría pueden escribirse como fracciones y que\, de\nhecho\, en muchos
sentidos se comportan como tales. Veremos también que\nesta categoría es
aditiva\, monoidal simétrica\, autodual y con una\ndescomposición de ti
po Krull-Schmidt para los objetos. Si el tiempo lo\npermite\, veremos su r
elación con la categoría de Burnside\, introducida\npor Lindner en 1976.
\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maru Sarazola (Cornell)
DTSTART;VALUE=DATE-TIME:20210428T180000Z
DTEND;VALUE=DATE-TIME:20210428T190000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/20
DESCRIPTION:Title: The stable homotopy hypothesis\nby Maru Sarazola (Cornell) a
s part of Categories seminar UNAM\n\n\nAbstract\nThe homotopy hypothesis i
s a well-known bridge between topology and category theory. Its most gener
al formulation\, due to Grothendieck\, asserts that topological spaces sho
uld be "the same" as infinity-groupoids. In the stable version of the homo
topy hypothesis\, topological spaces are replaced with spectra. \n\nIn thi
s talk we will review the classical homotopy hypothesis\, and then focus o
n the stable version. After discussing what the stable homotopy hypothesis
should look like on the categorical side\, we will use the Tamsamani mode
l of higher categories to provide a proof. This is based on joint work wit
h Moser\, Ozornova\, Paoli and Verdugo.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jamie Vicary (Cambridge)
DTSTART;VALUE=DATE-TIME:20210421T180000Z
DTEND;VALUE=DATE-TIME:20210421T190000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/21
DESCRIPTION:Title: Infinity categories with strict units\nby Jamie Vicary (Camb
ridge) as part of Categories seminar UNAM\n\n\nAbstract\nComposition in or
dinary 1-categories is strictly unital\, and it's known that every weak 2-
category is equivalent to a 2-category with strict units\, a useful theore
m that makes 2-categories easier to work with. But what does it mean for a
n n-category\, or even an infinity-category\, to have strict units? In thi
s talk I give an accessible introduction to infinity categories\, and use
lots of examples to illustrate the theory of strict units for infinity-cat
egories. This is joint work with Eric Finster and David Reutter (arXiv:200
7.08307).\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Makoto Yamashita (The University of Oslo)
DTSTART;VALUE=DATE-TIME:20210325T000000Z
DTEND;VALUE=DATE-TIME:20210325T010000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/22
DESCRIPTION:Title: Reflection equation and quantization of symmetric spaces\nby
Makoto Yamashita (The University of Oslo) as part of Categories seminar U
NAM\n\n\nAbstract\nThe reflection equation\, an analogue of the Yang-Baxte
r equation\, appeared from the boundary quantum field theory due to Chered
nik in the 80's. It came to known to have strong connection to quantizatio
n of homogeneous spaces\, and in particular symmetric spaces through Tanna
ka-Krein type duality. In this talk I will review the basic categorical pa
radigm behind this correspondence\, and an analogue of Kohno-Drinfeld rigi
dity theorem that gives a classification of monoidal categorical structure
(ribbon braided module category) quantizing compact symmetric spaces in t
erms of eigenvalues of solution to reflection equation. Based on joint wor
ks with Kenny De Commer\, Sergey Neshveyev\, and Lars Tuset.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernardo Uribe (Universidad del Norte)
DTSTART;VALUE=DATE-TIME:20210505T180000Z
DTEND;VALUE=DATE-TIME:20210505T190000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/23
DESCRIPTION:Title: Pontrjagin duality on multiplicative gerbes\nby Bernardo Uri
be (Universidad del Norte) as part of Categories seminar UNAM\n\n\nAbstrac
t\nMultiplicative gerbes can be understood as monoid objects on the 2-cate
gory of gerbes. We take this point of\nview on the 2-category of topologic
al gerbes in order to define appropriate representations of these multipli
cative gerbes. \nWe take an explicit model for topological gerbes using Gr
aeme Segal's cohomology of topological groups and we show that with this m
odel\nwe may replicate several constructions done over multiplicative gerb
es over finite groups.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ross Street (Macquarie University)
DTSTART;VALUE=DATE-TIME:20210513T000000Z
DTEND;VALUE=DATE-TIME:20210513T010000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/24
DESCRIPTION:Title: Views of centers\nby Ross Street (Macquarie University) as p
art of Categories seminar UNAM\n\n\nAbstract\nInitially\, the centre of a
monoidal category was used independently by V. Drinfeld\nin connection wit
h Hopf algebras and by A. Joyal and the speaker to study the\ncategory of
framed tangles. We were influenced by lectures of Yu. Manin in Montréal\n
and the work of D. Yetter and V. Turaev. In this talk I will give a gentle
introduction to\nhow the construction can be viewed in various ways. In p
articular\, it is a limit construction\nwhich can be performed in other pl
aces besides the cartesian monoidal 2-category of\ncategories. Some exampl
es from different fields will be provided.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dorette Pronk (Dalhousie University)
DTSTART;VALUE=DATE-TIME:20210526T190000Z
DTEND;VALUE=DATE-TIME:20210526T200000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/25
DESCRIPTION:Title: Orbispace Mapping Objects: Exponentials and Enrichment!\nby
Dorette Pronk (Dalhousie University) as part of Categories seminar UNAM\n\
n\nAbstract\nOrbifolds are defined like manifolds\, by local charts. Where
manifold charts are open subsets of Euclidean space\, orbifold charts con
sist of an open subset of Euclidean space with an action by a finite group
(thus allowing for local singularities). This affects the way that transi
tions between charts need to be described\, and it is generally rather cum
bersome to work with atlases. It has been shown in [Moerdijk-P] that one c
an represent orbifolds by groupoids internal to the category of manifolds\
, with etale structure maps and a proper diagonal\, I.e.\, combined source
-target map (s\,t): G_1 -> G_0 x G_0. We have since generalized this notio
n further to orbispaces\, represented by proper etale groupoids in the cat
egory of Hausdorff spaces. Two of these groupoids represent the same orbis
pace if they are Morita equivalent. However\, Morita equivalences are gen
erally not pseudo-invertible in this 2-category\, so we consider the bicat
egory of fractions with respect to Morita equivalences.\n\n \n\nFor a pair
of paracompact locally compact orbigroupoids G and H\, with G orbit-compa
ct\, we want to study the mapping groupoid [G\, H] of arrows and 2-cells i
n the bicategory of fractions. The question we want to address is how to d
efine a topology on these mapping groupoids to obtain mapping objects for
the bicategory of orbispaces. This question was addressed in [Chen]\, but
not in terms of orbigroupoids\, and with only partial answers.\n\n\nWe wil
l present the following results:\n\n\n1. When the orbifold G is compact\,
we define a topology on [G\,H] to obtain a topological groupoid OMap(G\, H
)\, which is Morita equivalent to an orbigroupoid. To obtain a Morita equi
valent orbigroupoid\, we need to restrict ourselves to so-called admissibl
e maps to form AMap(G\,H)\, and\n\n\nOrbispaces(K × G\, H) is equivalent
to Orbispaces(K\, AMap(G\, H)).\n\n\nSo AMap(G\,H) is an exponential objec
t in the bicategory of orbispaces.\n\n\n2. We will also show that AMap(G\,
H) thus defined provides the bicategory of orbit-compact orbispaces with b
icategorical enrichment over the bicategory of orbispaces: composition can
be given as a generalized map (an arrow in the bicategory of fractions) o
f orbispaces.\n\nIn this talk I will discuss how this work extends the wor
k done by Chen and I will show several examples. This is joint work with L
aura Scull.\n\n\n[Chen] Weimin Chen\, On a notion of maps between orbifold
s I: function spaces\, Communications in Contemporary Mathematics 8 (2006)
\, pp. 569-620.\n\n\n[Moerdijk-P] I. Moerdijk\, D.A. Pronk\, Orbifolds\, s
heaves and groupoids\, K-Theory 12 (1997)\, pp. 3-21.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ingo Runkel (Hamburg University)
DTSTART;VALUE=DATE-TIME:20210519T180000Z
DTEND;VALUE=DATE-TIME:20210519T190000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/26
DESCRIPTION:Title: Area dependent 2d QFT\nby Ingo Runkel (Hamburg University) a
s part of Categories seminar UNAM\n\n\nAbstract\nOne beautiful result one
learns early when studying the functorial approach to TQFTs is that in two
dimensions\, such theories are the same as commutative Frobenius algebras
. One furthermore learns that in functorial TQFTs\, state spaces are neces
sarily finite-dimensional. There are several ways to overcome this restric
tion\, and in two dimensions\, one possibility is to equip the surfaces wi
th an area. The most famous example of such a QFT is 2d Yang Mills theory
for a compact gauge group. Surprisingly\, one finds that a very similar cl
assification to the 2d TQFT still holds. Time permitting\, I will also dis
cuss defects in 2d area dependent QFTs\, of which Wilson line observables
in 2d Yang Mills are an example. This is joint work with Lorant Szegedy.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Gurski (Case Western Reserve University)
DTSTART;VALUE=DATE-TIME:20211006T180000Z
DTEND;VALUE=DATE-TIME:20211006T190000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/27
DESCRIPTION:Title: The truncated sphere spectrum in homological algebra\nby Nic
k Gurski (Case Western Reserve University) as part of Categories seminar U
NAM\n\n\nAbstract\nThe stable homotopy hypothesis predicts that "stable" n
-groupoids should model stable homotopy n-types. Stability on the categori
cal side is usually interpreted as a symmetric monoidal structure with inv
ertible objects\, while on the topological side these are spectra (instead
of spaces) with homotopy groups concentrated between dimensions 0 and n.
Proving this hypothesis is the first step in comparing spectra and higher
categories rather than the goal. I will discuss a very special case of goi
ng further than the hypothesis when n=1 and 2 (the dimensions in which the
stable homotopy hypothesis is a theorem rather than just conjecture)\, na
mely what categorical objects correspond to the truncated sphere spectrum.
We will recover some classical algebra for n=1\, and a complicated genera
lization of that algebra for n=2 that I don't think we really understand y
et.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleks Kissinger (Oxford)
DTSTART;VALUE=DATE-TIME:20211013T180000Z
DTEND;VALUE=DATE-TIME:20211013T190000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/28
DESCRIPTION:Title: A categorical logic of consistency for causal processes\nby
Aleks Kissinger (Oxford) as part of Categories seminar UNAM\n\n\nAbstract\
nI will talk about some recent developments in the framework of "black box
causal reasoning". In this minimal setting\, we assume access to some abs
tract process and attempt to describe\, quantify\, or prove properties abo
ut the causal relationships between its inputs and outputs. This works bot
h for first-order processes\, which can capture e.g. a device shared by mu
ltiple agents\, or higher-order processes\, which can capture the universe
in which those agents live. This higher-order picture leads naturally to
the structure of a *-autonomous category. Whereas first order processes (e
.g. quantum gates) only have two natural notions of composition (in series
and in parallel)\, higher-order processes have a rich and nuanced notion
of composition that must avoid inconsistency in the composition of causal
paths. I will show how provability in the internal logic of a *-autonomous
category gives sufficient conditions for causal consistency\, then discus
s several avenues of extension toward a complete characterisation.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toby St. Clere Smithe (Oxford/Topos Institute)
DTSTART;VALUE=DATE-TIME:20211020T180000Z
DTEND;VALUE=DATE-TIME:20211020T190000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/29
DESCRIPTION:Title: The changing shapes of cybercats\nby Toby St. Clere Smithe (
Oxford/Topos Institute) as part of Categories seminar UNAM\n\n\nAbstract\n
The ménagerie of categorical models of dynamical systems is becoming a ve
ritable zoo\, but what makes all these animals tick? In this talk\, I will
introduce a new specimen: a symmetric monoidal category of continuous-tim
e open Markov processes with general state spaces. I will explain how this
category is obtained from a category of "continuous-time coalgebras" opin
dexed by polynomials\, and describe how this recipe also gives categories
of nondeterministic systems in arbitrary (continuous) time. These new spec
imens are motivated by the cybernetic question of how to model systems tha
t are continuously performing approximate Bayesian inference. I will there
fore sketch why their better-known cousins weren't quite up to the job\, a
nd show that our new SMC admits Bayesian inversion. Finally\, I will attem
pt to make contact with the the "open games" branch of categorical cyberne
tics\, asking what makes the shapes of our structures seem so similar-but-
different\, and how we might begin to understand systems nested within sys
tems.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akif Mehmet Erdal (Yeditepe University)
DTSTART;VALUE=DATE-TIME:20211027T180000Z
DTEND;VALUE=DATE-TIME:20211027T190000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/30
DESCRIPTION:Title: Actions of monoidal categories and (co)stabilization\nby Aki
f Mehmet Erdal (Yeditepe University) as part of Categories seminar UNAM\n\
n\nAbstract\nSuppose that we are given a collection of endofunctors (e.g.\
, loop space functors) on a pointed homotopy theory $A$. We will call suc
h a homotopy theory stable if it is stable under these functors\; that is\
, each functor is an auto-equivaence. Alternatively\, one can consider thi
s as an action of a monoidal category\, and in this case stable means the
monoidal category acts by auto-equivalences. In this talk\, we discuss act
ions of monoidal categories on relative categories\, and applications in s
table homotopy theory. Given a monoidal category $I$ and an $I$-relative c
ategory $A$ (that is\, a relative category with an $I$-action)\, the (co)s
tabilization of $A$ is an $I$-relative category that is universal with re
spect to the property that every object of $I$ acts by auto-equivalences (
on homotopy category). We introduce a notion of $I$-equivariance for funct
ors between $I$-relative categories and give constructions of stabilizatio
n and costabilization in terms of (weak) ends and coends in a $2$-category
of $I$-relative categories and $I$-equivariant relative functors. Several
examples existing in the literature\, including various categories of spe
ctra and cohomology theories with exotic gradings\, can be seen as particu
lar instances of this setting after fixing $A$ and the $I$-action on it. I
n particular\, categories of sequential spectra\, coordinate free spectra\
, genuine equivariant spectra\, genuine parameterized spectra (indexed by
vector bundles)\, and cohomology theories with various exotic gradings can
be obtained in terms of weak ends. On the other hand\, the costabilizatio
n of a relative category with respect to an action gives a stable relative
category akin to a version of the Spanier-Whitehead category. This is a j
oint work with Özgün Ünlü.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Gogioso (Oxord)
DTSTART;VALUE=DATE-TIME:20211103T190000Z
DTEND;VALUE=DATE-TIME:20211103T200000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/31
DESCRIPTION:by Stefano Gogioso (Oxord) as part of Categories seminar UNAM\
n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Leinster (University of Edimburgh)
DTSTART;VALUE=DATE-TIME:20211117T190000Z
DTEND;VALUE=DATE-TIME:20211117T200000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/33
DESCRIPTION:Title: Large sets\nby Tom Leinster (University of Edimburgh) as par
t of Categories seminar UNAM\n\n\nAbstract\nLawvere's Elementary Theory of
the Category of Sets (ETCS) was conceived as an alternative to ZFC that r
epresents more accurately how mathematicians actually do mathematics. But
can ETCS do everything that ZFC can? I will present some evidence that yes
\, it can. Specifically\, I will sketch how the beginning of the theory of
large cardinals looks in ETCS\, describing both the similarities and the
differences between the two approaches. No prior familiarity with ETCS wil
l be assumed.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Davydov (Ohio University)
DTSTART;VALUE=DATE-TIME:20211201T190000Z
DTEND;VALUE=DATE-TIME:20211201T200000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/34
DESCRIPTION:Title: Autoequivalences of tensor categories and Bogomolov multiplier\nby Alexei Davydov (Ohio University) as part of Categories seminar UNAM
\n\n\nAbstract\nThe Bogomolov multiplier of a group is the subgroup of its
Schur multiplier\, of classes with vanishing restrictions to all abelian
subgroups. Bogomolov multiplier plays an important role in birational alge
braic geometry (Noether problem) and in topology (groups of singular subma
nifolds).\n\n\nIn the talk explain how Bogomolov multiplier appears in the
study of soft symmetries of modular tensor categories. Here soft means th
at a symmetry does not move objects. More precisely\, I will interpret Bog
omolov multiplier as a normal subgroup of the group of soft autoequivalenc
es of the Drinfeld double.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Riehl (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20220330T190000Z
DTEND;VALUE=DATE-TIME:20220330T200000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/35
DESCRIPTION:Title: Elements of ∞-Category Theory\nby Emily Riehl (Johns Hopki
ns University) as part of Categories seminar UNAM\n\n\nAbstract\nConfusing
ly for the uninitiated\, experts in weak infinite-dimensional category the
ory make use of different definitions of an ∞-category\, and theorems in
the ∞-categorical literature are often proven "analytically"\, in refer
ence to the combinatorial specifications of a particular model. In this ta
lk\, we present a new point of view on the foundations of ∞-category the
ory\, which allows us to develop the basic theory of ∞-categories --- ad
junctions\, limits and colimits\, co/cartesian fibrations\, and pointwise
Kan extensions --- "synthetically" starting from axioms that describe an
∞-cosmos\, the infinite-dimensional category in which ∞-categories liv
e as objects. We demonstrate that the theorems proven in this manner are "
model-independent"\, i.e.\, invariant under change of model. Moreover\, th
ere is a formal language with the feature that any statement about ∞-cat
egories that is expressible in that language is also invariant under chang
e of model\, regardless of whether it is proven through synthetic or analy
tic techniques. This is joint work with Dominic Verity.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Roberts
DTSTART;VALUE=DATE-TIME:20220406T230000Z
DTEND;VALUE=DATE-TIME:20220407T000000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/37
DESCRIPTION:Title: Geometric string structures on homogeneous spaces\nby David
Roberts as part of Categories seminar UNAM\n\n\nAbstract\nThe notion of st
ring structure on a space X goes back to work in the 1980s\, particularly
of Killingback\, starting as an analogue of a spin structure on the loop s
pace LX. In the decades since\, increasingly refined versions of string st
ructures have been defined. Ultimately\, one wants to have a full-fledged
String 2-bundle with connection\, a structure from higher geometry\, which
combines differential geometry and category-theoretic structures. A half-
way step\, due to Waldorf\, is known as a "geometric string structure". Gi
ving examples of such structures\, despite existence being know\, has been
an outstanding problem for some time. In this talk\, I will describe join
t work with Raymond Vozzo on our framework for working with the structure
that obstruct the existence of a geometric string structure\, which is a 2
-gerbe with connection\, as well as give a general construction of geometr
ic string structures on reductive homogeneous spaces.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Urs Schreiber (NYU Abu Dhabi and Czech Academy of Siences)
DTSTART;VALUE=DATE-TIME:20220413T170000Z
DTEND;VALUE=DATE-TIME:20220413T180000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/38
DESCRIPTION:Title: Anyonic Defect Branes in Twisted Equivariant Differential K-Theo
ry\nby Urs Schreiber (NYU Abu Dhabi and Czech Academy of Siences) as p
art of Categories seminar UNAM\n\n\nAbstract\nI'll start with an expositio
n of higher equivariant principal bundle\ntheory\, using a convenient cate
gory/homotopy-theoretic approach\,\nfollowing the notes here:\nncatlab.org
/schreiber/show/Higher+and+Equivariant+Bundles . By way of\nexample and ap
plication\, I'll then show how this provides a pleasantly\ntransparent way
to understand:\n 1. the CPT-twisting of equivariant K-theory\, which has
come to be\nknown as the "10-fold way"\,\n 2. the neglected twisting of eq
uivariant K-theory by "inner local\nsystems" appearing inside orbi-singula
rities.\nI'll close by briefly indicating how\, under the interpretation o
f\nK-cohomology as D-brane charge\, these two facts have remarkable\nconse
quences for the physics of exotic "defect branes" in string\ntheory (arxiv
.org/abs/2203.11838).\nThis is joint work with H. Sati. Slides will become
available at:\nncatlab.org/schreiber/show/Anyonic+defect+branes+in+TED-K-
theory .\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Rowell (Texas A&M)
DTSTART;VALUE=DATE-TIME:20220518T180000Z
DTEND;VALUE=DATE-TIME:20220518T190000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/39
DESCRIPTION:Title: Classification of Modular Fusion Categories\nby Eric Rowell
(Texas A&M) as part of Categories seminar UNAM\n\n\nAbstract\nThe classifi
cation of modular fusion categories has been pursued from various perspect
ives over the last 20 years\, and provides a hands-on introduction to the
intricacies of applied category theory. In this lecture we will review wha
t is known\, some open problems\, and a few of the successful techniques f
rom category theory\, algebraic geometry\, number theory and representatio
n theory.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Plavnik (How to zest your modular categories)
DTSTART;VALUE=DATE-TIME:20220601T180000Z
DTEND;VALUE=DATE-TIME:20220601T190000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/40
DESCRIPTION:Title: Modular categories arise naturally in many areas of mathematics\
, such as conformal field theory\, representations of braid groups\, quant
um groups\, and Hopf algebras\, and low dimensional topology\, and they ha
ve important applications in condensed matter phys\nby Julia Plavnik (
How to zest your modular categories) as part of Categories seminar UNAM\n
\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:César Galindo (University of Hamburg/Universidad de los Andes)
DTSTART;VALUE=DATE-TIME:20220615T180000Z
DTEND;VALUE=DATE-TIME:20220615T190000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/41
DESCRIPTION:Title: Equivariant fusion categories\nby César Galindo (University
of Hamburg/Universidad de los Andes) as part of Categories seminar UNAM\n
\n\nAbstract\nIn this talk\, I will report results from joint work with Co
rey Jones\, https://arxiv.org/abs/2111.09116. We describe all fusion subca
tegories of the equivariantization of group action on a fusion category. A
s applications\, we classify the Hopf subalgebras of Kac-Paljutkin type an
d recover the Naidu-Nikshych-Witherspoon classification of the fusion subc
ategories of the representation category of a twisted quantum double of a
finite group.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Samperton (Purdue)
DTSTART;VALUE=DATE-TIME:20220622T180000Z
DTEND;VALUE=DATE-TIME:20220622T190000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/42
DESCRIPTION:Title: Anyons\, defects\, and computational complexity\nby Eric Sam
perton (Purdue) as part of Categories seminar UNAM\n\n\nAbstract\nTopologi
cal invariants of objects like knots and 3-manifolds are only practically
useful insofar as one is able to efficiently compute them. So\, for any gi
ven invariant\, it is interesting to try to quantify its computational com
plexity. \nBeyond just being an interesting "theoretical" problem\, such c
omplexity-theoretic issues are foundational to topological quantum computa
tion. I'll spend most of the talk introducing these ideas. Time permitting
\, I'll report on work-in-progress with Colleen Delaney that says\, roughl
y: coupling a finite group gauge symmetry to a topological quantum compute
r can not create a more powerful computer.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colleen Delaney (University of Indiana Bloomington)
DTSTART;VALUE=DATE-TIME:20220629T180000Z
DTEND;VALUE=DATE-TIME:20220629T190000Z
DTSTAMP;VALUE=DATE-TIME:20231130T065208Z
UID:CategoriesatUNAM/43
DESCRIPTION:Title: Zesting\, modular isotopes\, and Reshetikhin-Turaev invariants\nby Colleen Delaney (University of Indiana Bloomington) as part of Cate
gories seminar UNAM\n\n\nAbstract\nI'll give an overview of the zesting co
nstruction on ribbon fusion categories through the lens of topological pha
ses of matter and topological quantum computation. In particular\, we'll s
ee that Reshetekhin-Turaev invariants of knots and links transform in a ni
ce way under zesting. As an application I will explain how zesting gives a
new way to understand Mignard and Schauenburg's ``modular isotopes" -- ex
amples of different modular categories with the same modular data.\n \nThi
s talk is based on joint work with Parsa Bonderson\, Cesar Galindo\, Sung
Kim\, Julia Plavnik\, Eric Rowell\, Alan Tran\, Zhenghan Wang\, and Qing Z
hang.\n
LOCATION:https://researchseminars.org/talk/CategoriesatUNAM/43/
END:VEVENT
END:VCALENDAR