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BEGIN:VEVENT
SUMMARY:Stephanie van Willigenburg (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20210618T150000Z
DTEND;VALUE=DATE-TIME:20210618T160000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071543Z
UID:ACPMS/1
DESCRIPTION:Title: Th
e e-positivity of chromatic symmetric functions\nby Stephanie van Will
igenburg (University of British Columbia) as part of Algebraic and Combina
torial Perspectives in the Mathematical Sciences\n\n\nAbstract\nThe chroma
tic polynomial was generalized to the chromatic symmetric function by Stan
ley in his seminal 1995 paper. This function is currently experiencing a f
lourishing renaissance\, in particular the study of the positivity of chro
matic symmetric functions when expanded into the basis of elementary symme
tric functions\, that is\, e-positivity.\nIn this talk we approach the que
stion of e-positivity from various angles. Most pertinently we resolve the
1995 statement of Stanley that no known graph exists that is not contract
ible to the claw\, and whose chromatic symmetric function is not e-positiv
e.\n\nThis is joint work with Soojin Cho\, Samantha Dahlberg\, Angele Fole
y and Adrian She\, and no prior knowledge is assumed.\n\nPlease note that
this talk **starts at 17:00 (GMT+2)** instead of the usual time.\n
LOCATION:https://researchseminars.org/talk/ACPMS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amy Pang (Hong Kong Baptist University)
DTSTART;VALUE=DATE-TIME:20210625T130000Z
DTEND;VALUE=DATE-TIME:20210625T140000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071543Z
UID:ACPMS/2
DESCRIPTION:Title: Ma
rkov chains from linear operators and Hopf algebras\nby Amy Pang (Hong
Kong Baptist University) as part of Algebraic and Combinatorial Perspecti
ves in the Mathematical Sciences\n\n\nAbstract\nIf you study a linear oper
ator that expands positively in some basis\, then your results may be appl
icable to a Markov chain\, whose transition probabilities are given by the
matrix of the operator. This is the idea behind the theory of random walk
s on groups and monoids\, where the eigen-data of the operator informs the
long-term behaviour of the chain. We point out a lesser-known advantage o
f this framework: if the linear operator descends to a specific subquotien
t of its domain\, then the corresponding Markov chain admits a projection
/ lumping. We apply this to a coproduct-then-product operator on Hopf alge
bras\, to explain Jason Fulman's observation regarding the RSK-shape under
card-shuffling. I hope this talk will enable and inspire you to explore n
ew examples.\n
LOCATION:https://researchseminars.org/talk/ACPMS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maciej Dołęga (Polish Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20210702T130000Z
DTEND;VALUE=DATE-TIME:20210702T140000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071543Z
UID:ACPMS/3
DESCRIPTION:by Maciej Dołęga (Polish Academy of Sciences) as part of Alg
ebraic and Combinatorial Perspectives in the Mathematical Sciences\n\nAbst
ract: TBA\n
LOCATION:https://researchseminars.org/talk/ACPMS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolina Benedetti (Universidad de los Andes\, Bogotá)
DTSTART;VALUE=DATE-TIME:20210709T130000Z
DTEND;VALUE=DATE-TIME:20210709T140000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071543Z
UID:ACPMS/4
DESCRIPTION:by Carolina Benedetti (Universidad de los Andes\, Bogotá) as
part of Algebraic and Combinatorial Perspectives in the Mathematical Scien
ces\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ACPMS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Susama Agarwala (University of Hamburg)
DTSTART;VALUE=DATE-TIME:20210903T130000Z
DTEND;VALUE=DATE-TIME:20210903T140000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071543Z
UID:ACPMS/5
DESCRIPTION:by Susama Agarwala (University of Hamburg) as part of Algebrai
c and Combinatorial Perspectives in the Mathematical Sciences\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/ACPMS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frédéric Chapoton (CNRS\, Strasbourg)
DTSTART;VALUE=DATE-TIME:20210910T130000Z
DTEND;VALUE=DATE-TIME:20210910T140000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071543Z
UID:ACPMS/6
DESCRIPTION:Title: Mu
ltiple zeta values and zinbiel algebras\nby Frédéric Chapoton (CNRS\
, Strasbourg) as part of Algebraic and Combinatorial Perspectives in the M
athematical Sciences\n\n\nAbstract\nWe will explain the construction\, usi
ng the notion of Zinbiel algebra\, of some commutative subalgebras $C_{u\,
v}$ inside an algebra of formal iterated integrals. There is a quotient ma
p from this algebra of formal iterated integrals to the algebra of motivic
multiple zeta values. Restricting this quotient map to the subalgebras $C
_{u\,v}$ gives a morphism of graded commutative algebras with the same gen
erating series. This is conjectured to be generically an isomorphism. When
$u+v = 0$\, the image is instead a sub-algebra of the algebra of motivic
multiple zeta values.\n
LOCATION:https://researchseminars.org/talk/ACPMS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chaitanya Leena Subramaniam (Université Paris Diderot)
DTSTART;VALUE=DATE-TIME:20210917T130000Z
DTEND;VALUE=DATE-TIME:20210917T140000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071543Z
UID:ACPMS/7
DESCRIPTION:Title: De
pendent type theory and higher algebraic structures\nby Chaitanya Leen
a Subramaniam (Université Paris Diderot) as part of Algebraic and Combina
torial Perspectives in the Mathematical Sciences\n\n\nAbstract\nIn classic
al universal algebra\, every family of algebraic structures (such as monoi
ds\, groups\, rings\, modules\, small categories\, operads\, sheaves) can
be classified by a syntactic (algebraic or essentially algebraic) equation
al theory. A cornerstone of universal algebra is the equivalence between a
lgebraic theories and finitary monads on the category of sets\, due to Law
vere\, B\\'enabou and Linton. Higher algebraic structures (such as loop sp
aces\, E-k spaces\, infinity-categories\, infinity-operads and their modul
es and algebras\, stacks\, spectra) are algebraic structures up to homotop
y in spaces ("spaces" = topological spaces\, simplicial sets or any other
model of homotopy types). It is a long-standing presupposition among homot
opy type theorists that the dependent types introduced by Martin-L\\"of ar
e particularly well-suited to providing syntactic theories and a universal
algebra for higher algebraic structures. In this talk\, we will see a (fe
w) definition(s) of "dependently sorted/typed algebraic theory" and descri
be a monad-theory equivalence strictly generalising that of Lawvere-Bénab
ou-Linton. With respect to their Set-valued models\, dependently sorted al
gebraic theories have the same expressive power as essentially algebraic t
heories. However\, as we will see in this talk\, dependently sorted algebr
aic theories have the advantage of having a good theory of models up-to-ho
motopy in spaces\, which generalises the theory of homotopy-models of alge
braic theories due to Schwede\, Badzioch\, Rezk and Bergner. We will see t
hat many familiar algebraic structures (such as n-categories\, omega-categ
ories\, coloured planar operads\, opetopic sets) are very naturally seen t
o be models of dependently sorted algebraic theories. The crux of these re
sults is a correspondence between the dependent sorts/types of any depende
ntly sorted algebraic theory T\, and a certain "cellularity" underlying ev
ery algebraic structure described by T (i.e. every T-model). The goal of t
his talk will be to explain this correspondence between type dependency an
d cellularity\, and why this cellularity marries well with homotopy theory
.\n
LOCATION:https://researchseminars.org/talk/ACPMS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gunnar Fløystad (University of Bergen)
DTSTART;VALUE=DATE-TIME:20210924T130000Z
DTEND;VALUE=DATE-TIME:20210924T140000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071543Z
UID:ACPMS/8
DESCRIPTION:Title: Sh
ift modules\, strongly stable ideals\, and their dualities\nby Gunnar
Fløystad (University of Bergen) as part of Algebraic and Combinatorial Pe
rspectives in the Mathematical Sciences\n\n\nAbstract\nPolynomial rings ov
er a field $k$ are the prime objects in algebra. Ideals in polynomial ring
s are the prime objects relating algebra and geometry via the zero set of
the ideal.\n\nTo understand ideals in a polynomial ring\, a common approac
h is to see what simpler ideals they degenerate to\, for instance what mon
omial ideals. But what are the most degenerate ideals you can find? Those
that cannot be degenerated any further? These are the so-called Borel-fixe
d ideals\, or\, when the field k has characteristic zero\, the strongly st
able ideals. This class is for instance the essential tool for understandi
ng numerical invariants of ideals in polynomial rings.\n\nWe enrich the se
tting of strongly stable ideals by:\n\n1. Extending them to a category of
modules\n\n2. Investigating the recently discovered duality on these ideal
s\n\n3. Getting a new type of projective resolution of such ideals\n\n4. L
etting the ambient polynomial ring be infinite dimensional\n
LOCATION:https://researchseminars.org/talk/ACPMS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franz Herzog (The University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20211001T130000Z
DTEND;VALUE=DATE-TIME:20211001T140000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071543Z
UID:ACPMS/9
DESCRIPTION:Title: Th
e Hopf algebra of IR divergences of Feynman graphs\nby Franz Herzog (T
he University of Edinburgh) as part of Algebraic and Combinatorial Perspec
tives in the Mathematical Sciences\n\n\nAbstract\nIt is by now very well k
nown that the structure of UV divergences Feynman Integrals\, and their as
sociated graphs\, can be described elegantly in a Hopf algebra originally
developed by Kreimer and Connes. Beyond UV divergences Feynman Integrals a
lso suffer from IR\, long-distance\, divergences. I will present a new Hop
f-algebraic formulation which allows to simultaneously treat both the IR a
nd the UV. Remarkably in this framework the IR and UV counterterm maps are
inverse to each other on the group of characters of the Hopf algebra.\n
LOCATION:https://researchseminars.org/talk/ACPMS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophie Spirkl (University of Waterloo)
DTSTART;VALUE=DATE-TIME:20211022T130000Z
DTEND;VALUE=DATE-TIME:20211022T140000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071543Z
UID:ACPMS/10
DESCRIPTION:Title: M
odular relations for the Tutte symmetric function\nby Sophie Spirkl (U
niversity of Waterloo) as part of Algebraic and Combinatorial Perspectives
in the Mathematical Sciences\n\n\nAbstract\nThe Tutte symmetric function
XB generalizes both the Tutte polynomial and the chromatic symmetric funct
ion X. In this talk\, I'll discuss a modular relation for XB analogous to
the Orellana-Scott relation for X\, general results for modular relations
for XB and X\, and applications.\nJoint work with Logan Crew.\n
LOCATION:https://researchseminars.org/talk/ACPMS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gerald Dunne (University of Connecticut)
DTSTART;VALUE=DATE-TIME:20211029T130000Z
DTEND;VALUE=DATE-TIME:20211029T140000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071543Z
UID:ACPMS/11
DESCRIPTION:Title: R
esurgent Trans-series in Hopf-Algebraic Dyson-Schwinger Equations\nby
Gerald Dunne (University of Connecticut) as part of Algebraic and Combinat
orial Perspectives in the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ACPMS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bérénice Delcroix-Oger (Université de Paris)
DTSTART;VALUE=DATE-TIME:20211217T140000Z
DTEND;VALUE=DATE-TIME:20211217T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071543Z
UID:ACPMS/12
DESCRIPTION:by Bérénice Delcroix-Oger (Université de Paris) as part of
Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/ACPMS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Gilliers (University of Toulouse)
DTSTART;VALUE=DATE-TIME:20211008T130000Z
DTEND;VALUE=DATE-TIME:20211008T140000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071543Z
UID:ACPMS/13
DESCRIPTION:Title: B
inary trees\, operads and Dykema’s T-transform in Free Probability\n
by Nicolas Gilliers (University of Toulouse) as part of Algebraic and Comb
inatorial Perspectives in the Mathematical Sciences\n\n\nAbstract\nIn this
talk\, we shall discuss an operadic perspective on K. Dykema’s twisted
factorization formula for the operator-valued T-transform in free probabil
ity. To begin with\, we introduce in the general setting of an operad with
multiplication two group products on formal series of operators\, besides
the one introduced by F. Chapoton. We explain how those products relate b
y means of certain transformation\, that we call (abstract) T-transform\,
borrowing terminology from free probability. Specializing in the endomorph
ism operad gives a new perspective on the twisted factorization of the T-t
ransform and to multiplicative free convolution. We will discuss connectio
ns to the work of A. Frabetti and C. Brouder by specializing our construct
ion to the duoidal and dendriform operads.\n
LOCATION:https://researchseminars.org/talk/ACPMS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yannic Vargas (University of Potsdam)
DTSTART;VALUE=DATE-TIME:20211015T130000Z
DTEND;VALUE=DATE-TIME:20211015T140000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071543Z
UID:ACPMS/14
DESCRIPTION:Title: M
onomial bases for combinatorial Hopf algebras\nby Yannic Vargas (Unive
rsity of Potsdam) as part of Algebraic and Combinatorial Perspectives in t
he Mathematical Sciences\n\n\nAbstract\nThe algebraic structure of a Hopf
algebra can often be understood in terms of a poset on the underlying fami
ly of combinatorial objects indexing a basis. For example\, the Hopf algeb
ra of quasisymmetric functions is generated (as a vector space) by composi
tions and admits a fundamental (F) basis and a monomial (M) basis\, relate
d by the refinement poset on compositions. Analogous bases can be consider
ed for other Hopf algebras\, with similar properties to the F basis\, e.g.
a product described by some notion of shuffle\, and a coproduct following
some notion of deconcatenation. We give axioms for how these generalised
shuffles and deconcatentations should interact with the underlying poset s
o that a monomial-like basis can be analogously constructed\, generalising
the approach of Aguiar and Sottile. We also find explicit positive formul
as for the multiplication on monomial basis and a cancellation-free and gr
ouping-free formula for the antipode of monomial elements. We apply these
results on classical and new Hopf algebras\, related by tree-like structur
es.\nThis is based on "Hopf algebras of parking functions and decorated pl
anar trees"\, a joint work with Nantel Bergeron\, Rafael Gonzalez D'Leon\,
Amy Pang and Shu Xiao Li.\n
LOCATION:https://researchseminars.org/talk/ACPMS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonard Schmitz (University of Greifswald)
DTSTART;VALUE=DATE-TIME:20230120T140000Z
DTEND;VALUE=DATE-TIME:20230120T150000Z
DTSTAMP;VALUE=DATE-TIME:20230208T071543Z
UID:ACPMS/15
DESCRIPTION:Title: T
wo-parameter sums signatures and corresponding quasisymmetric functions\nby Leonard Schmitz (University of Greifswald) as part of Algebraic and
Combinatorial Perspectives in the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ACPMS/15/
END:VEVENT
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