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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:20240329T052134Z
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:20240329T052134Z
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:20240329T052134Z
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:20240329T052134Z
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:20240329T052134Z
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:20240329T052134Z
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:20240329T052134Z
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:20240329T052134Z
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:20240329T052134Z
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:20240329T052134Z
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:20240329T052134Z
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:20240329T052134Z
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:20240329T052134Z
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:20240329T052134Z
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:20240329T052134Z
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
BEGIN:VEVENT
SUMMARY:Jaiung Jun (SUNY at New Paltz)
DTSTART;VALUE=DATE-TIME:20230317T140000Z
DTEND;VALUE=DATE-TIME:20230317T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/16
DESCRIPTION:Title: O
n the Hopf algebra of multi-complexes\nby Jaiung Jun (SUNY at New Palt
z) as part of Algebraic and Combinatorial Perspectives in the Mathematical
Sciences\n\n\nAbstract\nHopf algebras appear naturally in combinatorics i
n the following way: For a given class of combinatorial objects (such as g
raphs or matroids)\, basic operations (such as assembly and disassembly op
erations) often can be encoded in the algebraic structure of a Hopf algebr
a. One then hopes to use algebraic identities of a Hopf algebra to return
to combinatorial identities of combinatorial objects of interest. In this
talk\, I will introduce a general class of combinatorial objects\, which w
e call multi-complexes. They simultaneously generalize graphs\, hypergraph
s and simplicial and delta complexes. I will describe the structure of the
Hopf algebra of multi-complexes by finding an explicit basis of the space
of primitives. This is joint work with Miodrag Iovanov.\n
LOCATION:https://researchseminars.org/talk/ACPMS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annika Burmester (Bielefeld University)
DTSTART;VALUE=DATE-TIME:20230331T130000Z
DTEND;VALUE=DATE-TIME:20230331T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/17
DESCRIPTION:Title: P
ost-Lie algebras related to multiple (q-)zeta values\nby Annika Burmes
ter (Bielefeld University) as part of Algebraic and Combinatorial Perspect
ives in the Mathematical Sciences\n\n\nAbstract\nMultiple zeta values beca
me of more interest over the last 25 years due to their appearance in vari
ous fields of mathematics and also physics. First\, we will describe their
algebraic structure in terms of Hoffman’s quasi-shuffle algebras\, whic
h are certain deformations of the usual shuffle product. Following Racinet
this allows to relate a post-Lie algebra to the multiple zeta values\, th
e double shuffle Lie algebra equipped with the Ihara bracket\, which gives
a new insight into the algebraic structure of multiple zeta values. We ar
e interested in an analog approach for multiple q-zeta values\, which are
certain q-series degenerating to multiple zeta values for the limit q to 1
. In particular\, we will explain some results towards a post-Lie algebra
related to multiple q-zeta values.\n
LOCATION:https://researchseminars.org/talk/ACPMS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karine Beauchard (ENS Rennes)
DTSTART;VALUE=DATE-TIME:20230414T130000Z
DTEND;VALUE=DATE-TIME:20230414T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/18
DESCRIPTION:Title: O
n expansions for nonlinear systems\, error estimates and convergence issue
s\nby Karine Beauchard (ENS Rennes) as part of Algebraic and Combinato
rial Perspectives in the Mathematical Sciences\n\n\nAbstract\nExplicit for
mulas expressing the solution to non-autonomous differential equations are
of great importance in many application domains such as control theory or
numerical operator splitting. In particular\, intrinsic formulas allowing
to decouple time-dependent features from geometry-dependent features of t
he solution have been extensively studied.\nFirst\, we give a didactic rev
iew of classical expansions for formal linear differential equations\, inc
luding the celebrated Magnus expansion (associated with coordinates of the
first kind) and Sussmann’s infinite product expansion (associated with
coordinates of the second kind). Inspired by quantum mechanics\, we introd
uce a new mixed expansion\, designed to isolate the role of a time-invaria
nt drift from the role of a time-varying perturbation.\nSecond\, in the co
ntext of nonlinear ordinary differential equations driven by regular vecto
r fields\, we give rigorous proofs of error estimates between the exact so
lution and finite approximations of the formal expansions. In particular\,
we derive new estimates focusing on the role of time-varying perturbation
s.\nThird\, we investigate the local convergence of these expansions. In p
articular\, we exhibit arbitrarily small analytic vector fields for which
the convergence of the Magnus expansion fails\, even in very weak senses.\
nEventually\, we derive approximate direct intrinsic representations for t
he state\, particularly well designed for applications in control theory.\
n
LOCATION:https://researchseminars.org/talk/ACPMS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darij Grinberg
DTSTART;VALUE=DATE-TIME:20230428T130000Z
DTEND;VALUE=DATE-TIME:20230428T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/19
DESCRIPTION:by Darij Grinberg as part of Algebraic and Combinatorial Persp
ectives in the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ACPMS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gunnar Fløystad
DTSTART;VALUE=DATE-TIME:20230512T130000Z
DTEND;VALUE=DATE-TIME:20230512T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/20
DESCRIPTION:by Gunnar Fløystad as part of Algebraic and Combinatorial Per
spectives in the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ACPMS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara Meroni
DTSTART;VALUE=DATE-TIME:20230526T130000Z
DTEND;VALUE=DATE-TIME:20230526T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/21
DESCRIPTION:Title: P
ath signatures in convex geometry\nby Chiara Meroni as part of Algebra
ic and Combinatorial Perspectives in the Mathematical Sciences\n\n\nAbstra
ct\nHow can one compute the volume of the convex hull of a curve? I will t
ry to answer this question\, for special families of curves. This is a joi
nt work with Carlos Améndola and Darrick Lee. We generalise the class of
curves for which a certain integral formula works\, using the technique of
signatures. I will then give a geometric interpretation of this volume fo
rmula in terms of lengths and areas\, and conclude with examples and an op
en conjecture.\n
LOCATION:https://researchseminars.org/talk/ACPMS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emilie Purvine
DTSTART;VALUE=DATE-TIME:20230609T140000Z
DTEND;VALUE=DATE-TIME:20230609T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/22
DESCRIPTION:Title: A
pplied Topology for Discrete Structures\nby Emilie Purvine as part of
Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n\n\
nAbstract\nDiscrete structures have a long history of use in applied mathe
matics. Graphs and hypergraphs provide models of social networks\, biologi
cal systems\, academic collaborations\, and much more. Network science\, a
nd more recently hypernetwork science\, have been used to great effect in
analyzing these types of discrete structures. Separately\, the field of ap
plied topology has gathered many successes through the development of pers
istent homology\, mapper\, sheaves\, and other concepts. Recent work by ou
r group has focused on the convergence of these two areas\, developing and
applying topological concepts to study discrete structures that model rea
l data. This talk will survey our body of work in this area showing our wo
rk in both the theoretical and applied spaces. Theory topics will include
an introduction to hypernetwork science and its relation to traditional ne
twork science\, topological interpretations of graphs and hypergraphs\, an
d dynamics of topology and network structures. I will show examples of how
we are applying each of these concepts to real data sets.\n
LOCATION:https://researchseminars.org/talk/ACPMS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuele Verri (Universität Greifswald)
DTSTART;VALUE=DATE-TIME:20230623T130000Z
DTEND;VALUE=DATE-TIME:20230623T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/23
DESCRIPTION:Title: C
onjoined permutation patterns\nby Emanuele Verri (Universität Greifsw
ald) as part of Algebraic and Combinatorial Perspectives in the Mathematic
al Sciences\n\n\nAbstract\nSome time ago\, Bandt introduced the concept of
"permutation entropy" which proved very effective in the analysis of time
series.\nThis index is based on certain permutation patterns.\nPermutatio
n patterns play indeed a very central role in many areas of discrete mathe
matics.\nMore recently\, in algebraic combinatorics\, Vargas introduced th
e superinfiltration Hopf algebra whose operations behave well with respect
to occurrences of permutation patterns.\nInspired by both these works\, w
e introduce a new Hopf algebra which also includes the patterns used by Ba
ndt.\nIts algebraic operations behave well with respect to occurrences of
permutation patterns where is also specified whether values are consecutiv
e or arbitrarily far apart.\nTo encode whether two values are consecutive\
, we use interval partitions of finite subsets of positive integers and al
so introduce a new Hopf algebra on interval partitions.\nThis is joint wor
k with Joscha Diehl.\n
LOCATION:https://researchseminars.org/talk/ACPMS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART;VALUE=DATE-TIME:20230707T130000Z
DTEND;VALUE=DATE-TIME:20230707T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/24
DESCRIPTION:by TBA as part of Algebraic and Combinatorial Perspectives in
the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ACPMS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Olson-Harris (University of Waterloo)
DTSTART;VALUE=DATE-TIME:20230918T130000Z
DTEND;VALUE=DATE-TIME:20230918T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/25
DESCRIPTION:by Nick Olson-Harris (University of Waterloo) as part of Algeb
raic and Combinatorial Perspectives in the Mathematical Sciences\n\nAbstra
ct: TBA\n
LOCATION:https://researchseminars.org/talk/ACPMS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kasia Rejzner (University of York)
DTSTART;VALUE=DATE-TIME:20230929T130000Z
DTEND;VALUE=DATE-TIME:20230929T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/26
DESCRIPTION:Title: P
erturbative algebraic quantum field theory (introduction and examples)
\nby Kasia Rejzner (University of York) as part of Algebraic and Combinato
rial Perspectives in the Mathematical Sciences\n\n\nAbstract\nIn this talk
I will introduce the framework perturbative algebraic quantum field theor
y. It allows one to combine the method of Epstein-Glaser renormalisation w
ith the idea of BV quantization\, commonly applied to quantization of gaug
e theories. It straightforwardly generalizes to theories on a large class
of Lorentzian manifolds. The same formalism can also be applied when one r
eplaces the manifold with a finite collection of points\, equipped with a
partial order relation (modelling the causal order).\n
LOCATION:https://researchseminars.org/talk/ACPMS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Olson-Harris
DTSTART;VALUE=DATE-TIME:20231013T130000Z
DTEND;VALUE=DATE-TIME:20231013T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/27
DESCRIPTION:by Nick Olson-Harris as part of Algebraic and Combinatorial Pe
rspectives in the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ACPMS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Cabrera (Universidade Federal do Rio de Janeiro)
DTSTART;VALUE=DATE-TIME:20231027T130000Z
DTEND;VALUE=DATE-TIME:20231027T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/28
DESCRIPTION:Title: A
bout local symplectic groupoids and applications\nby Alejandro Cabrera
(Universidade Federal do Rio de Janeiro) as part of Algebraic and Combina
torial Perspectives in the Mathematical Sciences\n\n\nAbstract\nIn this ta
lk\, we will review the notion of local symplectic groupoid and its relati
on to Poisson geometry. We then summarize some recent results involving ex
plicit constructions and their relation to quantization. Finally\, we will
comment on applications to discretization of hamiltonian flows on Poisson
manifolds.\n
LOCATION:https://researchseminars.org/talk/ACPMS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Vallette
DTSTART;VALUE=DATE-TIME:20231117T140000Z
DTEND;VALUE=DATE-TIME:20231117T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/30
DESCRIPTION:by Bruno Vallette as part of Algebraic and Combinatorial Persp
ectives in the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ACPMS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matilde Marcolli
DTSTART;VALUE=DATE-TIME:20231201T140000Z
DTEND;VALUE=DATE-TIME:20231201T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/31
DESCRIPTION:by Matilde Marcolli as part of Algebraic and Combinatorial Per
spectives in the Mathematical Sciences\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ACPMS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Pechenik (University of Waterloo)
DTSTART;VALUE=DATE-TIME:20231215T140000Z
DTEND;VALUE=DATE-TIME:20231215T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/32
DESCRIPTION:Title: Q
uasisymmetric Schubert calculus\nby Oliver Pechenik (University of Wat
erloo) as part of Algebraic and Combinatorial Perspectives in the Mathemat
ical Sciences\n\n\nAbstract\nWe introduce projective schemes that are anal
ogues of the James reduced product construction from homotopy theory and b
egin to develop a Schubert calculus for such spaces. This machinery yields
K-theoretic and T-equivariant analogues of classic quasisymmetric functio
n theory. Based on joint works with Matt Satriano.\n
LOCATION:https://researchseminars.org/talk/ACPMS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Shiebler (Abnormal Security)
DTSTART;VALUE=DATE-TIME:20240126T140000Z
DTEND;VALUE=DATE-TIME:20240126T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/33
DESCRIPTION:Title: L
earning with Kan Extensions\nby Dan Shiebler (Abnormal Security) as pa
rt of Algebraic and Combinatorial Perspectives in the Mathematical Science
s\n\n\nAbstract\nA common problem in machine learning is "use this functio
n defined over this small set to generate predictions over that larger set
." Extrapolation\, interpolation\, statistical inference and forecasting a
ll reduce to this problem. The Kan extension is a powerful tool in categor
y theory that generalizes this notion. In this work we explore application
s of the Kan extension to machine learning problems. We begin by deriving
a simple classification algorithm as a Kan extension and experimenting wit
h this algorithm on real data. Next\, we use the Kan extension to derive a
procedure for learning clustering algorithms from labels and explore the
performance of this procedure on real data.\n
LOCATION:https://researchseminars.org/talk/ACPMS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolas Tapia (Weierstrass Institute)
DTSTART;VALUE=DATE-TIME:20240209T140000Z
DTEND;VALUE=DATE-TIME:20240209T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/34
DESCRIPTION:Title: B
ranched Itô Formula and natural Itô-Stratonovich isomorphism\nby Nik
olas Tapia (Weierstrass Institute) as part of Algebraic and Combinatorial
Perspectives in the Mathematical Sciences\n\n\nAbstract\nBranched rough pa
ths define integration theories that may fail to satisfy the integration b
y parts identity. The projection of the Connes-Kreimer Hopf algebra (\\(\\
mathcal{H}_{\\mathrm{CK}}\\)) onto its primitive elements defined by Broad
hurst-Kreimer and Foissy\, allows us to view \\(\\mathcal{H}_{\\mathrm{CK}
}\\) as a commutative \\(\\mathbf{B}_\\infty\\)-algebra and thus to write
an explicit change-of-variable formula for solutions to rough differential
equations (RDEs)\, which restricts to the well-known Itô formula for sem
imartingales. When compared with Kelly’s approach using bracket extensio
ns\, this formula has the advantage of only depending on internal structur
e. We proceed to define an isomorphism between \\(\\mathcal{H}_{\\mathrm{C
K}}\\) and \\(\\operatorname{Sh}(\\mathcal{P})\\) (the shuffle algebra ove
r primitives)\, which we compare with the previous constructions of Hairer
-Kelly and Boedihardjo-Chevyrev: while all three allow one to write branch
ed RDEs as RDEs driven by geometric rough paths taking values in a larger
space\, the key feature of our isomorphism is that it is natural when \\(\
\mathcal{H}_{\\mathrm{CK}}\\) and \\(\\operatorname{Sh}(\\mathcal{P})\\) a
re viewed as covariant functors \\(\\mathsf{Vec}\\to\\mathsf{Hopf}\\). Our
natural isomorphism extends Hoffman’s exponential for the quasi shuffle
algebra\, and in particular the usual Itô-Stratonovich correction formul
a for semimartingales. Special emphasis is placed on the 1-dimensional cas
e\, in which certain rough path terms can be expressed as polynomials in t
he trace path indexed by \\(\\mathcal{P}\\)\, which for semimartingales re
strict to the well-known Kailath-Segall polynomials.\n\nThis talk is based
on joint work with E. Ferrucci and C. Bellingeri.\n
LOCATION:https://researchseminars.org/talk/ACPMS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannes Kern (TU Berlin)
DTSTART;VALUE=DATE-TIME:20240301T140000Z
DTEND;VALUE=DATE-TIME:20240301T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/35
DESCRIPTION:Title: R
ough Flow techniques on manifolds\nby Hannes Kern (TU Berlin) as part
of Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n
\n\nAbstract\nIn 2020\, Armstrong et al managed to explicitly write down D
avie’s formula of the solution of a non-geometric RDE on a manifold for
the level N = 2. In this talk\, we introduce a new notion\, called pseudo
bialgebra map\, which allows us to construct similar expansions for higher
level rough pahs living in general Hopf algebras. To do this\, we prove a
local version of Bailleul’s sewing lemma for flows. Finally\, we go ove
r previous results and show that they do give rise to pseudo bialgebra map
s. Based on joint work with Terry Lyons.\n
LOCATION:https://researchseminars.org/talk/ACPMS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruggero Bandiera (Sapienza Università di Roma)
DTSTART;VALUE=DATE-TIME:20240315T140000Z
DTEND;VALUE=DATE-TIME:20240315T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/36
DESCRIPTION:Title: C
umulants\, Koszul brackets and homological perturbation theory for commuta
tive BVoo and IBLoo algebras\nby Ruggero Bandiera (Sapienza Universit
à di Roma) as part of Algebraic and Combinatorial Perspectives in the Mat
hematical Sciences\n\n\nAbstract\nn the first part of this talk we shall r
eview the classical homotopy transfer theorem in the context of Aoo and Lo
o algebras. We shall explain how the usual proof of this result for Aoo al
gebras\, based on the tensor trick and the homological perturbation lemma\
, can be adapted to Loo algebras using a symmetrized version of the tensor
trick. In the course of the discussion we shall review the construction o
f cumulants and Koszul brackets (as well as their coalgebraic analogs): th
ese are graded symmetric multilinear maps associated respectively to a mor
phism of graded commutative algebras $f\\colon A \\to B$ or to an endomorp
hism $d\\colon A \n\\to A$\, measuring the deviation of f from being an al
gebra morphism in the first case\, and the deviation of d from being an al
gebra derivation in the second case. A key technical lemma will be that un
der certain assumptions on the involved contraction\, these are compatible
with homotopy transfer in an appropriate sense. In the second part of the
talk we shall review commutative BVoo algebra in the sense of Kravchenko:
as an application of our previous discussion we shall introduce a new def
inition of morphisms between these objects in terms of cumulants. Moreover
\, we shall explain how to use homological perturbation theory to get a ho
motopy transfer theorem for commutative BVoo algebras\, under certain assu
mptions on the involved contraction. Finally\, IBLoo algebras\, that is\,
commutative BVoo algebras whose underlying algebra is free\, are known to
be a model for involutive Lie bialgebras up to coherent homotopies\, and h
ave recently found several applications in string topology and symplectic
field theory. \nAs an application of our results\, we shall explain how to
obtain a homotopy transfer theorem for IBLoo algebras via the symmetrized
tensor trick and the homological perturbation lemma.\n
LOCATION:https://researchseminars.org/talk/ACPMS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Joswig (TU Berlin)
DTSTART;VALUE=DATE-TIME:20240223T140000Z
DTEND;VALUE=DATE-TIME:20240223T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T052134Z
UID:ACPMS/37
DESCRIPTION:Title: Q
uantum automorphisms of matroids\nby Michael Joswig (TU Berlin) as par
t of Algebraic and Combinatorial Perspectives in the Mathematical Sciences
\n\n\nAbstract\nMotivated by the vast literature of quantum automorphism g
roups of graphs\, we define and study quantum automorphism groups of matro
ids. A key feature of quantum groups is that there are many quantizations
of a classical group\, and this phenomenon manifests in the cryptomorphic
characterizations of matroids. Our primary goals are to understand\, using
theoretical and computational techniques\, the relationship between these
quantum groups and to find when these quantum groups exhibit quantum symm
etry. Finally\, we prove a matroidal analog of Lovász's theorem character
izing graph isomorphisms in terms of homomorphism counts.\n\nJoint work wi
th Daniel Corey\, Julien Schanz\, Marcel Wack\, and Moritz Weber.\n
LOCATION:https://researchseminars.org/talk/ACPMS/37/
END:VEVENT
END:VCALENDAR