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BEGIN:VEVENT
SUMMARY:Kleene Stars in Shuffle Algebras
DTSTART;VALUE=DATE-TIME:20201203T123000Z
DTEND;VALUE=DATE-TIME:20201203T132000Z
DTSTAMP;VALUE=DATE-TIME:20210416T203304Z
UID:indico-contribution-6181-4951@indico.math.cnrs.fr
DESCRIPTION:Speakers: Gérard H. E. Duchamp (Université de Paris 13\, LIP
N)\nWe present some bialgebras and their monoid of characters. We entend\,
to the case of some rings\, the well-known theorem (in the case when the
scalars form a field) about linear independence of characters. Examples o
f algebraic independence of subfamilies and identites derived from their g
roups (or monoids) of characters are *provided. In this framework\, we det
ail the study of one-parameter groups of characters. It is a joint wor
k (arXiv:2009.10970) with Darij Grinberg (Drexel Universiy\, Philade
lphia\, US / currently Germany) and Hoang Ngoc Minh (LIPN\, Paris XIII Uni
versity).\n\nhttps://indico.math.cnrs.fr/event/6181/contributions/4951/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6181/contributions/4951/
END:VEVENT
BEGIN:VEVENT
SUMMARY:MRS Factorisations and Applications
DTSTART;VALUE=DATE-TIME:20201203T132000Z
DTEND;VALUE=DATE-TIME:20201203T141000Z
DTSTAMP;VALUE=DATE-TIME:20210416T203304Z
UID:indico-contribution-6181-4952@indico.math.cnrs.fr
DESCRIPTION:Speakers: Hoang Ngoc Minh (Université de Paris\, LIPN)\nWe r
eview simultaneously the essential steps to establish the equation bridgin
g the algebraic structures of converging polyzetas\, via their noncommutat
ive generating series put in factorised form MRS. This equation then al
lows us to describe polynomial relations\, homogenous in weight\, a
mong these polyzetas\, via an identification of local coordinates.\n\nhttp
s://indico.math.cnrs.fr/event/6181/contributions/4952/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6181/contributions/4952/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Highly Noncommutative Words and Noncommutative Poisson Structures
DTSTART;VALUE=DATE-TIME:20201203T142000Z
DTEND;VALUE=DATE-TIME:20201203T151000Z
DTSTAMP;VALUE=DATE-TIME:20210416T203304Z
UID:indico-contribution-6181-4953@indico.math.cnrs.fr
DESCRIPTION:Speakers: Natalja K. Iyudu (Research Fellow\, University of E
dinburgh)\nI will talk on homology calculations for the higher cyclic Hoch
schild complex and on combinatorial description of Lie structure on highly
noncommutative words. \nIt is based on the texts: Arxiv:1906.07134 (J. A
Lgebra\, 2020)\, preprints IHES M/19/14.\n\nhttps://indico.math.cnrs.fr/
event/6181/contributions/4953/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6181/contributions/4953/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hopf-Algebraic Renormalization of Multiple Zeta Values and their q
-analogues
DTSTART;VALUE=DATE-TIME:20201203T153000Z
DTEND;VALUE=DATE-TIME:20201203T162000Z
DTSTAMP;VALUE=DATE-TIME:20210416T203304Z
UID:indico-contribution-6181-4954@indico.math.cnrs.fr
DESCRIPTION:Speakers: Dominique Manchon (LMBP\, CNRS (UMR 6620) Universit
é de Clermont Auvergne)\nAfter a brief introductory account\, I’ll expl
ain how a quasi-shuffle compatible definition (by no means unique) of mult
iple zeta values can be given for integer arguments of any sign\, through
Connes-Kreimer’s Hopf-algebraic renormalization. Finally\, I’ll introd
uce the Ohno-Okuda-Zudilin model of q-analogues for multiple zeta values\,
describe the algebraic structure which governs it\, and explain how it co
uld open a way to the more delicate renormalization of shuffle relations.\
n\nhttps://indico.math.cnrs.fr/event/6181/contributions/4954/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6181/contributions/4954/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On a Tropical Version of the Jacobian Conjecture
DTSTART;VALUE=DATE-TIME:20201203T100000Z
DTEND;VALUE=DATE-TIME:20201203T105000Z
DTSTAMP;VALUE=DATE-TIME:20210416T203304Z
UID:indico-contribution-6181-4948@indico.math.cnrs.fr
DESCRIPTION:Speakers: Dimitri Grigoryev (CNRS Painlevé Lab\, Univ. Lille)
\nWe prove that\, for a tropical rational map if for any point the convex
hull of Jacobian matrices at smooth points in a neighborhood of the point
does not contain singular matrices then the map is an isomorphism. We als
o show that a tropical polynomial map on the plane is an isomorphism if al
l the Jacobians have the same sign (positive or negative). In addition\, f
or a tropical rational map we prove that if the Jacobians have the same si
gn and if its preimage is a singleton at least at one regular point then t
he map is an isomorphism. This is a joint work with Danylo Radchenko\, ETH
(Zürich).\n\nhttps://indico.math.cnrs.fr/event/6181/contributions/4948/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6181/contributions/4948/
END:VEVENT
BEGIN:VEVENT
SUMMARY:From Reflection Equation Algebra to Matrix Models
DTSTART;VALUE=DATE-TIME:20201202T162000Z
DTEND;VALUE=DATE-TIME:20201202T171000Z
DTSTAMP;VALUE=DATE-TIME:20210416T203304Z
UID:indico-contribution-6181-4949@indico.math.cnrs.fr
DESCRIPTION:Speakers: Dimitry Gurevich (Valenciennes University\, France)\
nReflection Equation Algebra is one of the Quantum matrix algebras\, assoc
iated with a given Hecke symmetry\, i.e. a braiding of Hecke type. I plan
to explain how to introduce analogs of Hermitian Matrix Models arising fro
m these algebras. Some other applications of the Reflection Equation Algeb
ras will be discussed.\n\nhttps://indico.math.cnrs.fr/event/6181/contribut
ions/4949/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6181/contributions/4949/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantum Mechanics of Bipartite Ribbon Graphs: A Combinatorial Int
erpretation of the Kronecker Coefficient.
DTSTART;VALUE=DATE-TIME:20201202T142000Z
DTEND;VALUE=DATE-TIME:20201202T151000Z
DTSTAMP;VALUE=DATE-TIME:20210416T203304Z
UID:indico-contribution-6181-4946@indico.math.cnrs.fr
DESCRIPTION:Speakers: Joseph Bengeloun (Université de Paris 13\, LIPN)\nT
he action of subgroups on a product of symmetric groups allows one to enum
erate different families of graphs. In particular\, bipartite ribbon graph
s (with at most edges) enumerate as the orbits of the adjoint action on tw
o copies of the symmetric group (of order n!). These graphs form a basis o
f an algebra\, which is also a Hilbert space for a certain sesquilinear fo
rm. Acting on this Hilbert space\, we define operators which are Hermitia
ns. We are therefore in the presence of a quantum mechanical model. We sho
w that the multiplicities of the eigenvalues of these operators are precis
ely the Kronecker coefficients\, well known in representation theory. We
then prove that there exists an algorithm that delivers the Kronecker coef
ficients and allow us to interpret those as the dimension of a sub-lattice
of the lattice of the ribbon graphs.Thus\, this provides an answer to Mur
naghan’s question (Amer. J. Math\, 1938) on the combinatorial interpret
ation of the Kronecker coefficient.\n\nhttps://indico.math.cnrs.fr/event/6
181/contributions/4946/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6181/contributions/4946/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quotients of Symmetric Polynomial Rings Deforming the Cohomology o
f the Grassmannian
DTSTART;VALUE=DATE-TIME:20201202T153000Z
DTEND;VALUE=DATE-TIME:20201202T162000Z
DTSTAMP;VALUE=DATE-TIME:20210416T203304Z
UID:indico-contribution-6181-4947@indico.math.cnrs.fr
DESCRIPTION:Speakers: Darij Grinberg (Drexel University\, Philadelphia\, U
S / currently Germany)\nOne of the many connections between Grassmannians
and combinatorics is cohomological: The cohomology ring of a Grassmannian
${\\rm Gr}(k\,n)$ is a quotient of the ring $S$ of symmetric polynomials i
n $k$ variables. More precisely\, it is the quotient of $S$ by the ideal g
enerated by the k consecutive complete homogeneous symmetric polynomials $
h_{n-k}\, h_{n-k+1}\, \\ldots \, h_n$. We deform this quotient\, by replac
ing the ideal by the ideal generated by $h_{n-k} - a_1 \, h_{n-k+1} - a_2
\, \\ldots \, h_n - a_k$ for some $k$ fixed elements $a_1 \, a_2 \, \\ldot
s \, a_k$ of the base ring. This generalizes both the classical and the q
uantum cohomology rings of ${\\rm Gr}(k\,n)$. We find three bases for the
new quotient\, as well as an $S_3$-symmetry of its structure constants\,
a “rim hook rule” for straightening arbitrary Schur polynomials\, and
a fairly complicated Pieri rule. We conjecture that the structure constan
ts are nonnegative in an appropriate sense (treating the $a_i$ as signed i
ndeterminate)\, which suggests a geometric or\ncombinatorial meaning for t
he quotient.\n\nhttps://indico.math.cnrs.fr/event/6181/contributions/4947/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6181/contributions/4947/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Constructive Matrix Theory for Hermitian Higher Order Interaction
DTSTART;VALUE=DATE-TIME:20201202T132000Z
DTEND;VALUE=DATE-TIME:20201202T141000Z
DTSTAMP;VALUE=DATE-TIME:20210416T203304Z
UID:indico-contribution-6181-4945@indico.math.cnrs.fr
DESCRIPTION:Speakers: Vincent Rivasseau (Laboratoire de Physique Théoriqu
e\, Université de Paris-Sud)\nIn this seminar we study the constructive l
oop vertex expansion for stable matrix models with (single trace) interact
ions of arbitrarily high even order in the Hermitian and real symmetric ca
ses. It relies on a new and simpler method which can also be applied in t
he previously treated complex case. We prove analyticity in the coupling
constant of the free energy for such models in a domain uniform in the siz
e of the matrix.\n\nhttps://indico.math.cnrs.fr/event/6181/contributions/4
945/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6181/contributions/4945/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maximal Green Sequences for Certain Triangle Products
DTSTART;VALUE=DATE-TIME:20201203T105000Z
DTEND;VALUE=DATE-TIME:20201203T114000Z
DTSTAMP;VALUE=DATE-TIME:20210416T203304Z
UID:indico-contribution-6181-4950@indico.math.cnrs.fr
DESCRIPTION:Speakers: Volker Genz (Bochum)\nBernhard Keller introduced max
imal green sequences as a combinatorial tool for computing refined Donalds
on-Thomas invariants in the framework of cluster algebras. Maximal green s
equences furthermore can be used to prove the existence of nice bases of c
luster algebras and play a prominent role in the work on the full Fock-Gon
charov conjecture due to Gross-Hacking-Keel-Kontsevich. In Physics\, maxi
mal green sequences appear in the computation of spectra of BPS states. We
report on joint work with Gleb Koshevoy introducing maximal green sequenc
es for certain triangle products of quivers. As an application we comment
on the consequences regarding the full Fock-Goncharov conjecture for doubl
e Bruhat cells.\nJoint work with Gleb Koshevoy.\n\nhttps://indico.math.cnr
s.fr/event/6181/contributions/4950/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6181/contributions/4950/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tracelet Algebras
DTSTART;VALUE=DATE-TIME:20201202T093000Z
DTEND;VALUE=DATE-TIME:20201202T102000Z
DTSTAMP;VALUE=DATE-TIME:20210416T203304Z
UID:indico-contribution-6181-4942@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nicolas Behr (Université de Paris\, IRIF)\nStochast
ic rewriting systems evolving over graph-like structures are a versatile m
odeling paradigm that covers in particular biochemical reaction systems. I
n fact\, to date rewriting-based frameworks such as the Kappa platform [1]
are amongst the very few known approaches to faithfully encode the enormo
us complexity in both molecular structures and reactions exhibited by bioc
hemical reaction systems in living organisms. Since in practice experi
mental constraints permit to track only very limited information about a
given reaction system (typically the concentrations of only a handful of m
olecules)\, a fundamental mathematical challenge arises: which types of in
formation are meaningful to derive and computable from a stochastic rewrit
ing system in view of the limited empirical data? Traditionally\, the mai
n focus of the mathematical theory of stochastic rewriting theory has been
upon the derivation of ODE systems describing the evolution of averages a
nd higher moments of pattern counts (i.e. the concentrations of molecular
species). In this talk\, we present an alternative approach based upon s
o-called tracelets [2]. The latter are the precise mathematical encoding o
f the heuristic notion of pathways in biochemistry. We demonstrate a nove
l mathematical concept of tracelet algebras and highlight a computational
strategy that permits to derive structural\, high level insights into the
dynamics of pattern counts. In view of the focus of CAP on combinatorial a
spects\, we will illustrate this mathematical approach with an analysis of
planar rooted binary trees in a rewriting-based formulation utilizing the
Rémy generator.\n\n[1] Pierre Boutillier et al.\, ”The Kappa platform
for rule-based modeling.”\, Bioinformatics 34.13 (2018): pp. 583-592.\n
\n[2] Nicolas Behr\, ”Tracelets and Tracelet Analysis Of Compositional R
ewriting Systems”\, Electronic Proceedings in Theoretical Computer Scien
ce 323 (2020)\, pp. 44-71.\n\nhttps://indico.math.cnrs.fr/event/6181/contr
ibutions/4942/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6181/contributions/4942/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Unifying Colour $SU(3)$ with ${\\mathbb Z}_3$-Graded Lorentz-Poinc
aré Algebra
DTSTART;VALUE=DATE-TIME:20201203T162000Z
DTEND;VALUE=DATE-TIME:20201203T171000Z
DTSTAMP;VALUE=DATE-TIME:20210416T203304Z
UID:indico-contribution-6181-4955@indico.math.cnrs.fr
DESCRIPTION:Speakers: Richard Kerner (LPTMC\, Sorbonne Université\, Paris
)\nA generalization of Dirac’s equation is presented\, incorporating the
three-valued colour variable in a way which makes it intertwine
with the Lorentz transformations. We show how the Lorentz-Poincaré gr
oup must be extended to accomodate both $SU(3)$ and the Lorentz transforma
tions. Both symmetries become intertwined\, so that the system can be diag
onalized only after the sixth iteration\, leading to a six-order character
istic equation with complex masses similar to those of the Lee-Wick model.
The spinorial representation of the ${\\mathbb Z}_3$-graded Lorentz algeb
ra is presented\, and its vectorial counterpart acting on a ${\\mathbb Z}_
3$-graded extension of the Minkowski space-time is also constucted. Appli
cation to new formulation of the QCD and its gauge-field content is briefl
y evoked.\n\nhttps://indico.math.cnrs.fr/event/6181/contributions/4955/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6181/contributions/4955/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tropical Convexity\, Mean Payoff Games and Nonarchimedean Convex P
rogramming
DTSTART;VALUE=DATE-TIME:20201203T090000Z
DTEND;VALUE=DATE-TIME:20201203T095000Z
DTSTAMP;VALUE=DATE-TIME:20210416T203304Z
UID:indico-contribution-6181-4956@indico.math.cnrs.fr
DESCRIPTION:Speakers: Stéphane Gaubert (INRIA and CMAP Ecole Polytechniqu
e)\nConvex sets can be defined over ordered fields with a non-archimedean
valuation. Then\, tropical convex sets arise as images by the valuation of
non-archimedean convex sets. The tropicalization of polyhedra and spectra
hedra are of special in- terest\, since they can be described in terms of
deterministic and stochastic games with mean payoff. In that way\, one get
s a correspondence between classes of zero- sum games\, with an unsettled
complexity\, and classes of semilagebraic convex op- timization problems o
ver non-archimedean fields. We shall discuss applications of this correspo
ndence\, including a counter example concerning the complexity of interior
point methods\, and the fact that non-archimedean spectrahedra have preci
sely the same images by the valuation as convex semi-algebraic sets. This
is based on works with Allamigeon\, Benchimol\, Joswig and Skomra.\n\nhttp
s://indico.math.cnrs.fr/event/6181/contributions/4956/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6181/contributions/4956/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dialogue Games and Logical Proofs in String Diagrams
DTSTART;VALUE=DATE-TIME:20201202T103000Z
DTEND;VALUE=DATE-TIME:20201202T112000Z
DTSTAMP;VALUE=DATE-TIME:20210416T203304Z
UID:indico-contribution-6181-4943@indico.math.cnrs.fr
DESCRIPTION:Speakers: Paul-André Melliès (Université de Paris\, IRIF)\n
After a short introduction to the functorial approach to logical proofs an
d programs initiated by Lambek in the late 1960s\, based on the notion of
free cartesian closed category\, we will describe a recent convergence wit
h the notion of ribbon category introduced in 1990 by Reshetikhin and Tura
ev in their functorial study of quantum groups and knot invariants. The co
nnection between proof theory and knot theory relies on the notion of ribb
on dialogue category\, defined by relaxing the traditional assumption that
duality is involutive in a ribbon category. We will explain first how to
construct the free such dialogue category using a logic of tensor and neg
ation inspired by the work by Girard on linear logic. A coherence theorem
for ribbon dialogue categories will be then established\, which ensures th
at two tensorial proofs are equal precisely when their underlying ribbon t
angles are equivalent modulo deformation. At the end of the talk\, we will
show how to understand these ribbon tangles as interactive Opponent/Playe
r strategies tracking the flow of negation functors in dialogue games. The
resulting diagrammatic description of tensorial proofs as interactive str
ategies is performed in the 3-dimensional language of string diagrams for
monoidal 2-categories (or more generally weak 3-\ncategories) initiated in
the mid 1990s by Street and Verity\, McIntyre and Trimble.\n\nA few refer
ences:\nhttps://www.irif.fr/ ̃mellies/hdr-mellies.pdf\nhttps://www.irif.f
r/ ̃mellies/tensorial-logic/1-game-semantics-in-string-diagrams.pdf\nhttp
s://www.irif.fr/ ̃mellies/papers/lics2018-ribbon-tensorial-logic.pdf\n\nh
ttps://indico.math.cnrs.fr/event/6181/contributions/4943/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6181/contributions/4943/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Untyped Linear Lambda Calculus and the Combinatorics of 3-valent G
raphs
DTSTART;VALUE=DATE-TIME:20201202T123000Z
DTEND;VALUE=DATE-TIME:20201202T132000Z
DTSTAMP;VALUE=DATE-TIME:20210416T203304Z
UID:indico-contribution-6181-4944@indico.math.cnrs.fr
DESCRIPTION:Speakers: Noam Zeilberger (Ecole Polytechnique)\nThe lambda ca
lculus was invented by Church in the late 1920s\, as part of an ambitious
project to build a foundation for mathematics around the concept of functi
on. Although his original system turned out to be logically inconsistent\,
Church was able to extract from it two separate usable systems\, with a t
yped calculus for logic and an untyped calculus for pure computation. Thro
ugh the work of Lawvere and Lambek in the 1970s\, a close connection was e
stablished between typed lambda calculus and the theory of cartesian close
d categories (cccs). Around the same time\, Dana Scott discovered the fir
st non-trivial mathematical models of untyped lambda calculus\, which he l
ater axiomatized using the notion of reflexive object in a ccc. After Jean
-Yves Girard’s formulation of Linear Logic in the 1980s\, some renewed a
ttention was paid to the linear subsystem of lambda calculus\, which has s
imilar relationships with the theory of symmetric monoidal closed categori
es\, in\nparticular untyped linear lambda calculus may be modelled as the
endomorphism operad of a reflexive object in a symmetric closed multicateg
ory. In the talk\, I will analyze a surprising bijection originally presen
ted by Bodini\, Gardy\, and Jacquot (2013) between untyped linear lambda t
erms and rooted 3-valent maps (= 3-valent graphs embedded on oriented surf
aces). Rather than being a mere coincidence\, this bijection appears to b
e part of a deeper connection between the combinatorics of lambda calculus
and the theory of map enumeration initiated by Tutte in the 1960s\, as w
itnessed by a host of correspondences between different natural subsystems
of linear lambda calculus and different natural families of maps.\n\nhttp
s://indico.math.cnrs.fr/event/6181/contributions/4944/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6181/contributions/4944/
END:VEVENT
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