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BEGIN:VEVENT
SUMMARY:Elliptic Curves Associated to Two-loop Graphs
DTSTART;VALUE=DATE-TIME:20201118T162000Z
DTEND;VALUE=DATE-TIME:20201118T171000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4771@indico.math.cnrs.fr
DESCRIPTION:Speakers: Spencer BLOCH (University of Chicago)\nAmplitudes of
one-loop graphs are known to be dilogarithms. What can one say about two-
loop graphs? In a surprising number of cases\, the motive of the second Sy
manzik of a two-loop graph involves (indeed\, the motive is actually built
around) the motive of an elliptic curve\, suggesting some relation betwee
n the amplitude and elliptic polylogarithms. I will discuss a number of ex
amples. This is joint work with C. Doran\, M. Kerr\, and P. Vanhove.\n\nht
tps://indico.math.cnrs.fr/event/4834/contributions/4771/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4771/
END:VEVENT
BEGIN:VEVENT
SUMMARY:New Techniques for Worldline Integration
DTSTART;VALUE=DATE-TIME:20201119T162000Z
DTEND;VALUE=DATE-TIME:20201119T171000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4777@indico.math.cnrs.fr
DESCRIPTION:Speakers: Christian SCHUBERT (Universidad Michoacana de San Ni
colas de Hidalgo)\nThe worldline formalism provides an alternative to Feyn
man diagrams in the construction of amplitudes and effective actions that
shares some of the superior properties of the organization of amplitudes i
n string theory. In particular\, it allows one to write down integral repr
esentations combining the contributions of large classes of Feynman diagra
ms of different topologies. However\, calculating these integrals analytic
ally without splitting them into sectors corresponding to individual diagr
ams poses a formidable mathematical challenge. I will summarize the histor
y and state of the art of this problem\, including some natural connection
s to the theory of Bernoulli numbers and multiple zeta values.\n\nhttps://
indico.math.cnrs.fr/event/4834/contributions/4777/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4777/
END:VEVENT
BEGIN:VEVENT
SUMMARY:2010-2020: a Decade of Quantum Computing
DTSTART;VALUE=DATE-TIME:20201120T103000Z
DTEND;VALUE=DATE-TIME:20201120T112000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4778@indico.math.cnrs.fr
DESCRIPTION:Speakers: Oliver SCHNETZ (FAU Erlangen-Nürnberg)\nSupported b
y Dirk Kreimer\, in 2010 I started analyzing and calculating high loop-ord
er amplitudes in perturbative quantum field theory. The main tools were gr
aphical functions\, generalized single-valued hyperlogarithms (GSVHs)\, an
d the c_2-invariant. I will report on the progress that has been achieved
in the past decade and give a brief account of what might be within reach
(of these techniques) in the future.\n\nhttps://indico.math.cnrs.fr/event/
4834/contributions/4778/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4778/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Solution of $\\phi^4_4$ on the Moyal Space
DTSTART;VALUE=DATE-TIME:20201119T141500Z
DTEND;VALUE=DATE-TIME:20201119T144500Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4775@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alexander Hock (Westfälische Wilhelms-Universität
Münster)\nWe show the exact solution of the self-dual $\\phi^4$-model on
the 4-dimensional Moyal space. Using the results explained in Raimar's tal
k\, an implicitly defined function converges to a Fredholm integral\, whic
h is solved\, for any coupling constant $\\lambda>-\\frac{1}{\\pi}$\, in t
erms of a hypergeometric function. We prove that the interacting model has
spectral dimension $4-2\\frac{\\arcsin(\\lambda\\pi)}{\\pi}$ for $|\\lamb
da|0$ avoids the triviality problem of the $\\phi^4_4$ model on the Moyal
space.\n\nhttps://indico.math.cnrs.fr/event/4834/contributions/4775/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4775/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On a Theorem of Kreimer
DTSTART;VALUE=DATE-TIME:20201118T153000Z
DTEND;VALUE=DATE-TIME:20201118T162000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4770@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marko BERGHOFF (University of Oxford)\nI will report
on joint work with Dirk on his vision of exploring\nquantum fields in out
er space. Our expeditions have so far uncovered an exciting wonderland of
algebraic\, geometric\, and topological relations in a magical galaxy\, po
pulated by Feynman graphs. Its inhabitants seem to play a mysterious game
of hide-and-seek\, hopfing around singularities of various kinds\, all rul
ed by the mighty King Cutkosky.\n\nhttps://indico.math.cnrs.fr/event/4834/
contributions/4770/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4770/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renormalization and Galois Theory
DTSTART;VALUE=DATE-TIME:20201118T123000Z
DTEND;VALUE=DATE-TIME:20201118T132000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4767@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alain CONNES (IHES)\nhttps://indico.math.cnrs.fr/eve
nt/4834/contributions/4767/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4767/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wick Products and Combinatorial Hopf Algebras
DTSTART;VALUE=DATE-TIME:20201116T121000Z
DTEND;VALUE=DATE-TIME:20201116T130000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4755@indico.math.cnrs.fr
DESCRIPTION:Speakers: Kurusch EBRAHIMI-FARD (NTNU Trondheim)\nWick product
s play a central role in both quantum field theory and stochastic calculus
. They originated in Wick’s work from 1950. In this talk we will describ
e Wick products using combinatorial Hopf algebra. Based on joint work with
F. Patras\, N. Tapia\, L. Zambotti.\n\nhttps://indico.math.cnrs.fr/event/
4834/contributions/4755/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4755/
END:VEVENT
BEGIN:VEVENT
SUMMARY:From Complementations on Lattices to Locality
DTSTART;VALUE=DATE-TIME:20201117T103000Z
DTEND;VALUE=DATE-TIME:20201117T112000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4760@indico.math.cnrs.fr
DESCRIPTION:Speakers: Sylvie PAYCHA (Institut für Mathematik Potsdam)\nA
complementation proves useful to separate divergent terms from convergent
terms. Hence the relevance of complementation in the context of renormalis
ation. The very notion of separation is furthermore related to that of loc
ality. We extend the correspondence between Euclidean structures on vector
spaces and orthogonal complementation to a one to one correspondence betw
een a class of locality structures and orthocomplementations on bounded la
ttices. This is joint work with P. Clavier\, Li Guo and Bin Zhang\n\nhttps
://indico.math.cnrs.fr/event/4834/contributions/4760/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4760/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toric Hall Algebras
DTSTART;VALUE=DATE-TIME:20201117T153000Z
DTEND;VALUE=DATE-TIME:20201117T162000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4764@indico.math.cnrs.fr
DESCRIPTION:Speakers: Matt SZCZESNY (Boston University)\nThe process of co
unting extensions in categories yields an associative (and sometimes Hopf)
algebra called a Hall algebra. Applied to the category of Feynman graphs\
, this process recovers the Connes-Kreimer Hopf algebra. Other examples ab
ound\, yielding various combinatorial Hopf algebras. I will discuss joint
work with J. Jun which attaches a Hopf algebra to a projective toric varie
ty X. This Hopf algebra arises as the Hall algebra of a category of cohere
nt sheaves on X locally modeled on n-dimensional skew partitions.\n\nhttps
://indico.math.cnrs.fr/event/4834/contributions/4764/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4764/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Resurgent Trans-series Analysis of Hopf Algebraic Renormalization
DTSTART;VALUE=DATE-TIME:20201119T153000Z
DTEND;VALUE=DATE-TIME:20201119T162000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4776@indico.math.cnrs.fr
DESCRIPTION:Speakers: Gérald DUNNE (University of Connecticut)\nIn the Kr
eimer-Connes Hopf algebraic approach to renormalization\, for certain QFTs
the Dyson-Schwinger equations can be reduced to nonlinear differential eq
uations. I describe methods based on Ecalle's theory of resurgent trans-se
ries to extract non-perturbative information from these Dyson-Schwinger eq
uations. Even in the absence of exact results\, there exist efficient meth
ods to uncover non-perturbative information numerically from perturbative
data.\n\nhttps://indico.math.cnrs.fr/event/4834/contributions/4776/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4776/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hopf-algebraic Renormalization of Multiple Zeta Values and their q
-analogues
DTSTART;VALUE=DATE-TIME:20201117T123000Z
DTEND;VALUE=DATE-TIME:20201117T132000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4761@indico.math.cnrs.fr
DESCRIPTION:Speakers: Dominique MANCHON (CNRS & Université Clermont-Auver
gne)\nMultiple zeta values are real numbers which appeared in depth one an
d two in the work of L. Euler in the Eighteenth century. They first appear
as a whole in the work of J. Ecalle in 1981\, as infinite nested sums. A
systematic study starts one decade later with M. Hoffman\, D. Zagier and M
. Kontsevich\, with multiple polylogarithms and iterated integral represen
tation as a main tool. After a brief historical account\, I'll explain how
a quasi-shuffle compatible definition (by no means unique) can be given t
hrough Connes-Kreimer's Hopf-algebraic renormalization when the nested sum
diverges. I'll also give an account of the more delicate renormalization
of shuffle relations. Finally\, I'll introduce the Ohno-Okuda-Zudilin mode
l of q-analogues for multiple zeta values\, and describe the algebraic str
ucture which governs it.\n\nhttps://indico.math.cnrs.fr/event/4834/contrib
utions/4761/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4761/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cointeracting Bialgebras
DTSTART;VALUE=DATE-TIME:20201117T132000Z
DTEND;VALUE=DATE-TIME:20201117T141000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4762@indico.math.cnrs.fr
DESCRIPTION:Speakers: Loïc FOISSY (Université du Littoral Côte d'Opale)
\nPairs of cointeracting bialgebras recently appears in the literature of
combinatorial Hopf algebras\, with examples based on formal series\, on tr
ees (Calaque\, Ebrahimi-Fard\, Manchon)\, graphs (Manchon)\, posets... We
will give several results obtained on pairs of cointeracting bialgebras: a
ctions on the group of characters\, antipode\, morphisms to quasi-symmetri
c functions... and we will give applications to Ehrhart poylnomials and ch
romatic polynomials.\n\nhttps://indico.math.cnrs.fr/event/4834/contributio
ns/4762/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4762/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Generalized Gross-Neveu Universality Class with Non-abelian Symmet
ry
DTSTART;VALUE=DATE-TIME:20201119T103000Z
DTEND;VALUE=DATE-TIME:20201119T112000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4772@indico.math.cnrs.fr
DESCRIPTION:Speakers: John GRACEY (University of Liverpool)\nWe use the la
rge N expansion to compute d-dimensional critical exponents at O(1/N^3) fo
r a generalization of the Gross-Neveu Yukawa universality class that inclu
des a non-abelian symmetry. Specific groups correspond to certain phase tr
ansitions in condensed matter physics such as graphene. The effect of the
non-abelian symmetry on the exponents is evidenced by the appearance of ra
nk 4 Casimirs in the higher order 1/N analytic corrections. These in effec
t tag the light-by-light diagrams. The main benefit of the final expressio
ns for the exponents is that one can recover previous results for a variet
y of universality classes in various limits.\n\nhttps://indico.math.cnrs.f
r/event/4834/contributions/4772/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4772/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dirk Kreimer through my Looking Glass
DTSTART;VALUE=DATE-TIME:20201120T132000Z
DTEND;VALUE=DATE-TIME:20201120T141000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4780@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marc BELLON (LPTHE (Sorbonne Université))\nFor the
last 13 years\, my research activities have been largely influenced by Dir
k Kreimer’s research. I will the speak of the prehistory\, the actuality
and the future of this influence.\n\nhttps://indico.math.cnrs.fr/event/48
34/contributions/4780/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4780/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spaces of Graphs\, Tori and Other Flat Gamma-complexes
DTSTART;VALUE=DATE-TIME:20201118T103000Z
DTEND;VALUE=DATE-TIME:20201118T112000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4766@indico.math.cnrs.fr
DESCRIPTION:Speakers: Karen VOGTMANN (University of Warwick)\nSpaces of fi
nite graphs play a key role in perturbative quantum field theory\, but als
o in many other areas of science and mathematics. Among these is geometric
group theory\, where they are used to model groups of automorphism of fre
e groups. Graphs can be thought of as 1-dimensional flat metric spaces.In
higher dimensions\, spaces of flat n-dimensional tori model automorphism
groups of free abelian groups.There are very interesting groups which inte
rpolate between free groups and free abelian groups\, called right-angled
Artin groups. I will describe a space of “Gamma-complexes”\, which are
a hybrid of tori and graphs\, and which model automorphism groups of righ
t-angled Artin groups\, by recent joint work with Bregman and Charney.\n\n
https://indico.math.cnrs.fr/event/4834/contributions/4766/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4766/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tasmanian Adventures
DTSTART;VALUE=DATE-TIME:20201120T162000Z
DTEND;VALUE=DATE-TIME:20201120T171000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4783@indico.math.cnrs.fr
DESCRIPTION:Speakers: David BROADHURST (The Open University)\nI report on
two adventures with Dirk Kreimer in Tasmania\, 25 years ago. One of these\
, concerning knots\, is not even wrong. The other\, concerning a conjectur
al 4-term relation\, is either wrong or right. I suggest that younger coll
eagues have powerful tools that might be brought to bear on this 4-term co
njecture.\n\nhttps://indico.math.cnrs.fr/event/4834/contributions/4783/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4783/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Classical Gravity at High Precision
DTSTART;VALUE=DATE-TIME:20201120T153000Z
DTEND;VALUE=DATE-TIME:20201120T162000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4782@indico.math.cnrs.fr
DESCRIPTION:Speakers: Johannes BLÜMLEIN (DESY Zeuthen)\nWe report on rece
nt progress in post-Newtonian precision calculations for the motion of con
servative binary gravitating systems.\n\nhttps://indico.math.cnrs.fr/event
/4834/contributions/4782/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4782/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renormalization Hopf Algebras and Gauge Theories: an Overview
DTSTART;VALUE=DATE-TIME:20201116T140000Z
DTEND;VALUE=DATE-TIME:20201116T145000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4756@indico.math.cnrs.fr
DESCRIPTION:Speakers: Walter van SUIJLEKOM (Radboud Universiteit Nijmegen
)\nWe give an overview of the Hopf algebraic approach to renormalization\,
with a focus on gauge theories. We illustrate this with Kreimer's gauge t
heory theorem from 2006 and sketch a proof. It relates Hopf ideals generat
ed by Slavnov-Taylor identities to the Hochschild cocycles that are given
by grafting operators.\n\nIn the second part of the talk I will briefly pr
esent Kreimer's unexpected influence on noncommutative geometry via my mor
e recent research. In joint work with Teun van Nuland we uncover a rich st
ructure of the spectral action functional. We express its Taylor expansion
in an inner perturbation in terms of Yang-Mills and Chern-Simons forms in
tegrated against even Hochschild and odd cyclic cocycles\, respectively.\n
\nhttps://indico.math.cnrs.fr/event/4834/contributions/4756/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4756/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogoliubov Type Recursions for Renormalisation in Regularity Struc
tures
DTSTART;VALUE=DATE-TIME:20201116T162000Z
DTEND;VALUE=DATE-TIME:20201116T171000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4759@indico.math.cnrs.fr
DESCRIPTION:Speakers: Yvain BRUNED (University of Edinburgh)\nHairer's re
gularity structures transformed the solution theory of singular stochastic
partial differential equations. The notions of positive and negative reno
rmalisation are central and the intricate interplay between these two reno
rmalisation procedures is captured through the combination of cointeractin
g bialgebras and an algebraic Birkhoff-type decomposition of bialgebra mor
phisms. We will revisit the latter by defining Bogoliubov-type recursions
similar to Connes and Kreimer's formulation of BPHZ renormalisation. This
is a joint work with Kurusch Ebrahimi-Fard.\n\nhttps://indico.math.cnrs.fr
/event/4834/contributions/4759/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4759/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geometrical Splitting and Reduction of N-point Feynman Diagrams
DTSTART;VALUE=DATE-TIME:20201116T130000Z
DTEND;VALUE=DATE-TIME:20201116T134500Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4757@indico.math.cnrs.fr
DESCRIPTION:Speakers: Andrei Davydychev (Moscow State University)\nA geom
etrical approach to the calculation of N-point Feynman diagrams is reviewe
d. It is shown how the geometrical splitting of N-point diagrams can be us
ed to simplify the parametric integrals and reduce the number of variables
in the occurring functions. Moreover\, such a splitting yields useful con
nections between Feynman integrals with different momenta and masses. Calc
ulation of the one-loop two-\, three-and four-point functions in general k
inematics is presented. The work on this approach was started in the 1990s
in Tasmania\, within a project where Bob Delbourgo and Dirk Kreimer were
involved.\n\nhttps://indico.math.cnrs.fr/event/4834/contributions/4757/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4757/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the enumerative structures in QFT
DTSTART;VALUE=DATE-TIME:20201117T141500Z
DTEND;VALUE=DATE-TIME:20201117T144500Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4769@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ali Assem Mahmoud (University of Waterloo)\nThe aim
of this talk is to display some enumerative results that are directly appl
ied in quantum field theory. We shall see how the number of connected chor
d diagrams can be used to count one-particle-irreducible (1PI) diagrams in
Yukawa theory. This translation of Feynman diagrams simplified the proces
s of calculating the asymptotic behaviour of the corresponding Green funct
ions.\n\nhttps://indico.math.cnrs.fr/event/4834/contributions/4769/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4769/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Solvable Dyson-Schwinger Equations
DTSTART;VALUE=DATE-TIME:20201119T123000Z
DTEND;VALUE=DATE-TIME:20201119T132000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4773@indico.math.cnrs.fr
DESCRIPTION:Speakers: Raimar WULKENHAAR (Westfälische Wilhelms-Universit
ät Münster)\nDyson-Schwinger equations provide one of the most powerful
non-perturbative approaches to quantum field theories. The quartic analogu
e of the Kontsevich model is a toy model for QFT in which the tower of Dys
on-Schwinger equations splits into one non-linear equation for the planar
two-point function and an infinite hierarchy of affine equations for all o
ther functions. The non-linear equation admits a purely algebraic solution
\, identified through insight from perturbation theory. The affine equatio
ns turn out to be affiliated with (and solved by) a universal structure in
complex algebraic geometry: blobbed topological recursion. As such they c
onnect to the geometry of the moduli space of complex curves.\n\nhttps://i
ndico.math.cnrs.fr/event/4834/contributions/4773/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4773/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Connes-Kreimer Hopf Algebras : from Renormalisation to Tensor Mode
ls and Topological Recursion
DTSTART;VALUE=DATE-TIME:20201119T132000Z
DTEND;VALUE=DATE-TIME:20201119T141000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4774@indico.math.cnrs.fr
DESCRIPTION:Speakers: Thomas KRAJEWSKI (CPT Aix-Marseille)\nAt the turn of
the millenium\, Connes and Kreimer introduced Hopf algebras of trees and
graphs in the context of renormalisation. We will show how the latter can
be used to formulate the analogue of Virasoro constraints for random tenso
rs\, which are natural generalisations of random matrices. Motivated by th
is example\, we will also sketch how these algebras appear in the formulat
ion of topological recursion proposed by Kontsevich and Soibelman.\n\nhttp
s://indico.math.cnrs.fr/event/4834/contributions/4774/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4774/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Random Loops and T-algebras
DTSTART;VALUE=DATE-TIME:20201116T153000Z
DTEND;VALUE=DATE-TIME:20201116T162000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4758@indico.math.cnrs.fr
DESCRIPTION:Speakers: Martin HAIRER (Imperial College London)\nThe stochas
tic quantization of the 1d non-linear sigma model (i.e. the natural Langev
in dynamic on loop space) naturally leads to the study of an algebraic str
ucture we call a T-algebra. We will discuss how they arise\, a few of thei
r properties\, as well as a concrete example of their application.\n\nhttp
s://indico.math.cnrs.fr/event/4834/contributions/4758/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4758/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cohomology of Graph Complexes\, Invariant Differential Forms and F
eynman Periods
DTSTART;VALUE=DATE-TIME:20201118T132000Z
DTEND;VALUE=DATE-TIME:20201118T141000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4768@indico.math.cnrs.fr
DESCRIPTION:Speakers: Francis BROWN (University of Oxford)\nKontsevich int
roduced the graph complex $GC_2$ in 1993 and raised the problem of determi
ning its cohomology. This problem is of renewed importance following the r
ecent work of Chan-Galatius-Payne\, who related it to the cohomology of th
e moduli spaces $M_g$ of curves of genus $g$. It is known by Willwacher th
at the cohomology of $GC_2$ in degree zero is isomorphic to the Grothendi
eck-Teichmuller Lie algebra $grt$\, but in higher degrees\, there are infi
nitely many classes which are mysterious and have no such interpretation.\
n\nIn this talk\, I will define algebraic differential forms on a moduli s
pace of graphs (outer space). Such a form is a map which assigns to every
graph an algebraic differential form of fixed degree\, satisfying some com
patibilities. Using the tropical Torelli map\, I will construct an infinit
e family of such differential forms\, which can in turn be integrated over
cells. Surprisingly\, these integrals are always finite\, and therefore o
ne can assign numbers to homology classes in the graph complex. They turn
out to be Feynman periods in phi^4 theory\, and can be used to detect gr
aph homology classes.\n\nThe upshot of all this is a new connection betwee
n graph cohomology\, Feynman integrals and motivic Galois groups. I will c
onclude with a conjectural explanation for the higher degree classes in gr
aph cohomology.\n\nhttps://indico.math.cnrs.fr/event/4834/contributions/47
68/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4768/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Euler Characteristic of Out(F_n) and the Hopf Algebra of Graph
s
DTSTART;VALUE=DATE-TIME:20201120T123000Z
DTEND;VALUE=DATE-TIME:20201120T132000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4779@indico.math.cnrs.fr
DESCRIPTION:Speakers: Michael BORINSKY (Nikhef)\nIn their 1986 work\, Har
er and Zagier gave an expression for the Euler characteristic of the modul
i space of curves\, M_gn\, or equivalently the mapping class group of a su
rface. Recently\, in joint work with Karen Vogtmann\, we performed a simil
ar analysis for Out(Fn)\, the outer automorphism group of the free group\,
or equivalently the moduli space of graphs. This analysis settles a 1987
conjecture on the Euler characteristic and indicates the existence of larg
e amounts of homology in odd dimensions for Out(Fn). I will illustrate the
se results and explain how the Hopf algebra of graphs\, based on the works
of Kreimer\, played a key role to transform a simplified version of Harer
and Zagier's argument\, due to Kontsevich and Penner\, from M_gn to Out(F
n). This combined technique can be interpreted as a `renormalized` topolog
ical field theory. I will also report on more recent results on the intege
r Euler characteristic of Out(Fn).\n\nhttps://indico.math.cnrs.fr/event/48
34/contributions/4779/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4779/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gauge/Gravity Double Copy from a Lie Bracket on the Shuffle Algebr
a
DTSTART;VALUE=DATE-TIME:20201118T141500Z
DTEND;VALUE=DATE-TIME:20201118T144500Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4763@indico.math.cnrs.fr
DESCRIPTION:Speakers: Hadleigh Frost (University of Oxford)\nThe 'field th
eory KLT' or 'double copy' relations express gravity amplitudes in terms o
f gauge theory partial amplitudes. I present an elementary proof of these
identities\, using only the properties of Lie polynomials and the shuffle
algebra. The work completes a project sketched by M Kapranov in 2012\, and
is joint with C Mafra.\n\nhttps://indico.math.cnrs.fr/event/4834/contribu
tions/4763/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4763/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tree-like Equations from the Connes-Kreimer Hopf Algebra and the C
ombinatorics of Chord Diagrams
DTSTART;VALUE=DATE-TIME:20201120T141500Z
DTEND;VALUE=DATE-TIME:20201120T144500Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4781@indico.math.cnrs.fr
DESCRIPTION:Speakers: Lukas Nabergall (University of Waterloo)\nWe describ
e how certain analytic Dyson-Schwinger equations and related tree-like equ
ations arise from the universal property of the Connes-Kreimer Hopf algebr
a applied to Hopf subalgebras obtained from combinatorial Dyson-Schwinger
equations in the work of Foissy. We then show how these equations can be s
olved as weighted generating functions of certain classes of chord diagram
s and obtain an explicit formula counting some of these combinatorial obje
cts.\n\nhttps://indico.math.cnrs.fr/event/4834/contributions/4781/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4781/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Categorical Interactions in Algebra\, Geometry and Physics: Cubica
l Structures and Truncations.
DTSTART;VALUE=DATE-TIME:20201117T162000Z
DTEND;VALUE=DATE-TIME:20201117T171000Z
DTSTAMP;VALUE=DATE-TIME:20210623T030346Z
UID:indico-contribution-4834-4765@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ralph KAUFMANN (Purdue University)\nThere are severa
l interactions between algebra and geometry coming from polytopic complexe
s as for instance demonstrated by several versions of Deligne's conjecture
. These are related through blow-ups or truncations. The polytopes and the
ir truncations also appear naturally as regions of integration for product
s\, which is an area of active study. Two fundamental polytopes are cubes
and simplices. The importance of cubes as a basic appears naturally in var
ious situations on which we will concentrate. In particular\, we will disc
uss cubical Feynman categories\, which afford a W-construction that is a c
ubical\ncomplex. \nThese relate combinatorics to geometry. Furthermore usi
ng categorical notions of push-forwards\, we show how to naturally constru
ction Moduli Spaces of curves and several of their compactifications. The
combinatorial ingredients are graphs and there is a universal way of decor
ating them to study different types. This makes the theory applicable to s
everal different geometries appearing in Moduli Spaces and Outer space. Wi
th respect to physics\, there is an additional relationship coming through
Hopf algebras which in turn also are related to multiple zeta values.\nWe
will discuss these constructions and relations on concrete examples.\n\nh
ttps://indico.math.cnrs.fr/event/4834/contributions/4765/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4765/
END:VEVENT
END:VCALENDAR