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BEGIN:VEVENT
SUMMARY:FIRE6: Feynman Integral REduction with Modular Arithmetic
DTSTART;VALUE=DATE-TIME:20190318T100000Z
DTEND;VALUE=DATE-TIME:20190318T110000Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2830@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Alexander Smirnov (Moscow State University)\nFIRE is
a program performing reduction of Feynman integrals to master integrals.
The C++ version FIRE was presented in 2014. There have been multiple chang
es and upgrades since then including the possibility to use multiple compu
ters for one reduction task and to perform reduction with modular arithmet
ic. The goal of this talk is to present the current version of FIRE that i
s 6.2.\n\nhttps://indico.mitp.uni-mainz.de/event/179/contributions/2830/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2830/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Four-loop quark form factor with quartic fundamental colour factor
DTSTART;VALUE=DATE-TIME:20190318T130000Z
DTEND;VALUE=DATE-TIME:20190318T133000Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2831@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Vladimir Smirnov (Moscow State University)\nAn analy
tical result for the four-loop QCD corrections for the colour structure (d
abcdF)^2 to the massless non-singlet quark form factor is obtained.\nThe e
valuation involves non-trivial non-planar integrals diagrams with master i
ntegrals in the top sector. To evaluate the master integrals second mass s
cale is introduced and the corresponding differential equations are solved
with respect to the ratio of the two scales. Analytical results for the c
usp and collinear anomalous dimensions\, and the finite part of the form f
actor are presented.\n\nhttps://indico.mitp.uni-mainz.de/event/179/contrib
utions/2831/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2831/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The algebraic Mellin transform\, after Loeser and Sabbah
DTSTART;VALUE=DATE-TIME:20190319T130000Z
DTEND;VALUE=DATE-TIME:20190319T134500Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2826@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Thomas Bitoun (University of Toronto)\nWe will prese
nt the essentials of Loeser and Sabbah's theory of the Mellin transform fo
r D-modules. It is a fundamental ingredient in our work with Bogner\, Klau
sen and Panzer on Feynman integral relations from parametric annihilators.
In particular\, for a holonomic D-module M\, we will express the dimensio
n of its Mellin transform as the Euler characteristic of M. We will not as
sume any prior knowledge of D-module theory\, so the talk should be access
ible to non-specialists.\n\nhttps://indico.mitp.uni-mainz.de/event/179/con
tributions/2826/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2826/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Counting master integrals with PSLQ
DTSTART;VALUE=DATE-TIME:20190319T141500Z
DTEND;VALUE=DATE-TIME:20190319T151500Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2828@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Stefano Laporta ()\nIn this talk I describe the use
of the integer relation algorithm PSLQ to determine with high reliability
the number of independent (master) integrals for some troublesome topologi
es\, using the Baikov representation.\n\nhttps://indico.mitp.uni-mainz.de/
event/179/contributions/2828/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2828/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laporta algorithm for multi-loop vs multi-scale problems
DTSTART;VALUE=DATE-TIME:20190318T083000Z
DTEND;VALUE=DATE-TIME:20190318T093000Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2829@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Johann Usovitsch (Trinity College Dublin)\nhttps://i
ndico.mitp.uni-mainz.de/event/179/contributions/2829/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2829/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Integration-by-parts reductions via unitarity cuts and syzygies
DTSTART;VALUE=DATE-TIME:20190320T083000Z
DTEND;VALUE=DATE-TIME:20190320T093000Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2832@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Kasper Larsen (University of Southampton)\nIn this t
alk I will discuss a new approach for generating integration-by-parts redu
ctions of Feynman integrals. The approach makes use of ideas from modern u
nitarity and from algebraic geometry\, which I will explain. I then demons
trate the power of the approach by performing fully analytically IBP reduc
tions relevant for two-loop five-gluon scattering in QCD. I will also disc
uss Azurite\, a publicly available code for providing bases of loop integr
als.\n\nhttps://indico.mitp.uni-mainz.de/event/179/contributions/2832/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2832/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Differential Reduction of Feynman Diagrams: status and perspective
DTSTART;VALUE=DATE-TIME:20190321T100000Z
DTEND;VALUE=DATE-TIME:20190321T110000Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2838@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Mikhail Kalmykov ()\nWe point out that the Mellin-Ba
rnes representation of Feynman Diagrams can be used for getting homogeneou
s system of linear differential equations of hypergeometric types. This se
t of equations are enough for reduction of original diagrams to some basis
with the following construction of coefficients of epsilon-expansion.\n\n
https://indico.mitp.uni-mainz.de/event/179/contributions/2838/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2838/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polynomials associated to graphs\, matroids\, and configurations
DTSTART;VALUE=DATE-TIME:20190322T083000Z
DTEND;VALUE=DATE-TIME:20190322T093000Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2841@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Mathias Schulze (Technische Universität Kaiserslaut
ern)\nKirchhoff (Symanzik) polynomials are obtained from a graph as a sum
of monomials corresponding to (non-)spanning trees. They are of particular
importance in physics in the case of Feynman graphs. One can consider the
m as special cases of matroid (basis) polynomials or of configuration poly
nomials. However the latter two generalizations differ in case of non-regu
lar matroids. This more general point of view has the advantage that the c
lasses of matroids and configurations are stable under additional operatio
ns such as duality and truncation. In addition there are important configu
ration polynomials\, such as the second graph polynomial\, which are not o
f Kirchhoff type. I will give an introduction to the topic and present new
results relating the algebro-geometric structure of the singular locus of
configuration hypersurfaces to the structure of the underlying matroid. T
heir proofs make essential use of matroid theory and\, in particular\, rel
y on duality.\n\nhttps://indico.mitp.uni-mainz.de/event/179/contributions/
2841/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2841/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reduction of multiloop Feynman integrals: an O(N) algorithm
DTSTART;VALUE=DATE-TIME:20190322T130000Z
DTEND;VALUE=DATE-TIME:20190322T140000Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2842@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Yan-Qing Ma (Peking University\, Beijing)\nWe modify
Feynman integrals by introducing an auxiliary parameter \\eta into each F
eynman propagator. The modified Feynman integrals are analytical functions
of \\eta\, and physical Feynman integrals can be obtained by taking \\eta
-> 0^+. Asymptotic expansions of the modified Feynman integrals at \\eta
-> \\infinity can be very easily calculated\, which contain only equal-mas
s vacuum integrals. Due to uniqueness theorem of analytical functions\, th
e asymptotic series determine both values of physical Feynman integrals an
d their linear relations. Based on the asymptotic expansion\, we construct
an algorithm to generate linear relations that can reduce arbitrary multi
-loop Feynman integral to master integrals. Computation complexity of nume
rically solving these linear relations is O(N) when the number of linear e
quations N is large. Our method may overcome the difficulty of IBP method\
, where linear equations are coupled and thus computation complexity is O(
N^3).\n\nhttps://indico.mitp.uni-mainz.de/event/179/contributions/2842/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2842/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Direct Reduction of Amplitude
DTSTART;VALUE=DATE-TIME:20190322T140000Z
DTEND;VALUE=DATE-TIME:20190322T143000Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2843@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Najam ul Basat (Chinese Academy of Sciences\, Beijin
g)\nWe propose an alternative approach based on series representation to d
irectly reduce multi-loop multi-scale scattering amplitude into set of fre
ely chosen master integrals. And this approach avoid complicated calculati
ons of inverse matrix and dimension shift for tensor reduction calculation
. During this procedure we further utilize the Feynman parametrization to
calculate the coefficients of series representation and obtain the form fa
ctors. Conventional methodologies are used only for scalar vacuum bubble i
ntegrals to finalize the result in series representation form. Finally\, w
e elaborate our approach by presenting the reduction of a typical two-loop
amplitude for W boson production.\n\nhttps://indico.mitp.uni-mainz.de/eve
nt/179/contributions/2843/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2843/
END:VEVENT
BEGIN:VEVENT
SUMMARY:direct solutions & conjugate polynomials
DTSTART;VALUE=DATE-TIME:20190322T100000Z
DTEND;VALUE=DATE-TIME:20190322T110000Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2845@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: David Kosower (Institut de Physique Théorique\, CEA
\, CNRS\, Université Paris-Saclay)\nhttps://indico.mitp.uni-mainz.de/even
t/179/contributions/2845/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2845/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Feynman Integrals and Intersection Theory
DTSTART;VALUE=DATE-TIME:20190320T130000Z
DTEND;VALUE=DATE-TIME:20190320T140000Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2834@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Pierpaolo Mastrolia (Padua University)\nI will discu
ss how intersection theory controls the algebra of Feynman integrals\, and
show how their direct decomposition onto a basis of master integrals can
by achieved by projection\, using intersection numbers. After introducing
a few basics concepts of intersection theory\, I will show the application
of this novel method\, first\, to special mathematical functions\, and\,
later\, to Feynman integrals on the maximal cuts\, also explaining how dif
ferential equations and dimensional recurrence relations for master integr
als can be directly built by means of intersection numbers. The presented
method exposes the geometric structure beneath Feynman integrals\, and off
ers the computational advantage of bypassing the system-solving strategy c
haracterizing the reduction algorithms based on integration-by-parts ident
ities.\n\nhttps://indico.mitp.uni-mainz.de/event/179/contributions/2834/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2834/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Feynman integral relations from Parametric annihilators
DTSTART;VALUE=DATE-TIME:20190319T134500Z
DTEND;VALUE=DATE-TIME:20190319T141500Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2848@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Erik Panzer ()\nhttps://indico.mitp.uni-mainz.de/eve
nt/179/contributions/2848/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2848/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kite diagram through Symmetries of Feynman Integrals
DTSTART;VALUE=DATE-TIME:20190321T144500Z
DTEND;VALUE=DATE-TIME:20190321T151500Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2840@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Subhajit Mazumdar ()\nThe Symmetries of Feynman Inte
grals (SFI) is a method for evaluating Feynman Integrals which exposes a n
ovel continuous group associated with the diagram which depends only on it
s topology and acts on its parameters. Using this method we study the kite
diagram\, a two-loop diagram with two external legs\, with arbitrary mass
es and spacetime dimension. Generically\, this method reduces a Feynman in
tegral into a line integral over simpler diagrams. We identify a locus in
parameter space where the integral further reduces to a mere linear combin
ation of simpler diagrams\, thereby maximally generalizing the known massl
ess case.\n\nhttps://indico.mitp.uni-mainz.de/event/179/contributions/2840
/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2840/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Constructing multi-loop scattering amplitudes with manifest singul
arity structure
DTSTART;VALUE=DATE-TIME:20190318T133000Z
DTEND;VALUE=DATE-TIME:20190318T140000Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2846@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Robert Schabinger (Michigan State University)\nThe i
nfrared exponentiation properties of dimensionally-regularized multi-loop
scattering amplitudes are typically hidden at the level of the integrand\,
materializing only after integral evaluation. In this talk\, we provide e
vidence that this long-standing problem may be addressed by introducing an
appropriate integral basis which is simultaneously finite and uniform wei
ght.\n\nhttps://indico.mitp.uni-mainz.de/event/179/contributions/2846/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2846/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Algorithmic approaches to syzygies for no-dot or no-numerator rela
tions
DTSTART;VALUE=DATE-TIME:20190320T140000Z
DTEND;VALUE=DATE-TIME:20190320T150000Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2836@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Andreas von Manteuffel (Michigan State University)\n
The calculation of syzygies for the generation of linear relations between
Feynman integrals can be challenging for state-of-the-art calculations in
quantum chromodynamics. I will discuss how basic linear algebra methods c
an be employed to efficiently compute the relevant syzygies for different
applications: relations in the Baikov representation which avoid squared p
ropagators (“dots”) and relations in the Lee-Pomeransky representation
which avoid numerators. In the latter case I will discuss applications fo
r relations involving also higher order differential operators.\n\nhttps:/
/indico.mitp.uni-mainz.de/event/179/contributions/2836/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2836/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Computer algebra and ring theory help Feynman integrals
DTSTART;VALUE=DATE-TIME:20190319T100000Z
DTEND;VALUE=DATE-TIME:20190319T110000Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2825@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Viktor Levandovskyy (RWTH Aachen)\nScientists\, deal
ing with Feynman integrals\, use plenty of algebraic techniques. We will g
ive an overview of appearing algebras\, morphisms between them and localiz
ations in a structured way\, also giving details on the arising algorithmi
c questions and possible realizations of the latter in modern computer alg
ebra systems. If the time allows\, Gel'fand-Kirillov dimension for algebra
s and modules (clarifying the overused notion of "holonomic module") as we
ll as the notion of a holonomic rank (of a localized module) will be expla
ined.\n\nhttps://indico.mitp.uni-mainz.de/event/179/contributions/2825/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2825/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Computation of holonomic systems for Feynman amplitudes associated
with some simple diagrams
DTSTART;VALUE=DATE-TIME:20190319T083000Z
DTEND;VALUE=DATE-TIME:20190319T093000Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2824@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Toshinori Oaku (Tokyo Woman's Christian University)\
nHolonomic systems are a class of systems of linear (partial or ordinary)
differential equations. One of the most fundamental properties of a holono
mic system is that its solution space is finite-dimensional. \n\nA Feynman
amplitude is the integral of a rational function\, or more generally\, th
e product of complex powers of polynomials. \nHence we can\, in principle\
, apply the following two facts in (computational) $D$-module theory: \n\n
1.\nFor (multivariate) polynomials $f_1\,\\dots\,f_d$ and complex numbers
$\\lambda_1\,\\dots\,\\lambda_d$\, the multi-valued analytic function $f_1
^{\\lambda_1}\\cdots f_d^{\\lambda_d}$ satisfies a holonomic system\, whic
h can be computed algorithmically. \n\n2.\nIf a function satisfies a holon
omic system\, its integral with respect to some of its variables also sati
sfies a holonomic system\, which can be computed algorithmically. \n\nIn t
he integration\, it would also be natural to ragard the integrand as a loc
al cohomology class associated with $f_1\,\\dots\,f_d$\, which roughly cor
responds to the 'residue' of \n$f_1^{\\lambda_1}\\cdots f_d^{\\lambda_d}$
at $\\lambda_1 = \\cdots = \\lambda_d = -1$ (at least in positive mass cas
e for external diagrams). \nThere are also algorithms for computing a holo
nomic system for such a cohomology class. \nHowever\, actual computation\,
especially of integration\, is hard in general because of the complexity.
\nI shall present some worked out examples together with an interpretatio
n based on microlocal analysis.\n\nhttps://indico.mitp.uni-mainz.de/event/
179/contributions/2824/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2824/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Functional reduction of Feynman integrals
DTSTART;VALUE=DATE-TIME:20190321T130000Z
DTEND;VALUE=DATE-TIME:20190321T140000Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2839@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Oleg Tarasov (Joint Institute for Nuclear Research\,
Dubna)\nA method for reducing Feynman integrals\, depending on \nseveral
kinematic variables and masses\, to a combination of\nintegrals with fewe
r variables is proposed. The method is based on iterative application of f
unctional equations proposed by the author. The reduction of the one-loop
scalar triangle\, box and pentagon integrals with massless internal propag
ators to simpler integrals will be described.\n\nThe triangle integral dep
ending on three variables is represented as a sum over three integrals dep
ending on two variables. By solving the dimensional recurrence relations f
or these integrals\, an analytic expression in terms of the $_2F_1$ Gauss
hypergeometric function and the logarithmic function was derived.\n\nBy us
ing the functional equations\, the one-loop box integral with \nmassless i
nternal propagators\, which depends on six kinematic variables\, was expre
ssed as a sum of 12 terms. These terms are proportional to the same integr
al depending only on three variables different for each term. For this int
egral with three variables\, an analytic result in terms of the $F_1$ App
ell and $_2F_1$ Gauss hypergeometric functions was derived by solving the
recurrence relation with respect to the spacetime dimension $d$. The redu
ction equations for the box integral with some kinematic variables equal
to zero are considered.\n\nWith the help of three step functional reductio
n the one-loop pentagon integral with massless propagators\, which depends
on 10 variables was reduced to a combination of 60 integrals depending on
4 variables. The on-shell pentagon integral depending on 5 variables was
reduced to 15 integrals depending on 3 variables. For the integrals with 3
variables an analytic result in terms of the $F_3$ Appell and $_2F_1$ Gau
ss hypergeometric functions was obtained.\n\nhttps://indico.mitp.uni-mainz
.de/event/179/contributions/2839/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2839/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Symmetries of Feynman Integrals: a new theory for FI evaluation
DTSTART;VALUE=DATE-TIME:20190321T140000Z
DTEND;VALUE=DATE-TIME:20190321T144500Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2864@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Barak Kol (The Racah Institute of Physics)\nSymmetri
es of Feynman Symmetries (SFI) is a general theory for the evaluation of F
eynman diagrams\, which is related to both IBP and DE. For any given diagr
am topology it defines a set of partial differential equations in terms of
the most general parameters - masses and kinematical invariants. The equa
tion system is associated with a group G whose orbits foliate the paramete
r space. The general integral is shown to reduce to its value at convenien
tly chosen parameters on the same G-orbit plus a line integral over simple
r diagrams - diagrams with one propagator contracted. Additional aspects o
f the theory and some applications will be discussed.\n\nhttps://indico.mi
tp.uni-mainz.de/event/179/contributions/2864/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2864/
END:VEVENT
BEGIN:VEVENT
SUMMARY:L-loop watermelon and sunrise graphs: differential equations\, ind
ex and dimension shifting relations\, and quadratic constraints
DTSTART;VALUE=DATE-TIME:20190321T083000Z
DTEND;VALUE=DATE-TIME:20190321T093000Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2837@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Roman Lee (Budker Institute of Nuclear Physics\, Nov
osibirsk)\nWe derive reduction formulae\, differential equations and dimen
sional recurrence relations for $L$-loop two-point massive tadpoles and su
nrises with arbitrary masses and regularized both dimensionally and analyt
ically. The differential system obtained has a Pfaff form and can be turne
d into $(\\epsilon+\\tfrac{1}{2})$-form when the analytic regularization i
s removed. For odd $d$ this form allows us to present coefficients of $\\e
psilon$-expansion explicitly in terms of Goncharov's polylogarithms. Using
the symmetry properties of the matrix in the right-hand side of the diffe
rential system\, we obtain quadratic constraints for the solutions of the
obtained differential system near any integer $d$.\n\nhttps://indico.mitp.
uni-mainz.de/event/179/contributions/2837/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2837/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Integrand reduction for particles with spins
DTSTART;VALUE=DATE-TIME:20190318T140000Z
DTEND;VALUE=DATE-TIME:20190318T143000Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2847@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Hui Luo ()\nScattering amplitudes with spinning part
icles are shown to decompose into multiple copies of simple building block
s to all loop orders\, which can be used to efficiently reduce these ampli
tudes to sums over scalar integrals. For example\, analytic results could
be obtained for the five gluon\, two loop\, and four gluon\, three loop pl
anar scattering amplitudes in pure Yang-Mills theory as well as for leadin
g singularities to even higher orders.\n\nhttps://indico.mitp.uni-mainz.de
/event/179/contributions/2847/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2847/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Massively Parallel Methods and Other Trends in the Design of Compu
ter Algebra Systems - With a Focus on Feynman Integral Reduction
DTSTART;VALUE=DATE-TIME:20190320T100000Z
DTEND;VALUE=DATE-TIME:20190320T110000Z
DTSTAMP;VALUE=DATE-TIME:20210125T044154Z
UID:indico-contribution-179-2833@indico.mitp.Uni-Mainz.DE
DESCRIPTION:Speakers: Janko Böhm (Technische Universität Kaiserslautern)
\nWith a view toward Feynman Integral Reduction\, I discuss fundamental al
gorithms in commutative algebra as implemented in the open source computer
algebra system Singular. I introduce a highly efficient framework for mas
sively parallel computations in computer algebra\, which combines Singular
with the workflow management system GPI-Space and is based on the idea of
separating coordination and computation. I also give an outlook on the po
tential of cross border methods in the next generation computer algebra sy
stem OSCAR\, which integrates Singular with the systems GAP for group theo
ry\, polymake for polyhedral geometry\, and Antic for number theory. Using
commutative algebra methods\, I address the complete analytic reduction o
f two-loop five-point non-planar hexagon-box integrals with degree-four nu
merators.\n\nhttps://indico.mitp.uni-mainz.de/event/179/contributions/2833
/
LOCATION:Mainz Institute for Theoretical Physics\, Johannes Gutenberg Univ
ersity 02.430
URL:https://indico.mitp.uni-mainz.de/event/179/contributions/2833/
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