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Sorana Scholtes (Max-Planck-Institut für Physik )14/10/2024, 08:30
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Johannes Henn14/10/2024, 09:15
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Ruth Britto (Trinity College Dublin)14/10/2024, 09:30
I will discuss integration contours for integrals over Feynman parameters that reveal discontinuities. I explore their variation in phase space, with a view towards deriving cut relations and understanding sequential discontinuities.
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Eric Pichon-Pharabod14/10/2024, 11:00
The period matrix of a smooth complex projective variety encodes the isomorphism between its singular homology and its algebraic De Rham cohomology. Numerical approximations with sufficient precision of the entries of the period matrix allow to recover some algebraic invariants of the variety, such as the Néron-Severi group in the case of surfaces. In this talk, we will present a method...
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14/10/2024, 13:00
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Clément Dupont14/10/2024, 14:00
Prompted by Arkani-Hamed and Trnka's discovery of the amplituhedra, the concept of positive geometry recently emerged as an important tool in the study of scattering amplitudes and related quantities in physics. Roughly speaking, a positive geometry is a semi-algebraic domain whose boundary structure matches the residue structure of a unique logarithmic form, called its canonical form. The...
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Gaia Fontana (University of Zürich)14/10/2024, 15:00
Reduction of Feynman integrals to a basis of linearly independent master integrals is a crucial step in any perturbative calculation, but also one of its main bottlenecks. In this talk I will present an improvement over the traditional approach to IBP reduction, that exploits transverse integration identities. Given an integral family to be reduced, the key idea is to find sectors whose corner...
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Karen Vogtmann (University of Warwick)14/10/2024, 16:45
A natural setting for studying the n-loop contribution to a Feynman amplitude is the appropriate moduli space of graphs. I will describe these moduli spaces, then explain how methods from both geometric group theory and quantum field theory can be used to explore their structure.
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Bernd Sturmfels15/10/2024, 09:30
We discuss practical methods for computing the space of solutions to an arbitrary homogeneous linear system of partial differential equations with constant coefficients. These rest on the Fundamental Principle of Ehrenpreis-Palamodov from the 1960’s. Our audience will have a chance to gain hands-on experience with primary ideals and the schemes they represent.
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Franziska Porkert (Universität Bonn)15/10/2024, 11:00
Feynman integrals are the building blocks of multi-loop scattering amplitudes and beyond one loop, many Feynman integrals are related to interesting geometries. In this talk, I will focus on Feynman integrals related to hyperelliptic curves and discuss ongoing work on finding canonical differential equations for maximal cuts of such Feynman integrals. This includes new ideas about the...
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Stefan Weinzierl (Universität Mainz)15/10/2024, 13:00
The differential equation for a system of Feynman integrals is encoded in a connection matrix. In this talk I will discuss that a specific choice of master integrals can lead to relations among the entries of the connection matrix. I will discuss self-duality and Galois symmetries.
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Bernd Sturmfels, Diana López-Falcón, Ruth Britto (Trinity College Dublin)15/10/2024, 14:00
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Paul-Hermann Balduf (University of Oxford)15/10/2024, 15:00
A Feynman integral is called "primitive" if it is superficially divergent and does not contain subdivergences. The "period" of a primitive graph is the coefficient of logarithmic energy dependence, or equivalently the simple pole in minimal subtraction. In recent work [2305.13506, 2403.16217] together with Kimia Shaban, we numerically computed the periods of 2 million Feynman integrals in...
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Konstantin Baune (ETH Zürich)15/10/2024, 15:15
Polylogarithms on higher-genus Riemann surfaces are necessary for systematic calculations of certain Feynman integrals and loop amplitudes in string theory. Employing the Schottky uniformization of a Riemann surface we construct higher-genus generating functions of polylogarithmic integration kernels, coinciding with the set of meromorphic differentials defined by Enriquez. This allows for...
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Hadrien Brochet (Inria Saclay)15/10/2024, 15:30
We consider the problem of computing all the linear relations between the integrals of the
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functions lying in a given holonomic D-module. We present in this poster a new integration
algorithm designed for handling multiple integrals of holonomic functions. This novel algorithm can be regarded as both an extension of Lairez’s reduction-based algorithm, which is limited to integrals of... -
Wojciech Flieger (University of Padova)15/10/2024, 15:45
We investigate the D-module structure of Feynman integrals and Euler-Mellin integrals by means of Griffiths theorem. We present first applications to special mathematical functions and one-and two-loop integrals, and discuss the generation of corresponding Pfaffian equation they obey, via Macaulay matrix method.
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Baran Hashemi (Origins Cluster)15/10/2024, 16:00
What happens when we let artificial intelligence tackle mathematical problems? This work explores how Transformer neural networks—initially designed for language processing—can learn and perform tasks in computational Algebraic Geometry. As a result, we introduce a neural network model that approximates psi-class intersection numbers on the moduli space of curves. Through our analysis, we...
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Carlos Rodriguez15/10/2024, 16:15
We study families of hypergeometric integrals given by one-dimensional integrals over a genus-g Riemann surface. These integrals are closely related to string amplitudes at loop-level in the chiral splitting formalism. Watanabe has studied the twisted cohomology of these integrals, and here we explore their twisted homology, with a goal of understanding the double copy at genus g > 1.
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Kajal Singh (Department of Mathematical Sciences, University of Liverpool)15/10/2024, 16:30
Study of correlation functions in AdS/CFT and in-in correlators in de Sitter space often requires the computation of Witten diagrams. Due to the complexity of evaluating radial integrals for these correlators, several indirect approaches have been developed to simplify computations. However, in momentum space, these methods have been limited to fields with integer spin. Here, we formulate...
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Felix Tellander (University of Oxford)15/10/2024, 16:45
I will present a method to calculate the Landau singularities of a Feynman integrals using Whitney stratifications. Whitney stratifications themselves are microlocal in nature, meaning that they naturally do not only live in the space we are stratifying but in the cotangent bundle of this space. With this in mind I introduce a microlocal (or rather distributional) framework for Feynman...
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Saiei Matsubara-Heo16/10/2024, 09:30
Recent years have seen a resurgence of old topics in quantum field theory. One of them is Landau singularity, which should be defined as the singular locus of a Feynman integral. In this talk, we develop a way to understand and compute Landau singularity from the perspective of hypergeometric system, which is a special class of D-modules. This explains why Landau singularity is a natural...
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Claudia Fevola (Inria Saclay)16/10/2024, 11:00
The Euler discriminant describes the locus of coefficients that cause a drop in the Euler characteristic of a very affine variety. In this talk, we focus on the case where the variety is the complement of hyperplanes. I will present formulas for two specific scenarios: when the coefficients are sparse and when they are restricted to a subspace of the parameter space. These formulas enable the...
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16/10/2024, 13:00
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Tobias Huber (Siegen U)16/10/2024, 14:00
Integral reduction based on integration-by-parts (IBP) identities are an indispensable tool for accomplishing higher-order calculations in perturbative quantum field theory. We approach this task from the point-of-view of algebraic geometry by solving the system of IBP equations symbolically. We formulate the problem as a non-commutative rational double-shift algebra Y and a left ideal that...
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Daniel Bath (KU Leuven)16/10/2024, 15:00
The comparison theorems of Grothendieck and Deligne tell us that to compute cohomology of the complement of a hypersurface with constant coefficients one must compute the cohomology of the meromorphic (or rational) de Rham complex. As this complex's objects lack finiteness, one wonders if a subcomplex of forms of order at most one along the hypersurface suffices. In verbiage: does the...
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Qinglin Yang (Max Planck Institute for Physics)16/10/2024, 16:45
In this talk, we will revisit Landau analysis for Feynman Integrals and their singularity study from a new geometrical viewpoint. The first part of the talk is about the foundation of our method. Through interpreting Landau loci by pinching of Schubert solutions, we will be able to uplift Landau singularities of an integral to its symbol letters automatically, and see our previous conjectural...
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Martina Juhnke17/10/2024, 09:30
A cosmological polytope is defined for a given Feynman diagram, and its canonical
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form may be used to compute the contribution of the Feynman diagram to the wavefunction of certain cosmological models. Given a subdivision of a polytope, its canonical form is obtained as a sum of the canonical forms of the facets of the subdivision. The goal of this talk to report on specific types of... -
Khazhgali Kozhasov (Université Côté d'Azur)17/10/2024, 11:00
Complete monotonicity of a smooth function on a convex cone is a strong property given by infinitely many sign conditions on the directional derivatives of the function. I will discuss results and questions around this concept that are motivated by research in convex optimization (interior-point methods), algebraic statistics (exponential families) and real algebraic geometry (hyperbolic and...
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17/10/2024, 13:00
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Ingrid Vazquez-Holm17/10/2024, 14:00
We study classical radiation fields at next-to-leading order using the
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methods of scattering amplitudes. The fields of interest to us are sourced when
two massive, point-like objects scatter inelastically, and can be computed from one-
loop amplitudes. The real and imaginary parts of the amplitudes play important
but physically distinct roles in the radiation field. We argue that the... -
Christoph Dlapa (DESY)17/10/2024, 15:00
I present work which provides evidence through two loops that rational
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letters of polylogarithmic Feynman integrals are captured by the Landau
equations, when the latter are recast as a polynomial of the kinematic
variables of the integral, known as the principal A-determinant.
Focusing on one loop, I further discuss how all square-root letters may
also be obtained, by re-factorizing the... -
Carsten Schneider17/10/2024, 16:45
We present tools from symbolic summation and integration that are tailored for Feynman integrals.
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In particular, we will present algorithms that enable one to produce linear differential or
difference equations that contain the input expression (e.g., in form of definite hypergeometric multisums, hyperexpontial multiintegrals or coupled systems of linear
differential equations) as solution.... -
Claudia Rella (Institut des Hautes Études Scientifiques, Université Paris-Saclay)18/10/2024, 09:30
Factorially divergent power series naturally arise as perturbative expansions in quantum theories but do not uniquely determine the original functions due to hidden non-analytic terms. In favourable circumstances, these terms can be systematically understood within the framework of resurgence. Growing evidence indicates that this is the case for topological string theory. In this talk, I will...
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Stephan Stieberger18/10/2024, 11:00
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18/10/2024, 13:00
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Zahra Zahraee18/10/2024, 14:00
In this pedagogical talk, we discuss non-perturbative methods to study planar N=4 SYM theory. Focusing on the four-point correlation function of the stress-energy tensor at the conformal point, we show how sum rules based on dispersion relations can be used to numerically bootstrap various objects in the theory, such as OPE coefficients, the four-point correlation function, and the...
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Anna-Laura Sattelberger (Max Planck Institute for Mathematics in the Sciences, Leipzig)18/10/2024, 15:00
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Baran Hashemi, Carlos Rodriguez, Felix Tellander, Hadrien Brochet, Kajal Singh, Konstantin Baune, Paul-Hermann Balduf, Sara Ditsch (MPP)
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Sara Ditsch (MPP)
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