Universe Online Seminar: MPI MIS

The seminar series will feature presentations and discussions on various topics relevant to the ERC UNIVERSE+ Synergy Project. Each session will offer valuable insights and opportunities for interaction, allowing us to keep the momentum going and delve deeper into our research areas. The Seminars will be held via Zoom bi-weekly, Wednesdays at 4:00 PM CET. Please register on the following website: indico.mpp.mpg.de/event/10448/

This activity is part of the ERC Synergy Grant UNIVERSE+ www.positive-geometry.com, funded by the European Union (ERC, UNIVERSE PLUS, 101118787). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.


30.04.25	Andrzej Pokraka (Brown University) : Hidden Zeros of the Cosmological Wavefunction Motivated by the recent discovery of hidden zeros in particle and string amplitudes, we characterize zeros of individual graphs contributing to the cosmological wavefunction. We construct polytopal realizations of the relevant graph associahedra and show that the cosmological zeros have natural geometric and physical interpretations as well as demonstrate that the wavefunction splits near these zeros. We also establish an equivalence between a family of flat-space wavefunction coefficients and $Tr[\phi^3]$ amplitudes, consequently rediscovering their hidden zeros.
02.04.25	Justin Berman (University of Michigan) : Characterizing the EFT-hedron High-energy physics can be encoded into low-energy effective field theories (EFTs) as an infinite set of Wilson coefficients. Requiring that the high-energy theory respects the fundamental physical principles of unitarity, locality, and causality bounds the values of these coefficients for 2->2 scattering amplitudes to live inside of a positive geometry in the space of Wilson coefficients known as the “EFT-hedron.” As constraints on an increasing number of Wilson coefficients are considered, the EFT-hedron has several surprising features that I will describe in my talk. I will additionally explain how requiring that Wilson coefficients live inside the EFT-hedron can place new constraints on what physics is allowed at high energies. Register
19.03.25	Matthias Oliver Wilhelm (University of Southern Denmark) : Functions in Scattering Amplitudes: From QFT to Gravitational Waves Multi-loop Feynman integrals for collider physics are known to contain intricate geometries and to evaluate to complicated transcendental numbers and functions. After an introduction to how those arise in Quantum Field Theory, I will investigate Feynman integrals contributing to the emission of gravitational waves in classical gravity. I will provide a full classification of the contributing Feynman integrals up to fifth order in the post-Minkowskian expansion, identifying new geometries that lead to new transcendental functions. Moreover, I will demonstrate how the corresponding differential equations can be solved by bringing them into canonical form. Register
05.03.25	Francis Brown (University of Oxford) : Canonical functions and rational approximations. Associating a “canonical form” associated to a semi-algebraic region in the complex points of an algebraic variety, whose poles lie along its boundary, has recently risen in popularity. In this talk I will introduce the notion of "canonical function" associated to two such regions. In brief, it is a rational function which has poles along the boundary of the first region, and zeros along the boundary of the second region. Associated to this data is a canonical Picard-Fuchs recurrence relation, periods and mysterious symmetry groups. Examples constructed in this way provide rare mathematical gems: for instance Apéry’s famous approximations to zeta(2), zeta(3), surprising connections with modular forms, and much more besides. Register
20.02.25	Agnese Bissi (Uppsala University) : AdS amplitudes from CFT
22.01.25	Mathieu Giroux (McGill University) : Recent progess in Landau Analysis: Schwinger, Baikov, and implementations The purpose of this talk is to review recent progress in Landau analysis, which aims to predict the singularity structure of Feynman integrals before explicitly evaluating them. In the first part, I will discuss the advantages and disadvantages of formulating this problem in both Schwinger parameter space and momentum (Baikov) space. In the second part, I will explain how the latter approach extends the powerful unitary-based method of arXiv:2406.05241 beyond two-particle cut-reducible graphs. To demonstrate its efficiency, I will present new results for multi-loop and multi-scale Feynman integrals, derived using an automatized Mathematica implementation in preparation. This activity is part of the ERC Synergy Grant UNIVERSE+ www.positive-geometry.com, funded by the European Union (ERC, UNIVERSE PLUS, 101118787). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. Register
08.01.25	Fabian Schmidt (MPA Garching) : Wilson-Polchinski renormalization group for large-scale structure Fabian Schmidt's research area is cosmology, with a main focus on theory, numerics, the analysis of quasilinear and nonlinear large-scale structures, and how they can inform us about gravity, dark energy, and the physics of inflation. The UNIVERSE+ Online Seminar Series is designed to foster dialogue and collaboration among project partners and those interested in positive geometry. This activity is part of the ERC Synergy Grant UNIVERSE+ www.positive-geometry.com, funded by the European Union (ERC, UNIVERSE PLUS, 101118787). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. Register

30.04.25

Andrzej Pokraka (Brown University) : Hidden Zeros of the Cosmological Wavefunction

Motivated by the recent discovery of hidden zeros in particle and string amplitudes, we characterize zeros of individual graphs contributing to the cosmological wavefunction. We construct polytopal realizations of the relevant graph associahedra and show that the cosmological zeros have natural geometric and physical interpretations as well as demonstrate that the wavefunction splits near these zeros. We also establish an equivalence between a family of flat-space wavefunction coefficients and $Tr[\phi^3]$ amplitudes, consequently rediscovering their hidden zeros.

02.04.25

Justin Berman (University of Michigan) : Characterizing the EFT-hedron

High-energy physics can be encoded into low-energy effective field theories (EFTs) as an infinite set of Wilson coefficients. Requiring that the high-energy theory respects the fundamental physical principles of unitarity, locality, and causality bounds the values of these coefficients for 2->2 scattering amplitudes to live inside of a positive geometry in the space of Wilson coefficients known as the “EFT-hedron.” As constraints on an increasing number of Wilson coefficients are considered, the EFT-hedron has several surprising features that I will describe in my talk. I will additionally explain how requiring that Wilson coefficients live inside the EFT-hedron can place new constraints on what physics is allowed at high energies.

19.03.25

Matthias Oliver Wilhelm (University of Southern Denmark) : Functions in Scattering Amplitudes: From QFT to Gravitational Waves

Multi-loop Feynman integrals for collider physics are known to contain intricate geometries and to evaluate to complicated transcendental numbers and functions. After an introduction to how those arise in Quantum Field Theory, I will investigate Feynman integrals contributing to the emission of gravitational waves in classical gravity. I will provide a full classification of the contributing Feynman integrals up to fifth order in the post-Minkowskian expansion, identifying new geometries that lead to new transcendental functions. Moreover, I will demonstrate how the corresponding differential equations can be solved by bringing them into canonical form.

05.03.25

Francis Brown (University of Oxford) : Canonical functions and rational approximations.

Associating a “canonical form” associated to a semi-algebraic region in the complex points of an algebraic variety, whose poles lie along its boundary, has recently risen in popularity. In this talk I will introduce the notion of "canonical function" associated to two such regions. In brief, it is a rational function which has *poles* along the boundary of the first region, and *zeros* along the boundary of the second region. Associated to this data is a canonical Picard-Fuchs recurrence relation, periods and mysterious symmetry groups. Examples constructed in this way provide rare mathematical gems: for instance Apéry’s famous approximations to zeta(2), zeta(3), surprising connections with modular forms, and much more besides.

20.02.25

Agnese Bissi (Uppsala University) : AdS amplitudes from CFT

22.01.25

Mathieu Giroux (McGill University) : Recent progess in Landau Analysis: Schwinger, Baikov, and implementations

The purpose of this talk is to review recent progress in Landau analysis, which aims to predict the singularity structure of Feynman integrals before explicitly evaluating them. In the first part, I will discuss the advantages and disadvantages of formulating this problem in both Schwinger parameter space and momentum (Baikov) space. In the second part, I will explain how the latter approach extends the powerful unitary-based method of arXiv:2406.05241 beyond two-particle cut-reducible graphs. To demonstrate its efficiency, I will present new results for multi-loop and multi-scale Feynman integrals, derived using an automatized Mathematica implementation in preparation. This activity is part of the ERC Synergy Grant UNIVERSE+ www.positive-geometry.com, funded by the European Union (ERC, UNIVERSE PLUS, 101118787). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.

08.01.25

Fabian Schmidt (MPA Garching) : Wilson-Polchinski renormalization group for large-scale structure

Fabian Schmidt's research area is cosmology, with a main focus on theory, numerics, the analysis of quasilinear and nonlinear large-scale structures, and how they can inform us about gravity, dark energy, and the physics of inflation. The UNIVERSE+ Online Seminar Series is designed to foster dialogue and collaboration among project partners and those interested in positive geometry. This activity is part of the ERC Synergy Grant UNIVERSE+ www.positive-geometry.com, funded by the European Union (ERC, UNIVERSE PLUS, 101118787). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.


04.12.24	Simon Telen (MPI MiS, Leipzig) : Landau Analysis and Euler Stratifications This activity is part of the ERC Synergy Grant UNIVERSE+ www.positive-geometry.com, funded by the European Union (ERC, UNIVERSE PLUS, 101118787). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.
20.11.24	Babis Anastasiou (ETH Zürich) : to be announced This activity is part of the ERC Synergy Grant UNIVERSE+ www.positive-geometry.com, funded by the European Union (ERC, UNIVERSE PLUS, 101118787). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.
06.11.24	Nima Arkani-Hamed (IAS Princeton) : The Cosmohedron This activity is part of the ERC Synergy Grant UNIVERSE+ www.positive-geometry.com, funded by the European Union (ERC, UNIVERSE PLUS, 101118787). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.
23.10.24	Bernd Sturmfels (MPI MiS, Leipzig) : Kinematic Varieties for Massless Particles This activity is part of the ERC Synergy Grant UNIVERSE+ www.positive-geometry.com, funded by the European Union (ERC, UNIVERSE PLUS, 101118787). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.
09.10.24	Johannes Henn (Max Planck Institute for Physics) : Completely Monotone Functions
25.09.24	Daniel Baumann (University of Amsterdam) : Hidden Patterns in Cosmological Correlations

04.12.24

Simon Telen (MPI MiS, Leipzig) : Landau Analysis and Euler Stratifications

20.11.24

Babis Anastasiou (ETH Zürich) : to be announced

06.11.24

Nima Arkani-Hamed (IAS Princeton) : The Cosmohedron

23.10.24

Bernd Sturmfels (MPI MiS, Leipzig) : Kinematic Varieties for Massless Particles

09.10.24

Johannes Henn (Max Planck Institute for Physics) : Completely Monotone Functions

25.09.24

Daniel Baumann (University of Amsterdam) : Hidden Patterns in Cosmological Correlations