Triangle Seminars
Tuesday, 2 Feb 2021
The Topology of Data: from String Theory to Cosmology to Phases of Matter
Gary Shiu
(University of Wisconsin)
Abstract:
We are faced with an explosion of data in many areas of physics, but very so often, it is not the size but the complexity of the data that makes extracting physics from big datasets challenging. As I will discuss in this talk, data has shape and the shape of data encodes the underlying physics. Persistent homology is a tool in computational topology developed for quantifying the shape of data. I will discuss three applications of topological data analysis: 1) identifying structure of the string landscape, 2) constraining primordial non-Gaussianity from CMB measurements and large scale structures data, and 3) detecting and classifying phases of matter. Persistent homology condenses these datasets into their most relevant (and interpretable) features, so that simple statistical pipelines are sufficient in these contexts. This suggests that TDA can be used in conjunction with machine learning algorithms and improves their architecture.
Based on https://arxiv.org/abs/2009.14231, https://arxiv.org/abs/2009.04819, https://arxiv.org/abs/1907.10072, https://arxiv.org/abs/1812.06960, https://arxiv.org/abs/1712.08159.
[please email a.held@imperial.ac.uk for zoom link or password]
We are faced with an explosion of data in many areas of physics, but very so often, it is not the size but the complexity of the data that makes extracting physics from big datasets challenging. As I will discuss in this talk, data has shape and the shape of data encodes the underlying physics. Persistent homology is a tool in computational topology developed for quantifying the shape of data. I will discuss three applications of topological data analysis: 1) identifying structure of the string landscape, 2) constraining primordial non-Gaussianity from CMB measurements and large scale structures data, and 3) detecting and classifying phases of matter. Persistent homology condenses these datasets into their most relevant (and interpretable) features, so that simple statistical pipelines are sufficient in these contexts. This suggests that TDA can be used in conjunction with machine learning algorithms and improves their architecture.
Based on https://arxiv.org/abs/2009.14231, https://arxiv.org/abs/2009.04819, https://arxiv.org/abs/1907.10072, https://arxiv.org/abs/1812.06960, https://arxiv.org/abs/1712.08159.
[please email a.held@imperial.ac.uk for zoom link or password]
Posted by: IC
Wednesday, 3 Feb 2021
Quantum Information Theory of the Gravitational Anomaly
Simeon Hellerman
(Tokyo U., IPMU)
Abstract:
I will explain that the notion of quantum entanglement is not defined for gravitationally anomalous two-dimensional theories, because they do not admit a local tensor factorization of the Hilbert space into local Hilbert spaces. Qualitatively, the modular flow cannot act consistently and unitarily in a finite region, if there are different numbers of states with a given energy traveling in the two opposite directions. I will make this precise by decomposing it into two observations: First, a two-dimensional conformal field theory admits a consistent quantization on a space with boundary only if it is not anomalous. Second, a local tensor factorization always leads to a definition of consistent, unitary, energy-preserving boundary condition. As a corollary I will establish a generalization of the Nielsen-Ninomiya theorem to all two-dimensional unitary local quantum field theories: No continuum quantum field theory in two dimensions can admit a lattice regulator unless its gravitational anomaly vanishes. I will advocate that these points be used to reinterpret the gravitational anomaly quantum-information-theoretically, as a fundamental obstruction to the localization of quantum information.
[Zoom link: please ask your local triangle organizer]
I will explain that the notion of quantum entanglement is not defined for gravitationally anomalous two-dimensional theories, because they do not admit a local tensor factorization of the Hilbert space into local Hilbert spaces. Qualitatively, the modular flow cannot act consistently and unitarily in a finite region, if there are different numbers of states with a given energy traveling in the two opposite directions. I will make this precise by decomposing it into two observations: First, a two-dimensional conformal field theory admits a consistent quantization on a space with boundary only if it is not anomalous. Second, a local tensor factorization always leads to a definition of consistent, unitary, energy-preserving boundary condition. As a corollary I will establish a generalization of the Nielsen-Ninomiya theorem to all two-dimensional unitary local quantum field theories: No continuum quantum field theory in two dimensions can admit a lattice regulator unless its gravitational anomaly vanishes. I will advocate that these points be used to reinterpret the gravitational anomaly quantum-information-theoretically, as a fundamental obstruction to the localization of quantum information.
[Zoom link: please ask your local triangle organizer]
Posted by: QMW
Islands in black holes and cosmology
Tom Hartman
(Cornell)
Abstract:
I will summarize recent developments on the information paradox involving "islands" and replica wormholes, and discuss the extent to which these ideas can be applied to cosmology.
[Zoom link: please ask your local triangle organizer]
I will summarize recent developments on the information paradox involving "islands" and replica wormholes, and discuss the extent to which these ideas can be applied to cosmology.
[Zoom link: please ask your local triangle organizer]
Posted by: QMW
Thursday, 4 Feb 2021
Wilson-'t Hooft lines as transfer matrices
Junya Yagi
(Tsinghua)
Abstract:
Supersymmetric gauge theories in four dimensions have various interrelated connections to quantum integrable systems. I will present a new correspondence which identifies Wilson-'t Hooft lines in N=2 circular quiver theories with transfer matrices of trigonometric systems. I will explain how this correspondence is related to Costello's 4d Chern-Simons theory and other similar correspondences. This is based on my joint work with Kazunobu Maruyoshi and Toshihiro Ota.
–––––––––– Part of the London Integrability Journal Club. New participants please register using the form at integrability-london.weebly.com.
Supersymmetric gauge theories in four dimensions have various interrelated connections to quantum integrable systems. I will present a new correspondence which identifies Wilson-'t Hooft lines in N=2 circular quiver theories with transfer matrices of trigonometric systems. I will explain how this correspondence is related to Costello's 4d Chern-Simons theory and other similar correspondences. This is based on my joint work with Kazunobu Maruyoshi and Toshihiro Ota.
–––––––––– Part of the London Integrability Journal Club. New participants please register using the form at integrability-london.weebly.com.
Posted by: CityU2