Fri, 28 Feb 2025
10:30
N4.01

Carrollian Fluids in 1+1 Dimensions: Mathematical Theory

Grigalius Taujanskas
(Cambridge)
Abstract

Due to connections to flat space holography, Carrollian geometry, physics and fluid dynamics have received an explosion of interest over the last two decades. In the Carrollian limit of vanishing speed of light c, relativistic fluids reduce to a set of PDEs called the Carrollian fluid equations. Although in general these equations are not well understood, and their PDE theory does not appear to have been studied, in dimensions 1+1 it turns out that there is a duality with the Galilean compressible Euler equations in 1+1 dimensions inherited from the isomorphism of the Carrollian (c to 0) and Galilean (c to infinity) contractions of the Poincar\'e algebra. Under this duality time and space are interchanged, leading to different dynamics in evolution. I will discuss recent work with N. Athanasiou (Thessaloniki), M. Petropoulos (Paris) and S. Schulz (Pisa) in which we establish the first rigorous PDE results for these equations by introducing a notion of Carrollian isentropy and studying the equations using Lax’s method and compensated compactness. In particular, I will explain that there is global existence in rough norms but finite-time blow-up in smoother norms.

Fri, 28 Feb 2025
09:15
N4.01

Carrollian Fluids: Carroll-Galilei Duality

Marios Petropoulos
(Ecole Polytechnique)
Abstract

Galilean and Carrollian algebras are dual contractions of the Poincaré algebra. They act on two-dimensional Newton--Cartan and Carrollian manifolds and are isomorphic. A consequence of this property is a duality correspondence between one-dimensional Galilean and Carrollian fluids. I will describe the algebras and the dynamics of these systems as they emerge from the relevant  limits of Lorentzian hydrodynamics, and explore the advertised duality relationship. This interchanges longitudinal and transverse directions with respect to the flow velocity, and permutes equilibrium and out-of-equilibrium observables, unveiling specific features of Carrollian physics. I will also discuss the hydrodynamic-frame invariance in Lorentzian systems and its fate in the Galilean and Carrollian avatars.

Tue, 15 Oct 2024

13:00 - 14:00
N4.01

Mathematrix: Meet and Greet

Abstract

Come along for free Pizza and to hear about the Mathematrix events this term. 

Fri, 26 May 2023

11:45 - 13:15
N4.01

InFoMM Group Meeting

Anna Berryman, Constantin Puiu, Joe Roberts
(Mathematical Institute)
Fri, 24 Feb 2023

11:45 - 13:15
N4.01

InFoMM Group Meeting

Sophie Abrahams, Oliver Bond, Georgia Brennan, Brady Metherall
(Mathematical Institute)
Fri, 25 Nov 2022

11:45 - 13:15
N4.01

InFoMM Group Meeting

Markus Dablander, James Harris, Deqing Jiang
(Mathematical Institute (University of Oxford))
Fri, 03 Jun 2022

16:00 - 17:00
N4.01

Hydrodynamic dispersion relations at finite coupling

Petar Tadic
(Yale University)
Further Information

It is also possible to join online via Microsoft Teams.

Abstract

Hydrodynamic excitations corresponding to sound and shear modes in fluids are characterized by gapless dispersion relations. In the hydrodynamic gradient expansion, their frequencies are represented by power series in spatial momenta. In this talk we will discuss the convergence properties of the hydrodynamic series by studying the associated spectral curve in the space of complexified frequency and complexified spatial momentum. For the N=4 supersymmetric Yang-Mills plasma at infinite 't Hooft coupling, we will use the holographic methods to demonstrate that the derivative expansions have finite non-zero radii of convergence. Obstruction to the convergence of hydrodynamic series arises from level-crossings in the quasinormal spectrum at complex momenta. We will discuss how finiteness of 't Hooft coupling affects the radius of convergence. We will show that the purely perturbative calculation in terms of inverse 't Hooft coupling gives the increasing radius of convergence when the coupling is decreasing. Applying the non-perturbative resummation techniques will make radius of convergence piecewise continuous function that decreases after the initial increase. Finally, we will provide arguments in favour of the non-perturbative approach and show that the presence of nonperturbative modes in the quasinormal spectrum can be indirectly inferred from the analysis of perturbative critical points.

Fri, 10 Jun 2022

16:00 - 17:00
N4.01

From Gravitational Orbits to Quantum Scars

Matthew Dodelson
(Cern)
Further Information

It is also possible to join online via Microsoft Teams.

Abstract

I will describe recent work with Zhibeodov on the boundary interpretation of orbits around an AdS black hole. When the orbits are far away from the black hole, these orbits describe heavy-light double-twist operators on the boundary. I will discuss how the dimensions of these operators can be computed exactly in terms of quasinormal modes in the bulk, using techniques from a paper to appear soon with Grassi, Iossa, Lichtig, and Zhiboedov. Then I will explain how these results are related to the concept of quantum scars, which are eigenstates that do not obey ETH. 

Fri, 27 May 2022

16:00 - 17:00
N4.01

Deconfining N=2 SCFTs

Matteo Lotito
(University of Massachusetts)
Further Information

It is also possible to join online via Microsoft Teams.

Abstract

In this talk I will describe a systematic approach, introduced in our recent work 2111.08022, to construct Lagrangian descriptions for a class of strongly interacting N=2 SCFTs. I will review the main ingredients of these constructions, namely brane tilings and the connection to gauge theories. For concreteness, I will then specialize to the case of the simplest of such geometrical setups, as in the paper, even though our approach should be much more general. I will comment on some low rank examples of the theories we built, that are well understood by (many) alternative approaches and conclude with some open questions and ideas for future directions to explore.

Fri, 13 May 2022

16:00 - 17:00
N4.01

The Supersymmetric Index and its Holographic Interpretation

Ohad Mamroud
(Weizmann Institute)
Further Information

It is possible to also join online via Microsoft Teams.

Abstract

I'll review 2104.13932, where we analyze the supersymmetric index of N=4 SU(N) Super Yang-Mills using the Bethe Ansatz approach, expressing it as a sum and concentrating on some family of contributions to the sum. We show that in the large N limit each term in this family corresponds to the contribution of a different euclidean black hole to the partition function of the dual gravitational theory. By taking into account non-perturbative contributions (wrapped D3-branes), we further show a one to one match between the contributions of the gravitational saddles and this family of contributions to the index, both at the perturbative and non-perturbative levels. I'll end with some new results regarding the Bethe Ansatz expansion and the information one could extract from it.

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