Publications related to Hermitian symmetric space

Optimal denoising of rotationally invariant rectangular matrices

Florent Gérard Krzakala, Lenka Zdeborová, Emanuele Troiani, Vittorio Erba

In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors, we completely ch ...

2022

From Trees to Barcodes and Back Again: A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem

Adélie Eliane Garin

In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view. Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B invol ...

EPFL2022

The cohomology of semi-simple Lie groups, viewed from infinity

Nicolas Monod

We prove that the real cohomology of semi-simple Lie groups admits boundary values, which are measurable cocycles on the Furstenberg boundary. This generalises known invariants such as the Maslov index on Shilov boundaries, the Euler class on projective sp ...

2022

Robust Differentiable SVD

Pascal Fua, Mathieu Salzmann, Zheng Dang, Wei Wang, Yinlin Hu

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) ...

2021

Spherical birational sheets in reductive groups

Filippo Ambrosio

We classify the spherical birational sheets in a complex simple simply-connected algebraic group. We use the classification to show that, when G is a connected reductive complex algebraic group with simply-connected derived subgroup, two conjugacy classes ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

Local invertibility and sensitivity of atomic structure-feature mappings

Michele Ceriotti, Sergey Pozdnyakov

Background: The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the variety o ...

2021

Energy distribution of harmonic 1-forms and Jacobians of Riemann surfaces with a short closed geodesic

Jürgpeter Buser, Robert Silhol

We study the energy distribution of harmonic 1-forms on a compact hyperbolic Riemann surface S where a short closed geodesic is pinched. If the geodesic separates the surface into two parts, then the Jacobian variety of S develops into a variety that split ...

2021

Handedness-dependent quasiparticle interference in the two enantiomers of the topological chiral semimetal PdGa

Roland Widmer, Samuel Thomas Stolz, Yi-Chiang Sun, Timur Kim

It has recently been proposed that combining chirality with topological band theory results in a totally new class of fermions. Understanding how these unconventional quasiparticles propagate and interact remains largely unexplored so far. Here, we use sca ...

Nature Research2020

From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives

Kathryn Hess Bellwald, Lida Kanari, Adélie Eliane Garin

Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors, such as persistence diagrams. While there are many powerful ...

2020

Haldane Gap of the Three-Box Symmetric SU(3) Chain

Frédéric Mila, Pierre Marcel Nataf, Samuel Gozel

Motivated by the recent generalization of the Haldane conjecture to SU(3) chains [Lajko et al., Nucl. Phys. B924, 508 (2017)] according to which a Haldane gap should be present for symmetric representations if the number of boxes in the Young diagram is a ...

2020

Perfect soliton crystals in optical microresonators

Tobias Kippenberg, Junqiu Liu, Maxim Karpov, Hairun Guo, Martin Hubert Peter Pfeiffer, Wenle Weng

We demonstrate the existence of perfect soliton crystal states and develop the deterministic procedure for their excitation in Si3N4 microresonators. We show that despite exceptional symmetrical properties, their behavior is strongly linked to the chaotic ...

IEEE2019

The Center of Small Quantum Groups I: The Principal Block in Type A

Anna Lachowska

We develop an elementary algebraic method to compute the center of the principal block of a small quantum group associated with a complex semisimple Lie algebra at a root of unity. The cases of sl(3) and sl(4) are computed explicitly. This allows us to for ...

OXFORD UNIV PRESS2018

Vibrational modes of Q-balls

Andrey Shkerin

We study linear perturbations of classically stable Q-balls in theories admitting analytic solutions. Although the corresponding boundary value problem is non-Hermitian, the analysis of perturbations can also be performed analytically in certain regimes. W ...

American Physical Society2018

Irreducible representations of simple algebraic groups in which a unipotent element is represented by a matrix with a single non-trivial Jordan block

Donna Testerman

Let G be a simply connected simple linear algebraic group of exceptional Lie type over an algebraically closed field F of characteristic p >= 0, and let u is an element of G be a non-identity unipotent element. Let phi be a non-trivial irreducible represen ...

2018

Toda frames, harmonic maps and extended Dynkin diagrams

Katharine Felicity Turner

We consider a natural subclass of harmonic maps from a surface into G/T, namely cyclic primitive maps. Here G is any simple real Lie group (not necessarily compact), T is a Cartan subgroup and both are chosen so that there is a Coxeter automorphism on G(C) ...

Elsevier2017

Disentangling constraints using viability evolution principles in integrative modeling of macromolecular assemblies

Dario Floreano, Matteo Dal Peraro, Matteo Thomas Degiacomi, Andrea Maesani, Giorgio Elikem Tamo, Sylvain Träger

Predicting the structure of large molecular assemblies remains a challenging task in structural biology when using integrative modeling approaches. One of the main issues stems from the treatment of heterogeneous experimental data used to predict the archi ...

Nature Research2017

On the geometrical interpretation of scale-invariant models of inflation

Georgios Karananas, Javier Rubio

We study the geometrical properties of scale-invariant two-field models of inflation. In particular, we show that when the field-derivative space in the Einstein frame is maximally symmetric during inflation, the inflationary predictions can be universal a ...

Elsevier2016

Bi-Jacobi Fields And Riemannian Cubics For Left-Invariant SO(3)

Tudor Ratiu

Bi-Jacobi fields are generalized Jacobi fields, and are used to efficiently compute approximations to Riemannian cubic splines in a Riemannian manifold M. Calculating bi-Jacobi fields is straightforward when M is a symmetric space such as bi-invariant SO(3 ...

Int Press Boston, Inc2016

Trace maps for Mackey algebras

Baptiste Thierry Pierre Rognerud

Let G be a finite group and R be a commutative ring. The Mackey algebra μR(G) shares a lot of properties with the group algebra RG however, there are some differences. For example, the group algebra is a symmetric algebra and this is not always the case fo ...

Elsevier2015

An indiscrete Bieberbach theorem: from amenable CAT$(0)$ groups to Tits buildings

Nicolas Monod

Non-positively curved spaces admitting a cocompact isometric action of an amenable group are investigated. A classification is established under the assumption that there is no global fixed point at infinity under the full isometry group. The visual bounda ...

2015