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Classe de Chern

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Weyl metallic state induced by helical magnetic order

Henrik Moodysson Rønnow, Jan Hugo Dil, Ivica Zivkovic, Jian Rui Soh, Xupeng Yang

In the rapidly expanding field of topological materials there is growing interest in systems whose topological electronic band features can be induced or controlled by magnetism. Magnetic Weyl semimetals, which contain linear band crossings near the Fermi ...

Berlin2024

Topological Effects in Carbon-based Two-dimensional Nanostructures

Yifei Guan

Recent advances on low-dimensional and topological materials has greatly inspired the research in condensed matter physics. This thesis is devoted to the computational and theoretical study of topological effects in two-dimensional materials, especially na ...

EPFL2023

Landau levels of the Euler class topology

Oleg Yazyev, Yifei Guan

Two-dimensional systems with C2T (PT) symmetry exhibit the Euler class topology E is an element of Z in each two-band subspace realizing a fragile topology beyond the symmetry indicators. By systematically studying the energy levels of Euler insulating pha ...

AMER PHYSICAL SOC2022

Serre-Tate theory for Calabi-Yau varieties

Maciej Emilian Zdanowicz

Classical Serre-Tate theory describes deformations of ordinary abelian varieties. It implies that every such variety has a canonical lift to characteristic zero and equips the base of its universal deformation with a Frobenius lifting and canonical multipl ...

WALTER DE GRUYTER GMBH2021

Local Theory of the Insulating State

Antimo Marrazzo

An insulator differs from a metal because of a different organization of the electrons in their ground state. In recent years this feature has been probed by means of a geometrical property, the quantum metric tensor, which addresses the system as a whole, ...

AMER PHYSICAL SOC2019

A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

Adrien Giuliano Marcone

The purpose of this thesis is to provide an intrinsic proof of a Gauss-Bonnet-Chern formula for complete Riemannian manifolds with finitely many conical singularities and asymptotically conical ends. A geometric invariant is associated to the link of both ...

EPFL2019

Characteristic classes as complete obstructions

Martina Rovelli

In the first part of this paper, we propose a uniform interpretation of characteristic classes as obstructions to the reduction of the structure group and to the existence of an equivariant extension of a certain homomorphism defined a priori only on a sin ...

SPRINGER HEIDELBERG2019

Topological states on the breathing kagome lattice

Adrien Bolens

We theoretically study the topological properties of the tight-binding model on the breathing kagome lattice with antisymmetric spin-orbit coupling (SOC) between nearest neighbors. We show that the system hosts nontrivial topological phases even without se ...

2019

Modular functors, cohomological field theories, and topological recursion

Nicolas Gerson Orantin

Given a topological modular functor V in the sense of Walker, we construct vector bundles Z (lambda) over bar, over (M) over bar (g,n) whose Chern characters define semi-simple cohomological field theories. This construction depends on a determinati ...

AMER MATHEMATICAL SOC2018

Towards new invariants for principal bundles

Martina Rovelli

We investigate the theory of principal bundles from a homotopical point of view. In the first part of the thesis, we prove a classification of principal bundles over a fixed base space, dual to the well-known classification of bundles with a fixed structur ...

EPFL2017