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Concept

Euler characteristic

Related publications (27)

Non-planarity of Markoff graphs mod p

Matthew De Courcy-Ireland

We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x2 + y2 + z2 = xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these gr ...

European Mathematical Soc-Ems2024

Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups

Nicolas Monod

We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring g ...

SPRINGER HEIDELBERG2023

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

Unconventional Flat Chern Bands and 2e Charges in Skyrmionic Moire Superlattices

Oleg Yazyev, Yifei Guan

The interplay of topological characteristics in real space and reciprocal space can lead to the emergence of unconventional topological phases. In this Letter, we implement a novel mechanism for generating higher-Chern flat bands on the basis of twisted bi ...

AMER CHEMICAL SOC2023

Dense Packings via Lifts of Codes to Division Rings

Vlad Serban, Nihar Prakash Gargava

obtain algorithmically effective versions of the dense lattice sphere packings constructed from orders in Q-division rings by the first author. The lattices in question are lifts of suitable codes from prime characteristic to orders O in Q-division rings a ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023

Magnetic orderings and electronic structure of complex oxides from advanced Hubbard functionals

Luca Binci

Transition metal oxides represent a class of materials displaying very unusual electronic, structural and magnetic properties. They are extremely interesting, both from a technological and fundamental point of view. The most important characteristic of the ...

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

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 numerical integration on curved polyhedra based on folded decompositions

Annalisa Buffa, Pablo Antolin Sanchez, Xiaodong Wei

We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces correspond to the g ...

ELSEVIER SCIENCE SA2022

Unramified F-divided objects and the etale fundamental pro-groupoid in positive characteristic

Giulio Orecchia

Let X /S be a flat algebraic stack of finite presentation. We define a new & eacute;tale fundamental pro-groupoid pi(1)(X /S), generalizing Grothendieck's enlarged & eacute;tale fundamental group from SGA 3 to the relative situation. When S is of equal pos ...

GEOMETRY & TOPOLOGY PUBLICATIONS2022

Collapse-invariant properties of spaces equipped with signals or directions

Stefania Ebli

Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...

EPFL2022

The role of convolutional neural networks in scanning probe microscopy: a review

Georg Fantner

Progress in computing capabilities has enhanced science in many ways. In recent years, various branches of machine learning have been the key facilitators in forging new paths, ranging from categorizing big data to instrumental control, from materials desi ...

BEILSTEIN-INSTITUT2021

Promoting Persistent Superionic Conductivity in Sodium Monocarba-closo-dodecaborate NaCB11H12 via Confinement within Nanoporous Silica

Mirjana Dimitrievska

Superionic phases of bulk anhydrous salts based on large cluster-like polyhedral (carba)borate anions are generally stable only well above room temperature, rendering them unsuitable as solid-state electrolytes in energy-storage devices that typically oper ...

AMER CHEMICAL SOC2021

Methods and systems for particle characterisation

Sandor Kasas, Anton Malovichko

A method and system for deriving particle characteristics is described. The method comprises imaging the movement of at least one free-floating particle in a liquid environment at at least one moment in time, determining for at least one moment in time a m ...

2020

A brief exposure to rightward prismatic adaptation changes resting-state network characteristics of the ventral attentional system

Patric Hagmann, Stephanie Clarke

A brief session of rightward prismatic adaptation (R-PA) has been shown to alleviate neglect symptoms in patients with right hemispheric damage, very likely by switching hemispheric dominance of the ventral attentional network (VAN) from the right to the l ...

2020

Regularity In Time Of Holder Solutions Of Euler And Hypodissipative Navier-Stokes Equations

Maria Colombo, Luigi De Rosa

In this work we investigate some regularization properties of the incompressible Euler equations and of the fractional Navier-Stokes equations where the dissipative term is given by (-Delta)(alpha) for a suitable power alpha is an element of (0, 1/2) (the ...

SIAM PUBLICATIONS2020

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

Presymplectic convexity and (ir)rational polytopes

Tudor Ratiu

In this paper, we extend the Atiyah-Guillemin-Sternberg convexity theorem and Delzant's classification of symplectic toric manifolds to presymplectic manifolds. We also define and study the Morita equivalence of presymplectic toric manifolds and of their c ...

2019

On the abundance problem for 3-folds in characteristic p > 5

In this article we prove two cases of the abundance conjecture for 3-folds in characteristic p>5: (i) (X,Delta) is klt and kappa(X,KX+Delta)=1, and (ii) (X,Delta) is klt, KX+Delta equivalent to 0 and X is not uniruled. ...

2019

Configuration Spaces Of Products

Kathryn Hess Bellwald

We show that the configuration spaces of a product of parallelizable manifolds may be recovered from those of the factors as the Boardman-Vogt tensor product of right modules over the operads of little cubes of the appropriate dimension. We also discuss an ...

2019

Related publications (27)

Promoting Persistent Superionic Conductivity in Sodium Monocarba-closo-dodecaborate NaCB11H12 via Confinement within Nanoporous Silica

Mirjana Dimitrievska

AMER CHEMICAL SOC2021

Methods and systems for particle characterisation

Sandor Kasas, Anton Malovichko

2020

A brief exposure to rightward prismatic adaptation changes resting-state network characteristics of the ventral attentional system

Patric Hagmann, Stephanie Clarke

2020