Concept

Polytope abstrait

Publications associées (22)

Anomalous and Chern topological waves in hyperbolic networks

Romain Christophe Rémy Fleury, Haoye Qin, Aleksi Antoine Bossart, Zhechen Zhang

Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental ...

Nature Research2024

Synthesis and properties of heterostructures in nanowires and 2-D materials

Akshay Balgarkashi

Modern solid-state devices were made possible by the discovery of semiconductor heterostructures. Heterostructures offer the ability to fabricate low-dimensional nanostructures such as quantum dots which can restrain carriers in all three-directions. Quant ...

EPFL2022

Generic vanishing in characteristic p > 0 and the geometry of theta divisors

Zsolt Patakfalvi

In this paper, we prove a strengthening of the generic vanishing result in characteristic p > 0 given in Hacon and Patakfalvi (Am J Math 138(4):963-998, 2016). As a consequence of this result, we show that irreducible Theta divisors are strongly F-regular ...

SPRINGER INTERNATIONAL PUBLISHING AG2022

The uniform symbolic topology property for diagonally F-regular algebras

Javier Alonso Carvajal Rojas

Let k be a field of positive characteristic. Building on the work of the second named author, we define a new class of k-algebras, called diagonally F-regular algebras, for which the so-called Uniform. Symbolic Topology Property (USTP) holds effectively. W ...

2020

Facet-driven formation of axial and radial In(Ga)As clusters in GaAs nanowires

Anna Fontcuberta i Morral, Lucas Güniat, Santhanu Panikar Ramanandan, Didem Dede, Martin George Friedl, Jean-Baptiste Leran, Wonjong Kim, Nicolas Tappy, Akshay Balgarkashi

Embedding quantum dots in nanowires (NWs) constitutes one promising building block for quantum photonic technologies. Earlier attempts to grow InAs quantum dots on GaAs nanowires were based on the Stranski-Krastanov growth mechanism. Here, we propose a nov ...

2020

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

b \in \Z^m

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

Tropical Ehrhart Theory and Tropical Volume

Matthias Schymura, Georg Peter Loho

We introduce a novel intrinsic volume concept in tropical geometry. This is achieved by developing the foundations of a tropical analog of lattice point counting in polytopes. We exhibit the basic properties and compare it to existing measures. Our exposit ...

2019

Extended Formulations from Communication Protocols in Output-Efficient Time

Yuri Faenza, Manuel Francesco Aprile

Deterministic protocols are well-known tools to obtain extended formulations, with many applications to polytopes arising in combinatorial optimization. Although constructive, those tools are not output-efficient, since the time needed to produce the exten ...

SPRINGER INTERNATIONAL PUBLISHING AG2019

On some problems related to 2-level polytopes

Manuel Francesco Aprile

In this thesis we investigate a number of problems related to 2-level polytopes, in particular from the point of view of the combinatorial structure and the extension complexity. 2-level polytopes were introduced as a generalization of stable set polytopes ...

EPFL2018

On 2-Level Polytopes Arising In Combinatorial Settings

Yuri Faenza, Manuel Francesco Aprile, Alfonso Bolívar Cevallos Manzano

2-level polytopes naturally appear in several areas of pure and applied mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. In this paper, we present a study of some 2-level polytopes arisi ...

SIAM Publications2018