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A Generalized Discrete Morse-Floer Theory

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Communications in Mathematics and Statistics 2019年第3期7卷 225-252页

作者： jürgen jost Sylvia Yaptieu Max Planck Institute for Mathematics in the Sciences Inselstrasse 2204103 LeipzigGermany Santa Fe Institute for the Sciences of Complexity Santa FeNM 87501USA

Forman has developed a version of discrete Morse theory that can be understood in terms of arrow patterns on a(simplicial,polyhedral or cellular)complex without closed orbits,where each cell may either have no arrows,receive a single arrow from one of its facets,or conversely,send a single arrow into a cell of which it is a *** following arrows,one can then construct a natural Floer-type boundary ***,we develop such a construction for arrow patterns where each cell may support several outgoing or incoming arrows(but not both),again in the absence of closed *** main technical achievement is the construction of a boundary operator that squares to 0 and therefore recovers the homology of the underlying complex.

关键词： CW complex Boundary operator Floer theory Poincarépolynomial Betti number Discrete Morsetheory Discrete Morse-Floertheory Conleytheory

Spectral Gap of the Largest Eigenvalue of the Normalized Graph Laplacian

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Communications in Mathematics and Statistics 2022年第3期10卷 371-381页

作者： jürgen jost Raffaella Mulas Florentin Münch Max Planck Institute for Mathematics in the Sciences LeipzigGermany

We offer a new method for proving that the maxima eigenvalue of the normalized graph Laplacian of a graph with n vertices is at least n+1/n−1 provided the graph is not complete and that equality is attained if and only if the complement graph is a single edge or a complete bipartite graph with both parts of size n−1/*** the same method,we also prove a new lower bound to the largest eigenvalue in terms of the minimum vertex degree,provided this is at most n−1/2.

关键词： Spectral graph theory Normalized Laplacian Largest eigenvalue Sharp bounds

Subelliptic Harmonic Maps with Values in Metric Spaces of Nonpositive Curvature

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Communications in Mathematical Research 2022年第4期38卷 516-534页

作者： Yaoting Gui jürgen jost Xianqing Li-jost School of Mathematical Sciences University of Science and Technology of ChinaHefeiChina Max Planck Institute for Mathematics in the Sciences LeipzigGermany

We prove the Holder continuity of a harmonic map from a domain of a sub-Riemannian manifold into a locally compact manifold with nonpositive curvature,and more generally into a non-positively curved metric space in th... 详细信息

关键词： Subelliptic harmonic maps nonpositive curvature Holder continuity

Dirac-harmonic maps with the trivial index

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Science China Mathematics 2024年

作者： jürgen jost Linlin Sun jingyong Zhu Max Planck Institute for Mathematics in the Sciences School of Mathematics and Statistics Guangxi Normal University School of Mathematics Sichuan University

For a homotopy class [u] of maps between a closed Riemannian manifold M and a general manifold N, we want to find a Dirac-harmonic map with the map component in the given homotopy class. Most known results require the index to be nontrivial. When the index is trivial, the few known results are all constructive and produce uncoupled solutions. In this paper, we define a new quantity. As a byproduct of proving the homotopy invariance of this new quantity, we find a new simple proof for the fact that all the Dirac-harmonic spheres in surfaces are uncoupled. More importantly, by using the homotopy invariance of this new quantity,we prove the existence of Dirac-harmonic maps from manifolds in the trivial index case. In particular, when the domain is a closed Riemann surface, we prove the short-time existence of the α-Dirac-harmonic map flow in the trivial index case. Together with the density of the minimal kernel, we get an existence result for Dirac-harmonic maps from closed Riemann surfaces to K¨ahler manifolds, which extends the previous result of the first and third authors. This establishes a general existence theory for Dirac-harmonic maps in the context of the trivial index.

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Boundary regularity for mean curvature flows of higher codimension

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Science China Mathematics 2024年

作者： Qi Ding jürgen jost Yuanlong Xin Shanghai Center for Mathematical Sciences Fudan University Max Planck Institute for Mathematics in the Sciences Institute of Mathematics Fudan University

In this paper, we derive global bounds for the H?lder norms of the gradient of solutions of graphic mean curvature flows with boundaries of arbitrary codimension.

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Computational History:Challenges and Opportunities of Formal Approaches

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journal of Social Computing 2023年第3期4卷 232-242页

作者： jürgen jost Roberto Lalli Manfred D.Laubichler Eckehard Olbrich jürgen Renn Guillermo Restrepo Peter F.Stadler Dirk Wintergrün the Max Planck Institute for Mathematics in the Sciences Leipzig 04103Germany the Santa Fe Institute Santa FeNM 87501USA the Max Planck Institute for the History of Science Berlin 14195Germany the School of Complex Adaptive Systems and the Global Biosocial Complexity Initiative Arizona State UniversityTempeAZ 85287USA the Department of Computer Science and Interdisciplinary Center for Bioinformatics Leipzig UniversityLeipzig 04109Germany

We propose a program for a computational analysis,based on large scale datasets,of deep conceptual and formal structures,representing the mechanisms of historical transformations in different domains ranging from biological to social,cultural,and knowledge *** conceptualize such systems as consisting of complex multi-layer *** properties of such networks may explain the spreading of *** relations between the dynamics of interacting networks may help to identify *** systems may show path and context *** illustrate our approach by case studies from all those types of systems.

关键词： computational history history of science network analysis big data

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几何分析中的基本概念与原理<英>

数学进展 2003年第2期32卷 129-140页

作者： jürgen jost 马普协会莱比锡数学所

本文是根据作者在中国科学院“中德几何分析伙伴小组”成立仪式上的演讲整理而成.主要目的在于通过回顾几何分析中的基本概念及基本定理,了解现阶段的研究情况和将来的研究线路.主要描述黎曼几何与量子场论中的思想,特别特别是极化物理... 详细信息

本文是根据作者在中国科学院“中德几何分析伙伴小组”成立仪式上的演讲整理而成.主要目的在于通过回顾几何分析中的基本概念及基本定理,了解现阶段的研究情况和将来的研究线路.主要描述黎曼几何与量子场论中的思想,特别特别是极化物理量与几何量产生的变分问题.

关键词：临界点 Morse理论上同调 Novikov理论几何分析向量从映射度量函数几何分析

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调和映照及其推广

中国科学：数学 2019年第2期49卷 125-138页

作者： jürgen jost 李先清陈群 Max-Planck Institute for Mathematics in the Sciences 武汉大学数学与统计学院武汉430072

本文概述了调和映照的各种推广,包括Hermite调和映照、Weyl调和映照、仿射调和映照、Finsler流形的调和映照、度量空间之间的调和映照、Dirac-调和映照等.

关键词：调和映照 Hermite Weyl 仿射调和映照 Finsler 流形的调和映照度量空间 Dirac-调和映照

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How sensing arsenite helps plants survive on toxic soils

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Molecular Plant 2021年第9期14卷 1424-1426页

作者： Ricarda jost Department of Animal Plant and Soil SciencesAustralian Research Council Centre of Excellence in Plant Energy BiologyAustralian Research HUB for Medicinal AgricultureLa Trobe Institute for Agriculture and Food(LIAF)La Trobe UniversityBundooraVICAustralia

Metals and metalloids are present in soils and ground *** constitute both essential plant nutrients and potent ***(As)is one of the most prevalent toxic compounds in soil with average concentrations between 5 and 7.5 mg kg 1 facing constant enrichment through anthropogenic activities,as well as soil weathering and volcanism Wenzel(2013).Both phosphorus(P)and As are non-metals found alongside nitrogen(N)in group 15 of the periodic table.

关键词： soils soil phosphorus