Robert Ghrist | Academic Influence

Robert Ghrist's AcademicInfluence.com Rankings

Robert Ghrist

Mathematics

#2028

World Rank

#3196

Historical Rank

#815

USA Rank

Algebraic Topology

#34

World Rank

#42

Historical Rank

#15

USA Rank

Topology

#28

World Rank

#45

Historical Rank

#11

USA Rank

Measure Theory

#2670

World Rank

#3193

Historical Rank

#772

USA Rank

mathematics Degrees

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Mathematics

Robert Ghrist's Degrees

PhD Mathematics University of California, Berkeley
Masters Mathematics University of California, Berkeley
Bachelors Mathematics University of Arizona

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Why Is Robert Ghrist Influential?

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According to Wikipedia, Robert W. Ghrist is an American mathematician, known for his work on topological methods in applied mathematics. Life and Work Ghrist received his bachelor's degree in mechanical engineering from the University of Toledo in 1991, and in 1994 his master's degree and in 1995 his PhD from Cornell University under Philip Holmes with thesis The link of periodic orbits of a flow. From 1996 to 1998, he was R. H. Bing Instructor at the University of Texas and from 1998 an assistant professor and then from 2002 an associate professor at the Georgia Institute of Technology. In 2002 he became an associate professor and in 2004 a professor at the University of Illinois at Urbana-Champaign. From 2007, he was at the Information Trust Institute. In 2008, he was appointed Andrea Mitchell Penn Integrating Knowledge University Professor in Mathematics and Electrical/Systems Engineering at the University of Pennsylvania.

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Robert Ghrist's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Barcodes: The persistent topology of data (2007) (1068)
Coverage in sensor networks via persistent homology (2007) (462)
Coverage and hole-detection in sensor networks via homology (2005) (345)
Two’s company, three (or more) is a simplex (2016) (265)
Coordinate-free Coverage in Sensor Networks with Controlled Boundaries via Homology (2006) (227)
Elementary Applied Topology (2014) (212)
HOMOLOGICAL SENSOR NETWORKS (2005) (174)
A grammatical approach to self-organizing robotic systems (2006) (154)
The importance of the whole: Topological data analysis for the network neuroscientist (2018) (136)
Blind Swarms for Coverage in 2-D (2005) (116)
Two's company, three (or more) is a simplex - Algebraic-topological tools for understanding higher-order structure in neural data (2016) (90)
Multi-robot coverage and exploration on Riemannian manifolds with boundaries (2014) (88)
Graph grammars for self assembling robotic systems (2004) (88)
Contact topology and hydrodynamics: I. Beltrami fields and the Seifert conjecture (2000) (87)
Persistent Homology for Path Planning in Uncertain Environments (2015) (84)
Contact Topology and Hydrodynamics (1997) (78)
Target Enumeration via Euler Characteristic Integrals (2009) (77)
Finding Topology in a Factory: Configuration Spaces (2000) (75)
Matroid Filtrations and Computational Persistent Homology (2016) (73)
Branched two-manifolds supporting all links (1997) (66)
Pursuit and Evasion in Non-convex Domains of Arbitrary Dimensions (2006) (64)
Distributed computation of coverage in sensor networks by homological methods (2012) (64)
Vietoris–Rips Complexes of Planar Point Sets (2009) (64)
The geometry and topology of reconfiguration (2007) (64)
Configuration spaces and braid groups on graphs in robotics (1999) (56)
Toward a spectral theory of cellular sheaves (2018) (55)
Computing Pareto Optimal Coordinations on Roadmaps (2005) (53)
State Complexes for Metamorphic Robots (2003) (52)
Mapping and Pursuit-Evasion Strategies For a Simple Wall-Following Robot (2011) (49)
Discrete Morse Theory for Computing Cellular Sheaf Cohomology (2013) (45)
Topological Localization Via Signals of Opportunity (2012) (44)
Nonpositive Curvature and Pareto Optimal Coordination of Robots (2006) (44)
Capture pursuit games on unbounded domains (2009) (44)
Safe Cooperative Robot Dynamics on Graphs (2000) (42)
Morse theory on spaces of braids and Lagrangian dynamics (2001) (42)
Knots and Links in Three-Dimensional Flows (1997) (41)
Contact topology and hydrodynamics III: knotted orbits (2000) (39)
Euler Calculus with Applications to Signals and Sensing (2012) (38)
Euler integration over definable functions (2009) (37)
Hadwiger’s Theorem for definable functions ☆ (2012) (36)
Persistent homology and Euler integral transforms (2018) (35)
Invariants for homology classes with application to optimal search and planning problem in robotics (2012) (34)
Total curvature and simple pursuit on domains of curvature bounded above (2009) (33)
AN ODE WHOSE SOLUTIONS CONTAIN ALL KNOTS AND LINKS (1996) (29)
Homological algebra and data (2018) (28)
Path homotopy invariants and their application to optimal trajectory planning (2017) (28)
Multi-robot Coverage and Exploration in Non-Euclidean Metric Spaces (2012) (27)
Contact topology and hydrodynamics II: solid tori (1999) (25)
Pareto Optimal Coordination on Roadmaps (2004) (24)
Applications of Sheaf Cohomology and Exact Sequences on Network Codings (2011) (24)
Opinion Dynamics on Discourse Sheaves (2020) (23)
CONFIGURATION SPACES, BRAIDS, AND ROBOTICS (2009) (21)
Bitbots: Simple Robots Solving Complex Tasks (2005) (20)
A topological max-flow-min-cut theorem (2013) (20)
Three examples of applied and computational homology (2008) (19)
An index for closed orbits in Beltrami fields (2001) (19)
Contact topology and hydrodynamics III: knotted flowlines (1999) (19)
Stratified integrals and unknots in invisid flows (1999) (19)
Topological exploration of unknown and partially known environments (2013) (19)
Surrounding Nodes in Coordinate-Free Networks (2006) (18)
Rips Complexes of Planar Point Sets (2007) (16)
Positive Alexander Duality for Pursuit and Evasion (2015) (16)
Homological sensing for mobile robot localization (2013) (16)
Cellular sheaves of lattices and the Tarski Laplacian (2020) (15)
Knots and Orbit Genealogies in Three Dimensional Flows (1993) (15)
BROWN-HEADED COWBIRD ( MOLOTHRUS ATER ) MORTALITY IN AN URBAN WINTER ROOST (2003) (14)
Persistence by Parts: Multiscale Feature Detection via Distributed Persistent Homology (2020) (13)
Toward the Regulation and Composition of Cyclic Behaviors (2001) (13)
Braid Floer homology (2009) (12)
Learning Sheaf Laplacians from Smooth Signals (2019) (12)
Inversion of Euler integral transforms with applications to sensor data (2011) (11)
Gradient flows within plane fields (1999) (11)
Generic Hydrodynamic Instability of Curl Eigenfields (2003) (11)
Target Enumeration via Integration over Planar Sensor Networks (2008) (11)
Flows on ³ supporting all links as orbits (1995) (10)
Closed characteristics of fourth-order twist systems via braids (2000) (10)
Chaotic knots and wild dynamics (1998) (10)
Safe Cooperative Robot Patterns via Dynamics on Graphs (1998) (10)
Knotting Within the Gluing Bifurcation (10)
Chapter 1 – On the Contact Topology and Geometry of Ideal Fluids (2007) (10)
Unimodal Category and Topological Statistics (2011) (9)
Resonant Gluing bifurcations (2000) (9)
Overtwisted energy-minimizing curl eigenfields (2004) (9)
Tight contact structures via dynamics (1999) (8)
Applications of Sheaf Cohomology and Exact Sequences to Network Coding (Frontiers in mathematical science through collaborations with other disciplines) (2011) (8)
Euler–Bessel and Euler–Fourier transforms (2010) (7)
Grammatical Self Assembly for Planar Tiles (2004) (6)
From Morse-Smale to all knots and links (1997) (6)
Steady Nonintegrable High-Dimensional Fluids (2001) (6)
Topological Features Of Inviscid Flows (2001) (6)
Path Signatures on Lie Groups (2020) (5)
Topology and Robotics (2007) (5)
Quiver Signal Processing (QSP) (2020) (5)
DTIME: Discrete Topological Imaging for Multipath Environments (2010) (4)
Distributed Optimization with Sheaf Homological Constraints (2019) (4)
Flowlines transverse to knot and link fibrations (2004) (4)
TARGET ENUMERATION IN SENSOR NETWORKS VIA INTEGRATION WITH RESPECT TO EULER CHARACTERISTIC (2007) (4)
Pursuit-evasion game for normal distributions (2014) (3)
Persistent Extension and Analogous Bars: Data-Induced Relations Between Persistence Barcodes (2022) (3)
A Novel Algorithm for Topological Persistence , with Application to Neuroscience (2015) (3)
TARGET ENUMERATION VIA EULER CHARACTERISTIC INTEGRALS I : SENSOR FIELDS (2007) (3)
Tight contact structures and Anosov flows (2002) (3)
Saecular persistence (2021) (3)
A Temporal Logic-Based Hierarchical Network Connectivity Controller (2020) (2)
Scalar parabolic PDE's and braids (2004) (2)
Cyclic network automata and cohomological waves (2012) (2)
Shape Complexes for Metamorhpic Robots (2002) (2)
Nusselt number of a sphere in creeping flow (1990) (1)
Braids and differential equations (2006) (1)
THREE EXAMPLES OF APPLIED & COMPUTATIONAL HOMOLOGY (2008) (1)
The link of periodic orbits of a flow (1995) (1)
Diffusion of Information on Networked Lattices by Gossip (2022) (1)
Path homotopy invariants and their application to optimal trajectory planning (2018) (1)
Accumulations of in nite links (1)
Hadwiger's Theorem for Data (2012) (1)
Decomposition of nonlinear persistence modules (2019) (1)
A GEOMETRIC APPROACH TO DIPATH CLASSIFICATION ON PROCESS GRAPHS (2005) (1)
Relationship Between Gradient of Distance Functions and Tangents to Geodesics (2012) (1)
Minimal Unimodal Decompositions on Trees (2018) (1)
Network SheafModels for Social Information Dynamics (2022) (1)
Opinion: MOOCs and the future of mathematics (2013) (1)
Minimal unimodal decomposition on trees (2019) (0)
2008 BARCODES : THE PERSISTENT TOPOLOGY OF DATA (2014) (0)
5.3.4 - Absolute and Conditional (2015) (0)
2.3.1 - Differentials (2015) (0)
5.3.2 - Convergence Tests I (2015) (0)
Submission for EPADEL Student Paper Competition (2013) (0)
Harmonicity in Networked Social Information Dynamics (2022) (0)
Minimal unimodal decomposition on trees (2019) (0)
4.4.3.1 - Moments and Gyrations (2015) (0)
Cyclic network automata for indoor sensor network (2012) (0)
5.2.1 - Numerical ODEs (2015) (0)
5.3.1 - Infinite Series (2015) (0)
Flowlines transverse to fibred knots and links (2003) (0)
1.4.3.1 - Orders of Growth (2015) (0)
5.1.1.1 - Sequences (2015) (0)
An optimal property of the hyperplane system in a finite cubing (2021) (0)
An optimal property of the hyperplane system in a finite cubing (2021) (0)
Distributed computation of coverage in sensor networks by homological methods (2012) (0)
Ja n 20 03 Flowlines transverse to fibred knots and links (2003) (0)
Stokes’s Theorem, Data, and the Polar Ice Caps (2018) (0)
4.2.1.1 - Volume & Dimension (2015) (0)
DTIME: Discrete Topological Imaging for (2010) (0)
3.2.2 - Integration by Parts (2015) (0)
SHEAF LAPLACIANS FROM SMOOTH SIGNALS (2019) (0)
4.5.3 - Expectation and Variance (2015) (0)
2.2.1 - Linearization (2015) (0)
Asynchronous Diffusion of Data on Networked Lattices (2022) (0)
3.2.1 - Integration by Submission (2015) (0)
4.5.1 - Fair Probability (2015) (0)
3.2.4.2 - Bonus (2015) (0)
3.1.2 - A Simple O.D.E. (2015) (0)
1.2.2.1 - Exponentials (2015) (0)
On Sensor Network Localization Exploiting Topological Constraints* (2020) (0)
Poster abstract: Cyclic network automata for indoor sensor network (2012) (0)
Network Sheaves Valued in Categories of Adjunctions and their Laplacians (2021) (0)
5.2.2 - Numerical Integration (2015) (0)
Braid Floer homology1 (2009) (0)
Distributed Locally Non-interfering Connectivity via Linear Temporal Logic (2020) (0)
3.2.4.1 - Partial Fractions (2015) (0)
Accumulations of infinite links (1997) (0)
1.3.4 - Expansion Points (2015) (0)
Topology and Robotics: July 10-14, 2006, Fim Eth, Zurich (2007) (0)
On Laplacians (Invited Talk) (2021) (0)
5.1.3 - Discrete Calculus (2015) (0)
70 80 11 v 1 2 2 A ug 1 99 7 Contact Topology and Hydrodynamics (2008) (0)
CIS 602-01 : Scalable Data Analysis Internet of Things (2017) (0)
Persistent homology and Euler integral transforms (2018) (0)
1.2.2.2 - Bonus (2015) (0)
Braid classes and their Floer homology (2009) (0)
Contemporary Mathematics WINDING NUMBERS FOR NETWORKS WITH WEAK ANGULAR DATA ROBERT GHRIST (2006) (0)
Sheaves and Sensors (2008) (0)
Reconstruction of Euclidean embeddings in dense networks (2016) (0)
Lattice dynamic analysis of Raman data from tin tetrabromide: Chains at high pressures (1994) (0)
Tight contact structures on 3-manifolds via dynamics (1998) (0)
1.3.2 - Computing Taylor Series (2015) (0)
Gradient ows within plane elds (1999) (0)
3.4.3 - Tables and Software (2015) (0)
4.5.2 - Probability Densities (2015) (0)
Invariants for homology classes with application to optimal search and planning problem in robotics (2013) (0)
5.4.3.1 - Approximation and Error (2015) (0)

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