Gunnar Carlsson

Q: What Schools Are Affiliated With Gunnar Carlsson

Gunnar Carlsson is affiliated with the following schools: University of California, San Diego, University of Chicago, Stanford University, Harvard University

Gunnar Carlsson's AcademicInfluence.com Rankings

Gunnar Carlsson

Mathematics

#582

World Rank

#1099

Historical Rank

Measure Theory

#1746

World Rank

#2143

Historical Rank

mathematics Degrees

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Mathematics

Gunnar Carlsson's Degrees

PhD Mathematics Stanford University

Why Is Gunnar Carlsson Influential?

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According to Wikipedia, Gunnar E. Carlsson is an American mathematician, working in algebraic topology. He is known for his work on the Segal conjecture, and for his work on applied algebraic topology, especially topological data analysis. He is a Professor Emeritus in the Department of Mathematics at Stanford University. He is the founder and president of the predictive technology company Ayasdi.

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Gunnar Carlsson'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

Topology and data (2009) (1955)
Computing Persistent Homology (2004) (1580)
Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition (2007) (576)
On the Local Behavior of Spaces of Natural Images (2007) (547)
Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival (2011) (497)
The Theory of Multidimensional Persistence (2007) (472)
Extracting insights from the shape of complex data using topology (2013) (456)
Topological estimation using witness complexes (2004) (395)
Persistence barcodes for shapes (2004) (385)
Zigzag Persistence (2008) (296)
Characterization, Stability and Convergence of Hierarchical Clustering Methods (2010) (286)
Topology of viral evolution (2013) (250)
Zigzag persistent homology and real-valued functions (2009) (233)
Topological pattern recognition for point cloud data* (2014) (217)
Topological analysis of population activity in visual cortex. (2008) (205)
Equivariant stable homotopy and Segal's Burnside ring conjecture (1984) (193)
A Topological Paradigm for Hippocampal Spatial Map Formation Using Persistent Homology (2012) (192)
Towards a new approach to reveal dynamical organization of the brain using topological data analysis (2018) (153)
Controlled algebra and the novikov conjectures for K- and L-theory (1995) (149)
A barcode shape descriptor for curve point cloud data (2004) (142)
Topological methods for exploring low-density states in biomolecular folding pathways. (2008) (129)
The Ring of Algebraic Functions on Persistence Bar Codes (2013) (119)
Computing Multidimensional Persistence (2009) (116)
Localized Homology (2007) (116)
Classification of hepatic lesions using the matching metric (2012) (99)
A Topology Layer for Machine Learning (2019) (91)
Classifying Clustering Schemes (2010) (91)
Structural Insight into RNA Hairpin Folding Intermediates (2008) (91)
Interconnection Networks Based on a Generalization of Cube-Connected Cycles (1985) (90)
An Algebraic Topological Method for Feature Identification (2006) (67)
Evasion paths in mobile sensor networks (2013) (65)
A Klein-Bottle-Based Dictionary for Texture Representation (2014) (64)
On the rank of abelian groups acting freely on(Sn)k (1982) (60)
Constructing Multi-Resolution Markov State Models (MSMs) to Elucidate RNA Hairpin Folding Mechanisms (2010) (58)
The integral K-theoretic Novikov conjecture for groups with finite asymptotic dimension (2004) (56)
Persistent Clustering and a Theorem of J. Kleinberg (2008) (54)
On the Nonlinear Statistics of Range Image Patches (2009) (53)
Axiomatic construction of hierarchical clustering in asymmetric networks (2013) (52)
Statistical topology via Morse theory, persistence and nonparametric estimation (2009) (52)
Equivariant stable homotopy and Sullivan's conjecture (1991) (51)
CHAPTER 13 – Stable Homotopy and Iterated Loop Spaces (1995) (49)
On homological coherence of discrete groups (2004) (49)
Computational topology for configuration spaces of hard disks (2011) (45)
Derived Completions in Stable Homotopy theory (2007) (44)
G. B. Segal's burnside ring conjecture for ? (1983) (44)
A counterexample to a conjecture of steenrod (1981) (41)
Exposition and Interpretation of the Topology of Neural Networks (2018) (40)
Topological Approaches to Deep Learning (2018) (40)
Topological methods reveal high and low functioning neuro‐phenotypes within fragile X syndrome (2014) (38)
Small Diameter Symmetric Networks from Linear Groups (1992) (37)
Multiparameter Hierarchical Clustering Methods (2010) (37)
Persistent Clustering and a Theorem of J . (2008) (36)
Topological approximation by small simplicial complexes (2003) (36)
On the homology of finite free (ℤ/2)n-Complexes (1983) (36)
Free (ℤ/2)k-actions and a problem in commutative algebra (1986) (34)
A simplicial group construction for balanced products (1984) (33)
Persistent homology and applied homotopy theory (2020) (30)
Cech homology and the Novikov Conjectures for K- and L-Theory (1998) (30)
On the algebraic $K$-theory of simply connected spaces (1996) (30)
Novikov Conjectures, Index Theorems and Rigidity: Bounded K-theory and the assembly map in algebraic K-theory (1995) (29)
The cyclic groups and the free loop space (1987) (29)
Higher topological cyclic homology and the Segal conjecture for tori (2008) (29)
On the algebraicK-theory of infinite product categories (1995) (28)
Hierarchical Quasi-Clustering Methods for Asymmetric Networks (2014) (28)
On the Non-Existence of Free Actions of Elementary Abelian Groups on Products of Spheres (1980) (27)
Topological methods for data modelling (2020) (27)
Applications of Zigzag Persistence to Topological Data Analysis (2011) (27)
Persistent Topology and Metastable State in Conformational Dynamics (2013) (26)
Nudged Elastic Band in Topological Data Analysis (2011) (25)
Foundations of numerical multilinear algebra: decomposition and approximation of tensors (2007) (25)
Covering Homology (2007) (25)
Parametrized homology via zigzag persistence (2016) (23)
Numeric invariants from multidimensional persistence (2014) (21)
Topological data analysis reveals genotype–phenotype relationships in primary ciliary dyskinesia (2021) (20)
The free loop space and the algebraic k-theory of spaces (1987) (20)
Dimension Independent Matrix Square using MapReduce (2013) (19)
Symmetric and r-symmetric tropical polynomials and rational functions (2014) (19)
Building Markov state models with solvent dynamics (2013) (19)
Continuously controlled algebraic $K$-theory of spaces and the Novikov conjecture (1998) (18)
Hierarchical clustering of asymmetric networks (2016) (17)
Algorithmic and statistical challenges in modern largescale data analysis are the focus of MMDS 2008 (2008) (17)
Persistent and Zigzag Homology: A Matrix Factorization Viewpoint (2019) (16)
Persistent homology of the sum metric (2019) (15)
Derived representation theory and the algebraic K‐theory of fields (2008) (15)
Topological De-Noising: Strengthening the Topological Signal (2009) (14)
Homology of complexes of degree one graphs (1995) (14)
The structure of odd L-groups (1979) (13)
Equivariant motivic homotopy theory (2014) (12)
Segal's Burnside ring conjecture and the homotopy limit problem (1987) (12)
Some exact sequences in the theory of Hermitian forms (1980) (12)
Controlled algebraic G-theory, I (2011) (12)
A geometric framework for sparse matrix problems (2004) (11)
Equivariant Formal Group Laws and Complex Oriented Cohomology Theories (2001) (11)
Algebraic K-theory of Geometric Groups (2013) (10)
Hierarchical clustering methods and algorithms for asymmetric networks (2013) (10)
A look at the topology of convolutional neural networks (2018) (9)
Alternative axiomatic constructions for hierarchical clustering of asymmetric networks (2013) (9)
A survey of equivariant stable homotopy theory (1992) (9)
Topological Data Analysis and Machine Learning Theory (2012) (8)
Structured stable homotopy theory and the descent problem for the algebraic k-theory of ?elds (2003) (8)
A near optimal coder for image geometry with adaptive partitioning (2008) (8)
The Shape of Data (2012) (8)
The shape of biomedical data (2017) (7)
BASE CHANGE FUNCTORS IN THE A1-STABLE HOMOTOPY CATEGORY (2001) (7)
Equivariant Stable Homotopy Theory and the Finite Descent Problem for Unstable Algebraic K-Theories (1991) (7)
Morse theory in topological data analysis (2011) (6)
Topological Deep Learning (2021) (6)
Deloopings in Algebraic K-theory (2010) (6)
The integral K-theoretic Novikov conjecture for groups with finite asymptotic dimension (2005) (6)
The topology of politics : voting connectivity in the US House of Representatives (2012) (6)
Proper Homotopy Theory and Transfers for Infinite Groups (1994) (6)
Advances in Homotopy Theory: Homotopy fixed points in the algebraic K-theory of certain infinite discrete groups (1989) (6)
Excisive Hierarchical Clustering Methods for Network Data (2016) (5)
Fibres of Failure: Classifying errors in predictive processes (2018) (5)
On the homotopy fixed point problem for free loop spaces and other function complexes (1991) (5)
Metric Representations of Network Data (2015) (5)
Recent developments in algebraic K-theory (2001) (5)
Admissible Hierarchical Clustering Methods and Algorithms for Asymmetric Networks (2016) (5)
A Topological Analysis of the Space of Natural Images (2007) (5)
Categories of acyclic graphs and automorphisms of free groups (1996) (5)
On modules over infinite group rings (2015) (5)
A geometric reformulation of the representational assembly conjecture for the K-theory of fields with pro-l absolute Galois group (2013) (4)
EQUIVARIANT STABLE HOMOTOPY METHODS IN THE ALGEBRAIC K-THEORY OF INFINITE GROUPS (2014) (4)
Topology, geometry, and algebra : interactions and new directions : Conference on Algebraic Topology in honor of R. James Milgram, August 17-21, 1999, Stanford University (2001) (4)
The space of sections of a smooth function (2020) (4)
ON THE WITT GROUP OF A 2-ADIC GROUP RING (1980) (4)
K-THEORY WITH FIBRED CONTROL (2014) (3)
Persistent Homology and Shape Description – I (2003) (3)
Algebraic Topology and Its Applications (2011) (3)
XIII. Free (ℤ/2)3 - Actions on Finite Complexes (1988) (3)
On the stable splitting of $b{\rm o}\wedge b{\rm o}$ and torsion operations in connective $K$-theory. (1980) (3)
Algebraic Techniques in Systolic Array Design. (1984) (3)
Genetic nets and dissipative structures: an algebraic approach. (1974) (3)
Some restrictions on finite groups acting freely on (ⁿ) (1981) (3)
Bounded G-theory with fibred control (2018) (3)
Data Analysis using Computational Topology and Geometric Statistics (2009) (2)
Dimension Independent Matrix Square using MapReduce (DIMSUM) (2013) (2)
Torsion with rings for orders and finite groups (1978) (2)
∈-entropy of piecewise polynomial functions and tree partitioning compression (2008) (2)
Homological Coordinatization (2011) (2)
K-theory of geometric modules with fibred control (2014) (2)
Motivic and \'Etale Spanier-Whitehead duality and the Becker-Gottlieb transfer (2020) (2)
MMDS 2008 : Algorithmic and Statistical Challenges in Modern Large-Scale Data Analysis are the Focus (2009) (2)
Higher topological cyclic homology (2007) (2)
Exterior Critical Series of Persistence Modules (2013) (2)
Galois descent for completed Algebraic K-theory (2013) (2)
K-theoretic descent and a motivic Atiyah-Segal theorem (2010) (2)
Wu invariants of Hermitian forms (1980) (2)
Excision in equivariant fibred G-theory (2019) (2)
Computational Algebraic Topology (2008) (2)
Some ideas for formalizing clustering schemes (2009) (2)
Atiyah-Segal Derived Completions for Equivariant Algebraic G-Theory and K-Theory (2019) (2)
Genetic nets and dissipative structures: An algebraic approach (1974) (1)
ON THE STABLE SPLITTING OF bo A bo AND TORSION OPERATIONS IN CONNECTIVE if-ΊΉEORY (2012) (1)
Algebraic topology : proceedings of an International Conference held in Arcata, California, July 27-August 2, 1986 (1989) (1)
MMDS 2008 : Algorithmic and Statistical Challenges in Modern Large-Scale Data Analysis , Part I (2009) (1)
Robust Hierarchical Clustering for Directed Networks: An Axiomatic Approach (2021) (1)
Topological algorithms mapping point cloud data (2009) (1)
A Prime Decomposition of Probabilistic Automata (2015) (1)
Computing Multidimensional Persistence * ½ Áòøöóù Blockinøóò (2009) (1)
A geometric framework for sparse matrix problem (2004) (1)
Topological Convolutional Neural Networks (2020) (1)
Desuspension in the symmetric L-groups (1979) (1)
Mapping geometry in heart rate data (2009) (1)
Representable Hierarchical Clustering Methods for Asymmetric Networks (2017) (1)
A Fast Geometric Clustering Method on Conformation Space of Biomolecules (2009) (1)
Topological Data Analysis Coupled with Machine Learning Reveals New Genotype-Phenotype Relationships in Primary Ciliary Dyskinesia (2020) (1)
The completion conjecture in equivariant cohomology (2006) (1)
ON THE STABLE SPLITTING OF bo A bo AND TORSION OPERATIONS IN CONNECTIVE if-ΊΉEORY (2012) (1)
CLASSIFICATION OF DI-EMBEDDINGS OF THE n-CUBE INTO R (2007) (1)
Approximating Absolute Galois Groups (2022) (0)
Topological Modeling of Complex Data (2018) (0)
Geometric Networks Analysis (2012) (0)
Union College Mathematics Conference Abstracts for the Algebraic Topology Session October 19-20 , 2013 (2013) (0)
AFRL-RY-WP-TM-2009-1057 ALGEBRAIC TOPOLOGY AND NEUROSCIENTIFIC DATA-NEOVISION 2 (2009) (0)
REAL COBORDISM AND GREEK LETTER ELEMENTS IN THE GEOMETRIC CHROMATIC SPECTRAL SEQUENCE (2005) (0)
Algebraic Topology and Neuroscientific Data - Neovision 2 (2009) (0)
Symmetric and r-Symmetric Tropical Polynomials and Max-Min Functions (2014) (0)
Numeric invariants from multidimensional persistence (2017) (0)
Algebraic techniques in systolic array design. Final report, October 1982-September 1983 (1984) (0)
From SIAM News , Volume 42 , Number 2 , March 2009 MMDS 2008 : Algorithmic and Statistical Challenges in Modern Large-Scale Data Analysis , Part II (2009) (0)
LARGE SCALE GRAPH COMPLETION A DISSERTATION SUBMITTED TO THE INSTITUTE FOR COMPUTATIONAL AND MATHEMATICAL ENGINEERING AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY (2014) (0)
Publisher's Note: Computational topology for configuration spaces of hard disks [Phys. Rev. E 85, 011303 (2012)] (2012) (0)
Asymptotic transfer maps in parametrized K-theory (2020) (0)
IDEMPOTENTS AND LANDWEBER EXACTNESS IN BRAVE NEW ALGEBRA (1999) (0)
Characterizing Properties for Q-Clustering (2012) (0)
Hierarchical clustering of asymmetric networks (2017) (0)
SURIM 2017 Project: Persistent Homology of Molecular Rotation Projections (2017) (0)
BOUNDED K -THEORY OF EXACT CATEGORIES (2003) (0)
K and L-theory (1989) (0)
Topological Methods for Data Fusion (2014) (0)
Topological mapping and exploration of genotyping data using Iris (2013) (0)
Topology in sensor networks (2008) (0)
A CHAIN COALGEBRA MODEL FOR THE JAMES MAP (2007) (0)
Meeting: Algorithms for Modern Massive Data Sets (2008) (0)
Classifying Clustering Schemes (2013) (0)
Evasion paths by homotopy limits (2022) (0)

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