Add to ORKGIt is widely known that persistent homology in more than one parameter is significantly more "complicated" than in the single-parameter setting. In this talk I will discuss in what sense it is more complicated from the point of view of representation theory, and from the point of view of algorithms. I will also give examples of how multi-parameter persistence modules naturally appear in applications.Non UBCUnreviewedAuthor affiliation: Technical University Munich/VU AmsterdamPostdoctora
A fundamental tool in topological data analysis is persistent homology, which allows extraction of i...
In various applications of data classification and clustering problems, multi-parameter analysis is ...
The extension of persistent homology to multi-parameter setups is an algorithmic challenge. Since mo...
It is widely known that persistent homology in more than one parameter is significantly more "compli...
We explore Persistence Theory in its full generality. As a particular instance, we first discuss one...
I have been thinking about this problem for a couple of years, first alone, then with a grad student...
In their paper "The theory of multidimensional persistence", Carlsson and Zomorodian write "Our stud...
The stability of persistent homology is rightly considered to be one of its most important propertie...
Kernels for one-parameter persistent homology have been established to connect persistent homology ...
Persistent homology is a recent grandchild of homology that has found use in science and engineering...
Motivated by the problem of optimizing sensor network covers, we generalize the persistent homology ...
We present a new proof of the algebraic stability theorem, perhaps the main theorem in the theory of...
A fundamental tool in topological data analysis is persistent homology, which allows extraction of i...
Persistent homology is a field within Topological Data Analysis that uses persistence modules to stu...
Persistent homology allows for tracking topological features, like loops, holes and their higher-dim...
A fundamental tool in topological data analysis is persistent homology, which allows extraction of i...
In various applications of data classification and clustering problems, multi-parameter analysis is ...
The extension of persistent homology to multi-parameter setups is an algorithmic challenge. Since mo...
It is widely known that persistent homology in more than one parameter is significantly more "compli...
We explore Persistence Theory in its full generality. As a particular instance, we first discuss one...
I have been thinking about this problem for a couple of years, first alone, then with a grad student...
In their paper "The theory of multidimensional persistence", Carlsson and Zomorodian write "Our stud...
The stability of persistent homology is rightly considered to be one of its most important propertie...
Kernels for one-parameter persistent homology have been established to connect persistent homology ...
Persistent homology is a recent grandchild of homology that has found use in science and engineering...
Motivated by the problem of optimizing sensor network covers, we generalize the persistent homology ...
We present a new proof of the algebraic stability theorem, perhaps the main theorem in the theory of...
A fundamental tool in topological data analysis is persistent homology, which allows extraction of i...
Persistent homology is a field within Topological Data Analysis that uses persistence modules to stu...
Persistent homology allows for tracking topological features, like loops, holes and their higher-dim...
A fundamental tool in topological data analysis is persistent homology, which allows extraction of i...
In various applications of data classification and clustering problems, multi-parameter analysis is ...
The extension of persistent homology to multi-parameter setups is an algorithmic challenge. Since mo...