Applied Topology and Complex Networks
5–9 February, 2024
About the workshop
This workshop will feature the following two mini courses:
- Exploring the Borsuk-Ulam Theorem: Applications in Geometry and Combinatorics
by Arijit Ghosh (ISI Kolkata, India)
The Borsuk-Ulam Theorem, a fundamental result in algebraic
topology, establishes a fundamental connection between
symmetry and topology. It states that any continuous mapping
from an n-dimensional sphere to n-dimensional Euclidean space
must necessarily map a pair of diametrically opposite points
to the same point. This theorem provides profound insights
into the inherent relationship between geometric and
algebraic properties. Throughout this lecture series, our
primary objective is to understand the foundational
principles of the Borsuk-Ulam Theorem and explore its many
applications in addressing important questions across the
diverse domains of geometry and combinatorics.
Plan: A series of 5 lectures.
Course Material
- A tour of methods and algorithms for the manipulation and analysis of temporal networks
by Esteban Bautista-Ruiz (Universite du Littoral Cote d'Opale, France)
Computer networks, social networks, the web, or the
electric grid are examples of systems that play a crucial
role in modern society. In the last decade, the field of
complex networks has studied these systems through their
interrelated structure, revealing extremely valuable insights
about their behavior. As our understanding deepens, it
becomes evident that these systems not only possess
interrelated characteristics but also undergo evolution,
rendering the temporal dimension a powerful source of
information. The field of temporal networks emerges as the
key to unlocking this temporal wealth. However, leveraging
temporal information is not straightforward and it
necessitates sophisticated frameworks and ideas. Currently,
there is no unified theory, with numerous concepts and
methodologies being proposed and tested. The objective of our
mini-course is to provide a general tour of current ideas,
methods and algorithms in the realm of temporal networks.
Plan (Tentative):
- Day 1: Introduction
A reminder of graph theory and introduction to
temporal networks (basic definitions, challenges,
overview of course).
- Day 2: Updating algorithms for static graph properties
We begin by studying some algorithms that do not care
about temporal information. They aim to compute classical
graph properties but in a setting where the graph can
evolve. Thus, instead of recomputing the graph properties
from scratch every time the network changes, they try to
update a previously known result in a much more efficient
manner.
- Day 3: Temporal networks as a generalization of graphs
We study two formalisms that aim to extend graph
theory into a theory of temporal networks: the TVG and
Link Stream approaches.
- Day 4: Applications to node centrality and community detection
We study algorithms that leverage the formalisms
presented in Day 3 to do the concrete data mining
applications. In particular, that aim to estimate the
importance of vertices and the presence of communities in
the data.
- Day 5: Temporal networks as a generalization of time series
We study a formalism that aims to extend signal
processing into a theory of temporal networks.
Schedule
Date |
09:30–11:00 |
11:30–13:00 |
14:00–15:00 |
Mon 5 Feb |
Arijit Ghosh |
Esteban Bautista-Ruiz |
Discussion session |
Tue 6 Feb |
Arijit Ghosh |
Esteban Bautista-Ruiz |
Contributed talks |
Wed 7 Feb |
Arijit Ghosh |
Esteban Bautista-Ruiz |
Discussion session |
Thu 8 Feb |
Arijit Ghosh |
Esteban Bautista-Ruiz |
Contributed talks |
Fri 9 Feb |
Arijit Ghosh |
Esteban Bautista-Ruiz |
Discussion session |
|