Ph.D
Group : Graphs, ALgorithms and Combinatorics

Classification of P-oligomorphic groups, conjectures of Cameron and Macpherson

Starts on
Advisor : THIÉRY, Nicolas

Funding :
Affiliation : Université Paris-Saclay
Laboratory : l'amphithéâtre DIGITÉO du bâtiment CLAUDE SHANNON

Defended on 29/11/2019, committee :

Research activities :

Abstract :
Given an infinite permutation group G, consider the function that
maps every natural integer n to the number of orbits of n-subsets,
for the induced action of G on the subsets of elements.
Cameron conjectured that this counting function, the profile of G,
is asymptotically equivalent to a polynomial if it is bounded
above by a polynomial. Another, stronger conjecture was later made
by Macpherson. It involves a certain structure of graded agebra on
the orbits of subsets, created by Cameron, and states that if the
profile of G is bounded by a polynomial, then its orbit algebra is
finitely generated.
The main achievement of the thesis is to classify the permutation
with polynomially bounded profile (up to closure), which in
particular demonstrates the two conjectures. The approach involves
studying the lattice of block systems, an experimental exploration
on computer, and tools from group theory.

CAUSAL LEARNING FOR DIAGNOSTIC SUPPORT


CAUSAL UNCERTAINTY QUANTIFICATION UNDER PARTIAL KNOWLEDGE AND LOW DATA REGIMES


MICRO VISUALIZATIONS: DESIGN AND ANALYSIS OF VISUALIZATIONS FOR SMALL DISPLAY SPACES
The topic of this habilitation is the study of very small data visualizations, micro visualizations, in display contexts that can only dedicate minimal rendering space for data representations. For several years, together with my collaborators, I have been studying human perception, interaction, and analysis with micro visualizations in multiple contexts. In this document I bring together three of my research streams related to micro visualizations: data glyphs, where my joint research focused on studying the perception of small-multiple micro visualizations, word-scale visualizations, where my joint research focused on small visualizations embedded in text-documents, and small mobile data visualizations for smartwatches or fitness trackers. I consider these types of small visualizations together under the umbrella term ``micro visualizations.'' Micro visualizations are useful in multiple visualization contexts and I have been working towards a better understanding of the complexities involved in designing and using micro visualizations. Here, I define the term micro visualization, summarize my own and other past research and design guidelines and outline several design spaces for different types of micro visualizations based on some of the work I was involved in since my PhD.