5 citations · 7 across the 15 of their papers we have counts for
18 papers
What makes a theorem interesting? Operationalizing interestingness for open-ended exploration
Silvère Gangloff
An agent that explores, whether it generates conjectures or research ideas, must decide which of them are worth keeping. This judgment of interestingness is usually delegated to a…
Knowledge transfer between simple discrete worlds
Silvère Gangloff, Jan Hula
Adapting to a new world and reasoning correctly about which outcomes are possible under rules one has not met before is a basic capacity underlying general intelligence. We study i…
Assessing LLMs' mathematical abilities requires understanding the various mechanisms of mathematical creativity
Silvère Gangloff
How should we assess whether large language models can perform mathematical invention? I argue that this question is currently underspecified: mathematical creativity is not one ca…
Residual stratification and the Cantor-Bendixson structures of dual algebraic coframes
Silvère Gangloff, Alonso Nuñez
We introduce a notion of residual derivative for elements of a preordered set, a construction that generalizes both the Frattini subgroup in algebra and the Cantor-Bendixson deriva…
On the cohomology of homshifts
Nishant Chandgotia, Silvère Gangloff, Benjamin Hellouin de Menibus +1
We study the cohomology of symbolic dynamical systems called homshifts: they are the nearest-neighbour shifts of finite type whose adjacency rules are the same in ev…
Undecidability of the block gluing classes of homshifts
Nishant Chandgotia, Silvère Gangloff, Benjamin Hellouin de Menibus +1
A homshift is a -dimensional shift of finite type which arises as the space of graph homomorphisms from the grid graph to a finite connected undirected graph .…
The topological structure of isolated points in the space of -shifts
Silvère Gangloff, Alonso Núñez
R. Pavlov and S. Schmieding provided recently some results about generic -shifts, which rely mainly on an original theorem stating that isolated points form a residual…
Various questions around finitely positively expansive dynamical systems
Silvère Gangloff, Pierre Guillon, Piotr Oprocha
It is well-known that when a positively expansive dynamical system is invertible then its underlying space is finite. C.Morales has introduced a decade ago a natural way to general…
Short-range and long-range order: a transition in block-gluing behavior in Hom shifts
Silvere Gangloff, Benjamin Hellouin de Menibus, Piotr Oprocha
Hom shifts form a class of multidimensional shifts of finite type (SFT) and consist of colorings of the grid Z2 where adjacent colours must be neighbors in a fixed finite undirecte…
A Cantor dynamical system is slow if and only if all its finite orbits are attracting
Silvère Gangloff, Piotr Oprocha
In this paper, we completely solve the problem when a Cantor dynamical system can be embedded in with vanishing derivative everywhere. For this purpose, we con…
On the computability properties of topological entropy: a general approach
Silvere Gangloff, Alonso Herrera, Cristobal Rojas +1
The dynamics of symbolic systems, such as multidimensional subshifts of finite type or cellular automata, are known to be closely related to computability theory. In particular, th…
Asymptotic growth rate of square grids dominating sets: a symbolic dynamics approach
Silvère Gangloff, Alexandre Talon
In this text, we prove the existence of an asymptotic growth rate of the number of dominating sets (and variants) on finite rectangular grids, when the dimensions of the grid grow…
From algebraic to coordinate Bethe ansatz for square ice
Silvère Gangloff
In this text, we provide a detailed exposition of the Algebraic Bethe ansatz for square ice (or six vertex model), which allows the construction of candidate eigenvectors for the t…
A proof that square ice entropy is
Silvère Gangloff
In this text, we provide a fully rigorous, complete and self-contained proof of E.H.Lieb's statement that (topological) entropy of square ice (or six vertex model, XXZ spin chain f…
Simulation of minimal effective dynamical systems on the Cantor sets by minimal tridimensional subshifts of finite type
Silvère Gangloff, Mathieu Sablik
In this text, we prove then that any minimal effective dynamical system on a Cantor set can be simulated by a minimal -SFT, in a sense that…
A characterization of entropy dimensions of minimal tridimensional subshifts of finite type
Silvère Gangloff, Mathieu Sablik
We prove in this text a characterization of the possible entropy dimensions of minimal tridimensional subshifts of finite type with a computability condition, using Goldbach's theo…
Quantified block gluing, aperiodicity and entropy of multidimensional SFT
Silvère Gangloff, Mathieu Sablik
It is possible to define mixing properties for subshifts according to the intensity which allows to concatenate two rectangular blocks. We study the interplay between this intensit…
Effect of quantified irreducibility on the computability of subshift entropy
Silvère Gangloff, Benjamin Hellouin de Menibus
We study the difficulty of computing topological entropy of subshifts subjected to mixing restrictions. This problem is well-studied for multidimensional subshifts of finite type :…