Related papers: Introduction to Iterated Monodromy Groups
In this paper a relation between iterated cyclings and iterated powers of elements in a Garside group is shown. This yields a characterization of elements in a Garside group having a rigid power, where 'rigid' means that the left normal…
A fundamental problem from invariant theory is to describe the endomorphism algebra of multilinear functions on a representation V invariant under the action of a group G. According to Weyl's classic, a first main (later: fundamental)…
Recent results in control systems and numerical integration literature utilize invariant set theory to lift dynamical systems evolving on nonlinear manifolds to those evolving on vector spaces. We leverage this technique to propose an…
These are notes for a mini-course of 3 lectures given at the St. Petersburg School in Probability and Statistical Physics (June 2012). My aim was to explain, on the example of a particular model, how ideas from the representation theory of…
We extend the notions of nonautonomous dynamics to arbitrary groups, through groupoid morphisms. This also presents a generalization of classic dynamical systems and group actions. We introduce the structure of cotranslations, as a specific…
Magnitude homology is an invariant of enriched categories which generalizes ordinary categorical homology -- the homology of the classifying space of a small category. The classifying space can also be generalized in a different direction:…
This work presents a detailed analysis of the combinatorics of modular operads. These are operad-like structures that admit a contraction operation as well as an operadic multiplication. Their combinatorics are governed by graphs that admit…
In 2023, two striking, nearly simultaneous, mathematical discoveries have excited their respective communities, one by Greenfeld and Tao, the other (the Hat tile) by Smith, Myers, Kaplan and Goodman-Strauss, which can both be summed up as…
In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and also restricted sumsets and zero-sum problems on abelian…
In cooperative game theory, the social configurations of players are modeled by balanced collections. The Bondareva-Shapley theorem, perhaps the most fundamental theorem in cooperative game theory, characterizes the existence of solutions…
Given a family $X$ of complex varieties degenerating over a punctured disc, one is interested in computing related invariants called the motivic nearby fiber and the refined limit mixed Hodge numbers, both of which contain information about…
The method of monodromy is an important tool for computing Virasoro conformal blocks in a two-dimensional Conformal Field Theory (2d CFT) at large central charge and external dimensions. In deriving the form of the monodromy problem, which…
There has been increasing interest in the integrated information theory (IIT) ofconsciousness, which hypothesizes that consciousness is integrated information withinneuronal dynamics. However, the current formulation of IIT poses both…
Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will…
Planning for multi-robot teams in complex environments is a challenging problem, especially when these teams must coordinate to accomplish a common objective. In general, optimal solutions to these planning problems are computationally…
In this work we investigate dynamical systems designed to approach the solution sets of inclusion problems involving the sum of two maximally monotone operators. Our aim is to design methods which guarantee strong convergence of…
A generalization of recent group-theoretic matrix multiplication algorithms to an analogue of the theory of partial matrix multiplication is presented. We demonstrate that the added flexibility of this approach can in some cases improve…
A hybrid system is a system whose dynamics is given by a mixture of both continuous and discrete transitions. In particular, these systems can be utilised to describe the dynamics of a mechanical system with impacts. Based on the approach…
We consider three important and well-studied algorithmic problems in group theory: the word, geodesic, and conjugacy problem. We show transfer results from individual groups to graph products. We concentrate on logspace complexity because…
The representation theory of the symmetric groups S_n is intimately related to combinatorics: combinatorial objects such as Young tableaux and combinatorial algorithms such as Murnaghan-Nakayama rule. In the limit as n tends to infinity,…