Assaf Libman
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View article: Are free groups of different ranks bi-invariantly quasi-isometric?
Are free groups of different ranks bi-invariantly quasi-isometric? Open
We prove that a homomorphism between free groups of finite rank equipped with the bi-invariant word metrics associated with finite generating sets is a quasi-isometry if and only if it is an isomorphism.
View article: Are free groups of different ranks bi-invariantly quasi-isometric?
Are free groups of different ranks bi-invariantly quasi-isometric? Open
We prove that a homomorphism between free groups of finite rank equipped with the bi-invariant word metrics is a quasi-isometry if and only if it is an isomorphism.
View article: Abstract Weighted Based Gradual Semantics in Argumentation Theory
Abstract Weighted Based Gradual Semantics in Argumentation Theory Open
Weighted gradual semantics provide an acceptability degree to each argument representing the strength of the argument, computed based on factors including background evidence for the argument, and taking into account interactions between t…
View article: The complex of injective words of permutations which are not derangements is contractible
The complex of injective words of permutations which are not derangements is contractible Open
Let $D_n \subseteq Σ_n$ be the set of derangements in the symmetric group. We prove that the complex of injective words generated by $Σ_n \setminus D_n$ is contractible. This gives a conceptual explanation to the well known fact that the c…
View article: Punctured groups for exotic fusion systems
Punctured groups for exotic fusion systems Open
The transporter systems of Oliver and Ventura and the localities of Chermak are classes of algebraic structures that model the ‐local structures of finite groups. Other than the transporter categories and localities of finite groups, impor…
View article: Pricing Multi-Asset Contingent Claims in a Multi-Dimensional Binomial Market
Pricing Multi-Asset Contingent Claims in a Multi-Dimensional Binomial Market Open
We consider an incomplete multi-asset binomial market model. We prove that for a wide class of contingent claims the extremal multi-step martingale measure is a power of the corresponding single-step extremal martingale measure. This allow…
View article: European baskets in discrete-time continuous-binomial market models
European baskets in discrete-time continuous-binomial market models Open
We consider a discrete-time incomplete multi-asset market model with continuous price jumps. For a wide class of contingent claims, including European basket call options, we compute the bounds of the interval containing the no-arbitrage p…
View article: Minimum Cost Super-Hedging in a Discrete Time Incomplete Multi-Asset Binomial Market
Minimum Cost Super-Hedging in a Discrete Time Incomplete Multi-Asset Binomial Market Open
We consider a multi-asset incomplete model of the financial market, where each of $m\geq 2$ risky assets follows the binomial dynamics, and no assumptions are made on the joint distribution of the risky asset price processes. We provide ex…
View article: Directional asymptotic cones of groups equipped with bi-invariant metrics
Directional asymptotic cones of groups equipped with bi-invariant metrics Open
Given a bi-invariant metric on a group, we construct a version of an asymptotic cone without using ultrafilters. The new construction, called the directional asymptotic cone, is a contractible topological group equipped with a complete bi-…
View article: Analytical Solutions for the Inverse Problem within Gradual Semantics
Analytical Solutions for the Inverse Problem within Gradual Semantics Open
Gradual semantics within abstract argumentation associate a numeric score with every argument in a system, which represents the level of acceptability of this argument, and from which a preference ordering over arguments can be derived. Wh…
View article: Uniform boundedness for algebraic groups and Lie groups
Uniform boundedness for algebraic groups and Lie groups Open
Let $G$ be a semisimple linear algebraic group over a field $k$ and let $G^+(k)$ be the subgroup generated by the subgroups $R_u(Q)(k)$, where $Q$ ranges over all the minimal $k$-parabolic subgroups $Q$ of $G$. We prove that if $G^+(k)$ is…
View article: Punctured groups for exotic fusion systems
Punctured groups for exotic fusion systems Open
The transporter systems of Oliver and Ventura and the localities of Chermak are classes of algebraic structures that model the $p$-local structures of finite groups. Other than the transporter categories and localities of finite groups, im…
View article: Strong and uniform boundedness of groups
Strong and uniform boundedness of groups Open
A group [Formula: see text] is called bounded if every conjugation-invariant norm on [Formula: see text] has finite diameter. We introduce various strengthenings of this property and investigate them in several classes of groups including …
View article: Pricing and hedging contingent claims in a multi-asset binomial market
Pricing and hedging contingent claims in a multi-asset binomial market Open
We consider an incomplete multi-asset binomial market model. We prove that for a wide class of contingent claims the extremal multi-step martingale measure is a power of the corresponding single-step extremal martingale measure. This allow…
View article: Polytopes associated with lattices of subsets and maximising expectation\n of random variables
Polytopes associated with lattices of subsets and maximising expectation\n of random variables Open
The present paper originated from a problem in Financial Mathematics\nconcerned with calculating the value of a European call option based on\nmultiple assets each following the binomial model. The model led to an\ninteresting family of po…
View article: Polytopes associated with lattices of subsets and maximising expectation of random variables
Polytopes associated with lattices of subsets and maximising expectation of random variables Open
The present paper originated from a problem in Financial Mathematics concerned with calculating the value of a European call option based on multiple assets each following the binomial model. The model led to an interesting family of polyt…
View article: Stabilization of the homotopy groups of the self equivalences of linear\n spheres
Stabilization of the homotopy groups of the self equivalences of linear\n spheres Open
Let $G$ be a finite group. Let $U_1,U_2,\\dots$ be a sequence of orthogonal\nrepresentations in which any irreducible representation of $\\oplus_{n \\geq 1}\nU_n$ has infinite multiplicity. Let $V_n=\\oplus_{i=1}^n U_n$ and $S(V_n)$\ndenot…
View article: Stabilization of the homotopy groups of the self equivalences of linear spheres
Stabilization of the homotopy groups of the self equivalences of linear spheres Open
Let $G$ be a finite group. Let $U_1,U_2,\dots$ be a sequence of orthogonal representations in which any irreducible representation of $\oplus_{n \geq 1} U_n$ has infinite multiplicity. Let $V_n=\oplus_{i=1}^n U_n$ and $S(V_n)$ denote the l…