Related papers: The Modular Isomorphism Problem for small groups -…

This paper proposes an interior-point framework for constrained optimization problems whose decision variables evolve on matrix Lie groups. The proposed method, termed the Matrix Lie Group Interior-Point Method (MLG-IPM), operates directly…

We compute the full isometry group of any left invariant metric on a simply connected, non-unimodular Lie group of dimension three. As an application, we determine the index of symmetry of such metrics and prove that the singularities of…

We study the codegree isomorphism problem for finite simple groups. In particular, we show that such a group is determined by the codegrees (counting multiplicity) of its irreducible characters. The proof is uniform for all simple groups…

This paper addresses the problem of decomposing a numerical semigroup into m-irreducible numerical semigroups. The problem originally stated in algebraic terms is translated, introducing the so called Kunz-coordinates, to resolve a series…

The isomorphism problem for graphs (GI) and the isomorphism problem for groups (GrISO) have been studied extensively by researchers. The current best algorithms for both these problems run in quasipolynomial time. In this paper, we study…

In this paper we generalize the Interior Point-Proximal Method of Multipliers (IP-PMM) presented in [An Interior Point-Proximal Method of Multipliers for Convex Quadratic Programming, Computational Optimization and Applications, 78,…

Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only…

By double ideal quotient, we mean $(I:(I:J))$ where ideals $I$ and $J$. In our previous work [11], double ideal quotient and its variants are shown to be very useful for checking prime divisor and generating primary component. Combining…

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…

For every odd prime $p$ and every integer $n\geq 12$ there is a Heisenberg group of order $p^{5n/4+O(1)}$ that has $p^{n^2/24+O(n)}$ pairwise nonisomorphic quotients of order $p^{n}$. Yet, these quotients are virtually indistinguishable.…

Let $R$ be a standard graded polynomial ring that is finitely generated over a field, and let $I$ be a homogenous prime ideal of $R$. Bhatt, Blickle, Lyubeznik, Singh, and Zhang examined the local cohomology of $R/I^t$, as $t$ grows…

In this paper we consider the Ideal Membership Problem (IMP for short), in which we are given real polynomials $f_0,f_1,\dots, f_k$ and the question is to decide whether $f_0$ belongs to the ideal generated by $f_1,\dots,f_k$. In the more…

We describe three algorithms to determine the stable, semistable, and torus-polystable loci of the GIT quotient of a projective variety by a reductive group. The algorithms are efficient when the group is semisimple. By using an…

We investigate whether the group algebra of a finite group over a localisation of the integers is semiperfect. The main result is a necessary and sufficient arithmetic criterion in the ordinary case. In the modular case, we propose a…

In this paper we introduce a new problem called the Isogenous Embedding Problem (IEP). The existence of solutions to this problem is related to the primes of bad reduction of CM curves of genus $3$ and we can detect potentially good…

Ising machines (IM) are physics-inspired alternatives to von Neumann architectures for solving hard optimization tasks. By mapping binary variables to coupled Ising spins, IMs can naturally solve unconstrained combinatorial optimization…

Let V_* be the normalized unitary subgroup of the modular group algebra FG of a finite p-group G over a finite field F with the classical involution *. We investigate the isomorphism problem for the group V_*, that asks when the group V_*…

The Sparse Approximation problem asks to find a solution $x$ such that $||y - Hx|| < \alpha$, for a given norm $||\cdot||$, minimizing the size of the support $||x||_0 := \#\{j \ |\ x_j \neq 0 \}$. We present valid inequalities for Mixed…

Let $G$ be any connected reductive $p$-adic group. Let $K\subset G$ be any special parahoric subgroup and $V,V'$ be any two irreducible smooth $\overline {\mathbb F}_p[K]$-modules. The main goal of this article is to compute the image of…

We present a polynomial time exact quantum algorithm for the hidden subgroup problem in $Z_{m^k}^n$. The algorithm uses the quantum Fourier transform modulo m and does not require factorization of m. For smooth m, i.e., when the prime…