We study the complexity of isomorphism problems for tensors, groups, and polynomials.
These problems have been studied in multivariate cryptography, machine learning, quantum …

It is well-known that cohomology has a richer structure than homology. However, so far, in
practice, the use of cohomology in persistence setting has been limited to speeding up of …

A smooth cuboid can be identified with a $3\times 3$ matrix of linear forms, with coefficients
in a field $ K $, whose determinant describes a smooth cubic in the projective plane. To …

Like the lower central series of a nilpotent group, filters generalize the connection between
nilpotent groups and graded Lie rings. However, unlike the case with the lower central …

Tensors are multiway arrays of data, and transverse operators are the operators that change
the frame of reference. We develop the spectral theory of transverse tensor operators and …

Like the lower central series of a nilpotent group, filters generalize the connection between
nilpotent groups and graded Lie rings. However, unlike the case with the lower central …

Motivated by the problems of finding orthogonal decompositions and testing equivalence
(isomorphism) of multidimensional arrays of scalars (ie tensors), we introduce a …

We introduce an algorithm to decide isomorphism between tensors. The algorithm uses the
Lie algebra of derivations of a tensor to compress the space in which the search takes place …

We enumerate the number of isoclinism classes of semi-extraspecial p-groups with derived
subgroup of order p2. To do this, we enumerate GL (2, p)-orbits of sets of irreducible, monic …

We generalize the common notion of descending and ascending central series. The
descending approach determines a naturally graded Lie ring and the ascending version …