In this paper, we consider the sequence of Frobenius conjugacy classes for a Galois extension K/Q, ordered by the increasing sequence of rational primes. For a given K, we look at the frequencies of non-overlapping consecutive k-tuples in this sequence. We compare these frequencies to what would be expected by the Chebotarev Density Theorem, if there were statistical independence between succes...

We define certain extensions of Jacobi groups A<sub>1</sub>, prove an analogue Chevalley theorem for their invariants, and construct a Dubrovin-Frobenius structure on its orbit space.

By a nonnegative matrix we mean a matrix whose entries are nonnegative real numbers. By positive matrix we mean a matrix all of whose entries are strictly positive real numbers. These notes give the core elements of the Perron-Frobenius theory of nonnegative matrices. This splits into three parts: (1) the primitive case (due to Perron) (2) the irreducible case (due to Frobenius) (3) the general...

We prove that the Chow motives of twisted derived equivalent K3 surfaces are isomorphic, not only as (due to Huybrechts), but also Frobenius algebra objects. Combined with a recent result Huybrechts, we conclude two complex projective isogenous (i.e. their second rational cohomology groups Hodge isometric) if and isomorphic objects; this can be regarded motivic Torelli-type theorem. ask whether...

We study quasi-Hopf algebras and their subobjects over certain commutative rings from the point of view of Frobenius algebras. We introduce a type of Radford formula involving an anti-automorphism and the Nakayama automorphism of a Frobenius algebra, then view several results in quantum algebras from this vantage-point. In addition, separability and strong separability of quasi-Hopf algebras ar...

Overview. My work is in the area of commutative algebra, and is motivated by the connections between algebra and geometry. Commutative algebra is the study of commutative rings (e.g. polynomial rings over fields and their quotients) and modules over these rings, while algebraic geometry is the study of finitely many polynomial equations in finitely many unknowns. The set of all solutions to suc...

We study the asymptotic behaviour of points under matrix cocyles generated by rectangular matrices. In particular we prove a random Perron-Frobenius and a Multiplicative Ergodic Theorem. We also provide an example where such products of random rectangular matrices arise in the theory of random walks in random environments and where the Multiplicative Ergodic Theorem can be used to investigate r...

We provide a proof for a Perron-type theorem on the principal eigenvalue of nonsymmetric elliptic operators based on the strong maximum principle. This proof is modeled after a variational proof of Perron’s theorem for matrices with positive entries that does not appeal to Perron-Frobenius theory.