Countably determined sets and a conjecture of C.W. Henson

Partially supported by NSF grants DMS-9208071 and DMS-9100383     

Non-negative hereditary polynomials in a free *−algebra

We prove a non-negative-stellensatz and a null-stellensatz for a class of polynomials called hereditary polynomials in a free *-algebra.Partially supported by NSF, DARPA and Ford Motor Co.Partially supported by NSF grant DMS-0140112Partially supported by NSF grant DMS-0100367     

A Morera type theorem forL 2 functions in the Heisenberg group

We obtain a Morera type characterization for the square integrable CR functions on the Heisenberg group. Partially supported by NSF Grant DMS-90524569. $Partially supported by NSF Grant DMS-9000968.     

Perturbation of Transition Functions and a Feynman-Kac Formula for the Incorporation of Mortality

Markov transition kernels are perturbed by output kernels with a special emphasis on building mortality into structured population models. A Feynman-Kac formula is derived which illustrates the interplay of mortality with a Markov process associated with the unperturbed kernel. partially supported by NSF grants DMS-0314529 and SES-0345945 partially supported by NSF grants DMS-9706787 and DMS-0314529     

On the Shintani zeta function for the space of binary quadratic forms

Partially supported by NSF Grant DMS-8803085, DMS-8610730     

On the eigenvalues of matrices with given upper triangular part

We give necessary and sufficient conditions for a set of numbers to be the eigenvalues of a completion of a matrix prescribed in its upper triangular part.Partially supported by the NSF Grant DMS-8701615-02Partially supported by the NSF Grant DMS-8802836 and United States-Israel Binational Science Foundation Grant 88-00304/I.     

The homology of irregular dihedral branched covers ofS 3

Partially supported by NSF grant DMS-9208052 and the MSRI NSF grant DMS-9022140. The author held an MSRI Research Professorship while the paper was being written     

The homology of cyclic branched covers ofS 3

Partially supported by NSF grant DMS-9208052 and the MSRI NSF grant DMS-9022140. The author held an MSRI Research Professorship while the paper was being written     

Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field

Partially supported by NSF Grant DMS-9123742     

Unstable minimal surfaces and Heegaard splittings

Partially supported by NSF grant DMS-8701746     

The refined\mathfrak{p}-adic abelian Stark conjecture in function fields

Partially supported by NSF grant DMS-8702716     

Nonisomorphic algebraic models of a smooth manifold

The second author was supported by NSF grants DMS-8905538 and DMS-9096119     

Artin groups of finite type are biautomatic

Partially supported by NSF grant DMS-8905378     

L 2 Riemann-Roch theorem for elliptic operators

Partially supported by NSF grant DMS-9222491.     

Compactness of isospectral conformal metrics onS 3

Research supported by NSF grants DMS-88-16321 and DMS-87-02871.     

Exponential sums on (G m ) n

Partially supported by NSF Grant No. DMS-8803085     

On the main conjecture of Iwasawa theory for imaginary quadratic fields

Partially supported by NSF grant DMS-8501937 and by a Sloan fellowship     

On extensions of the Baer-Suzuki Theorem

We find a necessary and sufficient condition for an element of prime order in a finite group to be in a normalp-subgroup. This generalizes the Baer-Suzuki Theorem. Our proof depends on a result about elements of prime order contained in a unique maximal subgroup containing a result of Wielandt. We discuss various consequences, linear and algebraic group versions of the result. For John Thompson Partially supported by NSF grant DMS-91011407. Partially supported by NSF grant DMS-9208667.     

Bounds on Scott rank for various nonelementary classes

Partially supported by NSF Grant DMS-8602557     

Exponents of almost simple groups and an application to the restricted Burnside problem

Partially supported by NSF DMS-8721480 and NSA MDA 90-88-H-2032