We consider zeros of two-dimensional sums over rectangular lattices, and in particular a sum first studied by Potter and Titchmarsh in 1935. They proved several properties of the zeros of sums over the rectangular lattice, and commented on the fact that a particular sum had zeros off the critical line. We investigate the behaviour of one such zero as a function of the ratio of the periods of th...

We characterise the Weyl-Hörmander symbol classes S ( M , g ) via growth of action corresponding ΨDOs on time-frequency shifts a single test function. For this purpose, we introduce geometric short-time Fourier transform which is well-suited for analysis . define new modulation spaces and achieve characterisation by showing that they are intersections such suitable characterisation.

We study Darboux-type transformations associated with the focusing nonlinear Schrödinger equation (NLS−) and their effect on spectral properties of the underlying Lax operator. The latter is a formally J -selfadjoint (but non-self-adjoint) Dirac-type differential expression of the form M(q) = i d dx −q −q − d dx , satisfying JM(q)J = M(q), where J is defined by J = 0 1 1 0 C, and C denotes the ...

Abstract. We use a reflection argument, introduced by Gessel and Zeilberger, to count the number of k-step walks between two points which stay within a chamber of a Weyl group. We apply this technique to walks in the alcoves of the classical affine Weyl groups. In all cases, we get determinant formulas for the number of k-step walks. One important example is the region m > x1 > x2 > · · · > xn ...

We compare the K-theories of symplectic quotients with respect to a compact connected Lie group and with respect to its maximal torus, and in particular we give a method for computing the former in terms of the latter. More specifically, let G be a compact connected Lie group with no torsion in its fundamental group, let T be a maximal torus of G, and let M be a compact Hamiltonian G-space. Let...

The contours =Λ(s) = 0 of the function which satisfies ζ(1− s) = Λ(s)ζ(s) cross the critical strip on lines which are almost horizontal and straight, and cut the critical line alternately at Gram points and points where ζ(s) is imaginary. The real part of ζ(s), when averaged in a modified manner, for fixed values of σ over the values on the “Gram lines”, satisfies a relation which extends a the...

Recently a great deal of attention has been focused on condensed matter systems which have zero-gap electronic structures analogous to the massless relativistic particles. The Weyl semimetal, which is recently discovered, has a peculiar band structure characterized by the nodal touching points (Weyl nodes) and the topological surface bands connecting the Weyl nodes. In this talk, I introduce ou...