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q-Deformed harmonic oscillator algebra for real and root of unity values of the deformation parameter is discussed by using an extension of the number concept proposed by Gauss, namely the Q-numbers. A study of the reducibility of the Fock…

We prove that, for a K3 surface in characteristic p > 2, the automorphism group acts on the nef cone with a rational polyhedral fundamental domain and on the nodal classes with finitely many orbits. As a consequence, for any non-negative…

Let $X$ be a Gorenstein minimal projective 3-fold with at worst locally factorial terminal singularities. Suppose the canonical map is of fiber type. Denote by $F$ a smooth model of a generic irreducible component in fibers of the canonical…

We describe two approaches to classifying the possible monodromy cones C arising from nilpotent orbits in Hodge theory. The first is based upon the observation that C is contained in the open orbit of any interior point N in C under an…

Dalitz-plot analyses of $B\rightarrow K\pi\pi$ decays provide direct access to decay amplitudes, and thereby weak and strong phases can be disentangled by resolving the interference patterns in phase space between intermediate resonant…

We will announce two theorems. The first theorem will classify all topological types of degenerate fibers appearing in one-parameter families of Riemann surfaces, in terms of ``pseudoperiodic'' surface homeomorphisms. The second theorem…

Recent years have seen considerable research success in the field of dynamic homogenization which seeks to define frequency dependent effective properties for heterogeneous composites for the purpose of studying wave propagation. There is…

We look at two methods to determine the weak phases $\phi_2$ and $\phi_3$ from $B \to \pi\pi$ and $K\pi$ decays within the perturbative QCD approach. We obtain quite interesting bounds on $\phi_2$ and $\phi_3$ from experimental measurements…

S. Kond\=o defined a birational period map from the moduli space of genus three curves to a moduli space of degree four polarized K3 surfaces. In this paper we extend the period map to a surjective morphism on a suitable compactification of…

We study in detail the degeneration of K3 to T^4/Z_2. We obtain an explicit embedding of the lattice of collapsed cycles of T^4/Z_2 into the lattice of integral cycles of K3 in two different ways. Our first method exploits the duality to…

The ground state degeneracy of an $SU(N)_k$ topological phase with $n$ quasiparticle excitations is relevant quantity for quantum computation, condensed matter physics, and knot theory. It is an open question to find a closed formula for…

Motivated by the Swampland Distance and the Emergent String Conjecture of Quantum Gravity, we analyse the infinite distance degenerations in the complex structure moduli space of elliptic K3 surfaces. All complex degenerations of K3…

Let $S_{g}$ be a general prime K3 surface in $P^g$ of genus $g \geq 3$ or a general double cover of $P^2$ ramified along a sextic curve for $g = 2$ and $S = S_{i,g}$ its {\it i}-th Veronese embedding. In this article we compute the corank…

Kagome antiferromagnets are known to be highly frustrated and degenerate when they possess simple, isotropic interactions. We consider the entire class of these magnets when their interactions are spatially anisotropic. We do so by…

We define a period pairing for flat, irregular singular, rank one connections, satisfying a technical condition regarding its stationary set, on complex surfaces between de Rham cohomology of the connection and a modified singular homology,…

We investigate decoherence effects in the recently suggested quantum computation scheme using weak nonlinearities, strong probe coherent fields, detection and feedforward methods. It is shown that in the weak-nonlinearity-based quantum…

In this note we compare the moduli spaces of the heterotic string compactified on a two-torus and F-Theory compactified on an elliptic K3 surface for the case of an unbroken E8 x E8 gauge group. The explicit map relating the deformation…

We prove a parabolic analogue of Wolff's inequality adapted to the intrinsic scaling $\delta_c(x,t)=(cx,c^2t)$ and formulated in terms of time-backward parabolic dyadic rectangles. As a consequence, we obtain equivalent characterizations of…

We construct several examples of genus-one fibered K3 surfaces without a global section with type $I_{n}$ fibers, by considering double covers of a special class of rational elliptic surfaces lacking a global section, known as Halphen…

We prove a local self-improving property for the gradient of very weak solutions to degenerate parabolic double-phase systems. The result is based on a reverse H\"older inequality with constants that are independent of the solution.…