Related papers: A mass formula for unimodular lattices with no roo…
In this paper, new extremal odd unimodular lattices in dimension $36$ are constructed. Some new odd unimodular lattices in dimension $36$ with long shadows are also constructed.
We deal with suitable nonlinear versions of Jauregui's isocapacitary mass in 3-manifolds with nonnegative scalar curvature and compact outermost minimal boundary. These masses, which depend on a parameter $1<p\leq 2$, interpolate between…
A classic theorem of Kazhdan and Margulis states that for any semisimple Lie group without compact factors, there is a positive lower bound on the covolume of lattices. H. C. Wang's subsequent quantitative analysis showed that the…
The isodiametric inequality states that the Euclidean ball maximizes the volume among all convex bodies of a given diameter. We are motivated by a conjecture of Makai Jr.~on the reverse question: Every convex body has a linear image whose…
For quantized universal enveloping algebras we construct weight modules by inducing representations of the centralizer of the Cartan subalgebra in the quantized universal enveloping algebra. The induced modules arising from…
A first study of numerical Monte Carlo simulations with two quark doublets, a mass-degenerate one and a mass-split one, interpreted as u, d, s and c quarks, is carried out in the framework of the twisted mass Wilson lattice formulation.…
We extend Witten's spinor proof of the positive mass theorem to large classes of complete asymptotically flat non-spin manifolds, including all manifolds of dimension less than or equal to 11 and all manifolds of dimension less than 26…
In this paper we describe a method for computing a basis for the space of weight $2$ cusp forms invariant under a non-split Cartan subgroup of prime level $p$. As an application we compute, for certain small values of $p$, explicit…
Lattices with a circulant generator matrix represent a subclass of cyclic lattices. This subclass can be described by a basis containing a vector and its circular shifts. In this paper, we present certain conditions under which the norm…
The automorphism groups of the three known extremal even unimodular lattices of dimension 48 and the one of dimension 72 are computed using the classification of finite simple groups. Restrictions on the possible automorphisms of…
We prove an expansion theorem on scalar-flat asymptotically conical K\"ahler metrics. Consider an AC K\"ahler manifold with asymptotic to a Ricci-flat K\"ahler metric cone with complex dimension n. Assuming the weak decay conditions…
We prove a positive mass theorem for $n$-dimensional asymptotically flat manifolds with a non-compact boundary if either $3\leq n\leq 7$ or if $n\geq 3$ and the manifold is spin. This settles, for this class of manifolds, a question posed…
Ultra-light axions (ULAs) with masses in the range 10^{-33} eV <m <10^{-20} eV are motivated by string theory and might contribute to either the dark-matter or dark-energy density of the Universe. ULAs could suppress the growth of structure…
We describe a unitary matrix model which is constructed from discrete analogs of the usual projective modules over the noncommutative torus and use it to construct a lattice version of noncommutative gauge theory. The model is a…
We classify the holomorphic Borcherds products of singular weight for all simple lattices of signature $(2,n)$ with $n \geq 3$. In addition to the automorphic products of singular weight for the simple lattices of square free level found by…
We give a list of $113$ holomorphic eta-quotients of integral weight ($66$ of which are primitive) and provide a uniform closed formula for their Fourier coefficients $c(l)$ where $l\equiv1\bmod{m}$ with some fixed $m\mid24$. The proof…
In a recent preprint, we constructed a sesquiharmonic Maass form $\mathcal{G}$ of weight $\frac{1}{2}$ and level $4N$ with $N$ odd and squarefree. Extending seminal work by Duke, Imamo\={g}lu, and T\'{o}th, $\mathcal{G}$ maps to Zagier's…
We apply the resummed version of the L\"uscher formula to analyze finite volume corrections to the mass of the nucleon and of heavy mesons. We show that by applying the subthreshold expansion of the scattering amplitudes one can express the…
We obtain a growth estimate for the number of lattice points inside any Q-Gorenstein cone. Our proof uses the result of Futaki-Ono-Wang on Sasaki-Einstein metric for the toric Sasakian manifold associated to the cone, a Yau's inequality,…
Recent theoretical developments have shown that extra spacetime dimensions can lower the fundamental GUT, Planck, and string scales. However, recent evidence for neutrino oscillations suggests the existence of light non-zero neutrino…