Related papers: Strong Szeg\H{o} Limit Theorems for Multi-Bordered…
The summation over spin structures, which is required to implement the GSO projection in the RNS formulation of superstring theories, often presents a significant impediment to the explicit evaluation of superstring amplitudes. In this…
The characterisation of small low conducting inclusions in an otherwise uniform background from low-frequency electrical field measurements has important applications in medical imaging using electrical impedance tomography as well as in…
This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We…
We generalize the notion of Erd\H{o}s-Ginzburg-Ziv constants -- along the same lines we generalized in earlier work the notion of Davenport constants -- to a ``higher degree" and obtain various lower and upper bounds. These bounds are…
The first main result is a topological rigidity theorem for complete immersed hypersurfaces of spherical space forms which extends similar results due to do Carmo/Warner, Wang/Xia and Longa/Ripoll. Under certain sharp conditions on the…
We extend our recent results on propagation of semiclassical resolvent estimates through trapped sets when a priori polynomial resolvent bounds hold. Previously we obtained non-trapping estimates in trapping situations when the resolvent…
In 1975 K. Michael Day produced an exact formula for the determinants of finite Toeplitz matrices whose symbols are rational. The answer is a sum that involves powers of the roots of the numerator of the symbol and whose coefficients depend…
Green, Tao and Ziegler prove ``Dense Model Theorems'' of the following form: if R is a (possibly very sparse) pseudorandom subset of set X, and D is a dense subset of R, then D may be modeled by a set M whose density inside X is…
It has been proved by S.L.Ziglin, for a large class of 2-degree-of-freedom (d.o.f) Hamiltonian systems, that transverse intersections of the invariant manifolds of saddle fixed points imply infinite branching of solutions in the complex…
Deep learning has shown strong potential for scientific discovery, but its ability to model macroscopic rigid-body kinematic constraints remains underexplored. We study this problem on spatial over-constrained mechanisms and propose…
We prove the necessity part of the higher-order Szeg\H{o} theorem on the unit circle for the single-critical-point weights $H_m(e^{i\theta})=(1-\cos\theta)^m$, $m\ge1$. If $\{\alpha_n\}_{n\ge0}$ are the Verblunsky coefficients of a…
Noncolliding Brownian motion (Dyson's Brownian motion model with parameter $\beta=2$) and noncolliding Bessel processes are determinantal processes; that is, their space-time correlation functions are represented by determinants. Under a…
We prove a central limit theorem for a certain class of functions on sparse rank-one inhomogeneous random graphs endowed with additional i.i.d. edge and vertex weights. Our proof of the central limit theorem uses a perturbative form of…
We prove a new "Toeplitz exactness" theorem for strong convergence. This is a machine to upgrade strong convergence in the general setting of $C^\ast$-correspondences, and has several applications.
A convergence theorem for martingales with c\`adl\`ag trajectories (right continuous with left limits everywhere) is obtained in the sense of the weak dual topology on Hilbert space, under conditions that are much weaker than those required…
We derive a central limit theorem for the number of vertices of convex polytopes induced by stationary Poisson hyperplane processes in $\mathbb{R}^d$. This result generalizes an earlier one proved by Paroux [Adv. in Appl. Probab. 30 (1998)…
Let $\mathfrak{g}$ be a semisimple complex Lie algebra of finite dimension and $\mathfrak{h}$ be a semisimple subalgebra. We present an approach to find the branching rules for the pair $\mathfrak{g}\supset\mathfrak{h}$. According to an…
We study convergence of operator families of the form $A_\beta = A + \beta B$ towards an effective operator defined on $\ker(B)$, as the coupling constant $\beta$ tends to infinity. Crucially, we focus on the setting where neither $A$ nor…
Increasing interest is being dedicated in the last few years to the issues of exact computations and asymptotics of spin networks. The large-entries regimes (semiclassical limits) occur in many areas of physics and chemistry, and in…
We consider the multiparameter random simplicial complex on a vertex set $\{ 1,\dots,n \}$, which is parameterized by multiple connectivity probabilities. Our key results concern the topology of this complex of dimensions higher than the…