Related papers: Eynard-Mehta theorem, Schur process, and their pfa…
The convergence of a sequence of Cauchy sequences is conjectured; which if shown to be true, would prove the Riemann hypothesis by way of LeClair and Fran\c{c}a's transcendental equation criteria.
We develop a unified framework to compute band-geometric quantities in multiband systems whose low-energy Hamiltonians realize arbitrary $SU(2)$ representations. Exploiting the presence of a quantization axis, we use the Wigner--Eckart…
Egge, Loehr, and Warrington proved a formula for the Schur function expansion of a symmetric function in terms of its expansion in fundamental quasi-symmetric functions. Their formula involves the coefficients of a modified inverse Kostka…
Quantization of diffeomorphism invariant theories of connections is studied. A solutions of the diffeomorphism constraints is found. The space of solutions is equipped with an inner product that is shown to satisfy the physical reality…
Within a framework of noncommutative geometry, we develop an analogue of (pseudo) Riemannian geometry on finite and discrete sets. On a finite set, there is a counterpart of the continuum metric tensor with a simple geometric…
A theorem by Orlov states that any equivalence between the bounded derived categories of coherent sheaves of two smooth projective varieties, X and Y, is isomorphic to a Fourier-Mukai transform with kernel in the bounded derived category of…
We introduce interpolation analogues of Schur Q-functions - the multiparameter Schur Q-functions. We obtain for them several results: a combinatorial formula, generating functions for one-row and two-rows functions, vanishing and…
We construct Pfaffian L-ensembles related to the z-measures on partitions and to the Plancherel measures on partitions with the Jack parameters 1/2 or 2. The results imply that these measures on partitions lead to Pfaffian point processes,…
Using techniques from integrable systems, we obtain a number of exact results for random partitions. In particular, we prove a simple formula for correlation functions of what we call the Schur measure on partitions (which is a far reaching…
There has been enormous progress in the last few years in designing neural networks that respect the fundamental symmetries and coordinate freedoms of physical law. Some of these frameworks make use of irreducible representations, some make…
The study of cosmological correlators, and more generally Feynman integrals, is greatly aided by considering them as solutions to differential equations. Often, such systems of differential equations are reducible, which, broadly speaking,…
The first part I talk about the motivation for Lu Qi-Keng conjecture and the results about the presence or absence of zeroes of the Bergman kernel function of a bounded domain in ${\bf{C^n}}$. The second part I summarize the main results on…
An extension of the theory of the Iterated Logarithmic Algebra gives the logarithmic analog of a Sheffer or Appell sequence of polynomials. This leads to several examples including Stirling's formula and a logarithmic version of the…
Two alternative, fairly compact proofs are presented of the Pfaffian integration theorem that is surfaced in the recent studies of spectral properties of Ginibre's Orthogonal Ensemble. The first proof is based on a concept of the Fredholm…
It is shown that the Gel'fand-Tsetlin realization of irreducible representations of the $A_n$ algebra is directly connected with a linear exactly integrable system in the n-dimensional space. General solution for this system is explicitly…
Following Manin's approach to renormalization in the theory of computation, we investigate Dyson-Schwinger equations on Hopf algebras, operads and properads of flow charts, as a way of encoding self-similarity structures in the theory of…
Let $ \overline B=\{ \overline B_{t},t\in R^{1} \}$ be Brownian motion killed after an independent exponential time with mean $2/\lambda^{2}$. The process $\overline B$ has potential densities, \[ u(x,y) ={e^{-\lambda |y-x|}\over…
We prove an identity relating the product of two opposite Schubert varieties in the (equivariant) quantum K-theory ring of a cominuscule flag variety to the minimal degree of a rational curve connecting the Schubert varieties. We deduce…
We first prove a Cauchy's integral theorem and Cauchy type formula for certain inhomogeneous Cimmino system from quaternionic analysis perspective. The second part of the paper directs the attention towards some applications of the…
We present a set of algebraic relations among Schur functions which are a multi-time generalization of the ``discrete Hirota relations'' known to hold among the Schur functions of rectangular partitions. We prove the relations as an…