Related papers: Some remarks on the Maslov index

We define commutants mod normed ideals associated with compact smooth manifolds with boundary. The results about the K-theory of these operator algebras include an exact sequence for the connected sum of manifolds, derived from the…

We give a parametrization of square roots of the ideal class of the inverse different of rings defined by binary forms in terms of the orbits of a coregular representation. This parametrization, which can be construed as a new integral…

We study the Chow classes of arbitrary matroids in the Grassmannian. We develop a new combinatorial approach for computing them, by first focusing on snake matroids and then extending our results via valuativity to any matroid. Our main…

In this paper we investigate the structure of algebraic cobordism of Levine-Morel as a module over the Lazard ring with the action of Landweber-Novikov and symmetric operations on it. We show that the associated graded groups of algebraic…

Let $\Sigma$ be a compact convex hypersurface in ${\bf R}^{2n}$ which is P-cyclic symmetric, i.e., $x\in \Sigma$ implies $Px\in\Sigma$ with P being a $2n\times2n$ symplectic orthogonal matrix and $P^k=I_{2n}$, where $n, k\geq2$,…

The first purpose of this paper is to generalize the well-known Maslov indices of maps of open Riemann surfaces with boundary lying on Lagrangian submanifolds to maps with boundary lying on coisotropic submanifolds in symplectic manifolds.…

We study symplectic linear algebra over the ring $\Rt$ of Colombeau generalized numbers. Due to the algebraic properties of $\Rt$ it is possible to preserve a number of central results of classical symplectic linear algebra. In particular,…

In this paper we are going to compute the $ \mathrm{KW} $-Euler classes for rank 2 vector bundles on the classifying stack $ \mathcal{B}N $, where $N$ is the normaliser of the standard torus in $SL_2$ and $\mathrm{KW}$ represents Balmer's…

In 2018, Kahle and Stump raised the following problem: identify sequences of finite Coxeter groups $W_n$ for which the two-sided descent statistics on a uniform random element of $W_n$ is asymptotically normal. Recently, Br\"uck and…

A.A. Suslin proved a normality theorem for an elementary linear group and V.I. Kopeiko extended this result of Suslin for a symplectic group defined with respect to the standard skew-symmetric matrix of even size. We generalized the result…

We use techniques from statistical mechanics to provide new formulas for Whittaker coefficients of metaplectic Eisenstein series on odd orthogonal groups, matching Friedberg and Zhang. We study a particular variation/generalization of the…

Quillen's algebraic K-theory is reconstructed via Voevodsky's algebraic cobordism. More precisely, for a ground field k the algebraic cobordism P^1-spectrum MGL of Voevodsky is considered as a commutative P^1-ring spectrum. There is a…

In this paper, we study the algebraic cobordism spectrum $MSL$ in the motivic stable homotopy category of Voevodsky over an arbitrary perfect field $k$. Using the motivic Adams spectral sequence, we compute the geometric part of the…

The Coulomb branch indices of Argyres-Douglas theories on $L(k,1)\times S^{1}$ are recently identified with matrix elements of modular transforms of certain $2d$ vertex operator algebras in a particular limit. A one parameter generalization…

A "squarefree module" over a polynomial ring $S = k[x_1, .., x_n]$ is a generalization of a Stanley-Reisner ring, and allows us to apply homological methods to the study of monomial ideals systematically. Let $Sq$ be the category of…

Let $X$ be a Noetherian separated scheme of finite Krull dimension. We show that the layers of the slice filtration in the motivic stable homotopy category $\stablehomotopy$ are strict modules over Voevodsky's algebraic cobordism spectrum.…

Recently, Darmon and Vonk initiated the theory of rigid meromorphic cocycles for the group $\mathrm{SL}_2(\mathbb{Z}[1/p])$. One of their major results is the algebraicity of the divisor associated to such a cocycle. We generalize the…

In this paper we investigate the endomorphism algebras of standard cluster tilting objects in the stably 2-Calabi-Yau categories $\Sub{\Lambda_w}$ with elements $w$ in Coxeter groups in \cite{BIRSc}. They are examples of the 2-Auslander…

This is the second paper in our sequence. Here, we apply our abstract Morse index formulation developed in the previous paper to study several optimization set-ups with constraints, including type I or/and type II considerations. A common…

Solomon's descent algebra is used to define a family of signed measures M(W,x) for a finite Coxeter group W and non-zero x. The measures corresponding to W of types A and B are known to arise from the theory of card shuffling and to be…