Related papers: Invitation to higher local fields, Part I, section…

PhD thesis TU-Vienna, May 1994. Table of Contents: 1. Introduction, 2. Poisson Structure Induced Two Dimensional Field Theories, 3. Models of Gravity in 1+1 Dimensions

Left and right "generalized Schur algebras", previously introduced by the author, are defined and analyzed. Filtrations of these algebras lead, in most cases, to parameterizations of the their irreducible representations over fields of…

Aiming at a comprehensive and concise tutorial survey, recap of variational inference and reinforcement learning with Probabilistic Graphical Models are given with detailed derivations. Reviews and comparisons on recent advances in deep…

The paper establishes a relationship between finite separable extensions and norm groups of strictly quasilocal fields with Henselian discrete valuations, which yields a generally nonabelian one-dimensional local class field theory.

We obtain two explicit formulas for the full local character expansion of any irreducible representation of a p-adic general linear group in principal blocks. The first, generalizing previous work of the author on the Iwahori-spherical…

For oscillatory functions on local fields coming from motivic exponential functions, we show that integrability over $Q_p^n$ implies integrability over $F_p ((t))^n$ for large $p$, and vice versa. More generally, the integrability only…

The notion of analyticity is studied in the context of hypercomplex numbers. A critical review of the problems arising from the conventional approach is given. We describe a local analyticity condition which yields the desired type of…

This introduction to Lifshitz-type field theories reviews some of its aspects in Particle Physics. Attractive features of these models are described with different examples, as the improvement of graphs convergence, the introduction of new…

In this paper we describe the blocks of the partition algebra over a field of positive characteristic.

As a natural generalization of the notion of `higher rank Euler system', we develop a theory of `higher special elements' in the exterior power biduals of the Galois cohomology of $p$-adic representations. We show, in particular, that such…

We study compressible types in the context of (local and global) NIP. By extending a result in machine learning theory (the existence of a bound on the recursive teaching dimension), we prove density of compressible types. Using this, we…

A review of the Hodge and Hopf-algebraic approach to QFT.

These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not homotopy theorists.

We study the validity of the local theta correspondence over a non-archimedean local field in the context of modular representation theory \textit{i.e.} for representations with coefficient fields of positive characteristic. For a…

Martin-L\"of's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of well-founded relations is presented. Using primitive…

Invariants of generalized tensor fields on a line are classified using special polynomials P_mk^(-1/lambda) introduced here for this purpose. For the case of positive characteristic, a new invariant of formal power series, a width, is…

Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.

In the first part of this article, we consider ruled surfaces defined over a finite field; we introduce invariants for them, and describe some explicit contructions that illustrate possible behaviour of these invariants. In the second part,…

We state and prove an analogue of the Kakeya conjecture for the local field $\mathbb{F}_q(\!(t)\!)$. This extends Arsovski's result on the Kakeya conjecture to local fields of positive characteristic. We also prove the Kakeya maximal…

We revisit Kolchin's results on definability of differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. In certain classes of differential topological…