Browse research papers in Algebra and Number Theory - Mathematics Discover 4 academic papers with AI-powered analysis

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Algebra and Number Theory

Abstract algebraic structures and properties of integers, including groups, rings, fields, algebraic geometry, arithmetic geometry, and applications to cryptography and coding theory

4 papers in this specialization

Papers

Non-intersecting ring currents in [12]infinitene

The study reveals that [12]infinitene exhibits two non-intersecting diatropic ring currents along its edges, leading to a shielding cone and aromatic behavior. This contradicts predictions based on the Möbius aromaticity rule for twisted annulenes. The dication, however, shows paratropic ring currents and antiaromatic character due to a strong through-space ring current between stacked rings.

New methods for conformal correlation functions

This paper introduces a novel uplift for quasi-primary operators in conformal field theory, enabling a unified treatment of all operators irrespective of their Lorentz representations. This leads to a simplified calculation of correlation functions and a new, more practical operator product expansion.

The spectral localizer for even index pairings

This paper introduces the spectral localizer, a finite-dimensional matrix that can be used to compute the topological invariant (even index pairing) associated with a topological insulator in even spatial dimensions. The key finding is that half the signature of this spectral localizer equals the index pairing, enabling its numerical calculation.

Renormalising SPDEs in regularity structures

This paper develops a general method for "renormalizing" a wide class of singular stochastic partial differential equations (SPDEs), showing that the renormalised solutions are equivalent to classical solutions of a modified equation with added counterterms. This provides a robust theoretical framework for studying the existence and behavior of solutions to complex systems driven by noise.