Related papers: Geometric Phases and Topological Effects
A phase-field formulation is introduced to simulate quantitatively microstructural pattern formation in alloys. The thin-interface limit of this formulation yields a much less stringent restriction on the choice of interface thickness than…
The present work proposes an approach for fluid-solid and contact interaction problems including thermo-mechanical coupling and reversible phase transitions. The solid field is assumed to consist of several arbitrarily-shaped, undeformable…
This article is meant as a gentle introduction to the "topological terms" that often play a decisive role in effective theories describing topological quantum effects in condensed matter systems. We first take up several prominent examples,…
This volume contains the post-proceedings of the Sixteenth International Workshop on Graph Computation Models (GCM 2025). The workshops took place in Koblenz, Germany on June 10 as part of STAF (Software Technologies: Applications and…
This article contains a collection of problems contributed during the course of the conference.
The antiferromagnetic Heisenberg model on a stacked triangular geometry with a finite number of layers is studied using Monte Carlo methods. A topological phase transition occurs at finite temperature for all film thicknesses. Our results…
The surface properties of solid-state materials often dictate their functionality, especially for applications where nanoscale effects become important. The relevant surface(s) and their properties are determined, in large part, by the…
These are expanded notes from a four lecture mini-course given by the author at the Spring School on Non-archimedean geometry and Eigenvarieties, held at the University of Heidelberg in March 2023. The course discusses coherent sheaves,…
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…
A new point of view about the deep origin of thermodynamic phase transitions is sketched. The main idea is to link the appearance of phase transitions to some major topology change of suitable submanifolds of phase space instead of linking…
This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions…
The Hopfield model, originally inspired by spin-glass physics, occupies a central place at the intersection of statistical mechanics, neural networks, and modern artificial intelligence. Despite its conceptual simplicity and broad…
We review recent experimental progresses on layered topological materials, mainly focusing on transitional metal dichalcogenides with various lattice types including 1T, Td and 1T' structural phases. Their electronic quantum states are…
This note is an expansion of three lectures given at the workshop "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces" held at Kyoto University in December of 2006 and will appear in the proceedings for this workshop.
Higher-order topological phases give rise to new bulk and boundary physics, as well as new classes of topological phase transitions. While the realization of higher-order topological phases has been confirmed in many platforms by detecting…
This is a book about computational aspects of modular forms and the Galois representations attached to them. The main result is the following: Galois representations over finite fields attached to modular forms of level one can, in almost…
Various topological phases, including topological insulators, topological semimetals, and topological superconductors, along with the controllable topological phase transitions, have attracted considerable attention due to their promising…
Topological phase classifications have been intensively studied via machine-learning techniques where different forms of the training data are proposed in order to maximize the information extracted from the systems of interests. Due to the…
Aim. This paper (Paper D) unifies the ideal-theoretic, computational, and homological layers developed in Papers A (Rao 2025), B (Rao 2025), and C (Rao 2025) into a geometric framework that includes fuzzy and computational geometries on the…
These are the extended notes of a talk I gave at the Geometric Topology Seminar of the Max Planck Institute for Mathematics in Bonn on January 30th, 2012. My goal was to familiarize the topologists with the basics of arithmetic hyperbolic…