Related papers: Introduction to tropical algebraic geometry
These are notes for the Bootcamp volume for the 2015 AMS Summer Institute in Algebraic Geometry. They are based on earlier notes for the "Positive Characteristic Algebraic Geometry Workshop" held at University of Illinois at Chicago in…
These are lecture notes of a course on Calogero-Moser systems and their connections with representation theory and geometry, given by the author in Zurich in May-June 2005.
Metric graphs are important models for capturing the structure of complex data across various domains. While much effort has been devoted to extracting geometric and topological features from graph data, computational aspects of metric…
We present an introduction to the theory of algebraic geometry codes. Starting from evaluation codes and codes from order and weight functions, special attention is given to one-point codes and, in particular, to the family of Castle codes.
Reproducing my talk at Algebra Symposium held at Hiroshima University, August 26--29, 2013, I review recent results on super algebraic groups, emphasizing results obtained by myself and my coauthors using Hopf algebraic techniques. The…
This paper is based on the first author's lectures at the 2012 University of Regina Workshop "Connections Between Algebra and Geometry". Its aim is to provide an introduction to the theory of higher secant varieties and their applications.…
We give an overview of recently implemented polymake features for computations in tropical geometry. The main focus is on explicit examples rather than technical explanations. Our computations employ tropical hypersurfaces, moduli of…
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
These notes cover and expand upon the material for two summer schools: The first, which was held at CIRM, Marseille, France, July 10-14, 2023, as part of "Renormalization and Visualization for packing, billiard and surfaces", was titled…
Let $G$ be a connected reductive algebraic group. We develop a Gr\"obner theory for multiplicity-free $G$-algebras, as well as a tropical geometry for subschemes in a spherical homogeneous space $G/H$. We define the notion of a spherical…
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
Tropical algebraic geometry offers new tools for elimination theory and implicitization. We determine the tropicalization of the image of a subvariety of an algebraic torus under any homomorphism from that torus to another torus.
These are lecture notes mainly aimed at graduate students on selected aspects of generalized geometry: in particular generalized complex and Kaehler structures and generalized holomorphic bundles. They are based on lectures given in March…
These lecture notes where presented as a course of the CIMPA summer school in Manila, July 20-30, 2009, Semidefinite programming in algebraic combinatorics. This version is an update June 2010.
These are extended notes for my lectures at the workshop ``Reconstructing the Gravitational Hologram'' held at Galileo-Galilei Institute, Florence, in June 2022.
These are lecture notes for a series of lectures given at the Les Houches Summer School on Integrability in Atomic and Condensed Matter Physics, 30 July to 24 August 2018. The same series of lectures has also been given at the Tokyo…
Historically, there have been many attempts to produce an appropriate mathematical formalism for modeling the nature of physical space, such as Euclid's geometry, Descartes' system of Cartesian coordinates, the Argand plane, Hamilton's…
This is the first paper in a series (of four) designed to show how to use geometric algebras of multivectors and extensors to a novel presentation of some topics of differential geometry which are important for a deeper understanding of…
This is an overview of math.AG/0310186, math.AG/0309290, math.AG/0501247, math.AG/0401002 and math.AG/0504584 written for the Proceedings of the AMS Meeting on Algebraic Geometry, Seattle, 2005.
We introduce a novel intrinsic volume concept in tropical geometry. This is achieved by developing the foundations of a tropical analog of lattice point counting in polytopes. We exhibit the basic properties and compare it to existing…