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Tropical Aspects in Geometry, Topology and Physics
Oberwolfach :
2015.
Under the general editorship: T. Ekholm, H. Markwig
The workshop Tropical Aspects in Geometry, Topology and Physics was devoted to a wide discussion and exchange of ideas between the leading experts representing various points of view on the subject. The development of tropical geometry is based on deep links between problems in real and complex enumerative geometry, symplectic geometry, quantum fields theory, mirror symmetry, dynamical systems and other research areas. On the other hand, new interesting phenomena discovered in the framework of tropical geometry (like refined tropical enumerative invariants) pose the problem of a conceptual understanding of these phenomena in the “classical” geometry and mathematical physics.
Chapters
Galkin S., , in: Tropical Aspects in Geometry, Topology and Physics.: Oberwolfach: [б.и.], 2015. P. 1269–1273.
Given a singular variety I discuss the relations between quantum cohomology of its resolution and smoothing. In particular, I explain how toric degenerations help with computing Gromov–Witten invariants, and the role of this story in “Fanosearch” programme. The challenge is to formulate enumerative symplectic geometry of complex 3-folds in a way suitable for extracting invariants ...
Added: December 2, 2015
Krivorol V., [б.и.], 2025.
We review some recent developments in 1st order GLSM construction, or so-called Gross–Neveu formalism for sigma models. We recall the general idea behind this framework and describe a 1st order GLSM data from which the general generalized Gross–Neveu model can be constructed, using CP^1 sigma model as simplest example. Then, we formulate a general statement that ...
Added: December 26, 2025
Krivorol V., Быков Д. В., Letters in Mathematical Physics 2025 Vol. 115 No. 4 Article 85
We revisit the classical aspects of N=(2,2) supersymmetric sigma models with Hermitian symmetric target spaces, using the so-called Gross–Neveu (“first-order GLSM”) formalism. We reformulate these models for complex Grassmannians in terms of simple supersymmetric Lagrangians with polynomial interactions. For maximal isotropic Grassmannians we propose two types of equivalent Lagrangians, which make either supersymmetry or the geometry ...
Added: December 26, 2025
Krivorol V., Быков Д. В., Advances in Theoretical and Mathematical Physics 2024 Vol. 28 No. 3 P. 1027–1079
We show that sigma models with orthogonal and symplectic Grassmannian target spaces admit chiral Gross-Neveu model formulations, thus extending earlier results on unitary Grassmannians. As a first application, we calculate the one-loop β-functions in this formalism, showing that they are proportional to the dual Coxeter numbers of the respective symmetry algebras. ...
Added: December 26, 2025
Yunhyung C., Eunjeong L., Mikiya M. et al., Fields Institute Communications 2024 Vol. 89 P. 107–119
Fano Bott manifolds bijectively correspond to signed rooted forests with some equivalence relation. Using this bijective correspondence, we enumerate the isomorphism classes of Fano Bott manifolds and the diffeomorphism classes of indecomposable Fano Bott manifolds. We also observe that the signed rooted forests with the equivalence relation bijectively correspond to rooted triangular cacti. ...
Added: August 30, 2025
Polotovskiy G., В кн.: Алгебра, теория чисел, дискретная геометрия и многомасштабное моделирование: Современные проблемы, приложения и проблемы истории: Материалы XXIII Международной конференции, посвященной 80-летию проф. А. И. Галочкина и 75-летию проф. В. Г. Чирского.: Тула: Тульский государственный педагогический университет им. Л.Н. Толстого, 2024. Гл. 11 С. 208–209.
Арифметическая и алгебраическая геометрия. ...
Added: February 9, 2025
Blank M., Проблемы передачи информации 2024 Т. 60 № 2 С. 53–58
Добрушинский семинар посвящен основным направлениям, которые развиваются в Добрушинской математической лаборатории ИППИ РАН: стохастической и детерминированной динамики больших систем, теории информации и теории кодирования, алгебраической геометрии и теории чисел, комбинаторным и вероятностным аспектам теории представлений. Представлена общая информация о семинаре, а также подробная информация о заседаниях семинара, прошедших с начала 2024 г. ...
Added: January 16, 2025
Springer, 2024.
This book explores toric topology, polyhedral products and related mathematics from a wide range of perspectives, collectively giving an overview of the potential of the areas while contributing original research to drive the subject forward in interesting new directions. Contributions to this volume were written in connection to the thematic program Toric Topology and Polyhedral Products held ...
Added: January 15, 2025
A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2024 Vol. 110 No. 2 Article 025004
It has been shown that non-Abelian solitonic vortex string supported in four-dimensional (4D) N = 2
supersymmetric QCD (SQCD) with the U(2) gauge group and Nf =4 quark flavors becomes a critical
superstring. This string propagates in the ten-dimensional space formed by a product of the flat 4D space
and an internal space given by a Calabi-Yau noncompact threefold, ...
Added: September 20, 2024
Birkhäuser, 2023.
This volume is dedicated to Ciro Ciliberto on the occasion of his 70th birthday and contains refereed papers, offering an overview of important parts of current research in algebraic geometry and related research in the history of mathematics. It presents original research as well as surveys, both providing a valuable overview of the current state ...
Added: November 13, 2023
Anton Shafarevich, Anton Trushin, Mathematical Communications 2023 Vol. 28 No. 2 P. 277–291
Let K be an algebraically closed field of characteristic zero. An affine algebraic variety X over K is toral if it is isomorphic to a closed subvariety of a torus K*. We study the group Aut(X) of regular automorpshims of a toral variety X. We prove that if T is a maximal torus in Aut(X), then X is ...
Added: October 19, 2023
Springer, 2016.
This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "Lie Theory and Its Applications in Physics", held near Varna, Bulgaria, in June 2015. Traditionally, Lie theory is a tool to build mathematical models for physical systems.
Recently, the trend has been towards geometrization of the mathematical ...
Added: October 18, 2023
A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2022 Vol. 106 No. 10 Article 106019
It has been shown that the non-Abelian solitonic vortex string supported in four-dimensional (4D)
N = 2 supersymmetric QCD (SQCD) with the U(2) gauge group and N_f = 4 quark flavors becomes a
critical superstring. This string propagates in the ten-dimensional space formed by a product of the flat 4D
space and an internal space given by a Calabi-Yau noncompact ...
Added: December 21, 2022
Gorsky A., E. Ievlev, A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2020 Vol. 101 No. 1 Article 014013
We study the dynamics of non-Abelian vortex strings supported in N =2 supersymmetric QCD with
the U(N) gauge group and N_f = N quark flavors deformed by the mass μ of the adjoint matter. In the limit
of large μ the bulk four-dimensional theory flows to N = 1 supersymmetric QCD. The dynamics of
orientational zero modes of the non-Abelian string ...
Added: October 31, 2022
Chen J., Sheu C., Shifman M. et al., Journal of High Energy Physics 2020 Vol. 2020 No. 10 Article 59
We study two-dimensional weighted N = (2; 2) supersymmetric CP models
with the goal of exploring their infrared (IR) limit. WCP(N, tildeN) are simplifed versions
of world-sheet theories on non-Abelian strings in four-dimensional N = 2 QCD. In the
gauged linear sigma model (GLSM) formulation, WCP(N, tildeN) has N charges +1 and tilde N
charges -1 fields. As well-known, at e N ...
Added: October 31, 2022
E. Ievlev, Shifman M., A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2020 Vol. 102 No. 5 Article 054026
We study non-Abelian vortex strings in four-dimensional (4D) N = 2 supersymmetric QCD with the
U(2) gauge group and N_f =4 flavors of quark hypermultiplets. It has recently been shown that these
vortices behave as critical superstrings. The spectrum of closed string states in the associated string theory
was found and interpreted as a spectrum of hadrons in 4D N ...
Added: October 31, 2022
S. Derkachov, Isaev A. P., Shumilov L., Physics Letters B 2022 Vol. 830 Article 137150
A convenient operator representation for zig-zag four-point and two-point planar Feynman diagrams relevant to the bi-scalar D-dimensional “fishnet” field theory is obtained. This representation gives a possibility to evaluate exactly diagrams of the zig-zag series in special cases. In particular, we give a fairly simple proof of the Broadhurst-Kreimer conjecture about the values of zig-zag multi-loop two-point diagrams ...
Added: October 27, 2022
E. Ievlev, A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2021 Vol. 104 No. 11 Article 114033
It has been shown that non-Abelian vortex string supported in four-dimensional (4D) N =2
supersymmetric QCD (SQCD) with the U(2) gauge group and N_f =4 quark flavors becomes a critical
superstring. This string propagates in the ten-dimensional space formed by a product of the flat 4D space
and an internal space given by a Calabi-Yau noncompact threefold, namely, ...
Added: October 26, 2022
Maslov, Victor P., Shvedov O., De Gruyter, 2022.
In this monograph we study the problem of construction of asymptotic solutions of equations for functions whose number of arguments tends to infinity as the small parameter tends to zero. Such equations arise in statistical physics and in quantum theory of a large number of fi elds. We consider the problem of renormalization of quantum ...
Added: July 1, 2022
Switzerland: Birkhauser/Springer, 2022.
The conference “Interactions between Representation Theory and Algebraic Geometry” was held at the University of Chicago on August 21–25, 2017. It brought together about 150 participants from several major universities in the USA and abroad, more than half of whom were junior mathematicians. It featured 21 talks by eminent mathematicians from the USA, Europe, and Asia on topics ...
Added: June 20, 2022
Shapiro D., Mirlin A., Shnirman A., Physical Review B: Condensed Matter and Materials Physics 2021 Vol. 104 No. 3 Article 035434
We consider an interferometer based on artificially induced topological superconductivity and chiral one-dimensional (1D) Majorana fermions. The (nontopological) superconducting island inducing the superconducting correlations in the topological substrate is assumed to be floating. This allows probing the physics of interfering Majorana modes via microwave response, i.e., the frequency-dependent impedance between the island and the earth. ...
Added: October 31, 2021
Shapiro D. S., Pogosov W. V., Lozovik Y., Physical Review A: Atomic, Molecular, and Optical physics 2020 Vol. 102 No. 2 Article 023703
In view of recent proposals for the realization of anisotropic light-matter interaction in such platforms as (i) nonstationary or inductively and capacitively coupled superconducting qubits, (ii) atoms in crossed fields, and (iii) semiconductor heterostructures with spin-orbital interaction, the concept of a generalized Dicke model, where coupling strengths of rotating wave and counter-rotating wave terms are ...
Added: October 31, 2021