Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Special Issue on Algebra, Topology, and Dynamics in Interaction in honor of Dmitry Fuchs' 80th anniversary

The Guest Editors for this special issue are

Boris Khesin (University of Toronto, Canada)
Fyodor Malikov (University of Southern California, USA)
Valentin Ovsienko (University of Reims Champagne-Ardenne, France)
Sergei Tabachnikov (Pennsylvania State University, USA)

This special issue of SIGMA is devoted to Dmitry Borisovich Fuchs, an outstanding mathematician and our teacher, on the occasion of his 80th birthday. It comprises 22 papers of his friends and colleagues, reflecting broad mathematical interests of Dmitry Borisovich himself, from fun problems to Verma modules (and back). The article “On the 80th Birthday of Dmitry Borisovich Fuchs” with many memories and semi-legendary stories in this volume can be viewed as an introduction to the volume itself.

We wish to thank also all the authors who have published papers in the issue, and to give our special thanks to all the referees for providing constructive reports.

The Guest Editors        

Papers in this Issue:

Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations
Sofiane Bouarroudj, Pavel Grozman, Alexei Lebedev, Dimitry Leites and Irina Shchepochkina
SIGMA 16 (2020), 089, 101 pages   [ abs   pdf ]
Uniform Lower Bound for Intersection Numbers of $\psi$-Classes
Vincent Delecroix, Élise Goujard, Peter Zograf and Anton Zorich
SIGMA 16 (2020), 086, 13 pages   [ abs   pdf ]
Evaluations of Noncommutative Polynomials on Algebras: Methods and Problems, and the L'vov-Kaplansky Conjecture
Alexei Kanel-Belov, Sergey Malev, Louis Rowen and Roman Yavich
SIGMA 16 (2020), 071, 61 pages   [ abs   pdf ]
Contingency Tables with Variable Margins (with an Appendix by Pavel Etingof)
Mikhail Kapranov and Vadim Schechtman
SIGMA 16 (2020), 062, 22 pages   [ abs   pdf ]
Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic
Wolfgang Ebeling and Sabir M. Gusein-Zade
SIGMA 16 (2020), 051, 15 pages   [ abs   pdf ]
Is There an Analytic Theory of Automorphic Functions for Complex Algebraic Curves?
Edward Frenkel
SIGMA 16 (2020), 042, 31 pages   [ abs   pdf ]
Permutation-Equivariant Quantum K-Theory X. Quantum Hirzebruch-Riemann-Roch in Genus 0
Alexander Givental
SIGMA 16 (2020), 031, 16 pages   [ abs   pdf ]
Horospherical Cauchy Transform on Some Pseudo-Hyperbolic Spaces
Simon Gindikin
SIGMA 16 (2020), 024, 10 pages   [ abs   pdf ]
On the 80th Birthday of Dmitry Borisovich Fuchs
Alice Fialowski, Ekaterina Fuchs, Elena Fuchs, Boris Khesin, Alexandre Kirillov, Fedor Malikov, Valentin Ovsienko, Alexei Sossinsky and Serge Tabachnikov
SIGMA 16 (2020), 023, 17 pages   [ abs   pdf ]
Counting Periodic Trajectories of Finsler Billiards
Pavle V.M. Blagojević, Michael Harrison, Serge Tabachnikov and Günter M. Ziegler
SIGMA 16 (2020), 022, 33 pages   [ abs   pdf ]
Geometric Approach to Quantum Theory
Albert Schwarz
SIGMA 16 (2020), 020,   3 pages   [ abs   pdf ]
A Faithful Braid Group Action on the Stable Category of Tricomplexes
Mikhail Khovanov and You Qi
SIGMA 16 (2020), 019, 32 pages   [ abs   pdf ]
Legendrian DGA Representations and the Colored Kauffman Polynomial
Justin Murray and Dan Rutherford
SIGMA 16 (2020), 017, 33 pages   [ abs   pdf ]
Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space
Kiumars Kaveh and Askold G. Khovanskii
SIGMA 16 (2020), 016, 12 pages   [ abs   pdf ]
Short Star-Products for Filtered Quantizations, I
Pavel Etingof and Douglas Stryker
SIGMA 16 (2020), 014, 28 pages   [ abs   pdf ]
New Examples of Irreducible Local Diffusion of Hyperbolic PDE's
Victor A. Vassiliev
SIGMA 16 (2020), 009, 21 pages   [ abs   pdf ]
Fun Problems in Geometry and Beyond
Boris Khesin and Serge Tabachnikov
SIGMA 15 (2019), 097, 21 pages   [ abs   pdf ]
Cohomology of Restricted Filiform Lie Algebras ${\mathfrak m}_2^\lambda(p)$
Tyler J. Evans and Alice Fialowski
SIGMA 15 (2019), 095, 11 pages   [ abs   pdf ]
Locally Nilpotent Derivations of Free Algebra of Rank Two
Vesselin Drensky and Leonid Makar-Limanov
SIGMA 15 (2019), 091, 10 pages   [ abs   pdf ]
Symplectic Frieze Patterns
Sophie Morier-Genoud
SIGMA 15 (2019), 089, 36 pages   [ abs   pdf ]
Twisted de Rham Complex on Line and Singular Vectors in $\widehat{{\mathfrak{sl}_2}}$ Verma Modules
Alexey Slinkin and Alexander Varchenko
SIGMA 15 (2019), 075, 26 pages   [ abs   pdf ]
Holomorphic Distributions and Connectivity by Integral Curves of Distributions
Vladimir A. Zorich
SIGMA 15 (2019), 070,   6 pages   [ abs   pdf ]

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