arXiv research

We construct an explicit topological model (similar to the topological Springer fibers appearing in work of Khovanov and Russell) for every two-row Springer fiber associated with the even orthogonal group and prove that the respective topological model is homeomorphic to its corresponding Springer fiber. This confirms …

Diagrammatic approach to Springer fibers for types C and D.

Shows natural quasi-Poisson structure on multiplicative Grothendieck-Springer space.

Lectures on link homology and its algebraic/geometric models.

Springer varieties appear in both geometric representation theory and knot theory. Motivated by knot theory and categorification Khovanov provides a topological construction of $(n/2, n/2)$ Springer varieties. We extend Khovanov's construction to all two-row Springer varieties. Using the combinatorial and diagrammatic …

Springer varieties are studied because their cohomology carries a natural action of the symmetric group $S_n$ and their top-dimensional cohomology is irreducible. In his work on tangle invariants, Khovanov constructed a family of Springer varieties $X_n$ as subvarieties of the product of spheres $(S^2)^n$. We show that…

This paper establishes an isomorphism between the Bar-Natan skein module of the solid torus with a particular boundary curve system and the homology of the (n,n) Springer variety. The results build on Khovanov's work with crossingless matchings and the cohomology of the (n,n) Springer variety. We also give a formula fo…

This is a review article for Encyclopedia of Complexity and System Science, to be published by Springer http://refworks.springer.com/complexity/. The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since late 1990s.

Summarizes geometric connections between sigma models and Gross-Neveu models.

Submitted to F. Schweitzer (ed.), Microscopic Models for Economic Dynamics, Lecture notes in physics, Springer, Berlin-Heidelberg 2002.kiel.tex

We prove that the Grothendieck-Springer simultaneous resolution viewed as a correspondence between the adjoint quotient of a Lie algebra and its maximal torus is Lagrangian in the sense of shifted symplectic structures. As Hamiltonian spaces can be interpreted as Lagrangians in the adjoint quotient, this allows one to …

We build extensions of the arc rings, relate their centers to the cohomology rings of the Springer varieties, and categorify all level two representations of quantum sl(N).

In this work we show that the systems of balance equations (balance systems) of continuum thermodynamics occupy a natural place in the variational bicomplex formalism. We apply the vertical homotopy decomposition to get a local splitting (in a convenient domain) of a general balance system as the sum of a Lagrangian pa…

Study local wild mapping class groups for irregular connections on complex curves.

For a fixed parabolic subalgebra p of gl(n,C) we prove that the centre of the principal block O(p) of the parabolic category O is naturally isomorphic to the cohomology ring of the corresponding Springer fibre. We give a diagrammatic description of O(p) for maximal parabolic p and give an explicit isomorphism to Braden…

A graph connects Specht and web bases; matrix is unipotent with vanishing entries.

Biography of mathematician Herbert Busemann.

A dangerously brief history of the developments of the main ideas in economics, as observed by a physicist, is given. This was published in 'Econophysics of Stock and Other Markets', Eds. A. Chatterjee, B. K. Chakrabarti, New Economic Windows Series, Springer, Milan, 2006, pp~219-224.

This is the second of three papers about the Compression Theorem. We give proofs of Gromov's theorem on directed embeddings [M Gromov, Partial differential relations, Springer--Verlag (1986); 2.4.5 C'] and of the Normal Deformation Theorem [The compression theorem I; 4.7], arxiv:math.GT/9712235.

Overview of Thurston's work in math.

Signature kernel handles sequential data with theoretical and practical advantages.

We present a new approximation to the normal distribution quantile function. It has a similar form to the approximation of Beasley and Springer [3], providing a maximum absolute error of less than $2.5 \cdot 10^{-5}$. This is less accurate than [3], but still sufficient for many applications. However it is faster than …

It is shown that a simple Lie group $G$ ($\neq {\rm SL}_2$) can be locally characterised by an integrability condition on an $\operatorname{Aut}(\mathfrak{g})$ structure on the tangent bundle, where $\operatorname{Aut}(\mathfrak{g})$ is the automorphism group of the Lie algebra of $G$. The integrability condition is t…

This a free translation with additional explanations of {\em Processus à Accroissement Independants Chapitre I: La Décomposition de Paul Lévy}, by J.L. Bretagnolle, in {\em Ecole d'Eté de Probabilités}, Lecture Notes in Mathematics 307, Springer 1973. The Lévy-Khintchine representation of infinitely divisible distribut…

Article explores Thurston's circle packing theorem in 3-manifold geometry.

Survey of work on quantum geometry and gravity.

A local Riemann-Hilbert correspondence for tame meromorphic connections on a curve compatible with a parahoric level structure will be established. Special cases include logarithmic connections on G-bundles and on parabolic G-bundles, where G is a complex reductive group. The corresponding Betti data involves pairs (M,…

In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkhäuser/Springer Basel AG] for continuous processes, we propose a framework enabling us to (asymptotically) optimize…

We consider the problem of adaptation to the margin and to complexity in binary classification. We suggest an exponential weighting aggregation scheme. We use this aggregation procedure to construct classifiers which adapt automatically to margin and complexity. Two main examples are worked out in which adaptivity is a…

Book reviews Riemann's work's impact on math, philosophy, physics.

This paper presents geometrical foundation for a systematic treatment of three main (elliptic, parabolic and hyperbolic) types of analytic function theories based on the representation theory of SL(2,R) group. We describe here geometries of corresponding domains. The principal role is played by Clifford algebras of mat…

This paper explores adiabatic solutions of Haydys-Witten equations for knot homology.

Delisle's projection explained by Euler in 18th century.

Base of fibered correspondence is arbitrary correspondence. Fibered correspondence is interesting when we consider relationship between different bundles. However composition of fibered correspondences may not always be defined. Reduced fibered correspondence is defined only between fibers over the same point of base. …

Extends Frohman and Rannard's result to Seifert fiber spaces with singular surfaces.

We are settling a longstanding quarrel in quantitative finance by proving the existence of trends in financial time series thanks to a theorem due to P. Cartier and Y. Perrin, which is expressed in the language of nonstandard analysis (Integration over finite sets, F. & M. Diener (Eds): Nonstandard Analysis in Practice…

Investigates conditions for GKM fiber bundles and realizability of fiber bundles of GKM graphs.

Teaches math, physics, and machine learning using Calabi-Yau spaces.

Study shows fibered knots' quandles have consistent structure.

Study fiber-preserving, orientation-reversing involutions on Seifert fibered 3-manifolds.

We give a positive answer to the Berry-Robbins problem for any compact Lie group G, i.e. we show the existence of a smooth W-equivariant map from the space of regular triples in a Cartan subalgebra to the flag manifold G/T. This map is constructed via solutions to Nahm's equations and it is compatible with the SO(3) ac…

We study the relationship between fibered ribbon 1-knots and fibered ribbon 2-knots by studying fibered slice disks with handlebody fibers. We give a characterization of fibered homotopy-ribbon disks and give analogues of the Stallings twist for fibered disks and 2-knots. As an application, we produce infinite families…

Historical notes on Thurston's 3-manifold geometry.

Introduces Darboux-Lie derivative for fiber bundles.

The study classifies vector fields tangent to Seifert fiberings.

The paper proves non-existence of positive scalar curvature on certain fiber bundles.

New examples show not all homology fiber bundles are topological.

Study shows simplicial volume of certain fiber bundles is zero.