arXiv research

This paper extends SLS controllers to two stocks, proving the RPE property with cross-coupling.

We present a generalization of the Simultaneous Long-Short (SLS) trading strategy described in recent control literature wherein we allow for different parameters across the short and long sides of the controller; we refer to this new strategy as Generalized SLS (GSLS). Furthermore, we investigate the conditions under …

New methods control false discoveries near the boundary in conformal novelty detection.

We prove Zimmer's conjecture for $C^2$ actions by finite-index subgroups of $\mathrm{SL}(m,\mathbb{Z})$ provided $m>3$. The method utilizes many ingredients from our earlier proof of the conjecture for actions by cocompact lattices in $\mathrm{SL}(m,\mathbb{R})$ but new ideas are needed to overcome the lack of compactn…

We explore the impact of learning paradigms on training deep neural networks for the Travelling Salesman Problem. We design controlled experiments to train supervised learning (SL) and reinforcement learning (RL) models on fixed graph sizes up to 100 nodes, and evaluate them on variable sized graphs up to 500 nodes. Be…

Geometric methods integrate Lie systems for optimal control problems.

Researchers found the longest arcs for specific sub-Lorentzian structures.

We consider the $SL(2,R)$ action on moduli spaces of quadratic differentials. If $μ$ is an $SL(2,R)$-invariant probability measure, crucial information about the associated representation on $L^2(μ)$ (and in particular, fine asymptotics for decay of correlations of the diagonal action, the Teichmüller flow) is encoded …

In any connected non-compact semi-simple Lie group without factors locally isomorphic to SL_2(R), there can be only finitely many lattices (up to isomorphism) of a given covolume. We show that there exist arbitrarily large families of pairwise non-isomorphic arithmetic lattices of the same covolume. We construct these …

Classifies limits of groups of involutions in SL(2,F) over local fields.

Define web algebras for annular SL(2) and SL(3) using foam TQFTs.

Classifies actions of SL(n,R) and SL(n,Z) on closed n-manifolds.

Study of Lagrangian submanifolds in pseudo-nearly Kähler SL(2,R)×SL(2,R).

The paper solves optimal control problems for various convex sets using convex trigonometry.

We show the correspondence between left invariant flat projective structures on Lie groups and certain prehomogeneous vector spaces. Moreover by using the classification theory of prehomogeneous vector spaces, we classify complex Lie groups admitting irreducible left invariant flat complex projective structures. As a r…

Explicitly found generators of cohomology for SL_n(Z) using sharbly cycles and cosharbly cocycles.

Extends $sl(3)$ invariant to tangles via webs and functors.

We construct an equivariant colored sl(N)-homology for links, which generalizes both the colored sl(N)-homology defined by the author and the equivariant sl(N)-homology defined by Krasner. The construction is a straightforward generalization of that of the colored sl(N)-homology. The proof of invariance is based on a s…

The paper classifies topological properties of specific geometric forms on manifolds.

The paper proves Zimmer's conjecture for non-uniform lattices by controlling mass escape and Lyapunov exponents.

New sl(2) action defined on a mathematical module.

It is showed that many examples of AMD submanifolds of higher dimensions come from SL normal bundles. A symmetry property of SL submanifolds and Björling type problem for SL normal bundles are also mentioned.

Classifies real-analytic SL(n,R) actions on closed manifolds.

We construct a categorification of the quantum sl_3 projectors, the sl_3 analog of the Jones-Wenzl projectors, as the stable limit of the complexes assigned to k-twist torus braids (as k goes to infinity) in a suitably shifted version of Morrison and Nieh's geometric formulation of sl_3 link homology (math.GT/0612754).…

We study the Chabauty compactification of two families of closed subgroups of $SL(n,\mathbb{Q}_p)$. The first family is the set of all parahoric subgroups of $SL(n,\mathbb{Q}_p)$. Although the Chabauty compactification of parahoric subgroups is well studied, we give a different and more geometric proof using various Le…

Decomposes $SL_3$ skein algebras for surfaces.

We define two functors from Elias and Khovanov's diagrammatic Soergel category, one targeting Clark-Morrison-Walker's category of disoriented sl(2) cobordisms and the other the category of (universal) sl(3) foams.

The study proves non-existence of hypercomplex structures on SL(3,R) and finds one on SL(2n+1,C).

We classify SL(2;C)-representations of a Brieskorn homology 3-sphere. We show any irreducible representation into SL(2;C) is conjugate to that into either SU(2) or SL(2;R). We also give a construction of SL(2;R)-representations for a Brieskorn homology 3-sphere from PSL(2;R)-representations of the base orbifold fundame…

Unsupervised learning representations generalize better than supervised learning under distribution shifts.

Odd-dimensional SL(n,Q) contains dense surface subgroups.

Two specific Einstein metrics found on a product of SL(2,R) groups.

The paper calculates colored Jones polynomials for specific link configurations.

Given a finite volume hyperbolic 3-manifold, we compose a lift of the holonomy in SL(2,C) with the n-dimensional irreducible representation of SL(2,C) in SL(n,C). In this paper we give local coordinates of the SL(n,C)-character variety around this representation. As a corollary, this representation is isolated among al…

We introduce two invariants called sl(3) Khovanov module and pointed sl(3) Khovanov homology for spatial webs (bipartite trivalent graphs). Those invariants are related to Kronheimer-Mrowka's instanton invariants $J^\sharp$ and $I^\sharp$ for spatial webs by two spectral sequences. As an application of the spectral seq…

The paper constructs bases for cluster varieties using ${ m SL}_3$-webs and laminations.

Study on cohomology of SL_n(Z) for n>=3, proving vanishing of certain cohomology groups.

SL(n) covariant valuations on Orlicz spaces are represented and characterized.

Lectures introduce evaluation of SL(3) foams and link homology.

The paper classifies totally geodesic Lagrangian submanifolds in a specific pseudo-nearly Kähler space.

Study SL(2,C) character schemes for finitely generated groups.

Extends knot invariant computation to symmetrically colored sl_N.

Paper proves zero stability for one-row colored sl₃-Jones polynomials.

New operator reveals unique features of sl(N) link homology.

In this paper I define certain interesting 2-functors from the Khovanov-Lauda 2-category which categorifies quantum sl(k), for any k>1, to a 2-category of universal sl(3) foams with corners. For want of a better name I use the term "foamation" to indicate those 2-functors. I conjecture the existence of similar 2-functo…

New central elements found in a quantum algebra related to knot theory.

Quantum cluster algebra constructed from web skein relations on surfaces.

Combining known spectral sequences with a new spectral sequence relating reduced and unreduced sl(N)-homology yields a relationship between the Homflypt-homology of a knot and its sl(N)-concordance invariants. As an application, some of the sl(N)-concordance invariants are shown to be linearly independent.