Common positive stabilisation found for isotopic contact structures.
problem Isotopic contact structures and open book decompositions.
method Sequence of positive stabilisations and destabilisations.
result Common positive stabilisation exists for isotopic contact structures.
We prove a homological stability theorem for moduli spaces of manifolds of dimension 2n, for attaching handles of index at least n, after these manifolds have been stabilised by countably many copies of Sn×Sn. Combined with previous work of the authors, we obtain an analogue of the Madsen--Weiss theorem …
Study stabilizers in handlebody group; meridians are undistorted, others are exponentially distorted.
problem Geometric properties of stabilizers in handlebody group.
method Analysis of stabilizers of meridians and primitive curves/annuli.
result Stabilizers of meridians are undistorted, others are exponentially distorted.
The stabilisation height of a fibre surface in the 3-sphere is the minimal number of Hopf plumbing operations needed to attain a stable fibre surface from the initial surface. We show that families of fibre surfaces related by iterated Stallings twists have unbounded stabilisation height.
Study of tree automorphisms via arc-stabilizers.
problem Understanding automorphisms of R-trees. method Analyzing actions over arc-stabilizers.
result Point-stabilizers are finitely generated.
This paper models and evaluates contagion and stabilisation in interconnected financial markets.
problem Understanding and managing contagion and resilience in multilayer financial networks.
method Formulates an interconnected multiplex structure, models contagion mechanism, and designs minimum-cost stabilisation strategies.
result Empirically validated minimum-cost stabilisation strategies for multichannel contagion containment.
Stabilizes deep Bayesian neural networks with self-stabilizing priors.
problem Brittleness and difficulty in training deep Bayesian neural networks.
method Signal propagation theory, reformulated ELBO, self-stabilizing priors.
result Improved convergence and robustness in training deeper networks and noisier settings.
New proof of Giroux Correspondence for tight contact 3-manifolds.
problem Proving the Giroux Correspondence for tight contact 3-manifolds.
method Introducing tight Heegaard splittings, using refinement process, and translating moves between splittings to moves between open books.
result Proves the tight Giroux Correspondence for contact 3-manifolds.
Computes slice genus of virtual knots up to 6 crossings.
problem Computing the slice genus of virtual knots.
method Diagrammatic definition and minimal genus surfaces.
result Computed and estimated slice genus of virtual knots.
Study Swan modules and homotopy types, resolving Wall and Dyer questions.
problem Homotopy classification of CW-complexes and Swan modules.
method Analysis of Swan modules and their stably free properties.
result Existence of non-free stably free Swan modules and implications for homotopy equivalence.
New distances defined between surfaces in 4-manifolds, with a new inequality proved.
problem Defining and comparing distances between surfaces in 4-manifolds.
method Using techniques similar to Gabai's proof, proving an inequality between two distance notions.
result Proved that stabilisation distance is at most one more than singularity distance.
In dimension 3 and above, Bredon cohomology gives an acurate purely algebraic description of the minimal dimension of the classifying space for actions of a group with stabilisers in any given family of subgroups. For some Coxeter groups and the family of virtually cyclic subgroups we show that the Bredon cohomological…
New method handles robust and adaptive control of linear systems with non-convex costs.
problem Robust and adaptive control of linear systems with unknown parameters.
method Combining non-asymptotic linear regression, interval prediction, and tree-based planning.
result First end-to-end suboptimality analysis for robust and adaptive MPC with non-convex costs.
The paper connects diffeomorphism groups and sphere embeddings, proving a group structure.
problem Understanding the homotopy types of diffeomorphism groups and sphere embeddings.
method Cerf's upgraded proof, scanning maps, canceling handles, Embedding Calculus.
result The monoid of Schoenflies spheres forms a group under connect-sum.
New method stabilizes GAN training by solving ODEs.
problem Stability issues in GAN training.
method Solving ordinary differential equations (ODEs) to stabilize GAN training.
result Well-known ODE solvers can stabilize GAN training.
Study stable equivalence relations on 4-manifolds, proving homotopy equivalent manifolds with abelian fundamental group are stably diffeomorphic.
problem Classifying stable equivalence relations on 4-manifolds.
method Combination of modified and classical surgery, focusing on homotopy equivalence up to stabilisation.
result Closed oriented homotopy equivalent 4-manifolds with abelian fundamental group are stably diffeomorphic.
It is one of the most important facts in 4-dimensional topology that not every spherical homology class of a 4-manifold can be represented by an embedded sphere. In 1978, M. Freedman and R. Kirby showed that in the simply connected case, many of the obstructions to constructing such a sphere vanish if one modifies the …
The study examines the realizability of a 4-manifold invariant for homeomorphisms.
problem Realizing the Casson-Sullivan invariant for homeomorphisms of 4-manifolds.
method Investigation of the invariant's realizability and application to surface isotopy.
result The invariant can be realized fully after stabilizing with a single S2imesS2 for all orientable pairs of homeomorphic 4-manifolds. Study stabilizes components of Galois cover moduli spaces.
problem Decide equivalence and stable equivalence of monodromy maps.
method Develop algebraic framework to study equivalence classes of monodromy maps.
result Recover a homological invariant that distinguishes equivalence classes.
Smoothly isotopic surfaces in a 4-manifold are stable isotopic if trivial in the 2-homology.
problem Investigating whether topologically isotopic surfaces are smoothly isotopic in stabilised 4-manifolds.
method Analyzing the triviality of surfaces in the 2-homology of the ambient 4-manifold and constructing stabilisations.
result The result holds for surfaces trivial in the 2-homology of the 4-manifold and for certain fundamental groups.
We prove a neighbourhood theorem for arbitrary knots in contact 3-manifolds. As an application we show that two topologically isotopic Legendrian knots in a contact 3-manifold become Legendrian isotopic after suitable stabilisations.
Contact Lie algebras have specific properties related to stabilizers and invariant polynomials.
problem Characterizing contact Lie algebras and their stabilizers.
method Analyzing algebraic Lie algebras of index 1 and their orbits.
result Contact Lie algebras have specific properties related to stabilizers and invariant polynomials.
Newly characterizes the Standard Model gauge group using spinors and geometry.
problem Characterize the Standard Model gauge group GSM within Spin(10).
method Characterizes GSM as a subgroup of Spin(10) using the geometry of pure spinors and Clifford algebras.
result GSM is the intersection of Georgi-Glashow SU(5) and Pati-Salam Spin(6) x Spin(4).
Using basic properties of one-sided Heegaard splittings, a direct proof that geometrically compressible one-sided splittings of RP^3 are stabilised is given. The argument is modelled on that used by Waldhausen to show that two-sided splittings of S^3 are standard.
New findings on group actions and stabilizers of infinite sets.
problem Understanding finiteness properties of stabilizers in group actions.
method Analyzing oligomorphic actions and permutational wreath products.
result Existence of finite subsets with non-FP∞ stabilizers. Abstract: Rational decomposition of homeomorphism spaces for manifolds.
problem Constructing rational homotopy pullback decompositions for homeomorphism spaces.
method Rational homotopy pullback decomposition, nullhomotopy of stabilisation maps, tensor products of truncated operads.
result Rational section of the stabilisation map for homeomorphisms of R^d.
New method classifies spin 4-manifolds using Kervaire-Milnor invariant.
problem Classifying spin 4-manifolds up to stabilisation.
method Using Kervaire-Milnor invariant to compute Arf invariants and classify.
result New stable classification of spin 4-manifolds with 2-dimensional fundamental groups.
Study symplectic mapping classes and their relations to surface mapping classes.
problem Comparing symplectic mapping classes with classical ones.
method Analogous configurations of Lagrangian submanifolds in Weinstein domains.
result Relations between Dehn twists in symplectic manifolds imply similar relations in surface mapping classes.
Study of automorphisms and splittings of special groups, showing infinite groups under certain conditions.
problem Understanding the structure and automorphisms of special groups G. method Constructing and analyzing non-small, stable G-actions on R-trees. result Conditions for the existence of infinite-order automorphisms and splittings.
Given a group action on a simplicial complex such that each simplex stabiliser admits a cocompact model of classifying space for proper actions, we give conditions implying the existence of a cocompact model of classifying space for proper actions for the whole group. This is used to generalise previous combination res…
Study of associative submanifolds in Berger space SO(5)/SO(3).
problem Characterizing and classifying associative submanifolds in Berger space.
method Geometric correspondence with pseudo-holomorphic curves, analysis of special Gauss maps.
result Existence of infinitely many topological types of compact associative 3-folds.
Researchers analyze sign choices for O-planes in orientifolds, proving stabilisation and deriving topological constraints.
problem Assigning sign choices to O-planes in orientifolds of type II string theory.
method Investigating sequences of invariant p-gerbes and coboundary maps to derive sign choices and topological constraints.
result Sign choice homomorphisms stabilise with the dimension of the orientifold and topological constraints on sign configurations are derived.
The brain optimizes memory by forgetting what's predictable, improving generalization.
problem Memory consolidation struggles with representational drift, semanticisation, and offline replay.
method Proposes predictive forgetting as a mechanism to optimize generalization by reducing complexity.
result Predictive forgetting improves information-theoretic generalization bounds on stored representations.
Surface groups found in interval diffeomorphisms without global fix points.
problem Existence of surface groups in interval diffeomorphisms.
method Analyzing the structure of diffeomorphisms of the interval.
result Surface groups with specific properties in interval diffeomorphisms.
An almost Robinson structure on an n-dimensional Lorentzian manifold $(\mcM,g)$, where n=2m+ε, ε∈{0,1}, is a complex m-plane distribution $\mcN$ that is totally null with respect to the complexified metric, and intersects its complex conjugate in a real null line distribution $\mcK$, say. When $\mcN$ an…
Investigates simplicial volume over finite fields and compares it with other coefficients.
problem Examines simplicial volume over Fp coefficients. method Analyzes simplicial volume and gradient invariants over Fp coefficients, comparing with other coefficient rings. result Compares simplicial volumes and Betti numbers over different coefficient rings.
We discuss the construction of Sp(2)Sp(1)-structures whose fundamental form is closed. In particular, we find 10 new examples of 8-dimensional nilmanifolds that admit an invariant closed 4-form with stabiliser Sp(2)Sp(1). Our constructions entail the notion of SO(4)-structures on 7-manifolds. We present a thorough inve…
Paper introduces Prob-SSI for robust OMA in noisy data.
problem Challenges in estimating modal parameters from noisy data.
method Probabilistic formulation of SSI, robust Prob-SSI algorithm.
result Robust Prob-SSI outperforms conventional SSI in corrupted data.
Study fibrations over S2 with same singularities, showing monodromies are equivalent up to direct sums.
problem Classifying torus fibrations over S2 up to fibre sum stabilisation. method Analyzing monodromies and using direct sums with certain torus Lefschetz fibrations.
result Global monodromies of fibrations with same singularities are Hurwitz equivalent after direct sums.
The goal of this paper is to give a conjectural census of complex hyperbolic sporadic groups. We prove that only finitely many of these sporadic groups are lattices. We also give a conjectural list of all lattices among sporadic groups, and for each group in the list we give a conjectural presentation, as well as a lis…
The virtual Betti number conjecture states that any hyperbolic three-manifold has a finite cover with positive first Betti number. We show that this would follow if it were known that the derived series of the fundamental group G of a hyperbolic three-manifold satisfies a certain stability property. The stability pro…
The paper explores non-amenability in infinite-type surfaces and graphs.
problem Determining non-amenability in mapping class groups of infinite-type surfaces and graphs.
method Analyzes mapping class groups of infinite-type surfaces and graphs, provides examples and exhibits classes of groups.
result Completely determines non-amenability of mapping class groups of infinite-type surfaces and graphs.
Let M be a surface (possibly nonorientable) with punctures and/or boundary components. The paper is a study of ``geometric subgroups'' of the mapping class group of M, that is subgroups corresponding to inclusions of subsurfaces (possibly disconnected). We characterise the subsurfaces which lead to virtually abelian ge…
Classifies tilings of Euclidean and hyperbolic planes using topological methods.
problem Classifying crystallographic tilings of Euclidean and hyperbolic planes.
method Topological approaches, including enumeration and classification of tilings as decorations of orbifolds.
result Classification up to equivariant equivalence achieved.
Recent deep network protection fails due to numerical limitations in gradient computations.
problem Numerical limitations in gradient computations weaken deep network protection from adversarial attacks.
method Analyzed saturated networks and showed attacks fail due to numerical limitations. Suggested stabilisation of gradient estimates for successful attacks.
result Numerical limitations in gradient computations are a key factor in the observed robustness of deep networks against adversarial attacks.
We study actions of Lie supergroups, in particular, the hitherto elusive notion of orbits through odd (or more general) points. Following categorical principles, we derive a conceptual framework for their treatment and therein prove general existence theorems for the isotropy (or stabiliser) supergroups and orbits thro…
Proves stable properties of proper maps between manifolds.
problem Stability of homotopy classes of proper maps and Pontryagin-Thom construction.
method Explicit construction and proof of bijection in a stable range.
result Stabilization of homotopy classes of proper maps and Pontryagin-Thom type bijection.
Affine diffeomorphisms are undistorted in half-translation surfaces.
problem Undistorted nature of affine diffeomorphism groups.
method Proof of undistorted subgroup property and systole map embedding.
result Finitely generated subgroups of affine diffeomorphisms are undistorted.