Advances in Mathematics

Items from 1 to 20 out of 33 results

article

Framed sheaves on root stacks and supersymmetric gauge theories on ALE spaces

Ugo Bruzzo, Mattia Pedrini, Francesco Sala, Richard J. Szabo

Advances in Mathematics > 2016 > 288 > C > 1175-1308

We develop a new approach to the study of supersymmetric gauge theories on ALE spaces using the theory of framed sheaves on root toric stacks, which illuminates relations with gauge theories on R4 and with two-dimensional conformal field theory. We construct a stacky compactification of the minimal resolution Xk of the Ak−1 toric singularity C2/Zk, which is a projective toric orbifold Xk such that...

article

Hochschild homology of structured algebras

Nathalie Wahl, Craig Westerland

Advances in Mathematics > 2016 > 288 > C > 240-307

We give a general method for constructing explicit and natural operations on the Hochschild complex of algebras over any prop with A∞-multiplication—we think of such algebras as A∞-algebras “with extra structure”. As applications, we obtain an integral version of the Costello–Kontsevich–Soibelman moduli space action on the Hochschild complex of open TCFTs, the Tradler–Zeinalian and Kaufmann actions...

article

A direct approach to Plateau's problem in any codimension

G. De Philippis, A. De Rosa, F. Ghiraldin

Advances in Mathematics > 2016 > 288 > C > 59-80

This paper proposes a direct approach to solve the Plateau's problem in codimension higher than one. The problem is formulated as the minimization of the Hausdorff measure among a family of d-rectifiable closed subsets of Rn: following the previous work [13], the existence result is obtained by a compactness principle valid under fairly general assumptions on the class of competitors. Such class is...

article

Different asymptotic behavior versus same dynamical complexity: Recurrence & (ir)regularity

Xueting Tian

Advances in Mathematics > 2016 > 288 > C > 464-526

For any dynamical system T:X→X of a compact metric space X with g-almost product property and uniform separation property, under the assumptions that the periodic points are dense in X and the periodic measures are dense in the space of invariant measures, we distinguish various periodic-like recurrences and find that they all carry full topological entropy and so do their gap-sets. In particular,...

article

Effective uniform bounding in partial differential fields

James Freitag, Omar León Sánchez

Advances in Mathematics > 2016 > 288 > C > 308-336

Motivated by the effective bounds found in [12] for ordinary differential equations, we prove an effective version of uniform bounding for fields with several commuting derivations. More precisely, we provide an upper bound for the size of finite solution sets of partial differential polynomial equations in terms of data explicitly given in the equations and independent of parameters. Our methods...

article

Cohomological finite-generation for finite supergroup schemes

Christopher M. Drupieski

Advances in Mathematics > 2016 > 288 > C > 1360-1432

In this paper we compute extension groups in the category of strict polynomial superfunctors and thereby exhibit certain “universal extension classes” for the general linear supergroup. Some of these classes restrict to the universal extension classes for the general linear group exhibited by Friedlander and Suslin, while others arise from purely super phenomena. We then use these extension classes...

article

Poisson bivectors and Poisson brackets on affine derived stacks

Valerio Melani

Advances in Mathematics > 2016 > 288 > C > 1097-1120

Let A be a commutative dg algebra concentrated in degrees (−∞,m], and let SpecA be the associated derived stack. We give two proofs of the existence of a canonical map from the moduli space of shifted Poisson structures (in the sense of [16]) on SpecA to the moduli space of homotopy (shifted) Poisson algebra structures on A. The first makes use of a more general description of the Poisson operad and...

article

On the radius pinching estimate and uniqueness of the CMC foliation in asymptotically flat 3-manifolds

Shiguang Ma

Advances in Mathematics > 2016 > 288 > C > 942-984

In this paper we consider the uniqueness problem of the constant mean curvature spheres in asymptotically flat 3-manifolds. We require the metric to have the form gij=δij+hij with hij=O4(r−1) and R=O(r−3−τ), τ>0. We do not require the metric to be close to Schwarzschild metric in any sense or to satisfy RT conditions. We prove that, when the mass is not 0, stable CMC spheres that separate a certain...

article

Affine symmetries of orbit polytopes

Erik Friese, Frieder Ladisch

Advances in Mathematics > 2016 > 288 > C > 386-425

An orbit polytope is the convex hull of an orbit under a finite group G⩽GL(d,R). We develop a general theory of possible affine symmetry groups of orbit polytopes. For every group, we define an open and dense set of generic points such that the orbit polytopes of generic points have conjugated affine symmetry groups. We prove that the symmetry group of a generic orbit polytope is again G if G is itself...

article

An approach to categorification of some small quantum groups II

Ben Elias, You Qi

Advances in Mathematics > 2016 > 288 > C > 81-151

We categorify an idempotented form of quantum sl2 and some of its simple representations at a prime root of unity.

article

Gromov–Witten gauge theory

Edward Frenkel, Constantin Teleman, A.J. Tolland

Advances in Mathematics > 2016 > 288 > C > 201-239

We introduce a modular completion of the stack of maps from stable marked curves to the quotient stack [pt/C×], and use this stack to construct some gauge-theoretic analogues of the Gromov–Witten invariants. We also indicate the generalization of these invariants to the quotient stacks [X/C×], where X is a smooth proper complex algebraic variety.

article

The multiplicative eigenvalue problem and deformed quantum cohomology

Prakash Belkale, Shrawan Kumar

Advances in Mathematics > 2016 > 288 > C > 1309-1359

We construct deformations of the small quantum cohomology rings of homogeneous spaces G/P, and obtain an irredundant set of inequalities determining the multiplicative eigen polytope for the compact form K of G.

article

Invariant theory in exterior algebras and Amitsur–Levitzki type theorems

Minoru Itoh

Advances in Mathematics > 2016 > 288 > C > 679-701

This article discusses invariant theories in some exterior algebras, which are closely related to Amitsur–Levitzki type theorems.First we consider the exterior algebra on the vector space of square matrices of size n, and look at the invariants under conjugations. We see that the algebra of these invariants is isomorphic to the exterior algebra on an n-dimensional vector space. Moreover we give a...

article

Suffridge's convolution theorem for polynomials and entire functions having only real zeros

Martin Lamprecht

Advances in Mathematics > 2016 > 288 > C > 426-463

We present a q-extension of Pólya's and Schur's characterization of multiplier sequences and a q-extension and a converse of Newton's inequalities.

article

The asymptotic k-SAT threshold

Amin Coja-Oghlan, Konstantinos Panagiotou

Advances in Mathematics > 2016 > 288 > C > 985-1068

Since the early 2000s physicists have developed an ingenious but non-rigorous formalism called the cavity method to put forward precise conjectures on phase transitions in random problems (Mézard et al., 2002 [37]). The cavity method predicts that the satisfiability threshold in the random k-SAT problem is rk-SAT=2kln⁡2−12(1+ln⁡2)+εk, with limk→∞⁡εk=0 (Mertens et al., 2006 [35]). This paper contains...

article

Bridgeland stability conditions on the acyclic triangular quiver

George Dimitrov, Ludmil Katzarkov

Advances in Mathematics > 2016 > 288 > C > 825-886

Using results in our previous paper “Non-semistable exceptional objects in hereditary categories”, we focus here on studying the topology of the space of Bridgeland stability conditions on Db(Repk(Q)), where Q= and k is an algebraically closed field. In particular, we prove that this space is contractible (in the previous paper it was shown that it is connected).

article

The Brown–Comenetz dual of the K(2)-local sphere at the prime 3

Paul G. Goerss, Hans-Werner Henn

Advances in Mathematics > 2016 > 288 > C > 648-678

We calculate the homotopy type of the Brown–Comenetz dual I2 of the K(2)-local sphere at the prime 3 and show that there is an equivalence in the K(2)-local category between I2 and a smash product of the determinant twisted sphere and an exotic element P in the Picard group. We give a characterization of P as well. A secondary aim of the paper is to extend our library of calculations in the K(2)-local...

article

Kronecker products, characters, partitions, and the tensor square conjectures

Igor Pak, Greta Panova, Ernesto Vallejo

Advances in Mathematics > 2016 > 288 > C > 702-731

We study the remarkable Saxl conjecture which states that tensor squares of certain irreducible representations of the symmetric groups Sn contain all irreducibles as their constituents. Our main result is that for sufficiently large n they contain representations corresponding to Young diagrams of hooks, two row and diagrams obtained from hooks and two rows by adding a finite number of squares. For...

article

The Dirichlet problem for nonlocal operators with singular kernels: Convex and nonconvex domains

Xavier Ros-Oton, Enrico Valdinoci

Advances in Mathematics > 2016 > 288 > C > 732-790

We study the interior regularity of solutions to the Dirichlet problem Lu=g in Ω, u=0 in Rn∖Ω, for anisotropic operators of fractional typeLu(x)=∫0+∞dρ∫Sn−1da(ω)2u(x)−u(x+ρω)−u(x−ρω)ρ1+2s. Here, a is any measure on Sn−1 (a prototype example for L is given by the sum of one-dimensional fractional Laplacians in fixed, given directions).When a∈C∞(Sn−1) and g is C∞(Ω), solutions are known to be C∞ inside...

article

Descent for n-bundles

Jesse Wolfson

Advances in Mathematics > 2016 > 288 > C > 527-575

Given a Lie group G, one constructs a principal G-bundle on a manifold X by taking a cover U→X, specifying a transition cocycle on the cover, and descending the trivialized bundle U×G along the cover. We demonstrate the existence of an analogous construction for local n-bundles for general n. We establish analogues for simplicial Lie groups of Moore's results on simplicial groups; these imply that...

Number:
C
Volume:
288
Year:
2016

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Keywords

AFFINE QUIVER (1)
AFFINE SYMMETRY (1)
ALE SPACES (1)
AMITSUR–LEVITZKI THEOREM (1)
ANISOTROPIC MEDIA (1)
ARTIN STACK (1)
ASYMPTOTICALLY FLAT MANIFOLD (1)
BLOWUP FORMULAS (1)
BOUNDED HEIGHT (1)
BRIDGELAND STABILITY CONDITIONS ON TRIANGULATED CATEGORIES (1)
BRILL–NOETHER THEORY (1)
BROAD DOMAIN (1)
BROWN–COMENETZ DUALITY (1)
BUNDLE GERBES (1)
CATEGORIFICATION (1)
CAYLEY–HAMILTON THEOREM (1)
CHROMATIC STABLE HOMOTOPY THEORY (1)
COHERENT SYSTEMS (1)
COHOMOLOGICAL FINITE GENERATION (1)
COMPLEX DYNAMICS (1)
CONSTANT MEAN CURVATURE (1)
CONTRACTIBLE SPACE (1)
CURVATURE MEASURE (1)
DEFORMATION THEORY (1)
DIFFERENTIAL FIELDS (1)
DYNAMICS (1)
EDGE-DECOMPOSITIONS OF GRAPHS (1)
EISENSTEIN SERIES (1)
EXCEPTIONAL COLLECTIONS (1)
EXTERIOR ALGEBRA (1)
EXTREMAL GRAPH THEORY (1)
FINITE GROUP SCHEMES (1)
FRACTAL GEOMETRY (1)
FRACTIONAL LAPLACIAN (1)
FRAMED SHEAVES (1)
FROBENIUS ALGEBRAS (1)
GAUGE THEORY (1)
GEOMETRIC MEASURE THEORY (1)
GROMOV–WITTEN (1)
GROUP REPRESENTATION (1)
HALF-SPACE (1)
HILBERT SCHEME (1)
HOCHSCHILD HOMOLOGY (1)
INTEGER PARTITIONS (1)
INTEGRO-DIFFERENTIAL EQUATIONS (1)
INVARIANT THEORY (1)
IRREDUCIBLE REPRESENTATIONS OF THE SYMMETRIC GROUP (1)
JULIA SET (1)
K-THEORY (1)
KRONECKER COEFFICIENTS (1)
LIMIT LINEAR SERIES (1)
LLC2 SET (1)
LOG-CONCAVE SEQUENCES (1)
MEASURABLE NONLINEARITY (1)
MEDVEDEV–SCANLON THEOREM (1)
MEROMORPHIC CONTINUATION (1)
MODULI SPACE OF RIEMANN SURFACES (1)
MULTIPLICATIVE EIGENVALUE PROBLEM (1)
NAVIER–STOKES FLOW (1)
NEWTON'S INEQUALITIES (1)
NONLINEAR ELLIPTIC EQUATION (1)
NORMAL VARIETY (1)
OPERATIONS (1)
ORBIT POLYTOPE (1)
PARTITION FUNCTIONS (1)
PERIODIC, ALMOST PERIODIC POINT, WEAKLY ALMOST PERIODIC POINT AND QUASI-WEAKLY ALMOST PERIODIC POINT (1)
PERMUTATION POLYTOPE (1)
PHASE TRANSITIONS (1)
PLATEAU'S PROBLEM (1)
POSITIVITY (1)
PROBABILISTIC COMBINATORICS (1)
PROBABILISTIC METHODS (1)
PROLONGATION SPACES (1)
PÓLYA–SCHUR MULTIPLIER SEQUENCES (1)
Q-BINOMIALS (1)
QUANTUM COHOMOLOGY (1)
QUANTUM GROUPS (1)
QUASICONFORMAL MAPPING (1)
QUASISYMMETRY (1)
RECTIFIABLE SETS (1)
REGULAR, QUASIREGULAR AND IRREGULAR POINT (1)
REGULARITY THEORY (1)
REIFENBERG DOMAIN (1)
REPRESENTATION POLYTOPE (1)
ROOTS OF UNITY (1)
ROUGH KERNELS (1)
SATISFIABILITY PROBLEM (1)
SECANT VARIETY (1)
SHEAF COHOMOLOGY (1)
SIMPLICIAL MANIFOLDS (1)
SOLUTION FORMULA (1)
SPECIFICATION PROPERTY (1)
SPECTRAL SEQUENCES (1)
SPLASH SINGULARITIES (1)
STACKS (1)
STOKES SYSTEM (1)
STRICT POLYNOMIAL FUNCTORS (1)
STRING 2-GROUP (1)
STRONG SOLUTION (1)
STRUCTURE THEOREM (1)
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INFONA - science communication portal

Advances in Mathematics

Framed sheaves on root stacks and supersymmetric gauge theories on ALE spaces

Hochschild homology of structured algebras

A direct approach to Plateau's problem in any codimension

Different asymptotic behavior versus same dynamical complexity: Recurrence & (ir)regularity

Effective uniform bounding in partial differential fields

Cohomological finite-generation for finite supergroup schemes

Poisson bivectors and Poisson brackets on affine derived stacks

On the radius pinching estimate and uniqueness of the CMC foliation in asymptotically flat 3-manifolds

Affine symmetries of orbit polytopes

An approach to categorification of some small quantum groups II

Gromov–Witten gauge theory

The multiplicative eigenvalue problem and deformed quantum cohomology

Invariant theory in exterior algebras and Amitsur–Levitzki type theorems

Suffridge's convolution theorem for polynomials and entire functions having only real zeros

The asymptotic k-SAT threshold

Bridgeland stability conditions on the acyclic triangular quiver

The Brown–Comenetz dual of the K(2)-local sphere at the prime 3

Kronecker products, characters, partitions, and the tensor square conjectures

The Dirichlet problem for nonlocal operators with singular kernels: Convex and nonconvex domains

Descent for n-bundles

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