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 Annals of MathematicsJournal Prestige (SJR): 10.923 Citation Impact (citeScore): 5Number of Followers: 5      Subscription journal ISSN (Print) 0003-486X Published by Princeton University Press  [1 journal]
• Pseudorandom sets in Grassmann graph have near-perfect expansion

Authors: mak
Abstract: We prove that pseudorandom sets in Grassmann graph have near-perfect expansion. This completes the proof of the $2$-to-$2$ Games Conjecture (albeit with imperfect completeness). Some implications of this new result are improved hardness results for Minimum Vertex Cover, improving on … Continue reading →
PubDate: Sat, 21 Jan 2023 16:34:55 +000

• Existence of infinitely many minimal hypersurfaces in closed manifolds

Authors: mak
Abstract: Using min-max theory, we show that in any closed Riemannanian manifold of dimension at least 3 and at most 7, there exist infinitely many smoothly embedded closed minimal hypersurfaces. It proves a conjecture of S.-T. Yau. This paper builds on … Continue reading →
PubDate: Sun, 15 Jan 2023 03:58:48 +000

• Two theorems on semi-simple Lie groups

Fri, 06 Jan 2023 21:10:39 +000

• Pseudo-differential operators and non-elliptic boundary problems

Fri, 06 Jan 2023 21:09:53 +000

• Cobordism of combinatorial manifolds

Fri, 06 Jan 2023 21:09:11 +000

• On the fundamental group of a compact minimal submanifold

Fri, 06 Jan 2023 21:07:19 +000

• SU-cobordism, KO-characteristic numbers, and the Kervaire invariant

Fri, 06 Jan 2023 21:06:58 +000

• Cobordism classes of squares of orientable manifolds

Fri, 06 Jan 2023 21:06:42 +000

• On the meromorphic function field of a Stein variety

Fri, 06 Jan 2023 21:06:24 +000

• Stable minimal hypersurfaces in $\mathbb{R}^{N+1+\ell}$ with singular set
an arbitrary closed $K\subset \{0\} \times \mathbb{R}^\ell$

Fri, 16 Dec 2022 06:30:12 +000

• Statistical dynamics of a hard sphere gas: fluctuating Boltzmann equation
and large deviations

Authors: mak
Abstract: We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that: (1) fluctuations of the empiral measure from the solution of the Boltzmann equation, scaled with the square root of the … Continue reading →
PubDate: Fri, 09 Dec 2022 16:07:30 +000

• Infinite volume and infinite injectivity radius

Abstract: We prove the following conjecture of Margulis. Let $G$ be a higher rank simple Lie group, and let $\Lambda \le G$ be a discrete subgroup of infinite covolume. Then, the locally symmetric space $\Lambda \backslash G/K$ admits injected balls of … Continue reading →
PubDate: Wed, 23 Nov 2022 20:43:00 +000

• On the Brumer–Stark conjecture

Abstract: Let $H/F$ be a finite abelian extension of number fields with $F$ totally real and $H$ a CM field. Let $S$ and $T$ be disjoint finite sets of places of $F$ satisfying the standard conditions. The Brumer–Stark conjecture states that … Continue reading →
PubDate: Wed, 23 Nov 2022 20:43:00 +000

• Special subvarieties of non-arithmetic ball quotients and Hodge theory

Abstract: Let $\Gamma \subset \mathrm {PU}(1,n)$ be a lattice and $S_\Gamma$ be the associated ball quotient. We prove that, if $S_\Gamma$ contains infinitely many maximal complex totally geodesic subvarieties, then $\Gamma$ is arithmetic. We also prove an Ax–Schanuel … Continue reading →
PubDate: Wed, 23 Nov 2022 20:41:00 +000

• Smooth mixing Anosov flows in dimension three are exponentially mixing

Abstract: We show that a topologically mixing $C^\infty$ Anosov flow on a 3-dimensional compact manifold is exponentially mixing with respect to any equilibrium measure with Hölder potential.
PubDate: Wed, 23 Nov 2022 20:40:00 +000

• There is no Enriques surface over the integers

Abstract: We show that there is no family of Enriques surfaces over the ring of integers. This extends non-existence results of Minkowski for families of finite étale schemes, of Tate and Ogg for families of elliptic curves, and of Fontaine and … Continue reading →
PubDate: Wed, 23 Nov 2022 20:40:00 +000

• Dimension formulae and generalised deep holes of the Leech lattice vertex
operator algebra

Abstract: We prove a dimension formula for the weight-$1$ subspace of a vertex operator algebra $V^{\mathrm {orb}(g)}$ obtained by orbifolding a strongly rational, holomorphic vertex operator algebra $V$ of central charge $24$ with a finite-order automorphism $g$. Based on an upper … Continue reading →
PubDate: Wed, 23 Nov 2022 19:42:00 +000

• On complex-spin manifolds

Sun, 20 Nov 2022 04:14:10 +000

• Hopf structures attached to $K$-theory: Hodgin’s theorem

Sun, 20 Nov 2022 04:13:46 +000

• On the double suspension of certain homotopy 3-spheres

Sun, 20 Nov 2022 04:12:12 +000

• The Nielsen number of a fibre map

Sun, 20 Nov 2022 04:12:05 +000

• Immersing projective spaces

Sun, 20 Nov 2022 04:11:41 +000

• On heights of algebraic subspaces and diophantine approximations

Sun, 20 Nov 2022 04:11:32 +000

• Representations of complex semi-simple Lie groups and Lie algebras

Sun, 20 Nov 2022 04:11:17 +000

• A duality in the representation theory of $C^\ast$-algebras

Sun, 20 Nov 2022 04:11:09 +000

• On compact subgroups of the diffeomorphism groups of Kervaire spheres

Sun, 20 Nov 2022 04:10:55 +000

• Transversality and super-rigidity for multiply covered holomorphic curves

Authors: mak
Abstract: We develop new techniques to study regularity questions for moduli spaces of pseudoholomorphic curves that are multiply covered. Among the main results, we show that unbranched multiple covers of closed holomorphic curves are generally regular, and simple index $0$ curves … Continue reading →
PubDate: Sat, 12 Nov 2022 03:35:37 +000

• Redshift and multiplication for truncated Brown–Peterson spectra

Abstract: We equip $\mathrm {BP} \langle n \rangle$ with an $\mathbb {E}_3$-$\mathrm{BP}$-algebra structure for each prime $p$ and height $n$. The algebraic $K$-theory of this ring is of chromatic height exactly $n+1$, and the map $\mathrm {K}(\mathrm{BP}\langle n \rangle )_{(p)} … Continue reading → PubDate: Thu, 27 Oct 2022 16:06:00 +000 • Prisms and prismatic cohomology • Free pre-print version: Loading... Authors: annadmin Abstract: We introduce the notion of a prism, which may be regarded as a “deperfection” of the notion of a perfectoid ring. Using prisms, we attach a ringed site — the prismatic site — to a$p$-adic formal scheme. The resulting … Continue reading → PubDate: Thu, 27 Oct 2022 16:05:00 +000 • One can hear the shape of ellipses of small eccentricity • Free pre-print version: Loading... Authors: annadmin Abstract: We show that if the eccentricity of an ellipse is sufficiently small, then up to isometries it is spectrally unique among all smooth domains. We do not assume any symmetry, convexity, or closeness to the ellipse, on the class of … Continue reading → PubDate: Thu, 27 Oct 2022 16:04:00 +000 • Universal optimality of the$E_8$and Leech lattices and interpolation formulas • Free pre-print version: Loading... Authors: annadmin Abstract: We prove that the$E_8$root lattice and the Leech lattice are universally optimal among point configurations in Euclidean spaces of dimensions eight and twenty-four, respectively. In other words, they minimize energy for every potential function that is a completely … Continue reading → PubDate: Thu, 27 Oct 2022 16:03:00 +000 • Invariant measures and measurable projective factors for actions of higher-rank lattices on manifolds • Free pre-print version: Loading... Authors: annadmin Abstract: We consider smooth actions of lattices in higher-rank semisimple Lie groups on manifolds. We define two numbers$r(G)$and$m(G)$associated with the roots system of the Lie algebra of a Lie group$G$. If the dimension of the manifold … Continue reading → PubDate: Thu, 27 Oct 2022 16:01:00 +000 • Zimmer’s conjecture: Subexponential growth, measure rigidity, and strong property (T) • Free pre-print version: Loading... Authors: annadmin Abstract: We prove several cases of Zimmer’s conjecture for actions of higher-rank, cocompact lattices on low-dimensional manifolds. For example, if$\Gamma$is a cocompact lattice in$\mathrm{SL}(n,\mathbb{R})$,$M$is a compact manifold, and$\omega$a volume form on$M$, we show … Continue reading → PubDate: Thu, 27 Oct 2022 16:00:00 +000 • Singularities for the Einstein vacuum equations: The exterior solution • Free pre-print version: Loading... Authors: mak Abstract: In this work we initiate the mathematical study of naked singularities for the Einstein vacuum equations in$3+1$dimensions by constructing solutions which correspond to the exterior region of a naked singularity. A key element is our introduction of a … Continue reading → PubDate: Wed, 19 Oct 2022 06:24:24 +000 • On the bound of the dimensions of the isometry groups of all possible riemannian metrics on an exotic sphere • Free pre-print version: Loading... Tue, 11 Oct 2022 02:51:27 +000 • Boundedness of translation invariant operators on Hölder spaces and$L^p$-spaces • Free pre-print version: Loading... Tue, 11 Oct 2022 02:51:17 +000 • Space of unitary vector bundles on a compact Riemann surface • Free pre-print version: Loading... Tue, 11 Oct 2022 02:51:06 +000 • Finite subgroups and isogenies of one-parameter formal Lie groups • Free pre-print version: Loading... Tue, 11 Oct 2022 02:50:42 +000 • Hecke polynomials as congruence$\zeta$functions in elliptic modular case • Free pre-print version: Loading... Tue, 11 Oct 2022 02:50:34 +000 • Differential geometry of complex hypersurfaces • Free pre-print version: Loading... Tue, 11 Oct 2022 02:50:21 +000 • Simplicial structures and transverse cellularity • Free pre-print version: Loading... Tue, 11 Oct 2022 02:50:13 +000 • Postnikov invariants and higher order cohomology operations • Free pre-print version: Loading... Tue, 11 Oct 2022 02:50:02 +000 • Solving diophantine problems modulo every prime • Free pre-print version: Loading... Tue, 11 Oct 2022 02:49:54 +000 • Construction of class fields and zeta functions of algebraic curves • Free pre-print version: Loading... Sat, 01 Oct 2022 00:29:41 +000 • On zeta functions of quadratic forms • Free pre-print version: Loading... Sat, 01 Oct 2022 00:29:36 +000 • Weierstrass points at cusps of$\Gamma_0(n)$• Free pre-print version: Loading... Sat, 01 Oct 2022 00:29:31 +000 • The spinning and twisting of a complex in a hyperplane • Free pre-print version: Loading... Sat, 01 Oct 2022 00:29:23 +000 • Piecewise linear embeddings • Free pre-print version: Loading... Sat, 01 Oct 2022 00:29:14 +000 • Algebraic number fields and symplectic discontinuous groups • Free pre-print version: Loading... Sat, 01 Oct 2022 00:03:23 +000 • Fixed point free conjugations on complex manifolds • Free pre-print version: Loading... Sat, 01 Oct 2022 00:03:17 +000 • Analysis in matrix spaces and some new representations of$\mathrm{SL}(N,\mathbf{C})$• Free pre-print version: Loading... Sat, 01 Oct 2022 00:03:10 +000 • On the algebraic curves uniformized by arithmetical automorphic functions • Free pre-print version: Loading... Sat, 01 Oct 2022 00:03:04 +000 • A$\Pi_\ast$-module structure for$\Theta_\ast$and applications to transformation groups • Free pre-print version: Loading... Sat, 01 Oct 2022 00:02:52 +000 • Some remarks on symplectic cobordism • Free pre-print version: Loading... Sat, 01 Oct 2022 00:02:46 +000 • Cohomology of arithmetic subgroups of algebraic groups. I. • Free pre-print version: Loading... Sat, 01 Oct 2022 00:02:34 +000 • A Lefschetz fixed point formula for elliptic complexes. I. • Free pre-print version: Loading... Fri, 30 Sep 2022 22:30:47 +000 • A concept of cobordism between links • Free pre-print version: Loading... Fri, 30 Sep 2022 22:30:23 +000 • Fields of tangent 2-planes on even-dimensional manifolds • Free pre-print version: Loading... Fri, 30 Sep 2022 22:30:10 +000 • Consistency proofs of subsystems of classical analysis • Free pre-print version: Loading... Fri, 30 Sep 2022 22:30:00 +000 • The structure of the spin cobordism ring • Free pre-print version: Loading... Fri, 30 Sep 2022 22:29:49 +000 • Existence theorems for analytic linear partial differential equations • Free pre-print version: Loading... Fri, 30 Sep 2022 22:29:40 +000 • Poincaré complexes. I. • Free pre-print version: Loading... Fri, 30 Sep 2022 22:28:56 +000 • On the non-vanishing of the Jacobian of a homeomorphism of harmonic gradients • Free pre-print version: Loading... Tue, 27 Sep 2022 04:22:42 +000 • Good reduction of abelian varieties • Free pre-print version: Loading... Tue, 27 Sep 2022 04:21:55 +000 • A Lefschetz fixed point formula for elliptic complexes. II. Applications • Free pre-print version: Loading... Tue, 27 Sep 2022 04:21:47 +000 • Cohomological dimension of algebraic varieties • Free pre-print version: Loading... Tue, 27 Sep 2022 04:21:38 +000 • The weakly complex bordism of Lie groups • Free pre-print version: Loading... Tue, 27 Sep 2022 04:21:32 +000 • On the characteristic Cauchy problem • Free pre-print version: Loading... Tue, 27 Sep 2022 04:21:21 +000 • On groups acting on locally finite graphs • Free pre-print version: Loading... Tue, 27 Sep 2022 04:00:51 +000 • On torsion-free groups with infinitely many ends • Free pre-print version: Loading... Tue, 27 Sep 2022 04:00:41 +000 • On the homotopy groups of$BPL$and$PL/O\$

Tue, 27 Sep 2022 04:00:29 +000

• On the set of non-locally flat points of a submanifold of codimension one

Tue, 27 Sep 2022 04:00:15 +000

• The word problem in fundamental groups of sufficiently large irreducible
3-manifolds

Tue, 27 Sep 2022 03:59:19 +000

• The elementary theory of finite fields

Tue, 27 Sep 2022 03:59:08 +000

• Formal cohomology. II. The cohomology sequence of a pair

Tue, 27 Sep 2022 03:58:43 +000

• Formal cohomology. I

Tue, 27 Sep 2022 03:58:35 +000

• Algebraic cycles on abelian varieties of complex multiplication type

Tue, 27 Sep 2022 03:58:21 +000

• Complexity of finite semigroups

Tue, 27 Sep 2022 03:14:47 +000

• Fatou’s theorem for symmetric spaces. I

Tue, 27 Sep 2022 03:14:38 +000

• Minimal varieties in Riemannian manifolds

Tue, 27 Sep 2022 03:14:22 +000

• On Schottky groups with applications to Kleinian groups

Tue, 27 Sep 2022 03:14:15 +000

• The structure of weakly compact sets in Banach spaces

Tue, 27 Sep 2022 03:14:08 +000

• On the deformation of rings and Algebras. III

Tue, 27 Sep 2022 03:13:59 +000

• Conjugate loci of constant order

Tue, 27 Sep 2022 02:49:53 +000

• Transversality for polyhedra

Tue, 27 Sep 2022 02:49:41 +000

• Representations of uniformly hyperfinite algebras and their associated von
Neumann rings

Tue, 27 Sep 2022 02:49:21 +000

• On a theorem of Bochner

Tue, 27 Sep 2022 02:49:13 +000

• On a problem of Philip Hall

Tue, 27 Sep 2022 02:49:05 +000

• Bounded analytic functions and Gleason parts

Tue, 27 Sep 2022 02:48:57 +000

• Grothendieck groups and Picard groups of abelian group rings

Tue, 27 Sep 2022 02:48:44 +000

• Conjugacy classes in Lie algebras and algebraic groups

Tue, 27 Sep 2022 02:48:37 +000

• Nonabelian level structures, Nielsen equivalence, and Markoff triples

Authors: mak
Abstract: In this paper we establish a congruence on the degree of the map from a component of a Hurwitz space of covers of elliptic curves to the moduli stack of elliptic curves. Combinatorially, this can be expressed as a congruence … Continue reading →
PubDate: Sun, 14 Aug 2022 14:55:10 +000

• On Frobenius exact symmetric tensor categories

Authors: mak
Abstract: A fundamental theorem of P. Deligne (2002) states that a pre-Tannakian category over an algebraically closed field of characteristic zero admits a fiber functor to the category of supervector spaces (i.e., is the representation category of an affine proalgebraic subgroup) … Continue reading →
PubDate: Sun, 14 Aug 2022 14:54:50 +000

• Structurally stable systems on open manifolds are never dense

Thu, 11 Aug 2022 03:48:30 +000

• The index of elliptic operators. III.

Thu, 11 Aug 2022 03:47:43 +000

• The index of elliptic operators. II.

Thu, 11 Aug 2022 03:47:37 +000

• The index of elliptic operators. I.

Thu, 11 Aug 2022 03:47:30 +000

• Block bundles. III. Homotopy theory

Thu, 11 Aug 2022 03:47:18 +000

• Embedding real projective spaces

Thu, 11 Aug 2022 03:46:31 +000

• Structure of inseparable extensions

Thu, 11 Aug 2022 03:46:22 +000

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