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Authors:
mak
Abstract: We give combinatorial descriptions of the Heegaard Floer homology groups for arbitrary three-manifolds (with coefficients in $\mathbb{Z}/2\mathbb{Z}$). The descriptions are based on presenting the three-manifold as an integer surgery on a link in the three-sphere, and then using a grid … Continue reading → PubDate: Wed, 17 Jul 2024 01:32:38 +000

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Authors:
mak
Abstract: We show Poincaré Duality for $\bf{F}_p$-étale cohomology of a smooth proper rigid-analytic space over a non-archimedean field $K$ of mixed characteristic $(0, p)$. It positively answers the question raised by P. Scholze in his paper “$p$-adic Hodge theory for rigid-analytic … Continue reading → PubDate: Thu, 11 Jul 2024 02:48:22 +000

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Authors:
mak
Abstract: Employing the Einstein-scalar field system, we demonstrate an approach for proving high co-dimensional nonlinear instability of naked-singularity solutions as constructed by Christodoulou in [18]. We further investigate the censorship of Christodoulou’s naked singularity and show that a tiny anisotropic perturbation … Continue reading → PubDate: Wed, 19 Jun 2024 18:39:45 +000

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Authors:
mak
Abstract: In a primitive integral Apollonian circle packing, the curvatures that appear must fall into one of six or eight residue classes modulo $24$. The local-global conjecture states that every sufficiently large integer in one of these residue classes appears as … Continue reading → PubDate: Mon, 17 Jun 2024 20:45:52 +000

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Authors:
mak
Abstract: We show that Lubin–Tate theories attached to algebraically closed fields are characterized among $T(n)$-local $\mathbb{E}_\infty$-rings as those that satisfy an analogue of Hilbert’s Nullstellensatz. Furthermore, we show that for every $T(n)$-local $\mathbb{E}_\infty$-ring $R$, the collection of $\mathbb{E}_\infty$-ring maps from $R$ … Continue reading → PubDate: Thu, 23 May 2024 18:58:15 +000

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:
mak
Abstract: We prove the P=W conjecture for $\mathrm{GL}_n$ for all ranks $n$ and curves of arbitrary genus $\ge 2$. The proof combines a strong perversity result on tautological classes with the curious Hard Lefschetz theorem of Mellit. For the perversity statement, … Continue reading → PubDate: Wed, 22 May 2024 00:39:27 +000

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Authors:
mak
Abstract: We prove in this paper the smoothability of cycles modulo rational equivalence below the middle dimension, that is, when the dimension is strictly smaller than the codimension. We introduce and study the class of cycles obtained as “flat pushforwards of … Continue reading → PubDate: Wed, 22 May 2024 00:36:46 +000

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Authors:
mak
Abstract: We develop a theory of linear Mahler systems in several variables from the perspective of transcendence and algebraic independence, which also includes the possibility of dealing with several systems associated with sufficiently independent matrix transformations. Our main results go far … Continue reading → PubDate: Wed, 22 May 2024 00:32:58 +000

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:
mak
Abstract: We show that Lubin–Tate theories attached to algebraically closed fields are characterized among $T(n)$-local $\mathbb{E}_\infty$-rings as those that satisfy an analogue of Hilbert’s Nellstellensatz. Furthermore, we show that for every $T(n)$-local $\mathbb{E}_\infty$-ring $R$, the collection of $\mathbb{E}_\infty$-ring maps from $R$ … Continue reading → PubDate: Wed, 22 May 2024 00:27:19 +000

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Authors:
mak
Abstract: It was conjectured by Milnor in 1968 that the fundamental group of a complete manifold with nonnegative Ricci curvature is finally generated. The main result of this paper is a counterexample, which provides an example $M^7$ with $\mathrm{Ric} \ge 0$ … Continue reading → PubDate: Tue, 21 May 2024 16:17:44 +000

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Authors:
mak
Abstract: We introduce a new class of $\mathfrak{sl}_2$-triples in a complex simple Lie algebra $\mathfrak{g}$, which we call magical. Such an $\mathfrak{sl}_2$-triple canonically defines a real form and various decompositions of $\mathfrak{g}$. Using this decomposition data, we explicitly parameterize special connected … Continue reading → PubDate: Fri, 17 May 2024 01:49:50 +000

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Authors:
mak
Abstract: We study the generalized doubling method for pairs of representations of$G\times\mathrm{GL}_k$ where $G$ is a symplectic group, split special orthogonal group or split general spin group. We analyze the poles of the local integrals, and prove that the global completed … Continue reading → PubDate: Fri, 17 May 2024 01:29:26 +000

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Authors:
mak
Abstract: Let $W$ be a smooth test function with compact support in $(0,\infty)$. Conditional on the Generalized Riemann Hypothesis for Hecke $L$-functions over $\mathbb{Q}(\omega)$, we prove that$$\lt br>\sum_{p \equiv 1 \pmod{3}} \frac{1}{2 \sqrt{p}} \cdot \Big ( \sum_{x \pmod{p}} e^{2\pi i x^3 … Continue reading → PubDate: Wed, 15 May 2024 05:22:19 +000

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Authors:
mak
Abstract: For a complex reductive group, we construct a semi-orthogonal decomposition of the cocenter of the universal variant of its affine Hecke category. We use this to calculate the endomorphisms of a Whittaker object in the cocenter via a diagram organizing … Continue reading → PubDate: Thu, 02 May 2024 20:44:41 +000

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Authors:
mak
Abstract: We prove a 1973 conjecture due to Erdős on the existence of Steiner triple systems with arbitrarily high girth. PubDate: Tue, 30 Apr 2024 18:16:41 +000

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Authors:
mak
Abstract: We complete the proof of Brauer’s Height Zero Conjecture from 1955 by establishing the open implication for all odd primes. PubDate: Sat, 27 Apr 2024 21:16:11 +000

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Authors:
mak
Abstract: We prove the Frenkel-Gaitsgory localization conjecture describing regular Kac-Moody representations at critical level via eigensheaves on the affine Grassmannian using categorical Moy-Prasad theory. This extends previous work of the authors. PubDate: Sat, 27 Apr 2024 20:54:00 +000

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Authors:
mak
Abstract: We consider the defocusing nonlinear Schrödinger equation on $\mathbb{T}^2$ with Wick ordered power nonlinearity, and prove almost sure global well-posedness with respect to the associated Gibbs measure. The heart of the matter is the uniqueness of the solution as limit … Continue reading → PubDate: Wed, 20 Mar 2024 17:55:03 +000

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Authors:
mak
Abstract: In this paper we consider the inductive Aleprin–McKay condition for quasi-isolated 2-blocks of exceptional groups of Lie type. Thereby, we complete the proof of the Alperin–McKay conjecture and Brauer’s Height Zero Conjecture for the prime 2 PubDate: Wed, 13 Mar 2024 20:12:25 +000

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Authors:
annadmin
Abstract: We compute the number of $\mathbb{F}_q$-points on $\overline{\mathcal{M}}_{4,n}$ for $n \leq 3$ and show that it is a polynomial in $q$, using a sieve based on Hasse–Weil zeta functions. As an application, we prove that the rational singular cohomology group … Continue reading → PubDate: Thu, 07 Mar 2024 00:00:00 +000

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Authors:
mak
Abstract: Of the $(2H+1)^n$ monic integer polynomials $f(x) = x^n +a_1x^{n-1}+\cdots a_n$ with $\max(\{|a_1| \dots,|a_n|\} \le H$, how many associated Galois group that is not the full symmetric group $S_n$' There are clearly $\gg H^{n-1}$ such polynomials, as may be obtained … Continue reading → PubDate: Wed, 06 Mar 2024 03:05:53 +000

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Authors:
annadmin
Abstract: For appropriate Gaussian processes, as a corollary of the majorizing measure theorem, Michel Talagrand (1987) proved that the event that the supremum is significantly larger than its expectation can be covered by a set of half-spaces whose sum of measures … Continue reading → PubDate: Wed, 06 Mar 2024 00:00:00 +000

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annadmin
Abstract: Let $f$ be a $C^{1+\alpha}$ diffeomorphism of a compact manifold $M$ preserving a smooth measure $\mu$. We show that if $f\colon (M,\mu)\to (M,\mu)$ is exponentially mixing, then it is Bernoulli. PubDate: Tue, 05 Mar 2024 00:00:00 +000

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annadmin
Abstract: We prove that the Borel space of torsion-free abelian groups with domain $\omega$ is Borel complete, i.e., the isomorphism relation on this Borel space is as complicated as possible, as an isomorphism relation. This solves a long-standing open problem in … Continue reading → PubDate: Mon, 04 Mar 2024 00:00:00 +000

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annadmin
Abstract: We prove the nonlinear inviscid damping for a class of monotone shear flows in $\mathbb{T}\times [0,1]$ for initial perturbation in Gevrey-$\frac{1}{s}$ class ($1\lt \frac{1}{s} PubDate: Sun, 03 Mar 2024 00:00:00 +000

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Authors:
annadmin
Abstract: We analyze the Poincaré and Log-Sobolev constants of logconcave densities in $\mathbb{R}^{n}$. For the Poincaré constant, we give an improved estimate of $O(\sqrt{n})$ for any isotropic logconcave density. For the Log-Sobolev constant, we prove a bound of $\Omega (1/D)$, where … Continue reading → PubDate: Sat, 02 Mar 2024 00:00:00 +000

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Authors:
annadmin
Abstract: The Nadler–Zaslow correspondence famously identifies the finite-dimensional Floer homology groups between Lagrangians in cotangent bundles with the finite-dimensional Hom spaces between corresponding constructible sheaves. We generalize this correspondence to incorporate the infinite-dimensional spaces of morphisms “at infinity,” given on the … Continue reading → PubDate: Fri, 01 Mar 2024 00:00:00 +000

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Authors:
annadmin
Abstract: For integers $s,t \geq 2$, the Ramsey number $r(s,t)$ denotes the minimum $n$ such that every $n$-vertex graph contains a clique of order $s$ or an independent set of order $t$. In this paper we prove \[ r(4,t) = \Omega\Bigl(\frac{t^3}{\log^4 … Continue reading → PubDate: Thu, 08 Feb 2024 00:00:00 +000

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Authors:
annadmin
Abstract: Our main theorem states that the complement of a compact holomorphically convex set in a Stein manifold with the density property is an Oka manifold. This gives a positive answer to the well-known long-standing problem in Oka theory whether the … Continue reading → PubDate: Wed, 07 Feb 2024 00:00:00 +000

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Authors:
annadmin
Abstract: Let $\Sigma _{g,n}$ be an orientable surface of genus $g$ with $n$ punctures. We study actions of the mapping class group $\mathrm {Mod}_{g,n}$ of $\Sigma _{g,n}$ via Hodge-theoretic and arithmetic techniques. We show that if $$\rho : \pi _1(\Sigma _{g,n})\to … Continue reading → PubDate: Tue, 06 Feb 2024 00:00:00 +000

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Authors:
annadmin
Abstract: We prove an effective form of Wilkie’s conjecture in the structure generated by restricted sub-Pfaffian functions: the number of rational points of height $H$ lying in the transcendental part of such a set grows no faster than some power of … Continue reading → PubDate: Mon, 05 Feb 2024 00:00:00 +000

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Authors:
annadmin
Abstract: We prove pointwise convergence for the scattering data of a Dirac system of differential equations. Equivalently, we prove an analog of Carleson’s theorem on almost everywhere convergence of Fourier series for a version of the non-linear Fourier transform. Our proofs … Continue reading → PubDate: Sun, 04 Feb 2024 00:00:00 +000

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annadmin
Abstract: We prove that for $n\in \{4,5\}$, a closed aspherical $n$-manifold does not admit a Riemannian metric with positive scalar curvature. Additionally, we show that for $n\leq 7$, the connected sum of a $n$-torus with an arbitrary manifold does not admit … Continue reading → PubDate: Sat, 03 Feb 2024 00:00:00 +000

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annadmin
Abstract: We establish a prime number theorem for all uniquely ergodic, analytic skew products on the $2$-torus $\mathbb{T}^2$. More precisely, for every irrational $\alpha$ and every $1$-periodic real analytic $g:\mathbb{R}\to\mathbb{R}$ of zero mean, let $T_{\alpha,g} : \mathbb{T}^2 \rightarrow \mathbb{T}^2$ be defined … Continue reading → PubDate: Fri, 02 Feb 2024 00:00:00 +000

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Authors:
annadmin
Abstract: We prove that the generic part of the $\mathrm{mod}\, \ell$ cohomology of Shimura varieties associated to quasi-split unitary groups of even dimension is concentrated above the middle degree, extending our previous work to a non-compact case. The result applies even … Continue reading → PubDate: Thu, 01 Feb 2024 00:00:00 +000

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annadmin
Abstract: \par Sharp $L^\infty $ estimates are obtained for general classes of fully non-linear PDE’s on non-Kähler manifolds, complementing the theory developed earlier by the authors in joint work with F. Tong for the Kähler case. The key idea is still … Continue reading → PubDate: Sat, 06 Jan 2024 00:00:00 +000

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Authors:
annadmin
Abstract: The periodic tiling conjecture asserts that any finite subset of a lattice $\mathbb {Z}^d$ that tiles that lattice by translations, in fact tiles periodically. In this work we disprove this conjecture for sufficiently large $d$, which also implies a disproof … Continue reading → PubDate: Fri, 05 Jan 2024 00:00:00 +000

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annadmin
Abstract: We show that every family of isolated hypersurface singularities with constant Milnor number has constant multiplicity. To achieve this, we endow the A’Campo model of “radius zero” monodromy with a symplectic structure. This new approach allows us to generalize a … Continue reading → PubDate: Thu, 04 Jan 2024 00:00:00 +000

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annadmin
Abstract: We prove a degree-one saving bound for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on $\mathrm{SL}_2$ over any number field that is not totally real. In particular, we establish a sharp bound … Continue reading → PubDate: Wed, 03 Jan 2024 00:00:00 +000

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annadmin
Abstract: Given a compact subset $\Sigma $ of $\mathbb{R}$ obeying some technical conditions, we consider the set of algebraic integers whose conjugates all lie in $\Sigma$. The distribution of conjugates of such an integer defines a probability measure on $\Sigma$; our … Continue reading → PubDate: Tue, 02 Jan 2024 00:00:00 +000

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Authors:
annadmin
Abstract: For every finite quasisimple group of Lie type $G$, every irreducible character $\chi $ of $G$, and every element $g$ of $G$, we give an exponential upper bound for the character ratio $|\chi (g)|/\chi (1)$ with exponent linear in $\log_{|G|} … Continue reading → PubDate: Mon, 01 Jan 2024 00:00:00 +000