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- publication . Preprint . 2019Open Access EnglishAuthors:Xu, Bin; Zhu, Xuwen;Project: NSF | Mathematical Sciences Res... (1440140)
We show that the monodromy of a spherical conical metric is reducible if and only if it has a real-valued eigenfunction with eigenvalue 2 in the holomorphic extension of the associated Laplace--Beltrami operator. Such an eigenfunction produces a meromorphic vector field...

- publication . Article . Preprint . Other literature type . 2019Open AccessAuthors:Guralnick, Robert M.; Tiep, Pham Huu;Publisher: Elsevier BVProject: NSF | Mathematical Sciences Res... (1440140), NSF | Group Representations and... (1840702)
Abstract Donovan's conjecture implies a bound on the dimensions of cohomology groups in terms of the size of a Sylow p-subgroup and we give a proof of a stronger bound (in terms of sectional p-rank) for dim H 1 ( G , V ) . We also prove a reduction theorem for higher ...

- publication . Preprint . 2016Open Access EnglishAuthors:Lin, Aijin; Shen, Liangming;Project: NSF | Mathematical Sciences Res... (1440140)
We prove that on one K\"{a}hler-Einstein Fano manifold without holomorphic vector fields, there exists a unique conical K\"{a}hler-Einstein metric along a simple normal crossing divisor with admissible prescribed cone angles. We also establish a curvature estimate for c...

- publication . Preprint . 2018Open Access EnglishAuthors:Abbott, Carolyn; Hume, David;Project: NSF | Mathematical Sciences Res... (1440140), NSF | RTG: Algebraic Geometry, ... (1502553)
Comment: 42 pages, 14 figures

- publication . Article . Preprint . 2018Open AccessAuthors:Blekherman, Grigoriy; Raymond, Annie; Singh, Mohit; Thomas, Rekha R.;Publisher: Springer Science and Business Media LLCProject: NSF | CAREER: Nonnegative Polyn... (1352073), NSF | Sums of Squares Polynomia... (1719538), NSF | CCF-BSF: AF: Small: New R... (1717947), NSF | Mathematical Sciences Res... (1440140)
Establishing inequalities among graph densities is a central pursuit in extremal combinatorics. A standard tool to certify the nonnegativity of a graph density expression is to write it as a sum of squares. In this paper, we identify a simple condition under which a gra...

- publication . Preprint . 2017Open Access EnglishAuthors:Ho, Meng-Che "Turbo";Project: NSF | Mathematical Sciences Res... (1440140)
The \emph{word problem} of a group $G = \langle \Sigma \rangle$ can be defined as the set of formal words in $\Sigma^*$ that represent the identity in $G$. When viewed as formal languages, this gives a strong connection between classes of groups and classes of formal la...

- publication . Preprint . Article . 2017Open Access EnglishAuthors:Joseph Maher; Alessandro Sisto;doi: 10.1093/imrn/rnx233Project: NSF | Mathematical Sciences Res... (1440140)
<jats:title>Abstract</jats:title> <jats:p>Let $G$ be an acylindrically hyperbolic group. We consider a random subgroup $H$ in $G$, generated by a finite collection of independent random walks. We show that, with asymptotic probability one, such a random subgroup $H$ of ...

- publication . Article . Preprint . 2019Open AccessAuthors:Liu, Fu; Solus, Liam;Publisher: Springer Science and Business Media LLCProject: NSF | Mathematical Sciences Res... (1440140)
Comment: 15 pages, 2 figures

- publication . Article . Other literature type . Preprint . 2019Open AccessAuthors:Boltje, R.; Kessar, R.; Linckelmann, M.;Publisher: eScholarship, University of CaliforniaProject: NSF | Mathematical Sciences Res... (1440140)
We show that the subgroup of the Picard group of a $p$-block of a finite group given by bimodules with endopermutation sources modulo the automorphism group of a source algebra is determined locally in terms of the fusion system on a defect group. We show that the Picar...

- publication . Article . Preprint . 2018Open AccessAuthors:Mitsuishi, Ayato; Yamaguchi, Takao;Publisher: Springer Science and Business Media LLCProject: NSF | Mathematical Sciences Res... (1440140)
Comment: We gave more details for the proofs of Theorems 1.1 and 1.2