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2018 Workshop on New Methods for Zimmer’s Conjecture
2018 Workshop New Methods for Zimmer’s Conjecture
2017/12/20
The purpose of this workshop is to bring focused attention on a recent breakthrough by Brown, Fisher and ZIM2018_imageHurtado on Zimmer’s Conjecture. The conjecture concerns low dimensional actions of...
We prove the Noether-Lefschetz conjecture on the moduli space of quasi-polarized K3 surfaces. This is deduced as a particular case of a general theorem that states that low degree cohomology classes o...
STRONG SHIFT EQUIVALENCE AND THE GENERALIZED SPECTRAL CONJECTURE FOR NONNEGATIVE MATRICES
STRONG SHIFT EQUIVALENCE GENERALIZED SPECTRAL CONJECTURE NONNEGATIVE MATRICES
2015/9/29
Given matrices A and B shift equivalent over a dense subring R of R,with A primitive, we show that B is strong shift equivalent over R to a primitive matrix. This result shows that the weak form of th...
THRESHOLD STATE AND A CONJECTURE OF POGHOSYAN,POGHOSYAN,PRIEZZHEV AND RUELLE
THRESHOLD STATE POGHOSYAN POGHOSYAN PRIEZZHEV RUELLE
2015/8/14
We prove a precise relationship between the threshold state of the fixed-energy sandpile and the stationary state of Dhar’s abelian sandpile: In the limit as the initial condition s0 tends to −∞...
Proof of a Conjecture of Hirschhorn and Sellers on Overpartitions
overpartition congruence theta function dissection formula (p k)-parametrization
2014/6/3
Let (n) denote the number of overpartitions of n. It was conjectured by Hirschhorn and Sellers that (40n + 35) ≡ 0 (mod 40) for n ≥ 0. Employing 2-dissection formulas of theta functions due to Ramanuj...
Let di(m) denote the coefficients of the Boros-Moll polynomials. Moll's minimum conjecture states that the sequence {i(i+1)(di2(m)-di-1(m)di+1(m))}1≤ i≤ m attains its minimum at i = m with 2-2mm(m+1)....
Proof of a Positivity Conjecture on Schur Functions
symmetric function Schur function multiplier sequence totally positive sequence
2014/6/3
In the study of Zeilberger's conjecture on an integer sequence related to the Catalan numbers, Lassalle proposed the following conjecture. Let (t)n denote the rising factorial, and let ΛR denote the a...
Even Galois Representations and the Fontaine--Mazur conjecture II
Even Galois Representations Fontaine--Mazur conjecture II
2011/2/24
We prove, under mild hypotheses, that there are no irreducible two-dimensional po-tentially semi-stable even p-adic Galois representations of Gal(Q/Q) with distinct Hodge–Tate weights.
Tree homology and a conjecture of Levine
Levine conjecture tree homology homology cylinders Whitney towers
2011/1/21
In his study of the group of homology cylinders, J. Levine [19] made the con-jecture that a certain homomorphism 0 : T ! D0 is an isomorphism. Here T is an abelian group on labeled oriented trees, an...
On a conjecture for a sixth order overdetermined elliptic boundary value problem
Overdetermined elliptic problems triharmonic operator
2010/9/20
In this note, we prove the conjecture of Payne and Schaefer [2], regarding an overdetermined boundary value problem for the triharmonic operator, Δ3 = ΔΔΔ. It is deduced that if a solution of the prob...
Notes on the Parity Conjecture
Notes Parity Conjecture
2010/12/14
The main purpose of these notes is to prove, in a reasonably self-contained way, that finiteness of the Tate-Shafarevich group implies the parity conjecture for elliptic curves over number fields. Alo...
Let X denote a smooth, projective, connected algebraic variety over C, of dimension n.
We prove that if positive integer p-surgery along a knot K S3 produces an L-space and it bounds a sharp 4-manifold, then the knot genus obeys the bound 2g(K) 1 pp 3p + 1:Moreo...
The srank Conjecture on Schur's Q-Functions
srank bar tableau Schur's Q-function power sum symmetric function strip tableau skew bar tableau
2014/6/3
We show that the shifted rank, or srank, of any partition λ with distinct parts equals the lowest degree of the terms appearing in the expansion of Schur's Qλ function in terms of power sum symmetric ...
We conjecture that the general mean of two positive numbers, as a function of its order, has one and only one inflection point. No analytic proof seems available due to the extreme complexity of the s...