Zobrazeno 1 - 10
of 103
pro vyhledávání: '"Roeder, Roland"'
Autor:
Rebelo, Julio, Roeder, Roland
We present several questions about the dynamics of the group of holomorphic automorphisms of the affine cubic surfaces $$S_{A,B,C,D} = \{(x,y,z) \in \mathbb{C}^3 \, : \, x^2 + y^2 + z^2 +xyz = Ax + By+Cz+D\},$$ where $A,B,C,$ and $D$ are complex para
Externí odkaz:
http://arxiv.org/abs/2307.10962
Autor:
Diller, Jeffrey, Roeder, Roland
We prove an equidistribution result for iterated preimages of curves by a large class of rational maps $f:\mathbb{CP}^2\dashrightarrow\mathbb{CP}^2$ that cannot be birationally conjugated to algebraically stable maps. The maps, which include recent e
Externí odkaz:
http://arxiv.org/abs/2304.00992
Autor:
Dasgupta, Aneesh, Roeder, Roland
Publikováno v:
The American Mathematical Monthly, 130:3, 279-284 (2023)
The Three Gap Theorem states that for any $\alpha \in \mathbb{R}$ and $N \in \mathbb{N}$, the fractional parts of $\{ 0\alpha, 1\alpha, \dots, (N - 1)\alpha \}$ partition the unit circle into gaps of at most three distinct lengths. We prove a result
Externí odkaz:
http://arxiv.org/abs/2208.01680
Autor:
Rebelo, Julio, Roeder, Roland
We study the dynamics of the group of holomorphic automorphisms of the affine cubic surfaces \begin{align*} S_{A,B,C,D} = \{(x,y,z) \in \mathbb{C}^3 \, : \, x^2 + y^2 + z^2 +xyz = Ax + By+Cz+D\}, \end{align*} where $A,B,C,$ and $D$ are complex parame
Externí odkaz:
http://arxiv.org/abs/2104.09256
Autor:
Haynes, Alan, Roeder, Roland
We study the statistical properties of the spacings between neighboring energy levels for the multi-dimensional quantum harmonic oscillator that occur in a window $[E,E+\Delta E)$ of fixed width $\Delta E$ as $E$ tends to infinity. This regime provid
Externí odkaz:
http://arxiv.org/abs/2006.06157
Publikováno v:
J. Math. Phys. 61, 073301 (2020)
We report exact results concerning the zeros of the partition function of the Potts model in the complex $q$ plane, as a function of a temperature-like Boltzmann variable $v$, for the $m$'th iterate graphs $D_m$ of the Diamond Hierarchical Lattice (D
Externí odkaz:
http://arxiv.org/abs/1911.04012
Autor:
Giraldo, Luis, Roeder, Roland
We prove that the preimage of a germ of a singular analytic hypersurface under a germ of a finite holomorphic map $g: (\mathbb{C}^n,0) \rightarrow (\mathbb{C}^n,0)$ is again singular. This provides a generalization of previous results of this nature
Externí odkaz:
http://arxiv.org/abs/1911.00628
Autor:
Gyurek, Croix, Roeder, Roland
We present a notion of mutation of hyperbolic polyhedra, analogous to mutation in knot theory, and then present a general question about commensurability of mutant pairs of polyhedra. We motivate that question with several concrete examples of mutant
Externí odkaz:
http://arxiv.org/abs/1906.08723
Autor:
Chio, Ivan, Roeder, Roland
Associated to any finite simple graph $\Gamma$ is the chromatic polynomial $P_\Gamma(q)$ whose complex zeroes are called the chromatic zeros of $\Gamma$. A hierarchical lattice is a sequence of finite simple graphs $\{\Gamma_n\}_{n=0}^\infty$ built r
Externí odkaz:
http://arxiv.org/abs/1904.02195
This paper is devoted to an in-depth study of the limiting measure of Lee--Yang zeroes for the Ising Model on the Cayley Tree. We build on previous works of M\"uller-Hartmann-Zittartz (1974 and 1977), Barata--Marchetti (1997), and Barata--Goldbaum (2
Externí odkaz:
http://arxiv.org/abs/1806.00403