Zobrazeno 1 - 10
of 126
pro vyhledávání: '"ATHREYA, JAYADEV S."'
We study the set of visible lattice points in multidimensional hypercubes. The problems we investigate mix together geometric, probabilistic and number theoretic tones. For example, we prove that almost all self-visible triangles with vertices in the
Externí odkaz:
http://arxiv.org/abs/2204.03147
Publikováno v:
Arnold Math. J. 9 (2023) 359-379
Motivated by the problem of counting finite BPS webs, we count certain immersed metric graphs, tripods, on the flat torus. Classical Euclidean geometry turns this into a lattice point counting problem in $\mathbb C^2$, and we give an asymptotic count
Externí odkaz:
http://arxiv.org/abs/2111.01891
We describe how certain properties of the extrema of the digits of Luroth expansions lead to a probabilistic proof of a limiting relation involving the Riemann zeta function and the Bernoulli triangles. We also discuss trimmed sums of Luroth digits.
Externí odkaz:
http://arxiv.org/abs/2110.01132
Publikováno v:
Geom Dedicata 217, 89 (2023)
Motivated by the study of the growth rate of the number of geodesics in flat surfaces with bounded lengths, we study generalizations of such problems for K3 surfaces. In one generalization, we give a result regarding the upper bound on the asymptotic
Externí odkaz:
http://arxiv.org/abs/2109.13824
Publikováno v:
In Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena October 2023 175 Part 1
Autor:
Athreya, Jayadev S., Lee, Dami
We study translation covers of several triply periodic polyhedral surfaces that are intrinsically Platonic. We describe their affine symmetry groups and compute the quadratic asymptotics for counting saddle connections and cylinders, including the co
Externí odkaz:
http://arxiv.org/abs/1912.08398
Given integers $g,n \geq 0$ satisfying $2-2g-n < 0$, let $\mathcal{M}_{g,n}$ be the moduli space of connected, oriented, complete, finite area hyperbolic surfaces of genus $g$ with $n$ cusps. We study the global behavior of the Mirzakhani function $B
Externí odkaz:
http://arxiv.org/abs/1907.06287
We study the translation surfaces obtained by considering the unfoldings of the surfaces of Platonic solids. We show that they are all lattice surfaces and we compute the topology of the associated Teichm\"uller curves. Using an algorithm that can be
Externí odkaz:
http://arxiv.org/abs/1811.04131
We consider systems of "pinned balls," i.e., balls that have fixed positions and pseudo-velocities. Pseudo-velocities change according to the same rules as those for velocities of totally elastic collisions between moving balls. The times of collisio
Externí odkaz:
http://arxiv.org/abs/1807.08320