Amita Malik

Amita Malik
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Amita Malik
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Mathematics - Dynamical Systems (2)
 
Mathematics - Combinatorics (1)
 
Mathematics - Number Theory (1)
 
Mathematics - Mathematical Physics (1)
 
Mathematics - Metric Geometry (1)
 
Mathematical Physics (1)

Publications Authored By Amita Malik

Apollonian gaskets are formed by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We experimentally study the pair correlation, electrostatic energy, and nearest neighbor spacing of centers of circles from Apollonian gaskets. Even though the centers of these circles are not uniformly distributed in any `ambient' space, after proper normalization, all these statistics seem to exhibit some interesting limiting behaviors. Read More

In 1982, Gessel showed that the Ap\'ery numbers associated to the irrationality of $\zeta(3)$ satisfy Lucas congruences. Our main result is to prove corresponding congruences for all sporadic Ap\'ery-like sequences. In several cases, we are able to employ approaches due to McIntosh, Samol--van Straten and Rowland--Yassawi to establish these congruences. Read More

The Farey sequence is a natural exhaustion of the set of rational numbers between 0 and 1 by finite lists. Ford Circles are a natural family of mutually tangent circles associated to Farey fractions: they are an important object of study in the geometry of numbers and hyperbolic geometry. We define two sequences of polygons associated to these objects, the Euclidean and hyperbolic Farey-Ford polygons. Read More