10 papers
Classifying Groups of Certain Orders
Shihan Kanungo
We will first discuss the question of which integers have exactly one group of order , namely the cyclic group . We will see that these are the integ…
Sobolev Spaces and Their Applications to Partial Differential Equations
Shihan Kanungo
This report provides an introduction to Sobolev spaces, a foundational concept in modern analysis and the theory of partial differential equations (PDEs). These spaces are useful t…
Elliptic Functions and Eisenstein Series
Shihan Kanungo
In this expository paper, we provide an introduction to elliptic functions and Eisenstein series from a classical analytic perspective while highlighting their broader mathematical…
The Grothendieck Group and K-Theory
Shihan Kanungo
In this expository paper, we develop the basic ideas underlying Grothendieck groups and to illustrate their appearance across algebra, topology, representation theory, and homologi…
Upper Bounds for Sequence Saturation
Shihan Kanungo
In this paper, we study the saturation function for sequences. Saturation for sequences was introduced by Anand, Geneson, Kaustav, and Tsai (2021), who proved t…
Representation Theory of the Twisted Yangians in Complex Rank
Arun S. Kannan, Shihan Kanungo
In 2016, Etingof defined the notion of a Yangian in a symmetric tensor category and posed the problem to study them in the context of Deligne categories. This problem was studied b…
Space-Filling Curves
Shihan Kanungo
We examine space-filling curves, which are surjective continuous maps from to some higher-dimensional space, usually the unit square . In particular, we define Pea…
On Product Formulas of Guillera and Sondow
Shihan Kanungo, Jordan Schettler
In this note, we evaluate a multivariable family of infinite products which generalize Guillera's infinite product for , and Ser's formula (rediscovered by Sondow) for . We…
Mixed Tensor Products, Capelli Berezinians, and Newton's Formula for
Sidarth Erat, Arun S. Kannan, Shihan Kanungo
In this paper, we extend the results of Grantcharov and Robitaille in 2021 on mixed tensor products and Capelli determinants to the superalgebra setting. Specifically, we construct…
A weaker notion of the finite factorization property
Henry Jiang, Shihan Kanungo, Harry Kim
An (additive) commutative monoid is called atomic if every given non-invertible element can be written as a sum of atoms (i.e., irreducible elements), in which case, such a sum is…