Apoorva Khare

activity

20242026

collaborators

10 papers

math.CO2026

A tight bound for affine-linearity, via universal ballot matrices

Apoorva Khare, Ashwin Sah

Based on work with Greenfeld and with Ziegler, Tao showed a concatenation result that if a map $f : F^{2} \to F$ is affine-linear on every line parallel to the coor…

math.CA2026

The entrywise calculus and dimension-free positivity preservers, with an Appendix on sphere packings

Apoorva Khare

We present an overview of a classical theme in analysis and matrix positivity: the question of which functions preserve positive semidefiniteness when applied entrywise. In additio…

math.CO2026

Majorization via positivity of Jack and Macdonald polynomial differences

Hong Chen, Apoorva Khare, Siddhartha Sahi

Majorization inequalities have a long history, going back to Maclaurin and Newton. They were recently studied for several families of symmetric functions, including by Cuttler--Gre…

math.NT2025

Maps preserving the sum-to-difference ratio

Sunil Chebolu, Apoorva Khare, Anindya Sen

For a field $F$ , what are all functions $f : F \to F$ that satisfy the functional equation $f \left( (x+y)/(x-y) \right) = (f(x) + f(y))/(f(…

math.FA2025

Numerical radius and $ℓ_{p}$ operator norm of Kronecker products and Schur powers: inequalities and equalities

Pintu Bhunia, Sujit Sakharam Damase, Apoorva Khare

Suppose $A = [a_{ij}] \in M_{n} (C)$ is a complex $n \times n$ matrix and $B \in B (H)$ is a bounded linear operator on a complex Hilbert space $\mat…

math.RT2025

Log-concavity of characters of parabolic Verma modules, and of restricted Kostant partition functions

Apoorva Khare, Jacob P. Matherne, Avery St. Dizier

In 2022, Huh-Matherne-MÃ©szÃ¡ros-St. Dizier showed that normalized Schur polynomials are Lorentzian, thereby yielding their continuous (resp. discrete) log-concavity on the positiv…