Aditya Kumar

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math.DG2026

Stable systolic inequalities via mod n covering

Aditya Kumar

We introduce a mod $n$ covering based approach to stable systolic inequalities. The idea is to prescribe a cohomology class mod $n$ which forces the desired cup product or index to…

math.DG2026

Urysohn width and macroscopic scalar curvature

Aditya Kumar, Balarka Sen

We show that the macroscopic version of Gromov's Urysohn width conjecture for scalar curvature is false in dimensions four and above. This is based on (1) a novel estimate on the c…

math.DG2025

Circle bundles with PSC over large manifolds

Aditya Kumar, Balarka Sen

We construct infinitely many examples of macroscopically large manifolds of dimension $m \geq 4$ equipped with circle bundles whose total spaces admit metrics of positive scalar cu…

math.DG2025

Positive scalar curvature and exotic structures on simply connected four manifolds

Aditya Kumar, Balarka Sen

We address Gromov's band width inequality and Rosenberg's $S^{1}$ -stability conjecture for simply connected smooth four manifolds. Both results are known to be false in dimension 4 d…