Szego Seminar: Supernatural Numbers: A Spooky Introduction

Abstract:  As the veil between worlds grows thin on this eerie Halloween night, we delve into the mystical realm of supernatural numbers, where math and magic intertwine. These numbers aren’t found in any ordinary textbook. Instead, they reside in the dark corners of number theory, where infinite sequences dance like restless spirits and prime powers echo like whispers in the wind. 

Supernatural numbers are ghostly beings that extend beyond the familiar integers. Each one is formed from an infinite product of prime powers, their components drifting through the infinite, much like the fog rolling through a haunted forest. They are tied to the ancient, primal forces of the primes, with their powers guiding the structure of all numbers like the unseen hand of fate. 

Unlike the numbers we use daily, supernatural numbers lurk in the shadows, haunting the study of ideal class groups, local fields, and the ghostly arithmetic of rings and modules. They don’t fit neatly into the real world; rather, they span across dimensions, offering mathematicians a glimpse into the infinite, as if gazing into a scrying mirror.  

So, dare you wander into this spectral world, where numbers go on forever, and the primes are the very bones upon which the infinite universe of math is built? If you’re brave enough to follow the trail of supernatural numbers, who knows what otherworldly secrets you might uncover?

Host: Pooja Joshi