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The Riemann integral does not work well with limits, so naturally one wishes to make something better. Thus, every high school or undergraduate math student should attempt to develop a better integral before learning any measure theory. Naturally, they come up with many strange ways to do it,…
There have been several recent approaches to defining a moduli space of L-parameters over Z[1/p], in order to obtain refined versions of the local Langlands conjecture ``at all primes away from p at once''. The components of this space are expected to be closely related to blocks in the category…
Various random graphs models satisfy that each edge appears independently of all other edges but those in a bounded degree graph. Examples include Erdös–Renyi random graphs, random Cayley graphs, random Latin square graphs, and random entangled graphs. We begin the systematic study of random…
Abstract: It is expected that the Klein-Gordon equation on a Schwarzschild black hole behaves very differently from the wave equation at late-time, due to the presence of stable (timelike) trapping. We present our recent work demonstrating that despite the presence of stable timelike trapping on…
Twist-roll spun knots are a well-studied family of knotted 2-spheres in the 4-sphere. The inputs for determining a twist roll spun knots are an integer number of twists, a number of rolls, and a choice of classical knot in the 3-sphere. I will explain why adding twists, while changing the…
Abstract
Choose your favourite, compact manifold M. How many rational points, with denominator of bounded size, are near M? We report on joint work with Damaris Schindler and Rajula Srivastava addressing this question. Our new method reveals an intriguing interplay between number theory, harmonic…
We will cover part of section 6 of [FP97].
Abstract
I will describe the construction of motivic cohomology classes on hypergeometric families of Calabi-Yau 3-folds using Hadamard convolutions. One can view this as a “higher” version of the Mordell-Weil group for families of elliptic curves, giving rise to sections of “higher” Jacobian…