Turbulent power-law spectra in the universe

Siyao Xu
September 17, 2020
Turbulence is ubiquitous in astrophysical media and plays an essential role in a variety of fundamental astrophysical processes. The turbulent power-law spectra have been observed in the solar wind, the interstellar medium, the intracluster medium, over a vast range of length scales. In our Galaxy, I will discuss pulsars as a unique tool for statistically studying the turbulence in the multi-phase interstellar medium over different ranges of length scales.

Simulating Multiscale Astrophysics to Understand Galaxy formation

Rachel Somerville
Rutgers University; Flatiron Institute
September 15, 2020
Building genuinely a priori models of galaxy formation in a cosmological context is one of the grand challenges of modern astrophysics. Most large volume simulations of galaxy formation currently adopt phenomenological scaling relations to model "small scale" processes such as star formation, stellar feedback, and black hole formation, growth, and feedback, which limits their predictive power.

Reeb dynamics in dimension 3 and broken book decompositions

Vincent Colin
Université de Nantes
September 11, 2020
In a joint work with Pierre Dehornoy and Ana Rechtman, we prove that on a closed 3-manifold, every nondegenerate Reeb vector field is supported by a broken book decomposition. From this property, we deduce that in dimension 3 every nondegenerate Reeb vector field has either 2 or infinitely periodic orbits and that on a closed 3-manifold that is not graphed, every nondegenerate Reeb vector field has positive topological entropy.

An asymptotic version of the prime power conjecture for perfect difference sets

Sarah Peluse
Institute for Advanced Study and Princeton University; Veblen Research Instructor, School of Mathematics
September 10, 2020
A subset D of a finite cyclic group Z/mZ is called a "perfect difference set" if every nonzero element of Z/mZ can be written uniquely as the difference of two elements of D. If such a set exists, then a simple counting argument shows that m=n2+n+1 for some nonnegative integer n. Singer constructed examples of perfect difference sets in Z/(n2+n+1)Z whenever n is a prime power, and it is an old conjecture that these are the only such n for which a perfect difference set exists.