Talks

Observational surveys of the distribution of matter in the universe are becoming ever more precise and continue to be extended to smaller scales. This necessitates accounting for the fact that baryons do not precisely trace the dark matter. The redistribution of baryons by galactic winds, which is the major bottleneck in our understanding of galaxy evolution, therefore requires a convergence between models of large-scale structure and cosmology. I will discuss some of the insights gained from cosmological, hydrodynamical simulations, and challenges that need to be overcome to make further progress. I will present recent results from the FLAMINGO suite of large-volume cosmological, hydrodynamical simulations, which provide insight into the importance of baryonic effects for cosmology using large-scale structure and galaxy clusters. Finally, I will present the COLIBRE simulations of galaxy formation, a new suite of cosmological hydrodynamical simulations that removes important shortcomings of previous simulations.

Terrestrial ecosystems exhibit ecological stability: If an ecosystem is perturbed, biological feedback drives it back toward an equilibrium state, but an ecosystem does not remain stuck in its equilibrium state because it is continually perturbed. Are galaxies really similar to biological ecosystems in that regard? My talk will consider whether the atmospheres of galaxies have feedback-regulated equilibrium states and what the observational consequences of those states might be. While considering those questions I will lay out a framework for classifying how halo-scale feedback loops operate.

The asymptotic behavior of the partition function was first determined by Hardy and Ramanujan in 1918 using their famous circle method. Since then, many new ways of deriving their asymptotic formula have been discovered. I will discuss these and report on my recent work with Karin Ikeda.

As a continuation of our previous lecture, we study the mock theta functions in the context of harmonic Maass forms, beginning with Zwegers' thesis in 2002. We discuss (1) universal mock theta functions, (2) a proof of the mock theta conjectures, and (3) exact formulas for coefficients of mock theta functions, beginning with Dragonette and Andrews.

In the first part of this talk, I will provide a brief introduction to classical summation formulas and their significance in number theory. We will review the foundational contributions of Bochner, Koshliakov, and the seminal work of Chandrasekharan and Narasimhan on summation formulas for a broad class of arithmetical functions.

In the second part, I will present recent developments involving new summation formulas in the theory of harmonic Maass forms. As an application of our summation formula, I will discuss the asymptotic behavior of the Riesz means of the Hurwitz class numbers.\\

This talk is based on recent joint work with Olivia Beckwith, Nikolaos Diamantis, Larry Rolen, and Kalani Thalagoda.