# School of Natural Sciences

## Evolutionary Dynamics and Population Genetics

## Learning Phylogeny Through Simple Statistical Genetics

## Introduction and Course Overview

## Building Unique Sequencing Platforms to View Different Parts of the Genome

## Geometric Extremization for Supersymmetric $AdS_3$ and $AdS_2$ Solutions

We consider supersymmetric $AdS_3\times Y_7$ solutions of type IIB supergravity dual to N=(0,2) SCFTs in d=2, as well as $AdS_2\times Y_9$ solutions of D=11 supergravity dual to N=2 supersymmetric quantum mechanics, some of which arise as the near horizon limit of supersymmetric, charged black hole solutions in $AdS_4$. The geometry underlying these solutions was first identified in 2005-2007. Around that time infinite classes of explicit supergravity solutions were also found but, surprisingly, there was little progress in identifying the dual SCFTs.

## Two Important Milestones in the History of the Universe: The Last Scattering Surface, the Black Body Photosphere of the Universe and Distortions of the CMB Spectrum

Our Universe is filled with Cosmic Microwave Background (CMB) radiation having an almost perfect black body spectrum with a temperature of To=2.7K. The number density of photons in our Universe exceeds the number density of electrons by a factor of more than a billion. In the expanding Universe the temperature at early times was higher than today: Tr = To (1+z), where z is the redshift.

## Inward Bound: Discovering and Exploring the Milky Way's Black Hole

## Globally Consistent Three-family Standard Models in F-theory

We present recent advances in constructions of globally consistent

F-theory compactifications with the exact chiral spectrum of the minimal

supersymmetric Standard Model. We highlight the first such example and

then turn to a subsequent systematic exploration of the landscape of

F-theory three-family Standard Models with a gauge coupling unification.

Employing algebraic geometry techniques, all global consistency

conditions of these models can be reduced to a single criterion on the

## Anomalies in the Space of Couplings and Dynamical Applications

Anomalies are invariants under renormalization group flow which lead to powerful constraints on the phases of quantum field theories. I will explain how these ideas can be generalized to families of theories labelled by coupling constants like the theta angle in gauge theory. Using these ideas we will be able to prove that certain systems, such as Yang-Mills theory in 4d, necessarily have a phase transition as these parameters are varied. We will also show how to use the same ideas to constrain the dynamics of defects where coupling constants vary in spacetime.