# ESP Biography

## BENJAMIN HOROWITZ, Yale Junior studying Mathematics and Physics

Major: Physics, Mathematics

College/Employer: Yale University

## Brief Biographical Sketch:

I am a math and physics double major, primarily interested in early universe cosmology and high energy theory. Over the past two years I've been part of the Quest-La Sila Variability Survey which does research on super nova's (cool dying star explosions). My work has been primarily on variable stars and galactic structure.

My current research has been quite different, focusing on behavior of Conformal Field Theories (related to String Theories via AdS/CFT) in three dimensions. In particular, I look at the transition between $\phi^4$ theories in 4d as they transform into the Ising model in 3d.

In my free time, I help run Splash at Yale.

## Past Classes

(Clicking a class title will bring you to the course's section of the corresponding course catalog)

M7920: Partial Differential Equations in Splash! 2013 (Nov. 23 - 24, 2013)
Partial Differential Equations are really fun and really cool. It is basically ordinary (single variable) differential equations, but BETTER! In this little class we will talk briefly about the main methods of solving partial differential equations. We will also talk about boundary value problems and finally solve “the heat equation” using Fourier Series and separation of variables.

S7921: Intensive Introduction to Cosmology in Splash! 2013 (Nov. 23 - 24, 2013)
In this class, we will give a whirlwind tour of the key concepts of modern cosmology. We will cover the dynamics of the expansion of the universe (the Friedmann equations), the history of the early universe (inflation, nucleosynthesis), formation of the cosmic microwave background, and dark matter. Depending on time, we can also dive into some more specialized topics like galaxy evolution, primordial black holes, and gravitational waves.

S7923: Supersymmetry and Physics Beyond the Standard Model in Splash! 2013 (Nov. 23 - 24, 2013)
Supersymmetry is a common aspect of many Beyond the Standard Model physical theories as it is one of the few non-trivial symmetries space-time can have beyond the traditional Lorenz transforms of Special Relativity. In this class we will talk in detail about the mathematics behind Supersymmetric theories and talk more broadly about Beyond the Standard Model theories, including the Minimally Supersymmetric Standard Model and String theories.

S6980: String Theory: How it is "Right" and Why it Doesn't Matter. in Spark! 2013 (Mar. 16, 2013)
String Theory is a popular topic that has extreme beauty from a mathematical perspective and is a very active field of research. In this class, I will go over the basics of string theory and related topics in cosmology and show how it is "right" (in that it is in all likelihood not false), and then go on to discuss some of the serious issues of viewing it as a "useful" physical theory. Along the way we will learn about the standard model, black hole information paradoxes, and so much more!

S5798: Intensive Introduction to Cosmology in Spark! 2012 (Mar. 10, 2012)
In this class, we will give a whirlwind tour of the key concepts of modern cosmology. We will cover the dynamics of the expansion of the universe (the Friedmann equations), the history of the early universe (inflation, nucleosynthesis), formation of the cosmic microwave background, and dark matter. Depending on time, we can also dive into some more specialized topics like galaxy evolution, primordial black holes, and gravitational waves.

S4986: Lagrangian Mechanics and an Introduction to Field Theory in Splash! 2011 (Nov. 19 - 20, 2011)
What shape of wire will minimize the time it takes for a bead to slide down it? How are classical mechanics, electricity and magnetism, and general relativity all fundamentally related? In this class we will do our best to answer these questions, learning handy ways to solve physics problems along the way as well as explore calculus of variations.

S4987: Cosmology in Splash! 2011 (Nov. 19 - 20, 2011)
Why is the universe expanding? What is cosmological inflation? Where is Dark Matter located? Come to learn all about the cosmology, the Friedmann Equations, and some of the still open questions!

M5049: Partial Differential Equations in Splash! 2011 (Nov. 19 - 20, 2011)
Partial Differential Equations are really fun and really cool. It is basically ordinary (single variable) differential equations, but BETTER! In this little class we will talk briefly about the main methods of solving partial differential equations. We will also talk about boundary value problems and finally solve “the heat equation” using Fourier Series and separation of variables.

M5050: Semi-Riemannian Geometry: the Mathematics of General Relativity in Splash! 2011 (Nov. 19 - 20, 2011)
Come learn about the very exciting field of Semi-Riemannian Geometry. In this class we will discuss: Manifolds, Diffeomorphisms, Vector Fields, One Forms, Dual Spaces, Tensors, Metrics, Connections, Curvature, and Topology on Manifolds. This is the mathematical foundation of General Relativity, and it will be a roller coaster of fun! There will be allocated time in the middle for a break and answering math (or other) questions.

M5051: A Quick and Dirty Introduction to Linear Algebra in Splash! 2011 (Nov. 19 - 20, 2011)
Ever wonder why your Algebra II teacher taught you how to add and subtract those little vectors? Vectors are just the first step into, what we consider, the most beautiful field of mathematics. From the basic properties of a vector space are built up linear transformations, determinants, Kramer's Rule, linear independence, eigenvalues and eigenvectors, and so much more.

M4546: A Quick and Dirty Introduction to Linear Algebra in Spark! 2011 (Mar. 12, 2011)
Ever wonder why your Algebra II teacher taught you how to add and subtract those little vectors? Vectors are just the first step into, what we consider, the most beautiful field of mathematics. From the basic properties of a vector space are built up linear transformations, determinants, Kramer's Rule, linear independence, eigenvalues and eigenvectors, and so much more.

M4547: Ordinary Differential Equations in Spark! 2011 (Mar. 12, 2011)
Differential Equations are the most powerful mathematical tools ever created to understand the world. They are essential to understanding economics, biology, chemistry, geology, physics, meteorology, sociology, and tons more. Also differential equations are interesting in a purely mathematical context, and have an extensive theory of existence and uniqueness of solutions. Come to embrace differential equations from both a computational and theoretical perspective; covering topics like separation of variables, homogeneous and non-homogeneous linear equations, Laplace transforms and systems of linear equations. Also, I will cover some cool qualitative methods (linearization of non-linear systems, phase diagrams) if time permits.

M4549: Semi-Riemannian Geometry: the Mathematics of General Relativity in Spark! 2011 (Mar. 12, 2011)
Come learn about the very exciting field of Semi-Riemannian (also known as psuedo-Riemannian) Geometry. In this class we will discuss: Manifolds, Diffeomorphisms, Vector Fields, One Forms, Dual Spaces, Tensors, Metrics, Connections, Curvature, and Topology on Manifolds. This is the mathematical foundation of General Relativity, and it will be a roller coaster of fun! There will be allocated time in the middle for a break and answering math (or other) questions. $$\operatorname{Ric} = R_{ij}\,dx^i \otimes dx^j$$

M4550: Introduction to Partial Differential Equations in Spark! 2011 (Mar. 12, 2011)
Partial Differential Equations are really fun and really cool. It is basically ordinary (single variable) differential equations, but BETTER! In this little class we will talk briefly about the main methods of solving partial differential equations. We will also talk about boundary value problems and finally solve “the heat equation” using Fourier Series and separation of variables.

M3735: A Quick and Dirty Introduction to Linear Algebra in Splash! 2010 (Nov. 20 - 21, 2010)
Ever wonder why your Algebra II teacher taught you how to add, subtract and multiply those pesky little matrices? Matrices are just the first step into, what we consider, the most beautiful field of mathematics. From the basic properties of matrices are built up determinants, Kramer's rule, linear transformations, vector spaces, linear independence, eigenvalues and eigenvectors, and so much more.

M3870: Differential Equations in Splash! 2010 (Nov. 20 - 21, 2010)
Differential Equations are the most powerful mathematical tools ever created to understand the world. They are essential to understanding economics, biology, chemistry, geology, physics, meteorology, sociology, and tons more. Also differential equations are interesting in a purely mathematical context, and have an extensive theory of existence and uniqueness of solutions. Come to embrace differential equations from both a computational and theoretical perspective; covering topics like separation of variables, homogeneous and non-homogeneous linear equations, Laplace transforms and systems of linear equations. Also, I will cover some cool qualitative methods (linearization of non-linear systems, phase diagrams) if time permits.

H3895: Introduction to Early Islamic History, the Quran and Islamic Law in Splash! 2010 (Nov. 20 - 21, 2010)
Ever wonder what at Fatwa was? What guides the Sharia (Islamic) law? In this class we will quickly cover (10 minutes) the early history of Islam, the split between Sunni's and Shia (10 minutes), and then go on to discuss Islamic law for the rest. We will discuss how the Quran is arranged, what the Hadith are, the timeline of Qu'ranic interpretation, the role of the Caliphate, the Hidden Imam, and anything else people are interested in and there is time for. Questions are encouraged!