Mathematics and Fundamental Physics
Here you will find a description of my mathematics and physics background, some papers I authored or co-authored, and a description of some of the things which still interest me. As this site develops, I hope to include some musings on physics and math as well.
Undergraduate Research
My main interests in mathematics are in the fields of geometry and topology. I was motivated in this largely in an effort to understand Einstein's theory of gravity, and how it might be reconciled with quantum theory. As a result, while an undergraduate at N.Y.U. I did a good deal of graduate work in Differential Geometry and Algebraic Topology. I also did some coursework in computational methods of Real Algebraic Geometry, which was quite refreshing in its constructivist approach to mathematics.
In a brief foray into experimental High Energy Particle Physics working under Peter Nemethy, I helped study the possibility of using L.E.D.'s to calibrate an array of photomultiplier tubes used in TeV scale cosmic ray air-shower detection. A copy of a paper on the larger effort, called Milagrito, can be found here.
Also as an undergraduate, under the guidance of Friedrich Ulfers, I spent some time attempting to understand how interpretive questions in quantum mechanics might provide input into a post-modern theory of ontology. Although not science itself, the effort led me to want to acquire a greater understanding of fundamental physics, and how basic ideas such as time, space, and knowing could be better described.
Graduate Research
Later, at Columbia, I began studying mathematical physics and Algebraic Geometry. I was interested in the Mirror Symmetry of Calabi-Yau threefolds, and also spent time wrestling with Quantum Field Theory and Conformal Field Theory as part of my String Theory education under Brian Greene.
Click here to see some preprints I have available online which were published while I was in graduate school at Columbia University. The common theme running through the papers is an effort to understand what mathematics needs to be brought to bear to understand the behavior of non-perturbative objects in String Theory (aka D-Branes).
The first paper attempts to understand how discrete quotients by non-abelian groups (such as the symmetric group on four letters) can be modeled within string theory. The second attempts to understand, via mechanisms present in Supergravity (a low-energy limit of String Theory), the behavior of D-Branes on a very "classical" (in the sense of being well-defined and fairly well-understood) background variety. The third tries to extend some earlier work on charge lattices of D-Branes to varieties which have no direct physical relevance, but rather extend the same mathematical structures to a higher dimension.
The individual papers are listed below:
- D-branes on Nonabelian Threefold Quotient Singularities. Brian R. Greene, C. I. Lazaroiu, Mark Raugas. Nucl.Phys. B553 (1999) 711-749.
- Split attractor flows and the spectrum of BPS D-branes on the Quintic. Frederick Denef, Brian R. Greene, Mark Raugas. JHEP 0105 (2001) 012.
- D-Branes and Vanishing Cycles in Higher Dimensions, Mark Raugas. [Preprint Only] 2001.
My Ph.D. thesis consisted of each of these papers as a chapter, as well as another chapter concerning some calculations of potentials for different singular del Pezzo surfaces (i.e. Fano varieties) in the context of the AdS/CFT correspondence.
A PDF file can found here.
Current Interests
I am currently trying to learn the methods of Loop Quantum Gravity -- I've been working through Rovelli's book and am curious as to what promise background independent methods may have in quanutm gravity. I've also been working through Conne's 2006 book on Noncommutative Geometry and the standard model, as well as trying to read some of Witten's recent preprints on Geometric Langlands. Unfortunately, my background in number theory is quite weak -- so I wind up having to do a lot of remedial reading at times and then get caught up in other things. Alas, doing physics research has been relegated to a bit of hobby for me, but something I want to spend more time on.