**Research Interests**
String theory is the only known solution to the problem which is at the core of modern physics: the incompatibility of quantum mechanics and gravity. Moreover, the most important physical principles: gauge theory and general relativity, are predicted by string theory. Finally, it is a realization of an old dream: that physics at the fundamental level should be determined by mathematical principles alone, and no arbitrary dimensionless parameters.
Duality is a cornerstone of our current understanding of string theory. Duality means that there can be different descriptions of the same theory, some very simple and classical, and others highly complicated and quantum mechanical. Dualities have taught us that what originally appeared as distinct superstring theories are in fact the weakly coupled descriptions of a single theory in various regimes. It is this uniqueness, together with the properties mentioned above, that make string theory the leading candidate for the fundamental theory of nature.
While duality as a phenomenon is not specific to string theory, in string theory duality is pervasive. The various dualities discovered in string theory have led to numerous advances in quantum field theory (e.g., the exact solutions of some supersymmetric gauge theories), mathematics (e.g. Calabi-Yau mirror symmetry), and quantum gravity (the counting of black hole entropy).
It is almost certain that we understand but a small corner of string theory, and that in many regimes string theory looks nothing like the theory of the small loops of string that it started out as. I work on improving our understanding this marvelous structure that we call string theory, uncovering its dualities and studying their consequences in the physics and mathematics contexts.
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Selected Publications**
M. Aganagic, H. Ooguri, N. Saulina and C. Vafa, “Black holes, q-deformed 2d Yang-Mills, and non-perturbative topological strings,” [arXiv:hep-th/0411280].
M. Aganagic, R. Dijkgraaf, A. Klemm, M. Marino and C. Vafa, “Topological strings and integrable hierarchies,” [arXiv:hep-th/0312085].
M. Aganagic, A. Klemm, M. Marino and C. Vafa, “The topological vertex,” [arXiv:hep-th/0305132].
M. Aganagic, A. Klemm, M. Marino and C. Vafa, “Matrix model as a mirror of Chern-Simons theory,” JHEP 0402, 010 (2004) [arXiv:hep-th/0211098].
M. Aganagic and C. Vafa, “Mirror symmetry, D-branes and counting holomorphic discs,” [arXiv:hep-th/0012041]. |