Harvard University

One Oxford Street

Cambridge, MA 02138, USA

I am a Benjamin Peirce Fellow in the Department of Mathematics at Harvard University . I am also a member of the Center for the Fundamental Laws of Nature, which is the Harvard University High Energy Theory Group. I work on the geometry of string theory and lecture on mathematics. My research is supported by the National Science Foundation (NSF) grant DMS-1406925 “Elliptic Fibrations and String Theory”.

Spring | 2016: | Introduction to Algebraic Geometry II (Math 232br) |

Fall | 2015: | Introduction to Algebraic Geometry I (Math 232a) |

Fall | 2015: | Sets, Groups and Topology (Math 101) |

Spring | 2015: | Introduction to Algebraic Geometry II (Math 232br) |

Spring | 2015: | Sets, Groups and Topology (Math 101) |

Fall | 2014: | Introduction to Algebraic Geometry I (Math 232a) |

Spring | 2014: | Introduction to Algebraic Geometry II (Math 232br) |

Spring | 2014: | Spin Geometry and SuperSymmetry (Math 255y) |

Fall | 2013: | Introduction to Algebraic Geometry I (Math 232a) |

Spring | 2013: | Calculus II (Math 1B) |

Fall | 2012: | Topics in Elliptic Fibrations and String Theory (Math 363) |

Spring | 2012: | Calculus I (Math MA) |

Fall | 2011: | Calculus II (Math 1B) |

Research

My area of research is at the interface of string theory and mathematics. I currently work closely with Professor S.T. Yau on the geometry of string theory, specially in the context of F-theory. String theory is an attempt to unify all the fundamental interactions of Nature into a unique consistent and elegant theory. Interestingly, this endeavor has produced a lot of new ideas and insights in many different areas of mathematics. It has built bridges between communities of scientists that at first look would not have much to talk about. Experimental proofs of string theory have yet to come but as a source of inspiration for mathematics, it is a success story.

I specifically study the geometry of elliptic fibrations as seen from the point of view of string theory. Elliptic curves are some of the oldest, yet most prominent objects across mathematics. My research has direct applications to gauge theories, Grand Unified Theories, and the study of topological defects in conformal field theories.

My research is supported by the National Science Foundation (NSF) grant DMS-1406925 “Elliptic Fibrations and String Theory”.- Fibrations, Mirror Symmetry and Calabi-Yau Geometry, 2015 CMS Winter Meeting, Montreal, December 2015
- XVIII International Congress on Mathematical Physics , Santiago do Chili, July 2015
- Geometric, Algebraic and Topological Methods for Quantum Field Theory, Villa de Layva, Colombia, July 2015
- University of Pennsylvania, Physics Seminar , Philadelphia, May 2015
- Third annual John U. Free Seminar Series , Eastern Nazarene College , March 2015
- Strings 2014 , CUNY, New York, October 2014
- Strings 2014 , Princeton University, Princeton, June 2014
- CAARMS 20, Princeton University, Princeton, June 2014
- Co-organizer of the Special Session on Singularities and Physics, AMS Sectional Meeting #1097, Knoxville, Princeton, March 2014
- University of Pennsylvania, Math-Phys Join Seminar , Philadelphia, May 2014
- University of Massachusetts, Boston, Colloquium in Mathematics, December 2013
- Harvard University, String Theory Family Talk, Cambridge, October 2013
- Boston University Geometry and Physics Seminar, Boston, September 2013
- Yau’s students seminar, Harvard University, Cambridge, April 2013
- Co-organizer of FRG Workshop 2012: Generalized Geometry , Harvard, Cambridge, August 2012
- Taida Institute, Algebraic Geometry Seminar , Taipei, Taiwan, June 2012
- UNH, New Hampshire, Particle Physic Seminar, March 2012
- MIT Center for Theoretical Physics, String seminar, Cambridge, March 2012
- TAMU, Higher Energy Theory Seminars, College Station, Texas, June 2012
- American Mathematical Society Fall Eastern meeting 2011 , Cornell University, Ithaca (NY), September 2011
- String-Math 2011 , University of Pennsylvania, Philadelphia, July 2011
- Caltech University, High Energy Physics seminar, Pasadina, May 2011
- UCSB, High Energy Physics seminar,Santa-Barbara, April 2011
- Stanford University, High Energy Physics seminiar,Palo Alta, April 2011
- Harvard University, String Theory Family Talk, Cambridge, March 2011
- MIT Center for Theoretical Physics, String seminar, Cambridge, March 2010
- Brandeis, Higher Energy and Gravity Group seminar, March 2010
- Harvard University Math Dept, Differential Geometry seminar, Cambridge, 2010
- Harvard University, High Energy Physics seminar, Cambridge, September 2009
- Stanford University, High Energy Physics seminar, Palo Alto, April 2009
- CEA-Saclay (IPhT), High Energy Physics seminar, Saclay (France), March 2009
- Marie-Curie University (LPTHE), High Energy Physics seminar, Paris (France), March 2009
- Brussels University, High Energy Physics seminar, Brussels (Belgium), March 2009
- Harvard University, String Theory Family Talk, Cambridge, November 2008
- Max Planck Institute for Mathematics, Conference ``The Manifold Geometry of Quantum Field Theory, July, Bonn (Germany), 2008

- M-theory on Elliptic Calabi-Yau Threefolds and 6d Anomalies , with Shu-Heng Shao, preprint.
- A New Model for Elliptic Fibrations with a Rank One Mordell-Weil Group : I. Singular Fibers and Semi-Stable Degenerations, with Monica Jinwoo Kang and Shing-Tung Yau, preprint.
- Singularities and Gauge Theory Phases II, with Shu-Heng Shao and Shing-Tung Yau, preprint.
- Singularities and Gauge Theory Phases, with Shu-Heng Shao and Shing-Tung Yau, preprint.
- Tate Form and Weak Coupling Limits in F-theory, with Raffaele Savelli, published in Journal of High Energy Physics.
- D5 elliptic fibrations: non-Kodaira fibers and new orientifold limits of F-theory , with James Fullwood and Shing-Tung Yau, preprint, accepted for publication (Communications in Number Theory and Physics)
- Small resolutions of SU(5)-models in F-theory with Shing-Tung Yau, published in Adv.Theor.Math.Phys. 17 (2013) 1195-1253
- New Orientifold Weak Coupling Limits in F-theory, with Paolo Aluffi, published in Journal of High Energy Physics.
- Stability of warped AdS(3) vacua of topologically massive gravity, with Dionysios Anninos and Monica Guica, published in Journal of High Energy Physics.
- Orientihholes, with Frederik Denef and Megha Padi, published in Journal of High Energy Physics.
- D-brane Deconstructions in IIB Orientifolds, with Andres Collinucci and Frederik Denef , published in Journal of High Energy Physics
- Chern class identities from tadpole matching in type IIB and F-theory, with Paolo Aluffi, , published in Journal of High Energy Physics.
- Half-BPS string in N=2 supergravity in the presence of a dilaton, with Kepa Sousa , published in Journal of High Energy Physics.
- D-term cosmic strings and Fayet-Ilioupoulos terms from N=2 supergravity, with A. Achucarro, J. Van den Bergh, A. Celi and A. Van Proeyen, published in Journal of High Energy Physics.
- On the renormalisability of gauge invariant extensions of the square gauge potential, with Filipe Freire, published in Physics Letters B.
- The Unphysical nature of the Sl(2 , R) symmetry and its associated condensates in Yang-Mills theories, with Filipe Freire, published in Physical Review D.
- A note on the uniqueness of D=4, N=1 supergravity, with Nicolas Boulanger, published in Classical and Quantum Gravity.

Last updated: June 25, 2015.