Research

Overview

My area of research is at the interface of string theory and mathematics. I explore 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.

Research Grants

My research is supported by the National Science Foundation (NSF) grant DMS-1406925 “Elliptic Fibrations and String Theory”.

I co-organize the NSF funded workshop series DMS-1603247 “A Three Workshop Series on the Physics and Mathematics of F-theory” (2016-2018) with Paolo Aluffi (Florida State) , Lara B. Anderson (Virginia Tech), and Shing-Tung Yau (Harvard) . The workshop series will rotate between Virginia Tech, Harvard University, and Florida State University. The goal of the workshop series is to facilitate progress on pressing problems at the interface of algebraic/differential geometry and string theory. The first workshop was held at Virginia Tech on October 8th and 9th, 2016.

Invited Seminars, Workshops and Conferences

• Mathematics Colloqium, University of Illinois at Urbana-Champaign, February 2017
• AMS Fall Southeastern Sectional Meeting Meeting, Special Session on Mathematical String Theory, November 2016
• AMS Fall Eastern Sectional Meeting Meeting, Special Session on Combinatorics Aspects of Nilpotent Orbits, Bowdoin College, October 2016
• Northeastern University, Singularities Seminar, October 2016
• Northeastern University, Math Club, October 13th, 2016
• Boston University, Boston University Geometry and Physics Seminar, October 12th, 2016
• Field Institute, Workshop on Singular Spaces and String Theory, August 2016
• Field Institute, Workshop on Stratified Spaces, August 2016
• University of Massachusetts in Boston, Physics Colloquium, April 2016
• Northeastern University, Singularities Seminar, March 2016
• University of Massachusetts in Boston, Physics Colloquium, April 2016
• Northeastern University, Singularities Seminar, March 2016
• McGill University, Special Math/Physics Seminar, February 2016
• Rutgers University, Mathematics Colloquium, January 2016
• University of California in Davis, January 2016
• 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 Alto, 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