Mathematical Sciences: Arithmetic of Abelian Varieties
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{'SignBlockName': 'Ann K. Boyle', 'PO_EMAI': None, 'PO_PHON': None}
This research concentrates on questions in number theory and               arithmetical algebraic geometry related to abelian varieties.                   Topics for research include the determination of "Mordell-Weil                  groups" of generic abelian varieties, bounding orders of torsion                points on abelian varieties defined over number fields, and the                 development of criteria for when an abelian variety has a model                 rational over its field of moduli.                                                   In arithmetical algebraic geometry one interprets the                      equations in number as a geometric object.  If the equations are                nice enough this geometric object has a way of combining points                 to get new points (i.e. combining solutions to get new                          solutions).  When this happens one has what is called an abelian                variety.  These types of equations are very important and contain               huge amounts of structure.  The P.I. will spend her time during                 this research studying this situation.  Even though she is a                    relatively new PhD she already has some excellent results to her                credit.  This research will undoubtedly result in many more.
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{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
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