This
seminar meets on Thursday on QVNTS
off weeks.

We will meet for talks from 1:10pm to 2:25pm in Waterman 402.

We will have lunch at Waterman Manor at noon on days when there are no department meetings.

We will meet for talks from 1:10pm to 2:25pm in Waterman 402.

We will have lunch at Waterman Manor at noon on days when there are no department meetings.

Thursday, February 2 |
Sophie Gonet, Elliptic curves over the complex numbers |

Thursday, February 15 |
Lloyd Simons, A brisk introduction to abelian varieties over the complex numbers |

Thursday, March 1 |
Taylor Dupuy, Complex tori vs abelian varieties |

Thursday, March 29 |
Taylor Dupuy, Triple product formula and universal vectorial extensions |

Thursday, April 12 |
Jonathan Sands, The Mordell-Lang conjecture on subvarieties of abelian varieties |

Thursday, April 26 |
David Dummit, Complex Multiplication Abelian Varieties |

Thursday, February 2, 2018,
1:10-2:25 p.m. Waterman 402

Sophie Gonet, Elliptic curves over the complex numbers

We introduce the projective plane, elliptic curves as abelian varieties, and the projective embedding of a complex 1-dimensional torus into projective space via the Weierstrass p-function. We then briefly discuss the endomorphism ring of a complex 1-dimensional torus. Time permitting, Christelle will discuss projective embeddings via theta functions.

We introduce the projective plane, elliptic curves as abelian varieties, and the projective embedding of a complex 1-dimensional torus into projective space via the Weierstrass p-function. We then briefly discuss the endomorphism ring of a complex 1-dimensional torus. Time permitting, Christelle will discuss projective embeddings via theta functions.

Thursday, February 15, 2018,
1:10-2:25 p.m. Waterman 402

Lloyd Simons, A brisk introduction to abelian varieties over the complex numbers

Thursday, March 1, 2018,
1:10-2:25 p.m. Waterman 402

Taylor Dupuy, Complex tori vs abelian varieties

Thursday, March 29, 2018,
1:10-2:25 p.m. Waterman 402

Taylor Dupuy, Triple product formula and universal vectorial extensions

Thursday, April 12, 2018,
1:10-2:25 p.m. Waterman 402

Jonathan Sands, The Mordell-Lang conjecture on subvarieties of abelian varieties

Following Mazur's expository article from the year 2000, we present a brief outline of the proof of the Mordell-Lang conjecture based on work of Vojta, Faltings, Buium, Voloch, and others. A version of this states that under standard hypotheses, a subvariety of an abelian variety is in fact a translate of an abelian subvariety. A consequence is the classical Mordell conjecture that a smooth projective irreducible algebraic curve over a number field is the Zariski closure of its rational points over some larger number field if and only if the curve has genus 0 or 1. For the purposes of exposition, we will focus on fields of characteristic 0.

Following Mazur's expository article from the year 2000, we present a brief outline of the proof of the Mordell-Lang conjecture based on work of Vojta, Faltings, Buium, Voloch, and others. A version of this states that under standard hypotheses, a subvariety of an abelian variety is in fact a translate of an abelian subvariety. A consequence is the classical Mordell conjecture that a smooth projective irreducible algebraic curve over a number field is the Zariski closure of its rational points over some larger number field if and only if the curve has genus 0 or 1. For the purposes of exposition, we will focus on fields of characteristic 0.

Thursday, April 26, 2018,
1:10-2:25 p.m. Waterman 402

David Dummit, Complex Multiplication Abelian Varieties

This talk will review the definitions and some of the basic information for "CM abelian varieties" - those abelian varieties 'with complex multiplication(s)'. This generalizes the results in the case of elliptic curves (the abelian varieties of dimension 1) and the talk will indicate some of the results for CM elliptic curves in greater detail as motivation for the higher dimensional case, in particular attempting to address the question "why would one care about CM abelian varieties?"

This talk will review the definitions and some of the basic information for "CM abelian varieties" - those abelian varieties 'with complex multiplication(s)'. This generalizes the results in the case of elliptic curves (the abelian varieties of dimension 1) and the talk will indicate some of the results for CM elliptic curves in greater detail as motivation for the higher dimensional case, in particular attempting to address the question "why would one care about CM abelian varieties?"

Old pages: Spring 2017, Fall 2017