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 |
Jonathan Sands, Mazur's Diophantine paper |

Thursday, April 12 |
George Melvin? |

Thursday, April 26 |
David Dummit, Complex multiplication |

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

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

Jonathan Sands

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

George
Melvin, Middleburry College

Crystals, Langlands duality and mirror symmetry

The Langlands philosophy has motivated significant advances in representation theory and geometry. For a reductive algebraic group G, having Langlands dual group G', the slogan is: the geometry associated to G controls the representation theory of G'. In algebraic and symplectic geometry, the philosophy of mirror symmetry states that the complex geometry of a (Fano, Kahler) complex variety X is controlled by the symplectic geometry of a mirror partner X'. Recently, Lam-Templier have described explicit realizations of the Langlands philosophy in the mirror symmetry of flag varieties. In this talk, I will define a version of mirror symmetry for flag varieties and describe recent work concerning the appearance of combinatorial representation-theoretic data, known as Kashiwara crystals, in this story. I will then describe a conjectural program relating the appearance of this combinatorial data to hierarchies of toric degenerations of flag varieties. The discussion will be kept down-to-earth and be guided by examples.

Crystals, Langlands duality and mirror symmetry

The Langlands philosophy has motivated significant advances in representation theory and geometry. For a reductive algebraic group G, having Langlands dual group G', the slogan is: the geometry associated to G controls the representation theory of G'. In algebraic and symplectic geometry, the philosophy of mirror symmetry states that the complex geometry of a (Fano, Kahler) complex variety X is controlled by the symplectic geometry of a mirror partner X'. Recently, Lam-Templier have described explicit realizations of the Langlands philosophy in the mirror symmetry of flag varieties. In this talk, I will define a version of mirror symmetry for flag varieties and describe recent work concerning the appearance of combinatorial representation-theoretic data, known as Kashiwara crystals, in this story. I will then describe a conjectural program relating the appearance of this combinatorial data to hierarchies of toric degenerations of flag varieties. The discussion will be kept down-to-earth and be guided by examples.

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

David Dummit

Old pages: Spring 2017, Fall 2017