unQVNTS (Vermont) Spring 2018

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.

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.

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.

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




Old pages: Spring 2017, Fall 2017