All talks will take place at the Cook Hotel, room Shelton1 (April 6-7th) and room Shelton2 (April 14th). There will be a screen/projector available, but no chalkboard.
Clicking on the speaker's name will bring up the slides from the talk.
9:30 - 10:30 Noriko Yui (Queen's)
10:30 - 11:00 Tea Break
11:00 - 12:00 Cameron Franc (Michigan)
12:00 - 2:00 Lunch Break
2:00 - 3:00 Jerome Hoffman (LSU)
3:00 - 3:30 Tea Break
3:30 - 4:00 Will Chen (PSU)
Clicking on the speaker's name will bring up the slides from the talk.
9:30 - 10:30 Fang-Ting Tu (NCTS Taiwan)
10:30 - 11:00 Tea Break
11:00 - 12:00 Luca Candelori (LSU)
12:00 - 2:00 Lunch Break
2:00 - 3:00 Yara Elias (McGill)
3:00 - 3:30 Tea Break
3:30 - 4:30 Alex Molnar (Queen's)
9:30 - 10:30 Fang-Ting Tu (NCTS Taiwan)
10:30 - 11:00 Tea Break
11:00 - 12:00 Jerome Hoffman (LSU)
12:00 - 1:00 Lunch Break
1:00 - 1:30 Henri Cohen (Bordeaux I)
1:30 - 1:45 Tea Break
1:45 - 2:45 Henri Cohen (Bordeaux I)
Noriko Yui: Automorphy of Calabi-Yau varieties over Q of dimension less than or equal to 3.
Link to abstract
Cameron Franc: Applications of vector-valued modular forms
We will discuss joint work with Geoff Mason on vector-valued modular forms in low dimensions, and their connection with hypergeometric series. Our talk will focus mainly on the three-dimensional case. We will discuss several applications of this work to the study of noncongruence modular forms associated with a finite order character of Gamma_0(2).
Jerome Hoffman: Families of curves with nontrivial endomorphisms in their jacobians
Link to abstract
Will Chen:
Quotients of the upper half plane by congruence subgroups of SL(2,Z) are well-known to be moduli spaces parametrizing elliptic curves with an “abelian” level structure. In my talk I will generalize the classical congruence level structures and show that quotients of the upper half plane by noncongruence subgroups are very naturally moduli spaces for elliptic curves equipped with "nonabelian" level structures.
Fang-Ting Tu (April 7th): Generalized Legendre Curves and Quternionic Multiplication
In this talk, we will first introduce the Jacobian varieties of generalized Legendre curves, whose periods can be expressed in terms of the Gauss hypergeometric functions. We will then discuss some results on their primitive subvarieties with Quternionic Multiplication, which are based on explicit computations on the corresponding Galois representations and periods.
Luca Candelori: Weil representations over abelian varieties
As analytic functions, theta functions possess a functional equation thanks to the Poisson summation formula. In this talk, we give an algebraic meaning to this functional equation, by viewing theta functions as sections of appropriate vector bundles over the moduli stack of abelian varieties. In particular, these vector bundles arise from the Weil representation attached to Heisenberg groups of non-degenerate line bundles over abelian varieties. We discuss applications towards the explicit construction of automorphic forms.
Yara Elias: On the Selmer group associated to a modular form twisted by an algebraic Hecke character
Kolyvagin uses an Euler system to bound the size of the Selmer group of certain elliptic curves over imaginary quadratic fields assuming the nonvanishing of a suitable Heegner point. This implies that they have rank 1, and that their associated Tate-Shafarevich group is finite. Combined with results of Gross and Zagier, this proves the Birch and Swinnerton-Dyer conjecture for analytic rank less than 1. Nekovar adapts Kolyvagin's method to the setting of a higher even weight modular form. In this talk, we will consider an extension of Nekovar's development to the case where the modular form is twisted by an algebraic Hecke character.
Alex Molnar: Explicit modularity of some Calabi-Yau threefolds
We discuss an approach to computing the L-function of some Calabi-Yau threefolds using modularity of smaller dimensional Calabi-Yau varieties. This approach works both with our rigid Calabi-Yau threefolds, re-verifying their modularity, and also with our non-rigid families where we can show the L-functions decompose into smaller pieces and are automorphic.
Fang-Ting Tu(April 14th): Hypergeometric Series and Gaussian Hypergeometric Functions
Our motivation is to investigate the relations between hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions (hypergeometric functions over finite fields). In this talk, we will study their relationships through the algebraic varieties that are analogues of Legendre curves.
Henri Cohen: L-functions: Survey, Algorithms, Implementations, Databases
In this talk I will first define L-functions in an elementary way, giving basic properties and conjectures. I will then explain the numerous ways in which L-functions occur in practice, and the relations between these, stressing in particular the fact that an L-function is "almost" characterized by its gamma factors and conductor. In a second part I will more specifically talk about the computational aspects: algorithms for computing L-functions, existing implementations and Databases. In a third part, I will give a computer demonstration of the new L-function package of Pari/GP developped jointly with several collaborators (no previous knowledge of the Pari/GP language is necessary).