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Talk_id	Date	Speaker	Title
19675	Wednesday 10/9 3:00 PM	Romyar Sharifi, UCLA	Cocycles valued in motivic cohomology New Window Algebra Speaker: Romyar Sharifi, UCLA Title: Cocycles valued in motivic cohomology Date: 10/09/2019 Time: 3:00 PM - 4:00 PM Place: C304 Wells Hall I will describe joint work in progress with Akshay Venkatesh on the construction of 1-cocycles on $\mathrm{GL}_2(\mathbb{Z})$ valued in a limit of second motivic cohomology groups of open subschemes of the square of (1) the multiplicative group over the rationals and (2) a universal elliptic curve. I’ll explain how these cocycles specialize to homomorphisms taking modular symbols to special elements in second cohomology groups of cyclotomic fields and modular curves in the respective cases.
19676	Wednesday 10/23 3:00 PM	Sumit Chandra Mishra, Emory University	Local-global principle for norms over semi-global fields New Window Algebra Speaker: Sumit Chandra Mishra, Emory University Title: Local-global principle for norms over semi-global fields Date: 10/23/2019 Time: 3:00 PM - 3:50 PM Place: C304 Wells Hall Let $K$ be a complete discretely valued field with residue field $\kappa$. Let $F$ be a function field in one variable over $K$ and $\mathscr{X}$ a regular proper model of $F$ with reduced special fibre $X$ a union of regular curves with normal crossings. Suppose that the graph associated to $\mathscr{X}$ is a tree (e.g. $F = K(t)$). Let $L/F$ be a Galois extension of degree $n$ with Galois group $G$ and $n$ coprime to char$(\kappa)$. Suppose that $\kappa$ is algebraically closed field or a finite field containing a primitive $n^{\rm th}$ root of unity. Then we show that an element in $F^*$ is a norm from the extension $L/F$ if it is a norm from the extensions $L\otimes_F F_\nu/F_\nu$ for all discrete valuations $\nu$ of $F$.
20689	Tuesday 11/5 3:00 PM	Carl Wang-Erickson, University of Pittsburg	Bi-ordinary modular forms New Window Algebra Speaker: Carl Wang-Erickson, University of Pittsburg Title: Bi-ordinary modular forms Date: 11/05/2019 Time: 3:00 PM - 4:00 PM Place: C304 Wells Hall It is known that p-ordinary cuspidal Hecke eigenforms give rise to 2-dimensional global Galois representations which become reducible after restriction to a decomposition group at p. For which such forms is this restriction not only reducible but also splittable? Complex multiplication (CM) forms satisfy this p-local property, but is such a restrictive global property as CM necessary? In classical weights at least 2, it is expected that this is the case. We present a construction of "bi-ordinary" p-adic modular forms, which can measure exceptions to this expectation. We also give evidence that there are non-CM but p-locally splittable forms in p-adic weights. This is joint work with Francesc Castella.

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