### Saturday, November 9, 2019 at The University of Maryland, College Park

### Henri Darmon (McGill University)

**Title:** Incoherent *p*-adic families of Eisenstein series and the RM values of rigid meromorphic cocycles

**Abstract:** I will express the Fourier coefficients of the ordinary projections of certain incoherent *p*-adic families of Hilbert Eisenstein series in terms of the RM values of appropriate rigid meromorphic cocycles. This transposes a seminal calculation of Gross and Zagier to a setting where the place infinity is replaced by a finite prime *p*, and (more importantly) where genus characters of real quadratic fields are replaced by arbitrary (odd) ring class characters.

This is joint work with Alice Pozzi amd Jan Vonk.

### Mark Andrea de Cataldo (Stony Brook University)

**Title:** The Hodge numbers of OG10 via Ngô strings

**Abstract: **I report on joint work with A. Rapagnetta (U.Rome) and G. Saccà (Columbia U.), where we compute the Hodge numbers of the hyperkähler manifolds in the deformation class of O’Grady’s 10-dimensional example by using the Ngô support theorem.

### Akhil Mathew (University of Chicago/IAS)

**Title:** *p*-adic deformations of algebraic cycle classes and topological cyclic homology

**Abstract:** Let *X* be a smooth projective scheme over the ring of integers in a *p*-adic field. The *p*-adic deformation problem (a weaker version of a conjecture of Fontaine-Messing) asks when a class in *K _{0}* of the special fiber can be lifted “infinitesimally” to

*K*. This question was considered by Bloch-Esnault-Kerz: in the unramified case (and with hypotheses on the dimension), the condition is exactly that the crystalline Chern classes should live in an appropriate step of the Hodge filtration. We use recent advances in the theory of topological cyclic homology to extend the Bloch-Esnault-Kerz theorem to arbitrary

_{0}(X)*p*-adic fields, and refine results of Beilinson on relative continuous

*K*-theory and cyclic homology. Joint with Benjamin Antieau, Matthew Morrow, and Thomas Nikolaus.

### Evangelia Gazaki (University of Virginia)

**Title:** Zero-cycles over arithmetic fields

**Abstract:** The Chow group of zero-cycles of a smooth projective variety is a generalization to higher dimensions of the Picard group of a curve. For a smooth projective variety *X* over a field *k*, this group provides a fundamental geometric invariant, but unlike the case of curves very little is known about its structure, especially when *k* is a field of arithmetic interest. In the mid 90’s Colliot-Thélène formulated a conjecture about zero-cycles over *p*-adic fields. A weaker form of this conjecture has been established, but the general conjecture is only known for very limited classes of varieties. In this talk I will present some joint work with Isabel Leal, where we prove this conjecture for a large family of products of elliptic curves, and discuss some work in progress about certain cases when serious obstructions seem to appear.

### Hang Xue (University of Arizona)

**Title:** Towards a factorization of linear periods

**Abstract:** I will explain how to relate local root numbers to the existence of linear models of representation of *GL(2n)*. I will also explain how to make use of this to prove conjectures of Sakellaridis and Venkatesh on the Plancherel formula for *GL(n, E) \ GL(2n, F)* and on the canonical factorization of linear periods.