Haruzo Hida (UCLA),
"Local indecomposability of Tate modules of abelian varieties of GL(2)-type"

We prove indecomposability of p-adic Tate modules over the p-inertia group for non CM (partially p-ordinary) abelian varieties with real multiplication. I will also discuss its application (given by Bin Zhao) to local indecomposability of Hilbert modular Galois representations.

Ana Caraiani (University of Chicago),
"Patching functors and p-adic local Langlands"

The p-adic local Langlands correspondence is well understood for GL_2(Q_p), but appears much more complicated when considering GL_n(F), where either n>2 or F is a finite extension of Q_p. I will discuss joint work with Matthew Emerton, Toby Gee, David Geraghty, Vytautas Paskunas and Sug Woo Shin, in which we approach the correspondence using global methods. We study the relationship between Taylor-Wiles-Kisin patching of completed cohomology and p-adic local Langlands, and give an application to the Breuil-Schneider conjecture.

Ana Caraiani is a Dickson Instructor and NSF Postdoctoral Fellow at the University of Chicago. She earned her Ph.D. from Harvard University in 2012 under the direction of Richard Taylor. She also holds a bachelor's degree in mathematics from Princeton University. Her research interests include the geometry and cohomology of Shimura varieties and the classical and p-adic Langlands program

Freydoon Shahidi (Purdue University),
"Some Arithmetic Consequences of Eisenstein Series"

In this talk we discuss two applications of the theory of L-functions obtained through Fourier-Whittaker coefficients of Eisenstein series. The first is a brief sketch of a proof of equality of root numbers for exterior and symmetric squares of n-dimensional representations of Weil-Deligne group with those defined for corresponding representations of GL(n,F) for a non-archimedean field F through Fourier coefficients of the Siegel Eisenstein series on GSp(2n,F) (joint with Cogdell and Tsai). The second is a brief discussion of how to define a p-adic measure to express the inverse of the p-adic L-function attached to a Dirichlet character by means of the Fourier coefficients of the corresponding standard SL(2) Eisenstein series (Langlands-Shahidi method). This is joint with Gelbart, Miller and Panchishkin.

George Pappas (Michigan State),
"The local structure of reductions of Shimura varieties"

We will discuss some recent results about the structure of the singularities of the reductions of Shimura varieties modulo primes at which the level subgroup is parahoric in the sense of Bruhat-Tits.

George Pappas received his PH.D. from Columbia University in 1992 and is currently a professor at Michigan State University. He has been a Sloan fellow, has previously taught at the University of Pennsylvania and at Princeton, and has also spent two years as a member of the Institute for Advanced Study.