Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, January 31, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    December 2018           January 2019          February 2019
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1          1  2  3  4  5                   1  2
2  3  4  5  6  7  8    6  7  8  9 10 11 12    3  4  5  6  7  8  9
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30 31


Thursday, January 31, 2019

11:00 am in 241 Altgeld Hall,Thursday, January 31, 2019

#### Monodromy for some rank two Galois representations over CM fields

###### Patrick Allen (Illinois Math)

Abstract: In the automorphic-to-Galois direction of Langlands reciprocity, one aims to construct a Galois representation whose Frobenius eigenvalues are determined by the Hecke eigenvalues at unramified places. It is natural to ask what happens at the ramified places, a problem known a local-global compatibility. Varma proved that the p-adic Galois representations constructed by Harris-Lan-Taylor-Thorne satisfy local-global compatibility at all places away from p, up to the so-called monodromy operator. Using recently developed automorphy lifting theorems and a strategy of Luu, we prove the existence of the monodromy operator for some of these Galois representations in rank two. This is joint work with James Newton.

2:00 pm in 347 Altgeld Hall,Thursday, January 31, 2019

#### Introduction to Percolation Theory (Part 2)

###### Grigory Terlov (UIUC Math)

Abstract: This is the second part of two talks designed to introduce students to Percolation Theory. We will discuss an upper bound for critical probability for $\mathbb{Z}^d$ via cut-sets and duality. This talk should be accessible for people who missed the first part.