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for events the day of Thursday, April 16, 2020.

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Thursday, April 16, 2020

11:00 am in Zoom (email Patrick Allen for the meeting ID and password),Thursday, April 16, 2020

The Wiles defect for Hecke algebras that are not complete intersections

Jeff Manning (University of California at Los Angeles)

Abstract: In his work on modularity theorems, Wiles proved a numerical criterion for a map of rings R->T to be an isomorphism of complete intersections. He used this to show that certain deformation rings and Hecke algebras associated to a mod p Galois representation at non-minimal level were isomorphic and complete intersections, provided the same was true at minimal level. In addition to proving modularity theorems, this numerical criterion also implies a connection between the order of a certain Selmer group and a special value of an L-function. In this talk I will consider the case of a Hecke algebra acting on the cohomology a Shimura curve associated to a quaternion algebra. In this case, one has an analogous map of ring R->T which is known to be an isomorphism, but in many cases the rings R and T fail to be complete intersections. This means that Wiles' numerical criterion will fail to hold. I will describe a method for precisely computing the extent to which the numerical criterion fails (i.e. the 'Wiles defect"), which will turn out to be determined entirely by local information at the primes dividing the discriminant of the quaternion algebra. This is joint work with Gebhard Bockle and Chandrashekhar Khare.

4:00 pm in Virtual Altgeld Hall,Thursday, April 16, 2020

Harnessing quantum entanglement

Laura Mancinska (University of Copenhagen)

Abstract: Entanglement is one of the key features of quantum mechanics. It lies at the heart of most cryptographic applications of quantum technologies and is necessary for computational speed-ups. However, given a specific information processing task, it is challenging to find the best way to harness entanglement and we are yet to uncover the full range of its potential applications. We will see that nonlocal games provide a rigorous framework for studying quantum entanglement and the advantage that it can offer. We will take a closer look at the question of how much entanglement can be needed to play a nonlocal game optimally. We will then use games requiring large amounts of entanglement to build protocols for certifying proper functioning of untrusted quantum devices. The meeting will be locked 4.15, contact me, if you need to get in.