Department of

# Mathematics

Seminar Calendar
for events the day of Friday, March 5, 2021.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, March 5, 2021

2:00 pm in Contact for zoom link,Friday, March 5, 2021

#### $L^{2}$ decoupling: An Introduction and Applications

###### Ryan McConnell (UIUC Math)

Abstract: Suppose one wants to decompose a function on into parts that have disjoint Fourier supports. Due to linearity of the Fourier transform, the sum of these parts must be the original function. Suppose, however, that you wish to understand how the norms of these parts relates to the norm of the original function. While this task isn’t so straight forward, Bourgain and Demeter (2015) were able to resolve a conjecture related to this: the $L^{2}$ Decoupling Conjecture.In this talk we will introduce the conjecture, provide applications of it to both PDEs and Number Theory, prove an earlier result of Bourgain for a smaller range of admissible exponents, and (time permitting) comment on how to adapt the ideas presented to prove the full result.

4:00 pm in Zoom,Friday, March 5, 2021

#### To (Conformal) Infinity and Beyond!

###### Hadrian Quan (UIUC)

Abstract: In this talk I'll describe a few geometric and analytic questions in the context of asymptotically hyperbolic spaces: manifolds which look like hyperbolic space at infinity. I'll do my best to gesture at which of these questions were inspired by conjectures of physicists (such as the AdS-CFT correspondence), while remaining firmly in the context of well-defined mathematical objects. At the end I'll discuss how the geometry of the hyperbolic space inside of Minkowski space can be used to prove theorems on such asymptotically hyperbolic spaces. Email basilio3 (at) illinois (dot) edu for Zoom details.