### 1:00- 1:50

#### log-log blow up solutions of the NLS at exactly m points

We will first introduce the log-log blow up solutions to NLS which have
been studied by Merle and Raphael and many other authors. Then, we will
illustrate our construction about certain solutions to NLS, which blow
up at $m$ prescribed points according to log-log law. The idea is to use
bootstrap to show the $m$ bubbles can be decoupled, and then use soft
topological argument to balance different bubbles, making them blow up
simultaneously at the prescribed points.

### 2:00 - 2:50

#### Random planar maps and Liouville quantum gravity

We begin with a well known bijection between planar trees and walks on
$\Z_{\ge 0}$. Then we present a bijection between spanning tree decorated
planar maps and walks on $\Z^2_{\ge 0}$. Both bijections can be understood
as quotient spaces. Thanks to that random walk converges to Brownian
motion, both bijections have continuum counterpart. In particular, the 2D
bijection amounts to gluing two continuum trees into a topological sphere
with a space filling curve. This construction gives us access to the
fascinating world of Liouville quantum gravity and 2D random geometry. No
background is required other than undergraduate probability.

### 3:30 - 4:20

#### Nondeterministic well-posedness for the periodic 4D cubic NLS

TBA

### 4:30 - 5:20

#### Spectral theory of von Neumann algebra valued
differential operators over non-compact manifolds

We provide criteria for selfadjointness and τ-Fredholmness of
first and second order differential operators acting on sections of
infinite dimensional bundles, whose fibers are modules of finite type over
a von Neumann algebra A endowed with a trace τ. We extend the Callias-type
index to operators acting on sections of such bundles and show that this
index is stable under compact perturbations. (Joint work with Maxim
Braverman).

Organized by Ken Ascher, Dori Bejleri, Mamikon Gulian, and Laura Walton at the Brown Math Department

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