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Series: PDE Seminar

Series: Geometry Topology Seminar

Series: Stochastics Seminar

Series: Analysis Seminar

Series: CDSNS Colloquium

In this talk I will present some results concerning the existence and the stability of quasi-periodic solutions for quasi-linear and fully nonlinear PDEs. In particular, I will focus on the Water waves equation. The proof is based on a Nash-moser iterative scheme and on the reduction to constant coefficients of the linearized PDE at any approximate solution. Due to the non-local nature of the water waves equation, such a reduction procedure is achieved by using techniques from Harmonic Analysis and microlocal analysis, like Fourier integral operators and Pseudo differential operators.

Series: CDSNS Colloquium

TBA

Series: ACO Student Seminar

Physical sensors (thermal, light, motion, etc.) are becoming ubiquitous and offer important
benefits to society. However, allowing
sensors into our private spaces has resulted in considerable privacy
concerns. Differential privacy has been developed to help alleviate
these privacy
concerns. In this
talk, we’ll develop and define a framework for releasing physical data
that preserves both utility and provides privacy. Our notion of
closeness of physical data will
be defined via the Earth Mover Distance and we’ll discuss the
implications of this choice. Physical data, such as temperature distributions, are often only accessible to us via a linear
transformation of the data.
We’ll analyse the implications of our privacy definition for linear inverse problems, focusing on those
that are traditionally considered to be "ill-conditioned”. We’ll
then instantiate our framework with the heat kernel on graphs and
discuss how the privacy parameter relates to the connectivity
of the graph. Our work indicates that it is possible to produce locally
private sensor measurements that both keep the exact locations of the
heat sources private and permit recovery of the ``general geographic
vicinity'' of the sources. Joint
work with Anna C. Gilbert.

Series: Job Candidate Talk

The mean field variational inference is widely used in statistics and
machine learning to approximate posterior distributions. Despite its
popularity, there exist remarkably little fundamental theoretical
justifications. The success of variational inference
mainly lies in its iterative algorithm, which, to the best of our
knowledge, has never been investigated for any high-dimensional or
complex model. In this talk, we establish computational and statistical
guarantees of mean field variational inference. Using
community detection problem as a test case, we show that its iterative
algorithm has a linear convergence to the optimal statistical accuracy
within log n iterations. We are optimistic to go beyond community
detection and to understand mean field under a general
class of latent variable models. In addition, the technique we develop
can be extended to analyzing Expectation-maximization and Gibbs sampler.

Wednesday, January 31, 2018 - 13:55 ,
Location: Skiles 006 ,
Sudipta Kolay ,
GaTech ,
Organizer: Anubhav Mukherjee

Series: Analysis Seminar

An overarching problem in matrix weighted theory is the so-called A2 conjecture, namely the question of whether the norm of a Calderón-Zygmund operator acting on a matrix weighted L2 space depends linearly on the A2 characteristic of the weight. In this talk, I will discuss the history of this problem and provide a survey of recent results with an emphasis on the challenges that arise within the setup.