Home » Connections for Women: Microlocal Analysis

Workshop

Connections for Women: Microlocal Analysis

August 29, 2019 - August 30, 2019

Registration Deadline:	August 30, 2019 almost 4 years ago
To apply for Funding you must register by:	June 03, 2019 about 4 years ago

Parent Program:	Microlocal Analysis
Location:	MSRI: Simons Auditorium, Atrium

Organizers

Tanya Christiansen (University of Missouri), LEAD Raluca Felea (Rochester Institute of Technology)

Speaker(s)

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Nalini Anantharaman (Université de Strasbourg)
Katya Krupchyk (University of California, Irvine)
Anna Mazzucato (Pennsylvania State University)
Julie Rowlett (Chalmers University of Technology/University of Göteborg)
Xuwen Zhu (Northeastern University)

Description

This workshop will provide a gentle introduction to a selection of applications of microlocal analysis. These may be drawn from among geometric microlocal analysis, inverse problems, scattering theory, hyperbolic dynamical systems, quantum chaos and relativity. The workshop will also provide a panel discussion, a poster session and an introduction/research session. This workshop is open to all mathematicians. Additional funding provided by:

Keywords and Mathematics Subject Classification (MSC)

Tags/Keywords

Microlocal analysis
singular spaces
scattering theory
quantum chaos
inverse problems

Primary Mathematics Subject Classification

Secondary Mathematics Subject Classification No Secondary AMS MSC

Funding & Logistics Show All Collapse

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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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MSRI does not hire an outside company to make hotel reservations for our workshop participants, or share the names and email addresses of our participants with an outside party. If you are contacted by a business that claims to represent MSRI and offers to book a hotel room for you, it is likely a scam. Please do not accept their services.

MSRI has preferred rates at the Hotel Shattuck Plaza, depending on room availability. Guests can call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Institute discount. To book online visit this page (the MSRI rate will automatically be applied).

MSRI has preferred rates at the Graduate Berkeley, depending on room availability. Reservations may be made by calling 510-845-8981. When making reservations, guests must request the MSRI preferred rate. Enter in the Promo Code MSRI123 (this code is not case sensitive).

MSRI has preferred rates at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select "Affiliated with the Space Sciences Lab, Lawrence Hall of Science or MSRI." When prompted for your UC Contact/Host, please list Chris Marshall (coord@msri.org).

MSRI has a preferred rates at Easton Hall and Gibbs Hall, depending on room availability. Guests can call the Reservations line at 510-204-0732 and ask for the MSRI- Mathematical Science Research Inst. rate. To book online visit this page, select "Request a Reservation" choose the dates you would like to stay and enter the code MSRI (this code is not case sensitive).

Additional lodging options may be found on our short term housing page.

Show Schedule, Notes/Handouts & Videos

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Aug 29, 2019
Thursday

09:15 AM - 09:30 AM		Welcome
Location MSRI: Simons Auditorium Video -- Abstract -- Supplements -- Show Detail
09:30 AM - 10:30 AM		Microlocal analysis/inverse problems/PSDOs Anna Mazzucato (Pennsylvania State University)
Location MSRI: Simons Auditorium Video -- Abstract I will motivate a quick introduction to pseudo-differential operators by discussing the so-called Calderon's problem, that is, whether knowledge of the Dirichlet-to-Neumann map (or the Neumann-to-Dirichlet map) at the boundary determines the conductivity of a body in the interior. This problem has applications in Electric Impedance Tomography (EIT). I will in particular discuss uniqueness at the boundary, interior uniqueness using Complex Geometrical Optics (CGO solutions), and if time permits, layer stripping reconstruction algorithms in the case of isotropic conductivities. Supplements -- Show Detail
10:30 AM - 11:00 AM		Tea
Location MSRI: Atrium Video -- Abstract -- Supplements -- Show Detail
11:00 AM - 12:00 PM		Quantum chaos Nalini Anantharaman (Université de Strasbourg)
Location MSRI: Simons Auditorium Video Abstract -- Supplements -- Show Detail
12:00 PM - 02:00 PM		Lunch
Location MSRI: Atrium Video -- Abstract -- Supplements -- Show Detail
02:00 PM - 03:00 PM		Introduction to inverse boundary problems Katya Krupchyk (University of California, Irvine)
Location MSRI: Simons Auditorium Video -- Abstract We provide a general introduction to the field of inverse boundary problems for elliptic PDE, with the celebrated Calderon problem serving as a prototypical example. The emphasis of the talk is on the techniques based on Carleman estimates and their role in the construction of complex geometric optics solutions. We also survey some of the more recent developments, including partial data problems, inverse boundary problems on manifolds, as well as inverse boundary problems for non-linear equations. Supplements -- Show Detail
03:00 PM - 03:30 PM		Tea
Location MSRI: Atrium Video -- Abstract -- Supplements -- Show Detail
03:30 PM - 04:30 PM		Introduction to microlocal analysis Xuwen Zhu (Northeastern University)
Location MSRI: Simons Auditorium Video Abstract This talk will be a (very gentle) introduction of real blow ups with applications in singular geometry. We will start with two motivating toy problems, including an eigenvalue resolution of self-adjoint matrices and a simple Fredholm operator on a manifold with boundary. Then if time permits we will mention some applications in singular uniformization problems, where the resolution or compactification via blow ups plays an important role in understanding the moduli spaces of constant curvature metrics with cusp and conical singularities. Supplements -- Show Detail
04:30 PM - 05:30 PM		Panel Discussion-applying for jobs
Location MSRI: Commons Room Video -- Abstract -- Supplements -- Show Detail
05:30 PM - 07:00 PM		Dinner at MSRI
Location -- Video -- Abstract -- Supplements -- Show Detail

Aug 30, 2019
Friday

09:30 AM - 10:30 AM		Microlocal analysis/inverse problems/PSDOs Anna Mazzucato (Pennsylvania State University)
Location MSRI: Simons Auditorium Video -- Abstract -- Supplements -- Show Detail
10:30 AM - 11:00 AM		Tea
Location MSRI: Atrium Video -- Abstract -- Supplements -- Show Detail
11:00 AM - 12:00 PM		Quantum chaos Nalini Anantharaman (Université de Strasbourg)
Location MSRI: Simons Auditorium Video -- Abstract -- Supplements -- Show Detail
12:00 PM - 02:00 PM		Lunch
Location MSRI: Atrium Video -- Abstract -- Supplements -- Show Detail
02:00 PM - 03:00 PM		Geometric analysis Julie Rowlett (Chalmers University of Technology/University of Göteborg)
Location MSRI: Simons Auditorium Video Abstract How do geometric features affect physics? In this talk I will start with a simple example in which we solve the initial value problem for the homogeneous heat equation on a half line, with the Dirichlet boundary condition at the origin. We will see how the Schwartz kernel of the fundamental solution, known as the heat kernel, ``feels'' the boundary at the origin, and how it also feels the boundary condition when we change between Dirichlet and Neumann boundary conditions. This is of course a very special example, because we can compute everything explicitly. However, even for a simple bounded domain in the plane, there is no analogous closed-form expression for the heat kernel. So, if we wish to understand how the geometric features of a domain in the plane affect the physical flow of heat, we need more tools: the tools of microlocal analysis! The main focus of this talk will be the microlocal construction of the heat kernel for curvilinear polygonal domains both in the plane and also in surfaces. This construction will introduce the concepts of ``blowing up'' and the incredible usefulness of ``blowing up.'' We will see how the microlocal construction can be applied to show that the heat kernel ``feels'' geometric features like curvature, boundary, and the presence (or lack thereof) of corners. Supplements -- Show Detail
03:00 PM - 03:30 PM		Tea
Location MSRI: Atrium Video -- Abstract -- Supplements -- Show Detail
03:30 PM - 04:30 PM		Poster Session
Location MSRI: Simons Auditorium Video -- Abstract -- Supplements -- Show Detail

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