UM PDE Reading Group: Winter 2011

We will be talking about various advanced topics in PDE. The plan for this semester is to talk about (1) spectral theory of unbounded operators, (2) calculus of variations, and (3) Morawetz estimates. (Last semester we talked about Strichartz estimates.) For more information, contact Jen Beichman (jbeich@); for matters pertaining to the webpage, email Rafe Kinsey (rkinsey@). To get on or off the email list, go to directory.umich.edu, search for "pde-reading-group," bind to your umich uniqname, and join the group, or email Jen or Rafe.

Logistics: Mondays 4pm-5pm, 3088 EH (New Room, starting 3/21), and Wednesdays 3-4pm, 4088 EH.
Date SpeakerTopic
Wed, January 5n/ano meeting
Mon, January 10, 4pmn/aorganization
Wed, January 12, 3pmJen BeichmanSpectral Theory of Bounded Operators
Mon, January 17, 4pmJen BeichmanSpectral Theory of Compact Bounded Operators
Wed, January 19, 3pmJoe RobertsAn application of spectral theory to PDE
Mon, January 24, 4pmJeff CalderSpectral Resolution of Bounded Linear operators I
Wed, January 26, 3pmTim FergusonSpectral Resolution of Bounded Linear Operators II
Mon, January 31, 4pmJoe RobertsAn application of spectral resolution to PDE
Wed, February 2, 3pmDan DeWoskinpostponed
Mon, February 7, 4pmDan DeWoskinSpectral Resolution of Symmetric and Unitary Operators (rescheduled from last week)
Wed, February 9, 3pmno talkno talk
Mon, February 14, 4pmMatthew MasarikApplication of Stone's Theorem and Formula to the Wave Equation.
Abstract: We will consider the Cauchy problem for the wave equation with compactly supported initial data in a general spherically symmetric black hole geometry. Our goal will be to apply Stone's Theorem and Stone's Formula to obtain a representation formula for the solution.
Wed, February 16, 3pmRafe KinseyAn Application of Spectral Theory to the Heat Operator
Mon, February 21, 4pmTim FergusonWolff's Solution to the Corona Problem
Wed, February 23, 3pmn/a(Tentative) Planning meeting for second half of semester talk
Wed, March 9, 3pmJen BeichmanIntro to/History of Calculus of Variations, Euler-Lagrange Equations
Mon, March 14, 4pmMatthew MasarikMy talk will consist of a brief historical account of the brachistochrone problem, followed by a brief solution. Then I'll move on to discuss the link between Lagrangians and conservation laws, ending with an application to the wave equation.
Wed, March 16, 3pmRafe KinseyCalculus of Variations: The Direct Method, Existence
Mon, March 21, 4pm
New Room for Mondays: 3088 EH
Joe RobertsCalculus of Variations: The Direct Method, Regularity
Wed, March 23, 3pmJeff CalderMinimal Surfaces
Mon, March 28, 4pm
New Room for Mondays: 3088 EH
Benson MuiteSome interesting examples in the scalar and vectorial cases.

Abstract: We give a survey of some interesting examples in the calculus of variations. We also discuss motivation for and possible means of weakening the convexity assumption in the calculus of variations.
Mon, April 3, 4pm
New Room for Mondays: 3088 EH
Jen BeichmanRelevant Facts about NLS, and Motivation for Morawetz Estimates
Wed, April 5, 3pmNate Totz/Jen BeichmanThe Viriel Identity.
Mon, April 10, 4pm
New Room for Mondays: 3088 EH
Nate TotzViriel Identity and Morawetz Estimates, Part II
Wed, April 12, 3pmJen BeichmanAn Application of Morawetz estimates to scattering for cubic, defocusing NLS

Archives:
Fall 2010 PDE Reading Group
Go back to the student analysis seminar homepage.

Email rkinsey (at) umich (dot) edu with comments, questions, and corrections on the webpage.
Last modified: Thu Apr 7 16:46:06 EDT 2011

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