Web page for Richard Melrose
My person can sometimes be found in Room 2-480, at MIT.
Telephone: 617-253-2950
E-mail: rbm@math.mit.edu
Fax 617-253-4358.
Cymbidium Kiri Te Kanawa (May 2013)
Teaching
Spring 2022:
18.157 Introduction to Microlocal Anlysis. TR 9:30-11.
Outline.pdf
Notes V1
Teaching
Fall 2021:
18.101 Analysis on Manifolds. TR 11-12:30, Room 2-132.
In person/remote:
This course is to be face-to-face. If anyone plans to take it
remotely, please contact me in advance.
Blurb:
Manifolds play a central role in modern Mathematics. This course is to
intended to present the basic facts about manifolds. As such it starts with
the differentiability properties of functions of several real variables,
proceeds with basic theorems related to these -- particularly Talyor's
theorem, the inverse function theorem and integration of vector fields. In
the second part these are used to define manifolds and discuss their properties.
Prerequisites:
This is a successor course to 18.100 -- which includes
differentiation and integration of functions of one real variable. Some
knowledge of ordinary differential equations (as in 18.03) is helpful. One
issue which arises is the distinction between 18.100A and 18.100B
especially concerning metric spaces, which are discussed in the latter but
not tyically in the former. There will be notes showing what I will use --
there is some time before this becomes significant.
Feel free to ask questions even before the semester starts. Those who are
preregistered have access to the Canvas site.
Newest
Extended abstract of talk at Oberwolfach, June 2021
Compactification of Semisimple Lie groups (with Albin, Dimakis and Vogan)
Geometry of Pseudodifferential algebra bundles
and Fourier Integral Operators
Generalized blow-up of corners and fiber
products
`Eta invariant on articulated manifolds'
Talk at CRM meeting, July 2012
`Calderon projector for manifolds with corners'
Talk at UNC meeting, July 2012
Talk for prospective grad students, March 2012
Equivariant cohomology and resolution
Resolution of smooth groups actions
Oberwolfach meeting on Singular spaces, June/July 2010
Jerusalem meeting for Werner Müller
Equivariant cohomology and resolution
Fredholm realizations of elliptic symbols on manifolds with boundary II: fibered boundary
Eta forms and the odd pseudodifferential families index
There will be a meeting `mmm2009' assocated to Singularities@mit (which is on Saturday 4th April) with talks on Friday 3rd April and Monday 6th April
posted 17 March 2009:
Lectures at Berkeley Fall 2008:Smooth Operator Algebras and K-theory
posted 17 March 2009:
Real Blow up
posted 17 March 2009:
Diffraction of singularities for the wave equation on manifolds with corners
posted 17 March 2009:
The index of projective families of elliptic operators: the decomposable case
Seminar Monza (Finished)
This is a virtual seminar, held weekly with 90 minute talks, with the first 30 minutes devoted to the setting of context.
I don't plan to maintain a detailed webpage for the seminar. For links to the talks (via zoom) send me an email request.
- 7 April, 2020, 12:30 ET. Rafe Mazzeo
- 14 April, 2020, 12:30 ET. Peter Hintz
- 21 April, 2020, 12:30 ET. Colin Guillarmou
- 28 April, 2020, 12:30 ET. Michael Singer
- 5 May, 2020, 12:30 ET. Jeff Galkowski
- 12 May, 2020, 12:30 ET. Paolo Piazza
- 19 May, 2020, 12:30 ET. Yaiza Canzani
- 26 May, 2020, 12:30 ET. Fr\'ed\'eric Rochon
- 2 June, 2020, 12:30 ET. Andr\'as Vasy
- 9 June, 2020, 12:30 ET. Maciej Zworski
- 16 June, 2020, 12:30 ET. Gunther Uhlmann
- 23 June, 2020, 12:30 ET. Dean Baskin
Mathematical entertainment
Real mathematics
A list of my graduate students
(I was a student of Gerard Friedlander)
- PhD 2020: Ethan Jafee
- PhD 2015: Xuwen Zhu
- PhD 2010: Chris Kottke
- PhD 2010: Fang Wang
- PhD 2007: Yakov Shapiro
- PhD 2005: Frédéric Rochon rochon@math.mit.edu
- Phd 2003: Gyula Lakos lakos@math.mit.edu
- Phd 2003: Raul Tataru grtataru@math.mit.edu
- PhD 1999: Sergiu Moroianu(moroianu@alum.mit.edu)
- PhD 1998: Sang Chin
- PhD 1998: Paul Loya (paul@math.binghamton.edu)
- PhD 1998: Jared Wunsch (jwunsch@math.northwestern.edu)
- PhD 1997: András Vasy (andras@math.mit.edu)
- PhD 1996: Edith A. Mooers (edie@tracfoundation.org)
- PhD 1994: Andrew Hassell (hassell@maths.anu.edu.au)
- PhD 1994: Mark S. Joshi (joshi@pmms.cam.ac.uk)
- PhD 1993: Tanya Christiansen (tjc@math.missouri.edu)
- PhD 1991: Paolo Piazza (piazza@mat.uniroma1.it)
- PhD 1990: Patrick T. McDonald (pmacdona@virtu.sar.usf.edu)
- PhD 1989: Julian Edward (edwardj@solix.fiu.edu)
- PhD 1989: Maciej Zworski (zworski@math.berkeley.edu)<
- PhD 1988: Catherine Durso
- PhD 1988: Boyd Livingston
- PhD 1988: Ant\^onio S\'a Barreto (sabarre@math.purdue.edu)
- PhD 1987: Chuan-yi Xu
- PhD 1986: Edoh Y. Amiran
- PhD 1986: Rafe R. Mazzeo (mazzeo@math.stanford.edu)
- PhD 1985: Ahmed Intissar intissar@fsr.ac.ma
- PhD 1985: Santiago Ramon Simanca Perez
- PhD 1984: Alan W. Magnusson
- PhD 1984: Niles D. Ritter
- PhD 1982: John M. (Jack) Lee
- PhD 1981: Frank Farris
- PhD 1981: Shahla Marvizi (Ahdout)
- PhD 1981: Mark Williams
Fruits, nuts, flowers, etc.
To the MIT Mathematics Department Home Page