Web page for Richard Melrose

My person can sometimes be found in Room 2-480, at MIT.
Telephone: 617-253-2950

Fax 617-253-4358.

Cymbidium Kiri Te Kanawa (May 2013)


Spring 2022:

18.157 Introduction to Microlocal Anlysis. TR 9:30-11. Outline.pdf
Notes V1


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.


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.


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.


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.

Mathematical entertainment

Real mathematics

A list of my graduate students

(I was a student of Gerard Friedlander)

Fruits, nuts, flowers, etc.

To the MIT Mathematics Department Home Page