Govind Menon

Division of Applied Mathematics,
Brown University.
Office : Room 104, 182, George St.,
Phone : 401-863-3793
Fax : 401-863-1355
Email : lastname at dam dot brown dot edu
Office hours and advising : Friday, 10 am - noon (Spring 2016).

Research interests

I have broad interests in applied mathematics. Most of my work is on the dynamics of disordered systems, especially:

Phase transitions (especially in materials science) and non-equilibrium statistical mechanics.
Integrable systems and random matrix theory.
Statistical analysis of numerical algorithms.
Models of turbulence.

These areas are linked through a common viewpoint. The kinetics of phase transitions and models of turbulence are important examples of dynamical systems in high dimensions. Surprisingly, several numerical algorithms may also be viewed as dynamical systems acting in high dimensional spaces and behave like glassy systems. This approach suggests new questions and (at the technical level) new equations and estimates that I hope will be valuable to practitioners in different fields.

My ideals are those of a mathematical physicist. I am constantly amazed by the mathematical beauty of fundamental physical models. Dirac's dictum that all physical principles must have mathematical beauty, seamlessly coexists with Cantor's view that the essence of mathematics resides in its freedom. We have no understanding of why this is the case, but it is a gift of knowledge that belongs to us all.

I am also fascinated with the idea that biology can inspire nanotechnology. While self-assembly today is principally driven by experimental advances, it is a promising field for mathematical contributions.


Recent teaching

I teach classes undergraduate and graduate classes in many areas of applied mathematics. In the past few years, I have developed several new classes.

APMA 1940V Spring 2017, Topics in information and coding theory.
APMA 1710 Fall 2016, Information theory.
APMA 2200 Spring 2016, Nonlinear dynamical systems, II.
APMA 2821X Spring 2016, Statistical theories of turbulence.
APMA 2811O Spring 2015, Dynamics and stochastics (random matrix theory) .
APMA 1330 Fall 2014, Methods of applied mathematics, III.
APMA 2200 Spring 2014, Nonlinear dynamical systems.
APMA 2190 Fall 2013, Nonlinear dynamical systems.
APMA 0360 Spring 2013, Methods of applied mathematics.

Editorial work

I am the associate managing editor for the Quarterly of Applied Mathematics . The Quarterly is published by Brown University and distributed by the American Mathematical Society. We are happy to publish papers in a wide range of areas of applied mathematics, and in many distinct formats. If you'd like to know if your work is suitable, please send me an email.

I currently serve on the editorial boards of the following journals.

Journal of Nonlinear Science (end 12/2016).
Physica D: Nonlinear Phenomena (end 12/2016).
SIAM Journal on Mathematical Analysis

As everyone who is involved in the publishing of mathematics knows, the cost of journals has skyrocketed, while most of the actual work involved in publishing (i.e. writing, editing and even typesetting papers) has been pushed onto authors. I find the situation as offensive as most, but I don't support boycotts of Elsevier or Springer. The main reason is that both these publishers support journals such as Physica D and the Journal of Nonlinear Science that are dedicated to interdisciplinary research in a way that the low-cost journals published by the AMS and SIAM are not. If you feel that your work is in this vein, and you would rather not support Physica D or JNLS, I'd be happy to consider your paper for QAM (which is distributed by the AMS).

I am also a contributing writer for The Mathematical Intelligencer .

Undergraduate advising

I am happy to serve as an advisor for an honors thesis. My typical expectation is that you work with me for at least two semesters, commiting time equivalent to at least one class per semester. I do not fund summer "internships" for international students.

Graduate advising

As of Fall 2016, I advise two graduate students and one postdoc. I expect to take on two or three new students, since my current students will graduate in 2017. If you are a graduate student in applied math or math at Brown, and would like to work with me, please email me. For a student with a taste for applications, I'm mainly interested in projects on self-assembly. There are also several `hard analysis' problems in random matrix theory, turbulence and phase transitions that are of great interest to me.

If you are a prospective student, and you'd like to work with me, please note that students at Brown are admitted to the graduate program, and are free to choose their advisor, so my "queue" should play no role in your decision to apply to Brown. Student plans often change (as they should) after some time in graduate school.