I am Professor of Mathematics in the Department of Mathematics and Statistics at Amherst College.

# Research

My research is in algebraic topology and homotopy theory.

## Goodwillie calculus

A large part of my research concerns Goodwillie's homotopy calculus. This theory provides analogues in the world of homotopy theory of ordinary calculus notions such as polynomial approximation, the Taylor series and its convergence, and derivatives. Much of my work is focused on the problem of reconstructing the corresponding 'Taylor tower' from its individual terms. Unlike in ordinary calculus there are many different ways to 'add up' terms.

## Operad theory and Koszul duality

The key objects that appear in my work on Goodwillie calculus are operads, and modules over them. Operads provide a way to keep track of complex collections of operations and how they interact. I have developed a geometric version of Ginzburg and Kapranov's 'Koszul' duality between the Lie and commutative operads.

## Tangent ∞-categories

The analogy between Goodwillie calculus and differential calculus of manifolds can be made precise via the theory of tangent categories and their ∞-categorical counterparts.

# Teaching

At Amherst College I have taught courses on calculus, analysis, topology, logic and Galois Theory, and also on math education and inequality. See my teaching page for more details.

# Previously

From 2008-2011, I was an Assistant Professor in the Math Department at the University of Georgia.

From 2005-2008, I was a J.J. Sylvester Assistant Professor at Johns Hopkins University.

I did my PhD at MIT and my undergraduate degree at Trinity College, Cambridge.

Before that I went to Oundle School and St. Faith's School, Cambridge.

Before that I grew up in Royston, Herts., UK.

## Michael Ching

Department of Mathematics and Statistics

Amherst College

PO Box 5000

Amherst, MA 01002

USA

Telephone: (413) 542-5530

Fax: (413) 542-2550

Email: mching@amherst.edu