# Michael Hopkins gives MSCS Distinguished Lectures March 5-7

Michael Hopkins (Harvard) will give the MSCS Distinguished Lectures on March 5-7.

Michael Hopkins has been a major leader in algebraic topology and homotopy theory and his work has links to elliptic curves and modular forms in number theory, and to string theory in physics. Michael Hopkins, (B.A. Northwestern University 1979, Rhodes Scholar, D.Phil., Oxford University 1984 and Ph.D., Northwestern 1984) received the AMS Veblen Prize in Geometry in 2001; and in 2012, he received the National Academy of Sciences Award in Mathematics for his work on algebraic topology leading to the resolution of the Kervaire invariant problem for framed manifolds. He has held faculty positions at Princeton University, University of Chicago, and MIT. Since 2005, he has been a professor of Mathematics at Harvard University.

#### Lecture 1: Wednesday March 5, 4:00 pm, BSB 250

**Invariants as the engine for mathematics**

This is a Public Lecture aimed at a broad audience. All are welcome. A reception will follow.

Abstract: In mathematics and in science an "invariant" of a system is a quantity, like the total energy, that does not change as the system evolves. The discovery and understanding of invariants is a significant part of what drives the development of mathematics. In this talk I will describe some simple mathematical invariants and the deep mathematics that has evolved from trying to understand them.

#### Lecture 2: Thursday, March 6, 4:00 pm, Lecture Center D5

**The Kervaire Invariant**

Abstract: The Kervaire invariant is subtle and important invariant lying at the interface of algebraic and differential topology. I will describe the history of this invariant, the problem it raised, and its eventual solution.

#### Lecture 3: Friday March 7, 3:00pm, Lecture Center D5

**Chern-Weil invariants and abstract homotopy theory**

Tea to follow in SEO 300.

Abstract: Nature does not come to us with a coordinate system. In writing down the equations describing the evolution of physical systems, it is therefore important that the mathematical entities that arise do not depend on a choice of coordinates. The Chern-Weil invariants are important examples of such entities. In this talk I will explain the Chern-Weil invariants and how one is led by by thinking carefully about them to modern day abstract homotopy theory.

Here is the poster for the series.

**October 28, 2020**