• ## Drew Heard

I am a third year graduate student studying mathematics at Melbourne University. My advisor is Craig Westerland. I am broadly interested in stable homotopy theory with a particular interest in chromatic homotopy theory. Currently I am thinking about the $$K(n)$$-local homotopy category, in particular the construction of so called exotic elements of the Picard group. See the research page for more information.

Update: New paper uploaded to the arxiv.

• ## Notes and Papers

Note that these notes are very rough, and may (indeed do) contain errors and simplifications introduced by me. Please keep this in mind.

GHMR Resolution: Slightly expanded version of the talk I gave at the 2013 Talbot on the Goerss-Henn-Mahowald-Rezk resolution of the $$K(2)$$-local sphere at the prime 3.

The Tate spectrum of higher real $$K$$-theories: Draft of a calulcation that shows that the Tate spectrum associated to $$EO_{p-1}$$ vanishes at height $$n=p-1$$.

## Preprints

$$K$$-theory, reality and duality . Joint with Vesna Stojanoska. We calculate the Anderson dual of $$KO$$, and give an algebro-geometric interpretation of this result. Last modified: 14/01/14

Here are some links to fellow algebraic topologists: Aaron Mazel-Gee Craig Westerland Dylan Wilson Eric Peterson Jon Beardsley Kyle Ormsby Mark Behrens Mike Catanzaro Sean Tilson TriThang Tran Vesna Stojanoska Vitaly Lorman
• ## Research

The $$K(n)$$-local stable homotopy category is symmetric monoidal under the $$K(n)$$-local smash product, and hence we can study its group of invertible elements, known as the Picard group, denoted $$\text{Pic}_n$$. This admits a cohomological approximation, $$\text{Pic}_n^\text{alg}$$ much like the Picard group of a scheme, and there is a natural map  $$\text{Pic}_n \to \text{Pic}_n^\text{alg}$$. The kernel of this map forms the group of exotic elements $$\kappa_n$$. In general not much is known about these groups; for a fixed $$n$$ it is known they vanish for large primes and further information is known at $$n=1,2$$. My work involves producing some exotic elements at height $$n=p-1$$, using the methods of Goerss-Henn-Rezk.

I also have various other interests in the stable homotopy category including various forms of duality, the Brauer group of the $$K(n)$$-local category and general compuational methods in homotopy theory.

• ## Contact

### Drew Heard

Richard Berry Building
Melbourne University
Victoria, Australia

E-mail: