Graduate Student

Department of Mathematics, UCLA

**Office:** MS 5351. I am more or less never there.

**Email:** smmiller@ucla.edu. Feel free to email me! I get surprisingly little spam.

I'm a fifth year graduate student. I mostly do gauge theory and its applications to low-dimensional (3+1) topology and differential geometry.

My advisor is Ciprian Manolescu.

**Publications**

**Equivariant instanton homology** ~ in preparation ~ draft as of 2/12/19 ~ comments welcome!

This is an essentially final draft. I expect an arXiv submission sometime between March 2019 and August 2073.

In this paper I develop some analysis of instanton moduli spaces, and present algebra related to the equivariant (co)homology of differential graded algebras and their modules.

Using these tools, I define four invariants of rational homology spheres that deserve to be called "equivariant instanton homology" and have some formal properties similar to those seen in Heegaard Floer and monopole Floer homology.

**Teaching**

I use StackExchange:

Image by Ryan Armand.

Department of Mathematics, UCLA

I'm a fifth year graduate student. I mostly do gauge theory and its applications to low-dimensional (3+1) topology and differential geometry.

My advisor is Ciprian Manolescu.

This is an essentially final draft. I expect an arXiv submission sometime between March 2019 and August 2073.

In this paper I develop some analysis of instanton moduli spaces, and present algebra related to the equivariant (co)homology of differential graded algebras and their modules.

Using these tools, I define four invariants of rational homology spheres that deserve to be called "equivariant instanton homology" and have some formal properties similar to those seen in Heegaard Floer and monopole Floer homology.

- Winter 2018: Math 123, Foundations of Geometry, with Marco Marengon

- Fall 2017: Math 32A, Multivariable Calculus, with Gang Liu

Math 225A, Differential Topology, with Ciprian Manolescu

- Winter 2017: Math 225B, Differential Geometry, with Ko Honda
- Fall 2016: Math 225A, Differential Topology, with Ko Honda
- Spring 2016: Math 225C, Algebraic Topology, with Ko Honda

- Winter 2016: Math 225B, Differential Geometry, with Kefeng Liu

- Fall 2015: Math 32A, Multivariable Calculus, with Lincoln Chayes

Math 225A, Differential Topology, with Ko Honda

- Summer 2015: Math 170B, Probability Theory II, with Sungjin Kim
- Spring 2015: Math 132, Complex Analysis, with Jesse Burke
- Winter 2015: Math 33A, Linear Algebra and Applications, with Tova Brown
- Fall 2014: Math 31B, Integration and Infinite Series, with Tova Brown

I use StackExchange:

Image by Ryan Armand.