# Clinton Conley

## Associate Professor, Director of Graduate Studies

**Address:**

7113 Wean Hall

Department of Mathematical Sciences

Carnegie Mellon University

5000 Forbes Avenue

Pittsburgh, PA 15213

412-268-2545

# Education

Ph.D. in Mathematics, University of California, Los Angeles

Postdoctoral Appointments:

- KGRC (Kurt Gödel Research Center), Vienna, Austria
- Cornell University

# Awards

- Julius Ashkin Award

# Research

I work in descriptive set theory, which is the study of how the ability to define a set (say of real numbers) confers useful information about its mathematical properties. Restricting your attention to definable sets rather than arbitrary sets can have counterintuitive consequences: sets can be partitioned into more pieces than there are elements in the original set, acyclic graphs can be hard to color, etc.

My specific work focuses on equivalence relations arising from measurable group actions or measurable graphs. Ergodic-theoretic properties of the group actions and combinatorial properties of the graphs often translate into set-theoretic properties of the induced equivalence relation. Thus, the area sits at the intersection of set theory, dynamics, and combinatorics.

# Select Publications

Conley, C.T. and Kechris, A.S. (2013). Measurable chromatic and independence numbers for ergodic graphs and group actions.

Clemens, J.D., Conley, C.T., Miller, B.D. (2016). The smooth ideal.

Conley, C.T., Marks, A.S., Tucker-Drob, R.D. (2016). Brooks' theorem for measurable colorings.

*Groups Geom. Dyn.,*7 (1), 127–180.Clemens, J.D., Conley, C.T., Miller, B.D. (2016). The smooth ideal.

*Proc. Lond. Math. Soc. (3),*112 (1), 57–80.Conley, C.T., Marks, A.S., Tucker-Drob, R.D. (2016). Brooks' theorem for measurable colorings.

*Forum Math. Sigma,*4 (16), 23.
Conley, C.T. and Miller, B.D. (2017). Measure reducibility of countable Borel equivalence relations.

Conley, C.T., Jackson, S.C., Kerr, D., Marks, A.S, Seward, B., and Tucker-Drob, R.D. (2018). Følner tilings for actions of amenable groups.

*Ann. of Math. (2),*185 (2), 347–402.Conley, C.T., Jackson, S.C., Kerr, D., Marks, A.S, Seward, B., and Tucker-Drob, R.D. (2018). Følner tilings for actions of amenable groups.

*Math. Ann,*371 (1-2), 663–683.