Alp Uzman's Webpage

E-mail: uzman at math dot utah dot edu
CV: pdf (Last Revised: 07/18/23)
Research Statement: pdf (Last Revised: 10/14/22)
Teaching Statement: pdf (Last Revised: 10/14/22)

I am a mathematician specializing in dynamics, and I currently work as a postdoc at the University of Utah. I received my PhD from Penn State in May 2023 under the supervision of Prof. Federico Rodriguez Hertz. My current research focus is nonuniform measure rigidity. I am also interested in higher rank actions at large, as well as other dynamical areas like ergodic optimization and subriemannian dynamics.

I hold a B.Sc. in mathematics and B.A. in philosophy from Koc University in Istanbul, Turkey. My philosophical studies are currently dormant but broadly speaking I am interested in (Husserl-adjacent) phenomenology.

Time crystal

Papers:

Arithmeticity for Maximal Rank Positive Entropy Actions of R^k by Diffeomorphisms [A short presentation at the Penn State 2021 Workshop] [A poster presented at the Simons Center Flexibility and Rigidity Conference] [Notes from a talk given to a non-dynamical audience at the University of Utah] [Dissertation Version, also available at the Penn State Dissertation Repository] [The presentation of my dissertation defense] [Arxiv Version, also available on Arxiv]

Some Notes:

An exposition of Cawley's "The Teichmuller Space of the standard action of SL(2,Z) on T^2 is trivial"

In Spring 2021 Prof. Rodriguez Hertz gave a topics course at Penn State on rigidity. For the course I acted as the cameraman. I am preparing an associated set of lecture notes (see this Overleaf document for the current state). I also have good quality footage of all classes (except the first class) that needs to be edited. [Currently this project is on hiatus.]

Below are handwritten notes associated to some of expository talks I gave:

2022 CC Geometry and Lyapunov Spectrum Rigidity Part I and Part II associated to this and this talk,

2021 Smooth Ergodic Theory of Higher Rank Abelian Actions associated to this talk,

2021 Young's Explicit Examples of Nonuniformly Hyperbolic Cocycles that are not Uniformly Hyperbolic associated to this talk,

2020 Decay of Correlations in Random Dynamics associated to this talk,

2019 The Problem of the Non-Integrability of the Center Distributions of Partially Hyperbolic Diffeomorphisms associated to this talk,

2019 Grigorchuk Group associated to this talk,

2018 Property (T) Groups associated to this talk,

2018 Amenable Groups associated to this talk,

2017 Hofstadter's Butterfly associated to this talk.

Service:

In Summer 2023 I served as a mentor in DRP Turkey. There I gave an introductory talk on Latex and supervised a project on time changes in parabolic dynamics.

In Summer 2022 I served as a mentor in DRP Turkey. There I gave an introductory talk on Latex and supervised a project on the Hiraide-Lewowicz Theorem (which states that a homeomorphism of a closed connected orientable surface is expansive iff it's topologically conjugate to pseudo-Anosov).

From Fall 2017 until the end of Spring 2021 I was the leading organizer of the Dynamics Student Seminar at Penn State; my coorganizers were Nawaf Alansari and Ignacio Correa.