Alp Uzman's Webpage

Alp Uzman's Webpage

Alp Uzman photo

[This website is last updated on 2025-11-06 14:25:56.]

E-mail: uzman dot ali alp at gmail dot com
or uzman at math dot utah dot edu
CV: pdf [Last Updated: 10/30/25]
Teaching Statement: pdf [Last Updated: 10/30/25]
Research Statement: pdf [Last Updated: 10/30/25]
Youtube: https://www.youtube.com/@alpuzman

I am a mathematician specializing in dynamics, and I currently work as a postdoc at the University of Utah. Here my postdoc supervisor is Prof. Kurt Vinhage. I received my PhD from Penn State in May 2023 under the supervision of Prof. Federico Rodriguez Hertz. I hold a B.Sc. in mathematics and B.A. in philosophy from Koc University in Istanbul, Turkey.

I consider teaching mathematics to be my craft, and while I have been primarily a research mathematician so far, my long-term career goal is to transition to a position centered on teaching and guiding undergraduate research.

My current research focus is smooth actions of compactly generated abelian Lie groups with some hyperbolicity. I am also interested in higher rank actions at large, as well as other dynamical areas like thermodynamic formalism, ergodic optimization and subriemannian dynamics.

In terms of philosophy I am interested in the problem of time, as well as the development of what I like to provisionally call dynamical phenomenology, a framework adjacent to Husserlian genetic phenomenology.

Teaching:

U of Utah Math 3220 - Foundations of Analysis II:
annotated lecture videos (Youtube),
all course materials (Github repo)
U of Utah Math 3210 - Foundations of Analysis I:
annotated lecture videos (Youtube),
all course materials (Github repo)
U of Utah Math 4800 - Undergraduate Research in Mathematics - Fractal Geometry and Dynamics:
annotated lecture videos (Youtube),
all course materials (Github repo)
U of Utah Math 2270 - Linear Algebra:
annotated lecture videos (Youtube),
all course materials (Github repo)
U of Utah Math 2250 - Differential Equations and Linear Algebra:
all course materials (Github repo)
Penn State Math 251 - Ordinary and Partial Differential Equations:
the harmonic oscillator with periodic forcing and beats (notes),
a long-winded application of the method of undetermined coefficients (notes),
the Laplace transform (notes),
linear PDE and Fourier Series (notes),
the brachistochrone problem (notes),
the solutions of the general second order linear constant coefficient homogeneous ODES (Desmos graph),
linearizations of the logistic equation (Desmos graph),
the Laplace transform (Desmos graph),
even and odd extensions and the Fourier series (Desmos graph)
Penn State Math 230 - Calculus and Vector Analysis:
analytic geometry (notes),
calculus of single variable vector valued functions (notes),
differential calculus of multivariable functions (notes),
integral calculus of multivariable functions (notes)
Penn State Math 036 - Insights into Mathematics:
coding (notes),
Halmos' "Mathematics as a Creative Art" (study questions),
Manin's "Mathematics as Metaphor" (study questions),
Weyl's Symmetry (study questions)
Penn State Math 022 - College Algebra II:
sets, logic, relations, and functions (notes)

Service:

In Summer 2025 I served as an organizer in DRP Turkey. Besides organizational matters I also gave an introductory talk on Latex and edited and annotated the colloquium and symposium talks.
In Spring 2025 I served as a mentor in the Introduction to Research program at the U of Utah. There I supervised Andrew Garzella on the ergodicity of the geodesic flow on the unit tangent bundle of a negatively curved closed surface.
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.

Research:

Higher Rank Plante Alternative joint with Kurt Vinhage, in preparation
Fragility of Rank One Factors joint with Kurt Vinhage, in preparation
Fried Average Entropy for Actions of Nilpotent Groups in preparation
2023 Arithmeticity for Smooth Maximal Rank Positive Entropy Actions of R^k Submitted to JMD, under review Dissertation Version, Arxiv

Expository:

2025 annotated lecture videos of Prof. Rodriguez Hertz' 2021 topics course at Penn State on rigidity
2024 notes on Cawley's "The Teichmuller Space of the standard action of SL(2,Z) on T^2 is trivial"
2022 notes on CC Geometry and Lyapunov Spectrum Rigidity Part I and Part II associated to this and this talk,
2021 notes on Smooth Ergodic Theory of Higher Rank Abelian Actions associated to this talk,
2021 notes on Young's Explicit Examples of Nonuniformly Hyperbolic Cocycles that are not Uniformly Hyperbolic associated to this talk,
2020 notes on 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 notes on Grigorchuk Group associated to this talk,
2018 notes on Property (T) Groups associated to this talk,
2018 notes on Amenable Groups associated to this talk,
2017 notes on Hofstadter's Butterfly associated to this talk.

Some Desmos Graphs:

Links: