Teaching

I am currently supervising:

-Fabian Lander, PhD Student (thesis expected 2027)

-Manvednra Somvanshi, Master Student (thesis expected 2025)

-Fernando Camacho Cadena, PhD Student (thesis expected 2025, co-adviserd with Anna Wienhard)

I have supervised:

-Fabian Lander, Master thesis on "Vertical foliations of triangulable dilation tori" January 2024

Leipzig

Here are notes on the ergodic theory of the geodesic and horocycle flows (updated as we go).

Heidelberg 2022-23

Here is the homepage for Introduction to Ergodic Theory for the Summer 2023 term.

I will be teaching a seminar course in geometry and dynamics on Lyapunov exponents and random matrix products for the 22-23 winter term.

I will be teaching a topics course in geometry on homogeneous dynamics on surfaces beginning June 14.

Yale Fall 2021

I taught two sections of MATH 115 (integral calculus).  

Heidelberg 2021

I am giving 6 RTG lectures during the 2021 summer semester on Aspects of Teichmüller-Thurston Theory.  Lecture notes will be posted here:

Lecture 1

Lecture 2

Lecture 3

Lecture 4

Lecture 5

Lecture 6

University of Utah

Here are the syllabi for courses I taught at the University of Utah.

• Spring 2018: Calculus I

• Spring 2017: Calculus I

• Fall 2015: Introduction to Statistical Inference

• Spring 2016: R Lab

Epsilon Camp

Epsilon Camp is two week long summer program for bright 9-11 year olds who love math.   Here is a description of the course I taught in 2017 and 2018.

Geometries:

In this course we study geometry in the plane beginning from axioms.  We emphasize theory, compass and straightedge constructions, and explore exotic geometric spaces.  We develop the geometry of the Euclidean plane and of the hyperbolic plane simultaneously, establishing some foundational results about triangle congruence, angle, and distance common to both geometries.  The theorems that are common to both geometries are known as neutral geometry.  At times, we add in the Euclidean axiom or the hyperbolic axiom for parallel lines.  We discover some very unusual properties of triangles in the hyperbolic plane and some very familiar properties of triangles in the Euclidean plane.  Highlights include proofs of Thales Theorem in Euclidean geometry and the Angle-Angle-Angle Triangle Congruence Theorem in hyperbolic geometry.  Detours to exotic geometric spaces include infinite graphs.  

Mathematics In Context

During the 2013-14 academic year, I ran a pilot program called Mathematics in Context (MIC) in the College of Natural Sciences at The University of Texas at Austin.  I worked  with Josh Beckham and Gwendolyn Stovall to introduce students participating in the Freshman Research Initiative (FRI) undergraduate research program in biochemistry to mathematical research.  The goal of the pilot program was to try to implement a sustainable model for students to ask and answer mathematical questions early on in their undergraduate career.  I worked with students who were working in the Aptamer research stream, where they developed short strands of ssDNA and RNA that could bind to target molecules.  I lead a small group of students who asked questions about the topology of DNA and DNA knotting.   

I helped write a book chapter about the FRI and the MIC pilot program.