Jonathan Passant

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Graduate Student
Advisor: Alex Iosevich
Office 710 Hylan
E-mail: jpassant at ur dot rochester period edu

My CV

Here is my CV.

Research

My research interests lie in the areas of geometric combinatorics, geometric incidence theory and geometric measure theory. In particular questions that arise from studying the structures of discrete point sets in real spaces. I have focused on a graphical variant of the Erd\H os distance problem, using incidence structures in higher dimensions. This has included using Fourier techniques that advanced the Falconer Conjecture to prove more general distance results in places out of reach of the current discrete methods. My future work will involve the interplay of techniques in finite fields, the Euclidean setting and Erd\H{o}s problems, using the latest breakthroughs to advance results in all settings.

Discrete geometry has also allowed me many opportunities to lead undergraduate research, particularly as the vast advances over the last decade have left many areas needing to be tackled with modern techniques. Such an effort in the Polymath REU over the last summer lead to a nice paper.

Please also see my research statement.

My publications

  1. Finite Point Configurations In The Plane, Rigidity And Erdős Problems, joint with Alex Iosevich. Published in J. Proc. Steklov Inst. Math. (2018) 303: 129, arXiv Link.

  2. On Erdős Chains in the Plane, arXiv Link, submitted.

  3. Distinct Distances from Points on a Circle to a Generic Set, joint with Alex McDonald, Brian McDonald and Anurag Sahay, arXiv Link, submitted.

  4. A multi-parameter variant of the Erdős distance problem (2017), joint with Alex Iosevich and Maria Janczak, arXiv Link.

Teaching

My teaching priorities are to ensure students are comfortable speaking up in lectures; to build their mathematical confidence and independence; and to be approachable for struggling students. As I near the completion of my PhD, I am looking forward to new teaching challenges, in particular having more responsibility to develop courses and teaching more challenging content.

Please read my teaching statement for more deatiled information on my approches, impacts and future plans. Please refer to my CV to see the courses I have taught. You can see my evaluations for the courses I have instructed at the bottom of this section.

Teaching Materials

See the tables below for samples of teaching materials I have developed. If you have questions or spot any typos please let me know.

Homework I wrote for a linear algebra and differential equation class.

Written Homework                      
MTH165 Written Homework 1 2 3 4 5 6 7 8 9 10 11

Scans of lecture notes. Scans are made available to students who miss class or need additional time to write.

Lecture Notes                    
MTH143 Lecture Notes Parametric Equations Polar Coordinates Sequences Series Integral Test Comparison Tests Alternating Series Test Root and Ratio Tests    
Power Series Representing Functions as Power Series Recap of Power Series Taylor and Maclaurin Series Taylor Series (Continued) Taylor Polynomials Final Review (Part B only) Midterm 1 Review Midterm 2 Review    

Notes provided for additional clarification on a topic.

Explainers  
An explainer of Geometric Series and Power series  
Series Tests Flow Chart  

Student Evaluations

Here are my student evaluations for the courses that I have been the instructor. Evaluations where I have been a Teaching assistant are available upon request.

Course Code Course Name Term Taught Report Comments
MTH141 Calculus 1 Summer ‘17 Report Comments
MTH142 Calculus 2 Spring ‘18 Report Comments
MTH150 Discrete Mathematics Fall ‘18 Report Comments
MTH165 Linear Alg. & Diff. Eqns. Summer ‘18 Report Comments
MTH143 Calculus 3 Spring ‘19 Report Comments
MTH165 Linear Alg. & Diff. Eqns. Summer ‘19 Report Comments
MTH161 Calculus 1A Fall ‘19 Report Comments
MTH161 Calculus 2A Spring ‘20 Report Comments