About Me
Hello! I'm Zichao Wang, and feel free to call me Franklin—after my favorite American historical figure, Benjamin Franklin. I am becoming a passionate research mathematician, currently in my first year of the Ph.D. program in Mathematics at Auburn University.
My academic journey began at Inner Mongolia University in Hohhot, where I studied Mathematics and physics. Recently, I earned my M.S. in Mathematics from Auburn University in 2024, graduating with a perfect GPA of 4.0.
I have a deep love for doing math, teaching math, and sharing math with others. My goal is to join the community of mathematicians and make meaningful contributions to the field. I am driven by the excitement of discovery, the challenge of solving problems, and the desire to leave a lasting impact through my research and dedication.
Research Interests
"The beauty of mathematics only shows itself to more patient followers." — Maryam Mirzakhani
As a first-year Ph.D. student, I am laying the groundwork for advanced research in algebraic geometry. My fascination with algebraic geometry was sparked while studying Dr. Hal Schenck's Computational Algebraic Geometry, and following Dr. Michael Brown's advice, I came to realize that algebraic geometry is an evolving field with significant potential for future developments. Moreover, it built upon the commutative algebra—a subject a subject I greatly enjoy.
Currently, I am engaged in studying commutative algebra under the guidance of Dr. Michael Brown, which is providing me with essential tools for my future research. At the same time, I am pursuing autodidactic study of Commutative Algebra by David Eisenbud to deepen my understanding. Next semester, I plan to delve into homological algebra with Dr. Prashanth Sridhar to further develop my mathematical toolkit. Following that, I aim to spend a year studying algebraic geometry using Robin Hartshorne's Algebraic Geometry (GTM 52), and here is a guide by the recommendations of Professor Botong Wang from University of Wisconsin-Madison and I have translated it to English—Some Suggestions for Reading GTM 52.
My interest in topology was nurtured by courses taught by Dr. Hannah Alpert, which led me to pursue my master's thesis in the field Computational Topology under the supervision of Dr. Ziqin Feng. Currently, I am collaborating with Ph.D. students Ian Tan and Mauricio Montes on studying topological data analysis, following the book Computational Topology for Data Analysis by Tamal Dey and Yusu Wang.
Paper
"We are continually faced with a series of great opportunities brilliantly disguised as insoluble problems." — John W. Gardner
- Wang, Z. (2024). Lower Bounds for Betti Numbers in Vietoris–Rips Complexes of Hypercubes. Master's Thesis, Auburn University. Advisor: Dr. Ziqin Feng.
In this thesis, I presented and analyzed the work of Henry Adams and Žiga Virk on new lower bounds for Betti numbers in Vietoris–Rips complexes of hypercube graphs across all dimensions and scales and corrected inaccuraies in their formula formulations.
Tutoring
"If you want to master something, teach it. Teaching is a powerful tool to learning." — Richard Feynman
I have served as a teaching assistant for the following courses at Auburn University:
- Linear Differential Equations (MATH 2650)
- Topics in Linear Algebra ( MATH 2660)
- Probablity and Statistics II (STAT 3610)
Recommended Resources
"君子生非异也，善假于物也。" — 荀子
Here are some resources that I highly recommend:
- Computational Algebraic Topology by Dr. Vidit Nanda - Dr. Vidit Nanda is a Professor of Mathematics at the University of Oxford. His lecture notes and Zoom recordings on computational algebraic topology were immensely helpful when I was writing my master's thesis.
- Richard E. Borcherds' YouTube Channel - Richard E. Borcherds is a Fields Medalist, and his channel is a true master class. I often watch his lectures on number theory and commutative algebra.
- Immersive Translate - A tool that integrates OpenAI's ChatGPT API to assist in translating content, including newspapers and YouTube videos. It enables access to foreign news in languages such as Hebrew and Chinese, breaking through information barriers and broadening perspectives.
Contact
"No man is an island, Entire of itself; Every man is a piece of the continent, A part of the main." — John Donne
If you would like to get in touch, please use the following contact information:
- Email: zzw0109@auburn.edu
- Office: 136 G, Department of Mathematics, Auburn University
You can also download my CV here: Download CV
Coursework
"There's Only One Thing To Do: Learn All We Can!" — Dorothy Vaughan
Below is a list of my M.S. and Ph.D coursework at Auburn University.
Fall 2024 (Ph.D First Year)
- Ring Theory
- Introduction To Commutative Algebra by M. F. Atiyah and I. G. MacDonald
- Topology I
- No Textbook
- Number Theory
- Number Theory Through Inquiry by David C. Marshall, Edward Odell, and Michael Starbird
Summer 2024 (Ph.D First Year)
- Computational Algebraic Geometry
- Computational Algebraic Geometry by Hal Schenck
Spring 2024 (M.S. Second Year)
- Algebra II
- Algebra 2nd Edition by Michael Artin
- Analysis II
- Real Analysis 2nd Edition by Gerald B. Folland
- Research And Thesis
- This course is dedicated to the completion of my master’s thesis
Fall 2023 (M.S. Second Year)
- Algebra I
- Algebra 2nd Edition by Michael Artin
- Analysis I
- Real Analysis 2nd Edition by Gerald B. Folland
- Introduction To Topology
- Topology Through Inquiry by Michael Starbird and Francis Su
Spring 2023 (M.S. First Year)
- Analysis II
- Introduction to Real Analysis 3rd Edition by Robert G. Bartle and Donald R. Sherbert
- Introduction To Abstract Algebra II
- A First Course in Abstract Algebra 8th Edition by John B. Fraleigh and Neal Brand
- The Art Of Presenting, Advanced Oral Communications
- No textbook
- Writting Proficiency In English For International Students
- No textbook
Fall 2022 (M.S. First Year)
- Analysis I
- Introduction to Real Analysis 3rd Edition by Robert G. Bartle and Donald R. Sherbert
- Introduction To Abstract Algebra I
- A First Course in Abstract Algebra 8th Edition by John B. Fraleigh and Neal Brand
- Eenglish For Professional Purposes
- No textbook