• Hi!
    I'm Albert

    ▶ The background photo was taken at the Astronomical Observatory in Huairou, Beijing, 2017.

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  • I am
    a Homotopist

    "How about doing something equivariantly?"

    ▶ The background photo was taken in Chicago, 2018.

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About

Who Am I?

Hi! I'm Jinghui (Albert) Yang (杨景辉). You may pronounce my name as "Jeeng-whee."

I am a first-year PhD student in math at the University of Pennsylvania. Email: yangjh@sas.upenn.edu

I received my B.S. in math from the University of Illinois, Urbana-Champaign, May 2021, and my M.S. in math from the University of Oxford, Jul 2022 (Thesis: Homotopy Groups of Spheres in Homotopy Type Theory).

Here is my CV (Last modified: Dec 2023).

I am interested in the homotopy theory. In particular, I am interested in topics in algebraic K-theory, and chromatic/equivariant/motivic (stable) homotopy theory.



I was the co-organizer of the seminar on Homological Mirror Symmetry in Oxford, Jun-Sep 2022. See here.

Watch this funny video about Klein bottle made by myself!

Eastern Standard Time (EST)
My Specialty

My Skills

Before transferring to the math major, I was a student in CS major. Here are some of the programming languages I can master with a corresponding skill level visualized in the progress bar.

LaTeX

90%

Java

85%

HTML5

85%

Python

90%

C

80%

MATLAB

75%

I am super interested in the recent development of AIGC (though I intend no profession in this area). Feel free to blast my brain with ultra-exciting things you know about the related technology!

Education

Education

Ph.D. in Mathematics, University of Pennsylvania, Aug 2023-present.

Advisor (Expected): Mona Merling.

Penn Logo

M.S. in Mathematics, University of Oxford, Jul 2022.

Thesis: Homotopy Groups of Spheres in Homotopy Type Theory.

Oxford Logo

Research Experience for Undergraduates, University of Chicago, Jun 2020 - Oct 2020.

Advisors: Peter May, Hana Jia Kong.

Chicago Logo

B.S. in Mathematics, University of Illinois, Urbana-Champaign, Aug 2018 - May 2021.

I was awarded the Most Outstanding Student in Mathematics Major, Mar 2021. More Details...

UIUC Logo

I received my high school diploma from Hefei No.8 High School, Anhui, China. There, I spent three years and met my girlfriend.

Photo of my high school 1 Photo of my high school 2
Experience

Work Experience

Asset Management Intern Jun-Sep 2021

I was engaged in investment banking at the Department of Asset Management, Guoyuan Securities Co. The main task is to analyze market conditions, select the best investment portfolio for clients, and assist in managing various asset management projects. I created a program to analyze several indicators of private equity funds (such as the Sharpe ratio).

My Research

Active Events

  • Equivariant Homotopy Theory. Reading seminar at Penn, Spring 2024. Supervisor: Mona Merling.
    • I will give talks about the Intro to equivariant homotopy theory, Smith theory, slice spectral, Atiyah's Real K-theory, and possibly something else.
    • The typed notes and exercises are under construction.
  • Homotopy Theory Seminar. Seminar at Fudan University and SCMS, Fall 2023. Supervisor: Guozhen Wang.
    • I will give a talk about the J-homomorphism (Adams J(X) series) in Mar 14 & 21, 2024. Notes under construction.

Past Events

  • Topological Hochschild Homology and Trace Method. Reading seminar at Penn, Fall 2023. Supervisor: Mona Merling.
    • I will give a talk about the classical approach to the trace method on Nov 14. Handwritten Notes.
    • I wrote a very naive, explosive paper on this topic at the University of Chicago, 2020. It is for someone who knows very little of this stuff. You can have a look here.
  • Algebraic K-theory. Reading seminar at Penn, Fall 2023. See this webpage: Math 999: Algebraic K-theory. All topics and notes are collected on the webpage.
  • Algebraic K-theory. Seminar at Fudan University and SCMS, Spring 2023. Supervisor: Guozhen Wang.
    • I will give a talk about the universal characterization of algebraic K-theory. (canceled due to personal reason)
  • Chromatic Homotopy Theory. Seminar at Fudan University and SCMS, Fall 2022. Supervisor: Guozhen Wang. You can review here.(last updated: Dec 30, 2022)
  • Prismatic Cohomology. Fall 2022. See my notes here.
  • Advanced Algebraic Topology. Fall 2022. See my notes here (last updated: Dec 27, 2022).
Read

Talks

  • The Trace Method in Algebraic K-theory, Nov 2023. BUGCAT conference, Binghamton University. slides here.
  • A Taste of Bott Periodicity, Dec 2019. pdf here.
  • Intro to Turán’s Method, Nov 2019.
    This is about Turán’s method towards exponential sum, based on Chapter 5 of Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis by Hugh L. Montgomery. No typed pdf available.
  • Kuratowski 14-Sets Theorem and Related Classifications of Topological Spaces via K-numbers, Oct 2019. No typed pdf, but you may find info here.
  • The Number N(T) and N(T, χ), Mar 2019. pdf here.
  • Perron’s Formula, Nov 2018. pdf here.


Writings



Quick Links

Art Gallery

Astrophotography

I am a big fan of astronomy. Previously, I was the president of the astronomy club at the university. Below are some photographs (taken by members) of the observation of the Gemini Meteor Shower in Huairou, Beijing, organized by me in Dec 2017.

Orion

Taken by Yang An

Overview

Taken by Yifei Li, Chen Chen, Daixi Jia

Overview

Taken by Dan Yang

Orion

Taken by Chen Huang

Meteor Shower

Taken by Ziyang Chen

Overview

Taken by Wenxin Pan, Tianren Luo
Get in Touch

Contact

yangjh@sas.upenn.edu

David Rittenhouse Laboratory, 209 S 33rd St, Philadelphia, PA 19104, United States

+86 185 5511 5286

+1 304-992-4866