Shang-Chun YU Curriculum Vitae

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Email puch40316+cv@gmail.com
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Maths graduate from ENS de Lyon, I am passionate about mathematics, IT, linguistics and design. I have a solid background in mathematics and am specialised in probability theory and quantum information theory. I am also very interested in maching learning, data science and web development. Enjoy working in a team and can also work independently.


École normale supérieure de Lyon, France
Normalien élève
Diploma of ENS, Mathematics
Diploma of ENS explained
Four years of study to obtain the Diploma of ENS:
  • 1st year: obtained the BSc in Mathematics
  • 3rd year: obtained the Msc in Advanced Mathematics
  • Final year: obtained the Diploma of ENS

During the final year, I did two research internships at TUM (Munich, Germany) and then at ICJ (Villeurbanne Lyon, France), where I learned higher-order quantum information theory (theoratical mathematics) and developed some results with probabilistic methods and representation theory.

In case you are interested, here are the courses I did at ENS:

1st year
  • Algebra
  • Complex Analysis
  • Measure Theory and Integration
  • Topology
  • Differential Calculus
  • Analysis and PDE
  • Probability Theory
  • Optimal Control Theory
2nd year (1st year of Master)
  • Advanced Algebra (Module Theory, Ring Theory)
  • Advanced Analysis (Functional Analysis, Distribution Theory, Spectral Theory)
  • Advanced Geometry (Differential Manifold)
  • Advanced Probability (Martingale, Markov Chain)
  • Stochastic Process (Brownian Motion)
  • Riemann Surface
  • Set Theory and Model Theory
  • Statistics
3rd year (2nd year of Master)
  • Stochastic Calculus - Emmanuel Jacob
  • Maching Learning - Aurélien Garivier
  • Statistic Physics (Percolation, Ising Model) - Oriane Blondel
  • Random Walks on Graphs - Grégory Miermont
  • Phenomena of Large Dimensions (Concentration of Measure) - Guillaume Aubrun
École normale supérieure de Lyon
Master of Science (MSc), Advanced Mathematics
Specialised in Probability Theory in the 2nd year of Master
École normale supérieure de Lyon
Bachelor of Science (BSc), Mathematics
Lycée Janson de Sailly, Paris, France
Scientific CPGE - MPSI, MP*
CPGE explained
CPGE, or Classe préparatoire aux grandes écoles, is a two-year intensive programme to prepare for the nationwide competitive exams to Grandes Écoles in France.

I did MPSI and MP* classes:
  • MPSI: mathematics, physics, informatics and engineering science (1st year)
  • MP* (MP star): mathematics, physics and informatics (2nd year)
Then was admitted by competition to l'ENS de Lyon and l'École Polytechnique.

Research experience

Weak approximate higher-order unitary designs
March 2020 - July 2020
with Guillaume Aubrun, Institut Camille Jordan (ICJ) - Lyon, France
I developed a mathematical framework (hierarchical structure) for higher-order (HO) objects in quantum information theory, such as HO twirling channels, HO designs and HO diamond norms, and generalised a super twirling channel approximation theorem to the whole quantum hierarchical structure using unitary group representation theory.
Super channels, higher-order quantum theory
October 2019 - March 2020
with Dr. Michael M. Wolf, Mathematics Centre M5, TUM - Munich, Germany
I first learned the basics of quantum mechanics and quantum channels, then studied super quantum channels and higher-order quantum theory.

I generalised common notions such as restriction, purification, and entropy to higher-order quantum objects, and also established the generalised purification theorem.

Eigenvalues of polynomials in random permutation matrices and their tensor product
April 2019 - July 2019
with Alice Guionnet, UMPA - Lyon, France
I studied the spectrum convergence of certain operators involving tensor products of random permutation matrices. In particular, I studied non-backtracking operator theory and trace methods.

Additionally, I had discussions with Charles Bordenave, the co-author of an article I read, and was later invited to a conference he organised at CIRM.

Random quantum circuits
May 2018 - June 2018
with Guillaume Aubrun, Institut Camille Jordan (ICJ) - Lyon, France

I studied papers about local random quantum circuits and unitary designs, and learned Haar measures, partial traces and path coupling techniques for random walks on unitary operators (probability theory).


Quantum spectrum estimation
May 2020
Quantum seminar, Lyon Quantum Information Group

I gave a talk on the spectrum estimation problem in quantum information theory with some representation theory. Here are the slides for the talk.

Volunteer experience

Dissemination of mathematics in secondary school
April 2018
At Collège Gabriel Rosset, organised by MathàLyon

I guided secondary school students in several hands-on mathematics experiments, with an aim to raise their interest in mathematics: helping them find solutions on their own, showing them mathematics can be interesting and fun, etc. It was a meaningful experience for me.

Here is a report (in French).


FISH UP Dictionary of Array
July 2020 - Present
Best website to learn and practice Array
What is Array?

Array is a free of license, open-source, shape-based Chinese input method, which is extremely easy to learn and is also the fastest free Chinese input method.

I built the best website to teach and promote Array by offering:

  • Best Array dictionary
  • Best Chinese typing practice website
  • Best Array tutorial... to name a few

Website available in English, French and traditional Chinese (Vue.js/python).

2k-3k visitors per month, and received many words of thanks and appreciation.

Very well ranked on Google, first result in Chinese language.

Daily Digest - COVID-19 IN FRANCE
January 2021 - Present
Daily Digest of COVID-19 in France: COVID-19 statistics and news

I built this website that presents daily COVID-19 statistics and news in France in the form of a daily digest.

Website available in traditional Chinese, simplified Chinese, English and French (React/python/Figma).

Shang-Chun YU's CV
February 2021 - Present
Aka what you are reading - Enjoy the dark mode I made (and many other ones)!


Ranked 1st for PhD Scholarship in Mathematics
For PhD Scholarship in Mathematics in Université Lyon 1
Asian International Teenagers Mathematical Olympiad
Represented Taiwan, won the Gold medal


Several years of experience in English-French translation in the scientific field
Also specialised in phonetics and phonology (pronounciation)

proficient English, French, Mandarin Chinese

learning German (A2-B1), Turkish (A1-A2)

others Japanese (A2-B1), Spanish (A1)

Tools & Technologies
I keep learning new things everyday.

prog. languages c++, javascript/typescript, python, rust

data science python, SQL

front-end css/sass, html, javascript/typescript, jquery, React.js, Vue.js, webpack

Marketing google analytics, google search console, SEO

productivity git, latex, vim


probability measure theory, probability theory, martingale, Brownian motion, stochastic process

analysis topology, real analysis, complex analysis, differential calculus

quantum information higher-order quantum theory, weak approximate design, twirling quantum channel