Jiahao Li

My name is Jiahao Li. Call me Justin.

I am an undergraduate Maths student at the University of British Columbia, Okanagan Campus. This is my website.

This statement include most of the academic background and interests I had during my undergraduate study

Research Interests

I am mainly interested in Homotopy Theoretic topics, such as Functor Calculus, Chromatic Homotopy Theory, Motivic Homotopy Theory, etc.

I am also interested in other topics such as Mathematical Quantum Physics, Mathematical Biology, Stochastic Processes, etc.

Papers

This is my research paper on the classifying space of homogeneous functors in manifold calculus. The main result of this paper shows that the classifying space of homogeneous functors over any manifolds is weakly equivalent to the classifying space of a simplicial monoid.

Presentations

This is the slide show for my presentation at the Mathematical Biology Research Group at UBCO on Geometric Quantization. It is the closing presentation for my directed study on Mathematical Quantum Physics under the supervision of Dr. Foxall at UBCO. It covers Hamiltonian mechanics on symplectic manifolds, basics in Quantum mechanics, and Geometric quantization, with each steps in the construction, prequantum line bundle, prequantization, polarization, half-form correction, and BKS construction explained.

This is the slide show for my presentation at the CMPS Undergraduate Research Conference, UBCO. This is the closing presentation for my research directed study under the supervision of Dr. Tsopméné at UBCO. Due to the background of the audiences, I have to sacrifice rigor and preciseness of my arguements for the understandability of the presentation. Therefore, many of the mathematical contents in the slideshow are inaccurate. The ones who are interested in the details should see my paper "On the Classifying Space of Homogeneous Functors".

My Own Learning Stuff

This is a website with my notes on chromatic homotopy theory, and how they interact with algebraic geometry. It is still updating. I also have a smaller note, Algebraic Geometry in Chromatic Homotopy Theory that this website intend to replace. The typed up notes contains contents such as localization, complex oriented cohomology, MU spectrum as universal complex orientation and formal group law, some algebraic geometry, formal groups, moduli stack of formal groups with the groupoid representation, chromatic layers E(n) as height filtration of p-local formal groups, Lubin-Tate theory of deformation of formal groups, and some K(n)-local theory

These are my answers to some of the practices in the book, starting at Chapter 2.

These are my answers to some of the practices in the book

My notes on OpenAI's proof of the finite generation of K(n)-local sphere.