Howard Xiao

I'm an incoming fourth year undergraduate student at University of Toronto.

I am currently working with Toronto Computational Imaging Group (TCIG) under Prof. Kyros Kutulakos and Prof. David Lindell. I'm currently doing research in the area of ultra-wideband single photon imaging.

I am also working with Prof. Boris Khesin at University of Toronto and Prof. Anton Izosimov at University of Arizona, in the area of Lie groupoids and Lie algebroids. On a related area of finite Lie Theory, I'm exploring with Prof. Eckhard Meinrenken from University of Toronto.

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Some Bio & Updates

I've spent quite some years of my childhood in Tianjin, China. I love the culture, the food and above all, the tea there.

Please see below to check out a recent code release for ICCV 2023's best paper Passive Ultra-wideband Single Photon Imaging!

In Fall 2024, I will be TA-ing for MAT240H1: Algebra I at University of Toronto, St. George campus.

I joined Dynamics Graphic Project of Toronto Computational Imaging Group (TCIG) since September, 2023. I received the Undergraduate Student Research Awards (USRA) from NSERC Canada for summer 2024.

In May, 2024, I completed a full year internship at Bell Canada as a software developer, completeing the university's internship program ASIP.

In spring 2024, I was a TA for MAT247H1: Algebra II course at University of Toronto, St. George campus with Prof. Eckhard Meinrenken.

From September 2023 to April 2024, I was also working with Prof. Almut Burchard in a project involving Steiner Symmetrizations.

Research

Broadly speaking, my current research interest is understanding the geometry of everything around us and of abstract mathematical structures. I believe computational imaging contributes more to the first part, while Lie theory contributes more to the second.

In general, I am interested in providing concrete mathematical principles together with cool computational imaging possibilities.

Projects

In short, I haven't published anything so far. However, there's some work in progress. There are some ongoing imaging projects not listed below too. This will be updated in the near future.

Code pipeline taking in an increasing stream of photon timestamps captured by unsynchronized single-photon avalanche diode (SPAD), and completes steps of ultra-wideband probing, frequency thresholding and 1-dimensional flux reconstruction for multiple asynchronous periodic sources (unsynchronized picosecond lasers, projectors, etc.)

Compute cocycle of central extensions on Virasoro Groupoid and Virasoro Algebroid, use it to find Poisson structure, and possibly interesting solutions to several equations like KdV.

Maximal Tori in Apposition for classical Lie groups.