Physics, Math, and CS blog

The double-centralizer theorem plays an important role in the modern theory of Hilbert space shattering. Here, I lay out the basics of the representation theory of semisimple algebras, prove the double centralizer theorem, and illustrate its application with Shur-Weyl duality. Lastly, I present a method for constructing the irreps of the symmetric group using the machinery of induced representations and Frobenius reciprocity.

In my undergrad stat mech class, I was fascinated by the fact that the Shannon entropy falls neatly out of the canonical ensemble. In this short review, I explore the content of this connection.

Here is a curious fact about the operator norm of the truncation of a matrix to the lower-left-triangle! This is based off an article by Rajendra Bhatia that I would recommend reading.

I am happy to report that I was a recipient of the FY 2025 NDSEG fellowship to support my research in quantum information dynamics! Although I found being a TA deeply fulfilling, I am excited for the opportunity to focus on research and looking forward to what we will uncover through this interesting new perspective on quantum dynamics in locally interacting quantum matter and the information processing capacity of quantum devices. If you are a prospective applicant, you can find my application materials attached!

I was inspired by this paper by Chao Yin to learn about the Schrieffer-Wolff transformation, which shows up in all sorts of areas of physics.