“Why did the two algebraic geometers get arrested at the airport? Because they were talking about blowing up six points on the plane.”

Anonymous

I spent my last week in Quebec attending the Canadian Undergraduate Mathematics Conference 2022. It was really an intense week of learning. I learned a lot and met many smart and interesting people. So I wanted to write about the things I learned and the people I met during the conference. There were so many excellent talks but unfortunately I could only attend some of them. In particular, there are some very good ones in geometry, topology, representation theory, algebra, logic theory, etc.

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Last week I gave a talk on the Canadian Undergraduate Mathematics Conference 2022 on Schubert calculus and cohomology of Grassmannians. Here are the slides of my talk.

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“Mathematics is the music of reason.”

James J. Sylvester

This week is the first week of the spring term and also my first week of undergraduate research with Prof. Satriano, so I decided to write about a research paper I’ve given to read, this one. In a nutshell, the paper proves a combinatorical conjecture posed by McKinnon, Satriano and Huang, about orbits on a hyperplane under permutation. Specifically, suppose that \(\sigma\in S_n\) acts on \(v\in\mathbf R^n\) by permutation, and let \(\mathcal{O}(v, w)=\{\sigma\in S_n: w\cdot \sigma v=0\}\). We prove a best bound for the number of vectors obtained by permutation of coordinates that are contained in a hyperplane through the origin except for \(\sum_ix_i=0\), where \(n\ge 3\). In notations, we have the following theorem.

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