Recently, I collected a short list of phrases for conjectures on a well-known social media platform and several people contributed to it. One can easily find more examples online, but I like my list, so I will keep it here and include references (as far as I have them). Probably, I will add more entries over time.
Firstly, I will give a list of phrases. Secondly, references for the phrases.
At the moment I am very busy writing things like grant applications and research papers, so I lack the time for blog posts. But then I wasted part of my evening reading this article on FiveThiryEight about the Democratic Party primaries in the US. For each democratic primary contender, they provide the following data:
- How many of their current supporter do not consider voting for another candidate. For instance for Biden this number is 21.9%, while for Buttigieg it is only 6.2%.
- Which other candidates their supporter are considering. For instance 52.2% of Biden’s supporter also consider Warren, 39.2% Sanders, 28.9% Harris, and 24.8% Buttigieg.
I spent the last few days in vain using several spectral arguments to bound the size of certain intersection problems. For instance what is the largest set of vectors in pairwise at Hamming distance at most (a problem solved by Kleitman, recently investigated by Huang, Klurman and Pohoata). Here the answer is and , , , , would be such an example. Or the largest set of vectors in pairwise at distance or . Here the answer is and an example is , , , , , , , . This is a problem which I recently investigated together with Hajime Tanaka, extending work by Frankl and others.
Usually, this playing around does not lead to anything. But this time …. It is actually the same. However, I did one useful thing which is the following: Generously counting, I do know five different easy spectral arguments which can be used to investigate these questions. This blog post presents these methods for the two problems mentioned above.
The following is mostly based on texts by Cordula Tollmien. I thank John Bamberg for his assistance, and Cordula Tollmien and Cheryl Praeger for their helpful comments on earlier drafts of this text.
Emmy Noether is one the most influential mathematicians of all time and one of the shining examples of the mathematics department at the Universität Göttingen during its glory days in the first third of the 20th century. Her most important contributions are in invariant theory with the celebrated Noether’s theorem in her habilitation and the invention modern algebra in a series of publications in the early 1920s. This text focusses on the context of her habilitation.
This is the announced post on my recent paper with Yuval Filmus on Boolean degree functions on association schemes. The post will focus on what motivates the problem from various points of view.
Before I start, a small remark. I am using latex2wp for the first time in this post. Thanks to Luca Trevisan for providing this nice script.
During this post I avoid using many definition, while I cite things that use all kind of terminology. For this I wrote this blog post as a reference. We will go through the main steps in the paper and focus more on the wider context of the research, so the parts for which there is less space in papers and not enough time in talks.