The power of negative thinking: Combinatorial and geometric inequalities

Just in time for the holidays, Colleen Robichaux and I wrote this paper on positivity of Schubert coefficients. This paper is unlike any other paper I had written, both in the content and the way we obtained the results. To me, writing it was a religious experience. No, no, the paper is paper is still […]

Is there anything new in Enumerative Combinatorics? Most experts would tell you about some interesting new theorems, beautiful bijections, advanced techniques, connections to other areas, etc. Most outsiders would simply scoff, as in “what can possibly be new about a simple act of counting?” In fact, if you ask traditional combinatorialists they...

The readers of this blog know know that I stay away from non-math related discussions. It’s not that I don’t have any political opinions, I just don’t think they are especially valuable or original. I do however get triggered by a clear anti-Semitism, discrimination of Jews by the universities, and by personal disrespect. The story […]

What follows is an unusual story of perseverance. We start with a conjecture and after some plot twists end up discussing the meaning of truth. While the title is a spoiler, you might not be able to guess how we got there… The conjecture The bunkbed conjecture (BBC) is a basic claim about random subgraphs. […]

By and large, math journals treat the authors like a pesky annoyance, sort of the way a local electric company treats its customers. As in — yes, serving you is our business, but if you don’t like our customer service where else are you going to go? Not all editors operate that way, absolutely not […]