a research blog by Dustin G. Mixon
After nearly five years, it s time to roll over the discussion. Aubrey s most recent comment in the previous thread seems interesting. I m reproducing it here for convenience: In the course of discussing Asger’s graph (see above) and the one I found shortly afterwards, a new conjecture has arisen: For all d = 2 and 3 Continue reading Polymath16, eighteenth thread: Back with a new conjecture!
This summer, 3Blue1Brown launched the third installment of the Summer of Math Exposition contest. Every year, I ve been impressed and inspired by the quality of some of the videos in this contest. Over the last couple of months, I worked with Boris Alexeev and John Jasper to throw our hat in the ring: I was Continue reading Math exposition on YouTube
Grant Sanderson (of 3Blue1Brown fame) recently launched the 3b1b podcast as part of the SoME1 math exposition challenge. This page annotates the third episode of the podcast: In this episode, Grant Sanderson (GS) interviews Steven Strogatz (SS) about research, pedagogy, and exposition, and what follows is some commentary by John Jasper (JJ), Emily King (EK), Clayton Shonkwiler (CS), and me (DM).…
Grant Sanderson (of 3Blue1Brown fame) recently launched the 3b1b podcast as part of the SoME1 math exposition challenge. To celebrate, some friends and I decided to launch an experiment on this blog by annotating the first episode of the podcast: In this episode, Grant Sanderson (GS) interviews Alex Kantorovich (AK) about all things academia, and Continue reading 3b1b podcast #1
This is the seventeenth “research” thread of the Polymath16 project to make progress on the Hadwiger–Nelson problem, continuing this post. This project is a follow-up to Aubrey de Grey’s breakthrough result that the chromatic number of the plane is at least 5. Discussion of the project of a non-research nature should continue in the Polymath proposal page. We will summarize progress on Continue…
Last summer, I launched an online seminar with Joey Iverson, John Jasper, and Emily King on the theory and applications of harmonic analysis, combinatorics, and algebra. We meet on Tuesdays at 1pm (Eastern time). We re kicking off the spring semester on January 26 with a talk from Steve Flammia on recent progress on Zauner s conjecture. Continue reading Codes and Expansions (CodEx) Seminar
What follows is a nice problem that was recently posed by Mario Krenn. Progress on this problem may lead to new insights in quantum physics (see this, this, this, and this for details). In addition, Mario has announced two cash prizes to encourage work in this direction. (!) Consider a weighted and edge-colored bipartite graph Continue reading A graph coloring problem from quantum physics (with…
This spring, I’m teaching a first-semester course on Linear Algebra at the Ohio State University. Click here for a draft of my lecture notes. I will update the above link periodically. Feel free to comment below. Update #1: Added two sections to Chapter 1. Update #2: Updated Chapter 1 and started Chapter 2. Update #3: Continue reading MATH 2568: Linear Algebra
At the end of his recent CodEx talk, Gene Kopp posed a problem with a prize attached to it. I was excited to learn about this, so I enlisted both Gene Kopp and Mark Magsino to help me write this blog entry to provide additional details. First, let denote the set of matrices in such Continue reading Kopp s Whisky Prize
This is the sixteenth “research” thread of the Polymath16 project to make progress on the Hadwiger–Nelson problem, continuing this post. This project is a follow-up to Aubrey de Grey’s breakthrough result that the chromatic number of the plane is at least 5. Discussion of the project of a non-research nature should continue in the Polymath proposal page. We will summarize progress Continue reading…