Saturday April 23rd

A trip to DMD

Colgate is not in Colgate

  • I’m currently just about to head to sleep after a conference at Colgate University, which actually isn’t in Colgate, but I’m staying not in either towns, but instead in Cazenovia.
  • Not only did I attend a Number Theory conf in person this year, but also a Combinatorics / Graph Theory conference, and it was pretty awesome! I made friends with a Combinatorialist in UMass Amherst (grad student) and a Topologist Prof in New York (at Niagara college who attended CalTech for his PhD), we ended up hiking and then walking downtown, having Pho (if I get the photo I’ll post it; it’s pretty hilarious because it’s a group of about ten of us eating Pho on park benches) and then getting coffee / tea afterwards. I ended up buying some coconut lavender tea to carry back.
  • On our trip down, we saw goats for sale and pondered buying a Combinatorial goat for our lab and naming him Catalan. We also ate deep dish pizza on the first night and both nights we stayed up pretty much close to midnight. We were supposed to make it down to the lake, but didn’t get around to that, but we found this awesome place downtown to chat. In the middle of that, I was somehow convinced to join a Category Theory course, which is hilarious (something like “you like Category Theory, right? Do you want to hang out with us to do that?” so now I’m literally the cliche of the student who goes to grad school and is learning Category Theory. So I went home on the night we checked in and emailed a professor about joining that (lol). The whole ride down went so quickly (it was about 5 hours long) chatting, and the view was beautiful.

Talks (not all included here, very abridged notes)

  • saw a talk on Descents for cones of a real hyperplane arrangement by M. Aguiar. Showed the monoid of compositions under lexicographic refinement. Spoke about antipodes as reversals, and chambers in hyperplane arrangements. Also the Tits Product and Simplicial arrangements.
  • Hopf monoids & polynomial invariants of combo structures as a follow up paper to read.
  • Second talk was on Tropicalization of Graph profiles. Loved this talk by A. Raymond with joint collaborators. Mentioned Sidorenko’s conjecture and Erdos-Simonovits conjecture. Key takeaways that Tropicalization is a useful object to study valid binomial inequalities and is an interesting tool for any set that has the Hadamard property. Also hepful to solve problems in extremal graph theory involving binomial inequalities
  • S. Walker gave a talk on Zero-Forcing power domination & Product power throttling of a graph. Propagation time was super interesting; how long before graph with white and blue turns all blue.
  • Which Neural Nodes are Convex by A. Shiu was amazing! Inspired by neuroscience place cells and grid cells and using place fields to form codewords. Spoke about (local) obstructions relating to convexity and Hochster’s theorem and Groebner basis came up!.

Other Stuff

  • Algebra : continue with saturation and ideals, irreducible ideals, annihilators and Noetherianity. I have one more lecture to catch up on tomorrow that I missed on Friday, as we left around 1pm to head to the conference.
  • Combinatorics: Higher rank Polyhedral Geometry, bounded polyhedra, Fourier-Motzkin elimination and Farkas’s Lemma. Normal fans, Minkowski-Wey decomposition, possible relation to Linear Programming for duality like Farkas’s Lemma
  • Elliptic Curves: Modular forms set up: complex analytic isomorphisms of complex lie groups, GAGA, relationship between algebraic and analytic definitions, q-series expansion, Eisenstein series, homothety property.
  • Number Theory: Quadratic congruences, lifting.
  • Random Prob Graphs: Harris Inequality and FKG, Janson
  • I attended a talk on the Math of Moneyball, in which a baseball analytics person spoke about their job.
  • Prob class: definitions of expectation of a random variable and conditional distributions, counting and lebesgue measures, density of a distribution, joint distributions, Borel sigma-fields
  • I attended two breathing meditation sessions which were pretty great, and also liked the analogy of your mind being like a kite, which you have to pull in to focus, particularly on the present.
  • Crypto group: learned about UFEDs used to scan phones and fingerprinting biometric devices, as well as how developers can determine what lives or is accessible in front of the lock screen or behind the lock screen.
  • I did some research (more to be done tomorrow as well).

Some photos from our trip

And that’s it

Written on April 23, 2022