For the last five weeks, I attended MCSP. Here is a recap of my experience:

Table of Contents

Favorite Events

1. Favorite classes: Khinchin's Constant and the Ergodic Theory; Homotopy Groups of Spheres; Polygons, Friezes, and Snakes; Linear Algebra Through Knots; How to Count Rings; The Outer Life of Inner Automorphisms; From the Sato-Tate Conjecture to Murmurations
2. Favorite colloquiums: Cluster Algebras; Hopf Fibrations; Shirts; You Can Hear the Shape of a Billiard Table; Random Matrix Theory
3. Favorite schedule board events: throw throw burrito; UVM trips; ping pong; water relays
4. Favorite weekend activities: trampolining; paddleboarding

Week 6

Academics

Classes

• Khinchin's Constant and the Ergodic Theorem. The class started off a bit slow but picked up pace towards the end. This might be because I was already familiar with the content of the first two days (introduction to measure theory and liminf/limsup), both of which I've seen before. But once the required background was covered, the class became quite enjoyable. As someone who hadn't heard of ergodic theory before this course, I found the Ergodic Theorem fascinating. While I'm not a huge fan of the proof (it's filled with slick algebraic tricks that make it bearable, but there's just so much technicality), I definitely enjoy applying it. I particularly liked solving the limit problems from Day 4 homework (verifying Borel's Normal Number Theorem) and the examples from Day 5 (applying it to Khinchin's constant).
• Homotopy Groups of Spheres. This class was insanely good; by far the best 2 chili class I attended, and I wish it lasted longer than just two days. I went into the class knowing nothing about homotopy groups of spheres since I don't know much topology, but day 1 was a perfect introduction. Learning about the Hopf fibration has turned me into a topology fan, and day 2 was even better! We took a quick trip through the history of this problem, which was really cool. I loved how well-paced the class was, covering a lot of material in a short period. In general, I really appreciate classes that focus on theorems, highlight the interesting bits, and avoid delving too deeply into time-consuming technicalities. This class did that perfectly. I'm a little sad that we didn't have time to discuss spectral sequences, but at least I got a reference to explore the topic further.
• Knot Invariants. The first day was a bit rough for me because the class felt too rigorous. Knot theory was new to me and I found the material quite challenging. However, the class improved significantly after that. It seems like many others had the same initial reaction, as the class size shrank to just eight students. This made the class feel more interactive, like a project rather than a lecture, which I really enjoyed. Knot theory turned out to be much cooler than I anticipated, and the highlight for me was the topological invariants discussed on Day 4. I ended up going down a rabbit hole learning more about Seifert surfaces after class.
• Bhargava's Cube. I have very mixed feelings about this class. The first day was a bit slow because I had already seen everything from Cox's Cox's Primes of the Form $x^2+ny^2$*. The homework was basically just linear algebra spam. Day 2 was amazing though and was my favorite class of the day. I spent a couple of hours after class reading Bhargava's original papers on the cube, which are excellent, and I highly recommend everyone reading this blog to check them out.
• The Transcendence of Many Numbers (including $\pi$ and $e$): Week 1. The class was well-taught, but I didn't find the topic as elegant as I had hoped. The first day on Schneider-Lang was interesting, and it was the only day of the week I enjoyed this class. On Day 2, the professor introduced complex analysis to explain the Maximum Modulus Principle, but since I've already encountered complex analysis in various contexts (including at last year's MCSP), I didn't gain much. Day 3 involved some rather tedious bounding using the Siegel and Derivative Lemma. While these are powerful and useful tools, I found the proofs tedious and unengaging, and they dominated the majority of the class. I hope next week improves.

Colloquium

• Day 36: Formulas for Solving Equations. This talk focused on Arnold's elementary proof of the unsolvability of the quintic. I really enjoyed the talk as the proof itself was beautiful, but I felt a bit dissatisfied with the level of rigor presented. A lot of details were skipped, which I understand given time constraints, but I felt that some essential details were omitted. Still, this colloquium was definitely worth attending, as it led me to research topics like the Tschirnhaus transformation and Bring radicals, sparking some entertaining discussions with fellow attendees.

• Day 37: Voting theory, Burlington, VT, and the Gibbard-Satterthwaite theorem. I had already seen most of this last year so this talk wasn't particularly noteworthy. Additionally, there was very little actual math, aside from some arithmetic, and the emphasis on historical context was not super interesting. The colloquium seemed quite popular though, and I heard plenty of other people really enjoyed it.
• Day 38: Mediants, Circles, and Stern-Brocot Patterns. Really cool colloquium topic, but I'm still not sure how the "the straight lines of a tetrahedron" problem is related to the rest of the talk. I had seen Farey sequences before but not Stern-Brocot, so I found the topic quite intuitive but ultimately I felt that the talk was too short and did not go deep enough for my likings. I've meant to spend some time exploring it further, but I haven't had the chance yet.

Other

• Day 41: Relays. Hardcore division, I'm still kind of annoyed that I botched the knot theory question. I felt the questions last year were better, but I'll admit that I'm more focused on just having fun this time around so I shouldn't be complaining too much.

Nonacademics

Field Trips

• Day 42: Rock climbing. Honestly, I kind of regret going on this trip. The bus rides were incredibly long for the little amount of time we actually spent rock climbing. The boulders were ridiculously difficult; I only completed two, and I failed repeatedly on a V0. I did have some good conversations with people on the bus, which made the ride somewhat bearable, but I feel I would have had more fun just exploring downtown Burlington or checking out UVM.
• Day 43: Bowling. This was a pretty fun trip, and the bowling-to-bus-ride time ratio was great. It was my first time bowling since 2019, and I somehow managed to get two strikes! That said, bowling is harder than I thought, as I kept getting the 0-0 score.

Other

• Day 35: Beating my monkeytype 15s record.
• Day 35: Trip to the lake.
• Day 36: July 4th trip to the lake. The fireworks were really nice! This was surprising since we sat there waiting for fireworks to go off for 2+ hours before they actually did.
• Day 37: Outdoor throw throw burrito
• Day 39: Target trip to buy throw throw avocado.
• Day 41: Soccer. Pretty mid, not that much fun, but at least I scored a handful of goals.
• Day 42: Indoor throw throw avocado. I had more fun in this round than with the burrito, but I definitely still prefer playing the burrito version.
• Day 43: Trip to the lake + Burlington book stores. I read A for Anonymous in the bookstore which I thought was mediocre. I felt like there wasn't enough drama added in the story to accurately reflect Anonymous' work.

Week 7

Academics

Classes

• Representation Theory of the Symmetric Groups. I really enjoyed the homework! The pacing of the class was a bit uneven at times, but I still learned a decent amount, especially on Day 4 when we covered Specht modules. The material is fascinating, so I'm definitely planning to read Sagan's book after camp to deepen my understanding of this topic.
• Polygons, Friezes, and Snakes - Oh My! The best class I've taken at MCSP. It was an algebraic combinatorics course connecting polygons, frieze patterns, and snake graphs. The class was taught incredibly well, and the most exciting part was learning how frieze patterns are linked to triangulations of unusual surfaces, like punctured polygons. I'm definitely planning to explore this more after camp. It seems like resources are limited, mostly consisting of original papers, so it might be tough, but I find the topic interesting enough to make it worth the effort.
• The Transcendence of Many Numbers (including $\pi$ and $e$): Week 2. The classes this week were quite good, especially in terms of learning about number fields. As usual, the material was taught very well, and I found it engaging enough that I'd like to revisit it in the near future, although it's not at the top of my list. My main takeaway from this class is that transcendence theory combines elegance with ugliness - it's full of difficult proofs and it's easy to get stuck. However, Week 2 was definitely more enjoyable than Week 1, and I'm glad I didn't switch classes.
• Packing Permutations Patterns. The first day was a bit slow as we were setting up, but Day 2 was much better. I finally learned why the packing problem is interesting for 132 patterns and got my first real explanation of what a "flag" is, both of which were completely new to me. The class was taught well, and the material turned out to be more interesting than I expected. I still don't love pure combinatorics, but my dislike has definitely lessened.

(Un)Colloquium

• Day 44: One-Half Factorial From Scratch. This talk was probably interesting for someone who hadn't seen the topic before, but since I'm already familiar with Wallis products, I didn't learn much. However, the visuals were enjoyable to watch, and the topic was presented clearly, so it was still somewhat entertaining.
• Day 45: Some Stories About Squares (mod $p$). This was an absolutely awesome colloquium. I learned about Heegner numbers and Ramanujan's constant, both of which were new to me. The visuals were fantastic, and the material was presented in a very approachable way. This was definitely one of my favorite colloquiums.
• Day 48: Cluster Algebras. This was a great introduction to cluster algebras. We defined cluster algebras, connected them to snake graphs, and explored some of their properties. The pictures and the connections were amazing. There wasn't much theory involved, focusing more on intuition, which seems to be a common trend in (un)colloquiums.
• Day 51: Hopf Fibrations. A nice short talk about $\mathbb{R}P^n, \mathbb{C}P^n, \mathbb{H}P^n,$ and $\mathbb{O}P^n$ as well as various concepts named after Hopf. Hopf fibrations are incredibly cool, but it's hard to fully grasp them. Nonetheless, the content was pretty mind-blowing, and I'll definitely dive deeper into these topics after camp.

Other

• Day 48: Project Fair. I got my top choice of quantum groups, so I am happy.
• Day 49: Relays. I participated in the mellow division. It was a pretty average round of relays, with nothing particularly noteworthy to mention here.

Nonacademics

Field Trips

• Day 49: Trampoling. Not really much to say here but it was fun.
• Day 50: Hardcore Hike. Slightly shorter than last year: 13.5 miles for me. Our original trail was flooded, so we switched to a sketchy one with extremely randomly placed and terrifying ladders. I got lost a couple of times, including once where I walked over a mile in the wrong direction. Despite that, it was pretty fun overall. The views were beautiful as well.

Other

• Day 46: Stanford Security Seminar. The talk was Threshold Signatures from Inner Product Argument: Succinct, Weighted, and Multi-threshold. Good talk.
• Day 48: RA ice cream trip. The ice cream was average and tasted just like the stuff in the dining hall.
• Day 48: Throw Throw Burrito/Avocado. As usual, this was fun. We had a bigger group this time, which wasn't as enjoyable, but as more people left, the group size became perfect again.
• Day 49: Ping pong king of the court. I dominated for 50 minutes until I threw a match to someone I'd already beaten like five times.
• Day ??: Chilling in my dorm room late at night. Some notable activities included fluffy koala hugging sessions and wrestling.

Week 8

Academics

Classes

• Linear Algebra Through Knots. This class was awesome - the only thing I would change about it is that I would make it longer. I learned how strings appear in linear algebra through tensor products and linear transformations, along with many new concepts, including the Cayley Algebra and exceptional Lie groups. The class was taught exceptionally well, and the homework was enjoyable. However, I wish the class was longer because the topic is quite complex, and there aren't many accessible references. It's deeply tied to physics that I'm not familiar with, and the material is a relatively new area of math. One of the last sentences of the handout was "Spin groups preserve some form on Clifford algebras" and I know nothing about either. I did get a reference so I will try to read it after camp, but there's an absurd amount of QFT stuff so it'll probably take me at least 10 years to understand it somewhat fully.
• How to Count Rings. I learned a lot of ring theory in this class, particularly about number fields and quadratic/cubic rings. Some new terminology, like ramification groups, was introduced, which I found fascinating. The class had a serious vibe but was well-taught, and the homework was both fun and challenging, which I enjoyed. While advertised as a ring theory class, I spent a surprising amount of time reading about Galois theory to avoid the homework, which led to the most outside-of-class reading I've done for any MCSP course, which was cool.
• All Aboard the Möbius. This class offered a standard introduction to Möbius inversion and related concepts. I didn't enjoy it as much because the material felt bland, with too many definitions to track and few challenging facts to engage with (often, you just had to match identities from the board). The most fun part was proving Selberg's identity. There were also plenty of exercises related to the Prime Number Theorem, but I didn't get to many of them. I've realized that I prefer analytic number theory involving actual integrals, so while this class was fun, it wasn't exactly what I hoped for.

(Un)Colloquium

• Day 50: Teaching Math to Computers. A basic talk about what lean theorem prover can do. I didn't really enjoy it that much, because the talk was basically just telling us that "lean can do certain things" and showing us random pieces of code without really explaining how to program in it or how it worked under the hood. The most surprising takeaway was that Lean can verify proofs but can't generate them - this contradicted my expectation that theorem provers were more advanced. While I think Lean is interesting and may explore it someday, it's not a priority for me right now.
• Day 51: Antinomy: Medications on Gödel's Undecidable Sentences. This talk covered paradoxes, specifically Quine's three types of paradoxes. The talk was probably good for someone who likes logic but I don't like logic so I didn't really like the talk.
• Day 55: Shirts. Shirts are spheres with four holes. This was a really cool talk and an area of math that I'm not familiar with. I learned a lot of things but the talk was also ranging from one to six peppers so I have a really rough idea of what some fancy things such as Teichmüller theory but I don't understand them well. The big picture, which connects Teichmüller spaces, mapping class groups, moduli spaces, and curve/marking graphs, is definitely something I want to dive deeper into later, especially since much of this was omitted due to time constraints.

Other

• Day 50: Tracking Pants. I read the notes from a 2022 class on tracking pants with one of the author's project mentors. The material was interesting, though it felt a bit disconnected, and some ideas emerged without much motivation. I didn't enjoy the proof sketches as they left out too much detail for me to fill in easily. Perhaps I just need more intuition in this area of math.
• Day 51: Project Meeting. We spent two hours working through difficult problems related to generalized eigenstuff and the representation theory of $\mathfrak{sl}(2)$, which was very difficult and not that interesting because every problem was to move symbols around using brackets and spamming ugly induction. Still, it was quite fun struggling on math with friends, even if the math was super tough.
• Day 53: Cluster Algebras. One of my project teammates sent me Schiffler's expository paper on cluster algebras, which I spent a few hours reading. It was enjoyable, and I plan to continue exploring it later.
• Day 55: Hot Ones. An event where a bunch of mentors proved Heine-Borel while eating increasingly spicy wings. I believe I've seen the exact proof before, so I was there mostly for the entertainment rather than the math. It was a pretty fun event and worth going to.
• Day 56: Project Meeting. This was by far my favorite project meeting so far. We explored the question, "Why should we care about quantum groups?" using a mix of geometric representation theory, how some representation is the electron, birdtracks, crystal bases, and quantized knot invariants. It was a bit chaotic, but I loved it.

Nonacademics

Field Trips

• Day 55: Beach and Ice Cream. We were supposed to go paddleboarding, but it got canceled due to rain. I spent about an hour on the beach and almost two hours wandering around, which was relaxing. I also had some delicious maple raspberry ice cream. While the beach itself was nice and the water was a good temperature, it was quite crowded, making it hard to do much. The ice cream was definitely the highlight.
• Day 56: Water Park. A classic small water park with a few fun rides, but nothing particularly extraordinary or thrilling. My favorite ride was the steep speed slide, where you get launched off at certain points, though I ended up getting a ton of water up my nose. After that, I opted for the calmer rides, including the lazy river and one that looked scary but turned out to be pretty mild. Nothing too memorable beyond that.

Other

• Day 52: Gym.
• Day 54: UVM Trip. UVM's campus had an eerie, liminal vibe. The massive hospital looked like an airport, and there were creepy, deformed statues scattered around, along with flickering lights in random buildings. Most buildings were locked, but we found the gym propped open, which felt oddly inviting. Walking around felt like I was in the backrooms, and I half-expected to get lost. It was a fun, mysterious adventure, and the walk back took us through dark streets I didn't even know existed.
• Day 55: Creepy Doll Music Party. SO GOOD!

Week 9

Academics

Classes

• Kuratowski's Game. In this class, I learned how to pronounce the letters "k" and "c" in a string as quickly as possible, and saw how "KFC" emerges in topology. The most interesting part was the explicit five-page list of the 120 operators forming the sharp bound discovered by Canilang, Cohen, Graese, and Song in 2019. While I didn't find the math itself particularly intriguing, the stupid aspects of the course were entertaining, and I enjoyed it. I did consider dropping the class after the first day, but I'm glad I stuck with it. The second half of the Day 3 handout turned out to be the best part of the course. While I don't see myself revisiting this material after camp, the class was still fun overall.
• McKelvey's Chaos Theorem. I attended the second day, and it felt more like a casual conversation with the teacher (with just one other camper) than a formal lecture, which was a refreshing change. The most interesting part was learning about the Rabinowitz-Macdonald non-special model of voting, though I still find voting theory depressing and not something I want to spend much time on.
• Gaussian Magic. This class was okay, but I didn't learn as much as I hoped. I expected a greater focus on random matrix theory, but instead, it was mostly about probability concepts like random variables and the central limit theorem, which I've already encountered. In hindsight, I probably would have gained more from a different class, but it's fine.
• The Outer Life of Inner Automorphisms. I'm a huge fan of this class—absolutely amazing. The material was highly technical and fast-paced, but it felt so rewarding when I understood the results. The proofs involved a blend of clever, sophisticated tricks and comically simple methods that worked surprisingly well. I came to MCSP with the goal of taking nonstandard courses I couldn't easily find elsewhere, and this class perfectly fit that objective. I encountered a lot of new math and received excellent textbook references to explore after camp. One challenge was the teacher's brilliance: he could explain almost anything off the top of his head, which was fantastic, but sometimes his explanations were too advanced for me to understand. Some texts I'm planning to read after camp include Central Simple Algebras and Galois Cohomology, An Invitation to General Algebra and Universal Constructions, and Parker's PhD thesis—though all are extremely technical, and I probably won't fully understand them for at least a decade.
• Braid Groups. I attended the last two days of this course. On the first day, we discussed a braid group-based key agreement protocol. It was interesting, but I don't see its advantages over traditional cryptographic methods, especially since it doesn't seem quantum-secure and is still relatively new (it was introduced last year in a PhD thesis by one of the teacher's colleagues). On the second day, we explored plats and a recent result by another of the teacher's colleagues. The result was fascinating, but honestly, I found the proof that the Göritz Unknot was the unknot to be the most satisfying and cool part of the course. Overall, I'm glad I attended, as both days focused on research that I wouldn't have encountered elsewhere.

(Un)Colloquium

• Day 58: The Geometry of Fractal Sets. I'm not sure why I attended this colloquium. I found many of the examples presented too standard, such as the Weierstrass function, Koch snowflake, and coastline paradox, which felt overexposed. Even though I've never studied fractals in depth before, I recognized a lot of the content. I did learn a bit about Brownian motion, but I was hoping this section would be longer. Unfortunately, it was very brief.
• Day 59: This was about as cool as logic gets in my opinion. I had never seen the infinite prisoners and hats problem before, and I found it really interesting. The talk had a good amount of humor, which made it enjoyable, and I found the brief connection to measure theory at the end particularly intriguing. After this, I'm motivated to explore the link to measure theory further, as the Week 6 Khinchin's constant class already convinced me that measure theory is fascinating.
• Day 60: The Evolution of Proofs in Computer Science. This was a basic introduction to zero-knowledge proofs. While I've seen variations of this talk multiple times, I'm a fan of zero-knowledge proofs, so it wasn't too bland. The best part was having a brief conversation with Yael Kalai about SNARGs. I hadn't realized SNARGs were relevant, so it was cool to learn more and compare them to SNARKs and STARKs.
• Day 61: You Can Hear the Shape of a Billiard Table. Unfortunately, I had to leave this talk early, but the portions I attended were incredible. I knew nothing about billiards going into it, so everything was new and fascinating. The results were often surprising, and this seems to be a rare area of math that's hard to learn elsewhere. I'm really glad I could attend at least part of this colloquium.

Other

This section is basically non stop project spam - I spent roughly 16 hours doing my project this week.

• Day 58: Project Meeting. My project group met to work through Chapter 2 of Jantzen together. We spent the whole TAU session on it and made some progress, though there's still a big chunk that makes no sense at all.
• Day 59: Project Meeting. We spent from 10 PM to midnight bombarding the mentors with questions about Chapter 2. We made some good progress, and I finally understood why the center matters. However, I'm still not sure why the roots of unity are important, other than their tendency to appear in random places.
• Day 60: We went over the structure of the Hopf algebra with the mentors. I understood the definition, but I still don't grasp why it exists or why it's significant, beyond the fact that it has some nice properties.
• Day 61: I tackled Sections 3.1-3.7 of Jantzen on my own in the outer office from 9 PM to midnight. These sections are making much more sense to me than Chapter 2 did.
• Day 62: Project Work. During the AA meetings slot, I revisited Sections 3.1-3.7 to ensure I understood everything. I think I've got a decent grasp of it now.
• Day 63: Project Write Up. After a break from reading Jantzen, I wrote up a 3-page expository piece on the representation theory of $\mathfrak{sl}_2(\mathbb{C})$, which took about 2.5 hours.
• Day 64: Project Work. I pushed through the rest of Chapter 3 in Jantzen. I don't fully understand the $\Theta$ stuff, but I skimmed it a few times. I spent about 3 hours on this.

Nonacademics

Field Trips

• Day 61: Paddleboarding. My group's paddleboarding trip was rescheduled after getting canceled on Day 55. At first, standing on the paddleboard was intimidating, but after about five minutes, I got the hang of it and was able to paddle around comfortably for the rest of the hour. I did realize halfway through that I was using the wrong grip, which made it harder, but once I corrected it, I was able to go much faster. Unfortunately, the mentors kept asking me to return every time I ventured too far, but it was still a fun experience.

Other

• Day 58: Gym. I found my favorite leg machine it's sooo fun.
• Day 58: Sidewalk
• Day 59: Modern art in the library after hours.
• Day 59: Water Buffet
• Day 61: Ping pong. I played ping pong for an hour; it was fun for a while but then it got a bit boring and I left.
• Day 61: Automorphic Forms Organisms Can 0nly Kawua
• Day 61-62: KEVIN CARDE CARD I NEED IT HOW DO I GET IT
• Day 62: Lake Trip. This trip was incredibly refreshing, and the view was stunning because the weather was perfect. There were many boats at the dock, so I couldn't nap, but the sight of the mountains in the background and massive ships floating around was beautiful. The only downside was almost being hit by a speeding car running a red light, as I was probably only six inches away from being paralyzed.
• Day 63: Dodgeball. Fairly fun but a bit too short.
• Day 63: Dinosaurs. The best part of the day!
• Day 63: Throw Throw Burrito Game. Standard throw throw burrito avocado game.

Week 10

Academics

Classes

• Flag Algebra Marathon. Flag algebras are really cool! I don't have much background in combinatorics, so this class was on the tougher side for me, but it was still fascinating. We covered topics like Goodman's theorem and systematic proofs using flag algebras. I really enjoyed the class, but I think my enjoyment was more due to how well it was taught rather than the topic itself. While I probably won't revisit this area of math after camp, I'm glad I attended.
• Schubert Calculus. I really enjoyed learning about Littlewood-Richardson coefficients! I felt like the class didn't cover as much as I wanted, and some sections moved a bit slowly, but overall, Schubert calculus is really cool and I'm glad I attended.
• Unicorns In Poland. I went to this class more for entertainment and as a break from my other classes rather than for the serious math. The math itself was very simple for the first part, mostly taught by JCs. The last half hour picked up pace and became more handwavy, so I didn't come away with a strong understanding, but the topic is still fascinating. I plan to revisit the notes later to learn more.
• From the Sato-Tate Conjecture to Murmurations. Possibly the coolest class of mcsp 2023! Day 1 gave a fantastic presentation of the Sato-Tate Conjecture, and on Day 2, we proved Hasse's theorem. On Day 3, we explored the modern research on murmurations, building from L-functions and modular forms. I got a lot of resources to dig into after camp—this topic is definitely high on my to-do list. I've seen little about elliptic curves beyond basic elliptic curve cryptography, so there's a ton to explore. Plus, I know almost nothing about L-functions and modular forms, so I'm really excited to dive into this material after camp.
• Why 0 Is The Biggest Prime. This class used model theory to prove results like Hilbert's Nullstellensatz. I thought it was interesting but the pace was too slow. The first day on model theory was a bit dry, but necessary for Day 2, which was more engaging. Unfortunately, the model theory section took up too much time, so we didn't finish the proof we were working on. Model theory isn't my favorite area, so I won't be looking into this after camp, but it was still a cool class to attend.
• The Ra(n)do(m) Graph. This was a one-day class exploring random graphs and some surprising counterintuitive results, like first-order statements and Alice's Restaurant Property. It was a really fun, engaging class!
• The Transcendence of a Single Number. This class focused on Liouville's theorem. Someone spoiled the answer to the problem before the class, which made it a bit less enjoyable, but it was still a fascinating topic. I'm glad I attended.
• Lastly, Choose Randomly. This class covered the Lovász Local Lemma, a topic I hadn't seen before. While I thought it was somewhat interesting, it wasn't super captivating for me.
• The Chevalley Warning Theorem. The first part of the class was fairly dry, but the last 10 minutes were awesome. We saw the Ax-Guth theorem and how it connects to the Riemann hypothesis. I had already seen most of the lecture before the last 40 minutes, but those final minutes definitely made it worthwhile.

(Un)Colloquium

• Day 66: A Magic Show. It was about taking a X and gluing mobius strips, and then cutting down the middle. This wasn't particularly mathematical, but it was an amazing and very entertaining performance.
• Day 67: Random Matrix Theory. By far the best uncolloquium I attended. One of the most mind-blowing facts was the connection between random matrix theory and the Riemann hypothesis. We also went over a random matrix theory central limit theorem proved by the lecturer, which was cool but really abstract. This talk covered what I had hoped to learn in the Gaussian Magic class, so I'm really glad I attended.
• Day 68: Banach-Tarski. I had already seen this talk before, so it wasn't as cool as the first time. However, it's still a fascinating topic and worth revisiting.

Other

• Day 67: Stanford Security Seminar. The talk was Distributed Broadcast Encryption from Bilinear Groups by Dimitris Kolonelos. Unfortunately, I didn't find it very engaging.
• Day 67: Project Prep. Made a poster.
• Day 68: Project Fair! I presented my project and saw others' work. The coolest project I saw was one on the three-colorability of knots using Arduinos.
• Day 69: Water Relays! The best relays by far, they were super super super fun. It's nice that my team finally placed in my last relays ever, on a team that included 2/3 of the members on my first ever relays team last year. I got super drenched, 15/10 literally more fun than the water park trip.
• Day 69: 30 in 30. This event was really fun for entertainment, though I didn't actually learn anything from it. My memories of the proofs are now a blur, so I won't even try to pick a favorite.

Nonacademics

• Day 65: Basketball.
• Day 67: Starless Gazing. Tried to go stargazing but there were no stars so I just stared into space in the cool, summer night air.
• Day 68: Talent Show. The venue was great, and many of the performances were impressive. The Tetris Just Dance performance was definitely the highlight.
• Day 69: Final assembly.
• Day 69: Throw Throw Burrito/Avocado at UVM. The game got cut short to celebrate someone's birthday, but it was still a lot of fun.
• Day 70: (Not) all nighter. Played ping pong for a while, signed yearbooks, and slept. Unfortunately, I slept through most of the chaos, so I didn't get to say a proper goodbye to everyone I wanted to. Oh well.
• Day 70: Departures. It was great seeing everyone, bye!