Jekyll2026-08-18T18:38:39+00:00https://juliptic.github.io/feed.xmlJulie ShieldsYour Name's academic portfolioJulie Shields4-15-26 - What do I know2026-04-15T00:00:00+00:002026-04-15T00:00:00+00:00https://juliptic.github.io/posts/2026/04/math-i-knowI want to teach absrtact algebra again. Its my favorite intro subject to advanced math and I’ve planned out how I would do it and I think I could give good perspective. I also sometimes think about how long it would take someone to learn everything neccesary to understand or do what I’m doing now. Assuming you’ve taken a proofs class you would need

Abstract Algbera (Groups, Rings and Fields, + Commutative Algebra)

Real and Complex Analysis

Topology

Algebraic Geometry

Algebraic Number Theory

Differeintial Geometry

Now that I look at it this doesn’t look like that much. I think I have to believe that because I do genuinely believe anyone could’ve gotten to where I’ve gotten to and comprehend this material. I also think most people could do it faster but idk.

]]>Julie Shields4-13-26 - Proud of Myself2026-04-13T00:00:00+00:002026-04-13T00:00:00+00:00https://juliptic.github.io/posts/2026/04/proudToday I was very proud of myself. I have these days every once in a while where I feel like I genuinely understand something I am working on. Without days like this I don’t know if I would’ve made it this far in my program.

Yesterday a few friends were discussing postgrad education and for anyone out there thinking about it, particularly in math, you should be aware that as you likely already have experienced, you will constantly feel outclassed by everything and everyone. Grad school has been the process of constantly feeling dumb, despite knowing that I know more math than almost anyone ever. Because you are around other smart people who also have dedicated even more of their lives than you your days are spent feeling dumb.

The other thing about grad school is you don’t have to be smart to make it. Like if you want to get a Ph.D or a master and have the moeny or time you can do it. The ceritifcation is nice but many Ph.D’s couldn’t explain any hard stuff after 20 years in industry not being forced to think about more than their own cog.

Now I get to be a nerd about what I learned today. I was sitting in on my advisors course on automorphic and modular forms and we were discussing Hecke operators. We gave the classical description as sums over representatives of a double coset and I asked about the relationship to the local spherical Hecke algebra in the adelic perspective. I then spent time on and off for the next week trying to see the fact that the action of char(K(p,0\0,1)K) on the adelization of a modular form should be the same as the action of the classical Hecke algebra and I think I understand it now. I was proud that as I wrote down my understanding on my own I correctly predicted how to translate between the two version (via the SL_2(Q) piece of the strong approximation decompostion). I found some exercises that note this here. https://bicmr.pku.edu.cn/upload/file/2021/20210802/20210802085307_22494.pdf

]]>Julie Shields4-18-26 - Gameplay is Paramount2026-04-13T00:00:00+00:002026-04-13T00:00:00+00:00https://juliptic.github.io/posts/2026/04/gameplayThe unique aspect of playing a video game in comparison to other forms of media is control. You have agency, albiet prescribed by the developers, to press the buttons at your fingertips and affect the world. From this comes my core opinion about whether I like a game or not, do I enjoy the gameplay.

If the core gameplay is not fun I will probably not like a game. A lot of games people like have gameplay that feels bad and while i recognize that it can have themactic value, for many games I find this as insuufiecient. As an example I bounced off uncharted 4 very hard because the gunplay felt horrible and the slow platforming in a number of sections did not feel fun enough to keep me going. Basically all my favorite games have gameplay I will defend with my life. Destiny has maybe the best feeling gunplay on account of bungie’s very good sound design and other systems to make everythign feel satisfying. Many games fall into the category of “fun dash” such as hollow knight, hades, celeste and ultrakill. Titanfall 2 has movement and gunplay unmatched by most modern fps’s. Even the rpgs I like have this core property.

This philsophy gives me an aversion to slower games which I do think about often. I played red dead 2 and it was fun with music and distractions. I might just have cooked my zoomer brain but I do think I can enjoy the gameplay of big rpg’s if it feels fun.

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