I would like help figuring out graduate school (2024, anything helps lol I am lost)

[BoatsandHoes56]

Hello anyone kind enough to search through profiles. I would like some help deciding what my next move should be. Unlike the majority of people here I have much more normal qualifications. I would like to know what you think I could and should do. I would like to get a PhD in Math, but I am open to other possibilities if they are better fits.
I have been looking at other posts and I will try and put what they had in my post so you can make an accurate assessment.

Undergraduate Institution: Medium State School (U.S)
Major: Mathematics (pure)
GPA: 3.85
Math GPA: 3.85
Type of Student: Domestic white male

GRE (updated, took very recently)
V: 153
Q: 160
AW: ?

GRE Math Subject: Haven't taken. I will take it if the school I want to go to asks for it.

Research Experience: I have been working on two projects. The first one I started with the math department head at my institution last January and we are continuing it through this fall. We are trying to push for a submission into an undergraduate journal but as of now I don’t know if that will work out. The second is new this summer. I am working with a professor at another state school, and we are mostly just working to figure some things out with parameter recovery of different partial differential equations.
Recommendations: I should have 4 or 5 letters of recommendations. I have had three research advisors at my current institution as well as one professor that I am very close with who has been a great mentor to me when I needed one. I have one more potential recommendation from the research this summer as mentioned above.
Teaching: I have been a tutor at my school for about two years now. Starting with lower-level math classes and freshmen general electives. I now tutor most if not all 300 and lower math classes my institution offers with some 400 classes sprinkled in. I am trying to be a TA / Grader, but the professor hasn’t gotten back to me.
Coursework: Calc I, Calc II, Calc III, Advanced Calc I, Advanced Calc II, Linear Algebra, Ordinary Differential Equations, Probability and Stats, Complex Analysis / Variables, Mathematical Proofs, Numerical Analysis, Numerical Methods with PDE’s, Intro to Programming, Three semesters of Undergraduate Research, and a short coding in math course. I think I got everything, but it’s been three years in the making.
Coursework I plan on taking: PDE’s, Abstract Algebra I - maybe the second level, Number Theory, Geometry, and Mathematical Modeling.
I was not able to take Applied Stats and Topology on account of me being an athlete for my school and the conflicting schedules, math professors don’t typically have to worry about that so no worries.
Extras: I have gotten a few honors and third-party scholarships, an athletic scholarship -after being on a team for a year, as well as a merit scholarship out of high school. I am also trying to become the representative of the math major at my school, I have an interview in the coming days -not guaranteed.
Clarifications: I don’t have any graduate work or publications -yet, hopefully- and I am not doing a senior thesis, to my knowledge, because of the research I have already been working on.

I do think I have a competitive application to some extent though not top tier. If there is anything that needs to be clarified, please ask and I will do my best to answer. I appreciate any help I can be offered as far as program suggestions or things to do to boost my resume.

This is kind of an extension off of the above post. As you can probably see I don't have a direction I want to go in, so I looked up happiest Universities in the U.S. and saw Tulane was number one. Among the other program suggestions, you may have if someone could tell me what I need to do to get into Tulane for a PhD I would greatly appreciate it. Again, it doesn't have to be math if I simply cannot bridge the gap. Anything helps and thank you for your time.

[activator73]

What field/fields of math are you looking to go into? This will help guide your search--you can go on the arXiv and search for papers in your intended field and then stalk the authors (online)

[BoatsandHoes56]

My emphasis in undergraduate is pure math so I would like to look into that field, PhD preferably. I would also be open to applied and computational math, and maybe even something to do with machine learning and AI. Also, thanks for clarifying to stalk them online lol, things could have gotten weird.

[eamath]

Hi, a few thoughts for you. 1) I don't think undergrad surveys for happiest students are relevant for PhD programs. How happy you are in grad school is dependent on your advisor and the culture of the department as a whole, as well as the nature of the town/city cost of living/weather/housing/etc relative to your preferences (also look at typical stipend levels to make sure you can afford the area). For example, anecdotally, Cornell undergrads seem to be stressed, where as the center for applied math at Cornell PhD program seems to have a pretty positive culture. Assessing the culture of a program and working styles of possible advisors is important, and ideally done via visits and/or talking with current grad students (most often done after acceptance). 2) It is ok to be somewhat undecided on specific topics you want to study in grad school, but you should have some idea beyond just pure math. Narrowing to at least broad categories like analysis, algebra, etc. would be very helpful in selecting schools to apply to, and help those schools better assess if you are a fit to them. As you seem undecided, and also list applied math or computer science, I would suggest focusing on large programs that have strengths in a number of areas , i.e. places like University of Illinois, U Michigan, Ga Tech, etc. 3) What are your post PhD goals? academia, national lab, industry? Unless firmly focusing on academia, suggest consider applied math programs as they can leave you in good stead for a variety of possible future job paths. Perhaps look at schools ranging from Cornell to U Colorado Boulder to Stony Brook, as well as the others previously mentioned. Perhaps use the US News math grad school rankings and specialty areas as a starting point for coming up with 8 to 15 schools to apply to (also look at QS rankings, Shanghai rankings, etc). Look on the school department websites, as mentioned previously look at google scholar, etc pages for professors you are interested in to help narrow down your search. Look at qualifying exam procedures, if the they have a core course program, how flexible they are, etc to decide best fit for you. You have a good undergrad record, if letters of support are strong, schools in the top 20-50 range may be achievable. Also take a shot at some top 20 programs as well, and don't ignore programs in the 50-100 range if they have a strong advisor that matches your interests. With regards to Tulane, they are ranked 73 in US news, but also have a NAS member Lisa Fauci who is well known, her interests are numerical analysis, scientific computing, fluid dynamics and mathematical biology. Not sure how old she is or if still taking PhD students, but that can be figured out with a little searching. Good luck!