Fall 2024

09/06: Mark Saving: The Constructive Multiverse; Whiz through the wild, wacky worlds of constructive mathematics. In these mad models, anything is possible; all real-valued functions can be continuous, calculus can be developed through the theory of infinitesimals, computers can calculate any function you like, and schemes are just plain old local rings. All this and more can be yours for the low-low price of throwing away logical laws and axioms undergirding the majority of modern mathematics! Just pay separate processing and handling.
09/13: Sai Sivakumar: Fourier analysis on LCA groups and Pontryagin Duality; We will recover from representation theory the classical Fourier transforms on the circle group and on the real line, and time permitting, briefly talk about Pontryagin duality. Topics to be discussed are irreducible unitary representations of locally compact Abelian groups, their characters, the dual group, the Fourier transform, Pontryagin duality, and Fourier inversion.
09/20: Jemma Schroder: Hybrid Optimal Control Problems in a Stochastic Environment; We present a question of optimal route planning in R^2 with time-penalized direction changes in a stochastic environment. We will begin with a single actor, then introduce multi-actor interaction dynamics, and time permitting we will consider the addition of cooperative team-based interactions in a game-theoretic framework.
09/27: Ansel Goh: <no title>; In this talk, we will be analyzing (watching) the adventures of panda warrior. With a stunning rating of 10.0 (mod 8.3) on IMDB, we answer a question posed by Sai: “is it skibidelicious and better than rent a girlfriend?” Come join us as we examine the best thing to come out of China since Zimao and the Chinese Remainder theorem.
10/04: Ioannis Karagiorgis: A deep dive into math drama; The only thing more interesting than math is math drama. In this talk, we’ll be doing a deep dive into the life of one of the most controversial characters in the MCU (Mathematics Cinematic Universe). Expect a story full of betrayals, rivalries, and bitter feuds between mathematicians. Who is this character you ask? Tune in on Friday to find out!
10/11: Unai Caja Lopez: Surprise talk; The contents of Friday’s talk will be a surprise. However, I will say that the following elements will make an appearance:
• Prisoner’s dilemma
• Cheating in relationships
• Vampire bats
10/18: John Teague: Opinions Were Like Kittens; Opinions — we all have them. Some have more opinions than others, and they take great joy in sharing them. In this Sophex talk, we will explore some particular opinions had by particular people. As such, this will be an interactive talk.
10/25: Daniel Koizumi: On a technique to solve deeper problems; As a mathematics PhD student, you’re surely familiar with the urge to acquire useless superpowers. In this talk, we will examine another, with some mind paid toward a quote by Grothendieck. Applying our newfound power, we will also examine whether descent is the correct way to solve exciting problems. We will end with finding bounds on the depth of a certain class of objects.
11/01: Flavio Argentieri: Opinions Are Back; I enjoyed John's talk so much, that I thought it deserved a sequel. I am very curious to collect your (anonymous) opinions on a variety of hot topics - even though some of them might have been hot 1000 years ago, and they are at best tepid now. This will be an interactive talk, so please bring a mobile phone. If, for some reason, you are unable to, Sai will provide one.
11/15: Sai Sivakumar: Video games I care about; Video games have been a large part of my life. In this talk I will discuss a few of them that have been very important to me and I would like to hear from the audience about other video games that were significant to them. Time and technology permitting, I will play some of these games.
11/22: Zimao Tian: O, P, E, R, A; So, what is OPERA?
One fine day we'll see, from every Mediterranean melody, the hidden sob of a heart pulsing with longing.
Punch sir, I punch your nose, what followed your knockdown was a century of iridescent shrieks and shattered beauty.
Ever just a dream, can't be true that we are together, together for all time till eternity, fervor and mastery.
Rejoice everyone smiles from somewhere, but no one will come to me, hands around my waist, tire me out with passionate embrace, my desolated land, steeped in grimness, deep as a bowl of black wheat wine; "poor wounded name, my bosom as a bed shall lodge thee…"
Always you, every thought I'll ever know, everywhere I'll go you'll be, you and me; rise with me, Amor Americano!
P. S. There are melodies accompanying each of some beginning words, i.e. an opera behind each of the five verses above. Even more - five countries, five styles.
12/06: Jake Wellington + Matt Verheul: You Decide; Matt and I will give a presentation based off of YOUR slides! Send in your wackiest, craziest slides you can imagine and we will stretch them into a talk. 2/3 slides per person should be appropriate.

Spring 2025

01/24: Mark Saving: On the Theory and History of Rings; The core principles of the theory of rings have drastically influenced the course of mathematics and of history. I will discuss the history of rings, with a focus on the terminal object in the category thereof and its relation to other objects in this category. Time permitting, I will discuss the cosmological implications and context of these concepts.
01/31: Iris Jiang: Beyond straightedge and compass; As you may recall from high school geometry, there are certain geometric constructions that are not possible via straightedge and compass, such as squaring the circle, trisecting the angle, and doubling the cube. It turns out that some of these constructions are still possible with a different set of axioms. In this talk, I will explore the techniques used in these constructions, and time permitting, we will apply these techniques to construct new objects.
02/07: Sudharshan K V: Backwards Through Time - Puzzles of an Ancient Game; Certainly, here is a possible abstract for your topic. We'll explore a world of intriguing puzzles inspired by an ancient game of strategy. Bring your curiosity and a mind ready to unravel mysteries.
02/14: Nathan Louie: Pokémon Lore 101; Many of us had watched, played, and/or collected Pokémon when we were kids (and maybe still now), but a lot of the in-game details about the world may have gone over our heads back then. We will discuss some of the chronological lore in the Pokémon world, including the creation of the universe and other random canon stories about certain Pokémon that I thought were interesting.
02/21: Sara Ansari: Movie night (evening?); We will be watching a movie about a quirky personality with a dicey relationship with the FBI. Based on a true story or at least that's what they say.
02/28: Zimao Tian: Intersection theory of Music and Literature; As you can guess, I will revisit the theme of music, incorporating significant elements of literature this time. Music has always served as my primary lens for exploring literature, and it continues to amaze me how music reinterpreting a text, selectively capturing and enhancing different spectrums of light.
03/07: Ansel Goh: On a functor from the category of sports + other stuff; We will be talking about how a particular functor from sports to a certain other category results in interesting phenomena in the appearances of sports teams. Depending on how lazy I am, I might not prepare enough of this to fill the hour, in which case, I will attempt to fill the remaining time with a lower effort topic (possibly books).
03/14: Matt Verheul: Universal Grammar; I will be talking about something called universal grammar, a linguistic theory by Noam Chomsky. We'll discuss what it is, and evidence for and against it. Eventually I will just start talking about cool chomsky facts such as:
-his youthfulness
04/04: Sai Sivakumar + Jake Wellington: April Fools' Sophex; <See the section on the April Fools' Talk below for details>
04/11: Michael Han: Dark Energy and the Expanding Universe; If you throw a stone straight up, it does not continue upward forever, but eventually comes back down because of the gravitational attraction exerted by the earth. Since stars and planets are pulled toward each other by the same force of gravity, one is led to ask the following question: Why doesn’t the universe collapse in on itself under its own gravity? Known as Bentley’s paradox, this reveals a problem with applying Newtonian mechanics on macroscopic scales. The answer to this paradox is two-fold. One reason is that the average density of matter in the universe is too low to exert sufficient gravity. The second reason is the presence of dark energy, which contributes about 68 percent of the mass-energy in the observable universe and is causing the universe to expand and accelerate indefinitely. Though scientists attribute the expansion of the universe to dark energy, none can say for certain what it is. In this talk, we discuss several theories on what dark energy may be. If time permits, we may discuss the tangentially-related topics of active galactic nuclei and apparent superluminal motion, which make our universe a truly fascinating place to live. We will enjoy complementary cosmic brownies and an outro song.
04/18: Sai Sivakumar: GitHub, TeX, and personal webpages; Git is a "version control system", which just means that it is software that lets users keep track of changes to their code and makes it possible to coordinate changes made to code by multiple users. GitHub is a server that hosts users' code and uses Git to keep track of changes to users' code. I will explain how to get started with GitHub, via the practical example of wanting to back up your TeX files so that in case anything goes wrong, you have (hopefully several) backups of the files you need. I will also showcase (but not explain) the interaction that Visual Studio Code has with GitHub and LaTeX, as well as Overleaf's interaction with GitHub. I will also explain how to produce a personal webpage via GitHub if in case you'd like to have a lightweight and free website. I am using a Windows device, but there should be ways to reproduce everything I will discuss on a macOS device. Bring your laptops and make a GitHub account!
04/25: Jemma Schroder: Mirror mirror on the wall, who's the most skibbidy of them all? Vote now<hyperlink removed>!; Please join me in honoring the esteemed members of the 2024 and 2025 cohorts with the titles and superlatives they have (unknowingly) worked towards earning their entire lives. Who will win the title of biggest gooner? Who is the biggest gossip? Despite the monarchical rule of Sai and Jake this semester, I believe everyone deserves a voice in decisions of such great import. To cast your vote, please vote via this<hyperlink removed> form by noon Friday; titles will be bestowed during Sophex via a baby guessing game Kahoot.

Please note that those who do not provide a baby picture as well will not be honored in this ceremony; instead, their titles will be taped to their office door for all to see.

Organizing the seminar

To reiterate, the Sophex seminar is a seminar run by first-year mathematics graduate students at UT Austin that is designed to be a safe space for first-year students to practice speaking and to facilitate getting to know each other. This is achieved by only letting first and second-year students attend talks. Typically, the Sophex seminar meets on Fridays from 4:00PM to 5:00PM in the 12th floor classroom, followed by dinner at a nearby location.

Two people are required to run the seminar. In my cohort, it was Jake Wellington and I that ran the seminar. The first-years who run the seminar volunteer or are volunteered the Friday of the first week of classes. The same day, a schedule is formed by assigning a first-year to each Friday in the semester, again by volunteering or being volunteered to do so. Form another schedule the same way for the spring semester at the first meeting of the spring semester. (The organizers may need to ask someone to speak on the first Friday of the spring semester in advance, but it doesn't matter exactly when the schedule is made or solidified. The most important thing is that as many Fridays in both semesters are populated by at least one speaker.)

Every week, the organizers will send a number of emails to a few addresses. On the Monday of the week, send an email to the speaker for the week asking for a title and abstract for their talk. Below is what I sent back in the day:

To: <speaker's email address>
Subject line: sophex title + abstract
Body: Hello <speaker's first name>,

I hope today has been treating you well. I am emailing you for an abstract and title for your Sophex talk this Friday at 4:00PM. Please try to get them to me before Wednesday night -- I will be emailing the two cohorts on Thursday and bumping them again on Friday.

Best,
Sai

Observe that I mentioned that I would email both cohorts later in the week. This is important! By both cohorts, I mean both the first-year cohort and the second-year cohort. Once the speaker emails back with a title and abstract for their talk, send an email on Thursday to both cohorts. Below is what I used to send to both cohorts on Thursdays of weeks with a Sophex talk:

To: math-cohort2024@utlists.utexas.edu; math-cohort2023@utlists.utexas.edu
Subject line: Sophex <date in MM/DD format>: <speaker's first and last name>
Body: Hello all,

Tomorrow, <speaker's first and last name> will speak about <brief description of what they're talking about> at Sophex (4PM, 12.166). The title and abstract:

<title the speaker provided>

<abstract the speaker provided>

<comments and/or plans after the talk>

Best,
Sai

The addresses above must be changed to reflect the current first and second-year cohorts. For example, if the first-years started their fall semester in August 2025, they belong to the 2025 cohort and hence may be contacted via email at math-cohort2025@utlists.utexas.edu. In this case the organizers would email both the 2025 and 2024 cohorts at math-cohort2025@utlists.utexas.edu and math-cohort2024@utlists.utexas.edu.

On Fridays, send a reminder email to both cohorts (this is easiest by replying all to the email sent on Thursday) that the talk is happening. This concludes the emailing portion of organizing the seminar. Naturally the organizers can do whatever they like in place of my samples above, but the important thing is that talks actually happen on Fridays and that both cohorts are informed well in advance.

Snacks appear at all Sophex talks. The rule is that last week's speaker would bring snacks for the next talk. Sometimes this rule is broken in order to bring more snacks, or for example if the Sophex seminar changes cohorts. The first-years should try their best to follow the rule and ensure that people have snacks during the talks.

Despite the low stakes, the organizers should still treat the Sophex seminar as a seminar. What I mean by this is that you do the usual song and dance at the start and end of the talks where an organizer will introduce the speaker and the title of their talk, and at the end an organizer will have everyone clap, ask questions, and then clap again just like Sophex were any other seminar. It's all part of the performance, I guess.

After the talk is done, try to organize dinner plans with the cohort. There are plenty of nearby locations that are suitable for a Sophex-sized party to have dinner at. I used to hold a vote between 3-4 nearby locations, where the options would exclude the place we went to last time to promote exploration. The organizers can do whatever they want, though.

Some miscellaneous details: There used to be a Sophex webpage prior to the math department's website redesign (which happened in Spring 2025), where a collection of most titles and abstracts from previous years were stored. At the time of writing, this webpage has not found its way back onto the new department website, so either I or someone else will have to request for someone with access to restore it. Furthermore, if it gets restored, we will have to request that the new Sophex organizers have edit permissions so that new titles and abstracts can be added to the existing list.

April Fools' Sophex

The April Fools' Sophex talk is an annual event that the first-years put on where essentially the slides are solicited from the entire body of graduate students (and sometimes even faculty). These slides are usually poke fun at various people in the department and it is a lot of fun. The exact way that the slides are obtained and how they are stitched together is rather elaborate, but the email I sent my year has a succinct explanation:

To: math-grad@utlists.utexas.edu
Subject line: April Fools' Sophex: April 4th 2025, 4PM, 12.166
Body: Most Valued Graduate Student,

A wise man once said, “Better a witty fool than a foolish wit.” – Feste (Twelfth Night)

We will gather once again next Friday, the 4th of April, at 4pm in 12.166 to explore the concept of tickling each other wirelessly using abstract concepts like Jokes and Shared Culture among other sources of joy and laughter. Consider contributing to and/or attending this bi-annual meeting of the finest jokers in the department.

Rules for Slides

- One (1) slide per person.

- For $n\geq 2$, the $n$-th slide will be based on the $(n-1)$-th slide. Our procedure for accomplishing this is as follows:
0) Sign up at https://docs.google.com/spreadsheets/d/13tk8mYLSQAoImskWCPCkmxmZyUyWQTDNpVNmyTrGJQM/edit?usp=sharing. Order matters.
1) Make one (1) slide in Google Slides.
2) Email a copy of the slide you made (and only that slide) to the person below you and CC me at sivakumars [at] utexas.edu.
3) Update your status to Done (also shade the appropriate cell green too).
4) Hope that you understood the previous slide correctly, and hope that the next person understands how to proceed given your slide.

- I will periodically check the form and poke people (possibly in real life) who need to make slides but have delayed their contribution for several hours. Our procedure is not dissimilar to a relay race.

- The deadline for slides is 3:00 AM on Friday, April 4th (the day of). Those who fail to submit slides on time will be assigned hours in the CalcLab without pay.

- Feel free to make your slides about anything you want. Obviously, expect to see jokes about our Grad-Advisor and Grad-Coordinator, among other notable figures in the department. Have some fun!

Again, the sign up form is at https://docs.google.com/spreadsheets/d/13tk8mYLSQAoImskWCPCkmxmZyUyWQTDNpVNmyTrGJQM/edit?usp=sharing.

Lastly: Bring snacks if you can. There are health benefits to eating.

Best,
Jen

With solemn regards,
Isaac Martin

Best,
Audrick

Salubriously,
Sai

The above links should still work, so you have an idea of how this works. The organizers should send an email like the one above to math-grad@utlists.utexas.edu two weeks before the actual April Fools' talk takes place. This ensures that there is enough time for slides to make their way down to the bottom. There will inevitably be issues closer to the date of the talk where people tarry in making their slides and sending them to the next person, and it is possible not everyone who signs up will be able to contribute a slide. Do your best.

The most important thing is that the speaker(s) for this talk may be anyone in the first-year cohort and that the speakers do not witness the slides. It may be possible to change things up so that the speakers do get to see the slides, but I think some of the magic is in not knowing.

Reorganizing the seminar

At the end of each semester, an organizer should email Tan Thai to reserve the 12th floor classroom for the Sophex seminar every Friday from 4:00PM-5:00PM for the following semester. Specifically, an organizer must do this sometime in December and sometime in May. (Note that this means that the incoming first-years do not have to do anything for reserving the room in the fall semester that they arrive in.)

The organizers should prepare the first talk of the fall semester and invite the incoming first-years and now second-years to come. This talk should explain how the Sophex seminar works and should set up new organizers and ideally get around to forming a schedule for the semester.

Meeting the incoming first-years

Later in the spring semester, the current first-years will be asked to host a dinner (followed by a chill hang out at Crown and Anchor) for the incoming first-years during their Open House/prospective visit day. The organizers of the Sophex seminar do not need to be the ones to organize this, but a pair of first-years should be the ones to do this. Below is an ordered(!) list of things to consider and address (in the listed order, please!):

Who?: The two organizers for this dinner should invite the entire graduate student body to this dinner.
When?: The prospective visit day is typically in late March or at worst early April (after all, this visit day should be at least a couple weeks before the decision deadline in April). Ask Robyn about the exact date maybe two months ahead of this time. The dinner should start at 6:30pm that evening.
Where?: Up to whoever is organizing, but make sure it is less than 15-20 minutes of walking distance away from the AT&T Hotel and Conference Center, which is where the prospective students will be staying.
Contacting Robyn: Whoever is organizing the dinner should get the details of the date, time, and logistics from Robyn. They will match the instructions here or otherwise be close to them. Let Robyn know also which restaurant the dinner will be at.
Reservations for the restaurant: After contacting Robyn, start by reserving spots for about 30-40 people as soon as you become aware of the visit day dates, if the restaurant takes reservations. It still makes sense to let the restaurant know that a large party will be arriving even if they do not take reservations.
Emails: Robyn will likely let the graduate students know about the dinner in her usual Friday email blasts, but you can also feel free to email math-grad@utlists.utexas.edu within a week of the evening the dinner falls on.
Tax-free form and reimbursement: Robyn will hand you a tax-free form which the organizers for the dinner should fill out and give to the restaurant when paying for the bill. One organizer will pay for the dinner, and Robyn will reimburse them.
Shepherding the incoming first-years: Robyn will forward all the dinner plans you make to the prospective students, and she will also tell them to come meet at the lobby of the AT&T Hotel and Conference Center. The organizers should bring a party of current first-year students with them to meet the prospective students there and to lead them, by walk, to the restaurant. Ideally you will find that any other interested graduate students will be waiting at the restaurant for you all.
Drinks at Crown and Anchor: Following the dinner, at around maybe 9:00pm or maybe even later, you can (should) invite the first years to Crown and Anchor for drinks and more chatting. This time you may opt to drive the prospective students there or walk with them; it will be dark. Make sure that all the prospective students get back to the hotel safely.