Sharing Research, Making Connections: A Tale of Two Mathematicians at JMM

Figure 1.

Maggie Miller takes notes while Devashi Gulati presents her talk at JMM 2024.

Maggie Miller had just one day to spend at JMM 2024 in San Francisco.

A first-year assistant professor at the University of Texas at Austin (UT) and a Clay Research Fellow, Miller had another math conference to go to that week. But having attended JMM for more than a decade meant she knew her way around.

On the opening morning of JMM, Miller would present her research. That afternoon, as people flooded to the awards ceremony elsewhere at JMM, Miller perched on a chair in the front row at “Searching for Triple Grid Diagrams” by Devashi Gulati.

“It’s sort of about two areas of math, one of which I know a lot about and one of which I know less about, so I like that it might make the second more accessible to me,” she said.

“But to be honest, part of the reason I’m looking forward to the talk is that the speaker is a PhD student, so I’m happy to see her doing something interesting. I feel like it would be more normal to say one of the plenary talks is interesting, but I honestly like the regular talks better.”

Miller had seen a few shorter versions of Gulati’s talk at other conferences and was intrigued. “I was surprised by a theorem she had proved with her coauthors—they proved that triple grid diagrams exist for any Lagrangian surface in CP2, which I believe she has stated as a conjecture in previous talks,” Miller said. “I had asked one of her coauthors, Sarah Blackwell, about it a long time ago and had the impression that a general existence theorem wasn’t likely on the horizon, so I thought that was quite good.”

Figure 2.

Devashi Gulati.

Devashi Gulati is a PhD candidate in mathematics at the University of Georgia in Athens. She attended BITS Pilani in Goa, India, for her master’s degree in mathematics and bachelor of engineering in computer science, earning both with honors.

JMM 2024 was Gulati’s first mathematical speaking engagement longer than a lightning talk. She had never attended JMM before.

Gulati explained her talk this way: “Sarah Blackwell, David Gay, and Peter Lambert-Cole defined what triple grid diagrams are… a one-dimensional higher analogue of grid diagrams, using trisections. Grid diagrams are useful since they are a combinatorial representation of smooth objects, which computers can work with. But triple grid diagrams are hard to find.

“My advisor [Lambert-Cole] and I tried to computationally search all grid diagrams, but that turned out to be a resource-intensive endeavor. We also found many, many examples which were combinatorially different but the underlying surface was mathematically equivalent. So, we decided to take advantage of the context of these diagrams to try to determine when they are equivalent.

“That led to us looking at the structure of the collection of all triple grid diagrams, called the moduli space. Doing so, we realized that if we fix the underlying graph, we get a space of triple grid diagrams associated with it which represent the same underlying surface. Furthermore, we were also able to define ‘moves’ on triple grid diagrams.”

Gulati’s talk was part of the AMS-AWM Special Session for Women and Gender Minorities in Symplectic and Contact Geometry and Topology, held every other year for the past eight years. Each time the session runs at JMM, the previous occurrence’s organizers find the leaders for the next installment.

“When choosing speakers for the session, the main goal is to invite people within this research network, with a particular focus on graduate students and early career mathematicians who are about to graduate and/or currently on the job market,” said the aforementioned Sarah Blackwell, an NSF Postdoctoral Fellow at the University of Virginia, who organized the 2024 session with Luya Wang of Stanford University and Nicole Magill of Cornell University.

This year, “we tried to invite speakers working on a wide range of topics within symplectic geometry,” Blackwell said. “As it turns out, I actually do happen to know more about Devashi’s topic, because I know her personally, and part of my dissertation was closely related to what she is doing.”

Figure 3.

Maggie Miller.

She is just 30—even named one of Forbes magazine’s “30 Under 30”—but Maggie Miller, winner of the Maryam Mirzakhani New Frontiers Prize, is an old hand at the JMM.

Sponsored by AMS travel grants, Miller attended the JMM as a UT undergraduate in 2013 (San Diego), 2014 (Baltimore), and 2015 (San Antonio). She participated in JMM 2020 in Denver while a graduate student at Princeton University.

For 2022’s virtual JMM, as a Visiting Clay Fellow at Stanford University, Miller organized the AMS Special Session on Knot Theory in Dimension Four with Jeffrey Meier (Western Washington University) and Patrick Naylor (Princeton). She also presented research undertaken with Mark Hughes (Brigham Young University) and Seungwon Kim (Sungkyunkwan University), and had an additional research project presented.

Flash back to her first JMM 11 years ago, where Miller earned a joint poster prize and gave her first math talk ever, “Community Detection by Maximizing Partition Efficiency.” The project, with Brendan Shah, an undergrad at Rochester Institute of Technology (RIT), combined math and computer science. “Our program was much slower than existing algorithms, so not at all practical—but it was an interesting problem mathematically,” she said.

“I made slides and then gave several practice talks in front of just Brendan,” she continued. “For me the hardest part was not speaking very quickly.

“I was really nervous the first time I spoke at JMM—even though the talk was only ten minutes long, it was my first time presenting in front of strangers. Of course, now that’s something I have to do all the time. Getting to practice early on gave me a start on developing public speaking abilities, so that by the time I was giving hour-long talks I was a little more confident.”

Miller said of her own talk earlier that day, “I always try to keep JMM or AMS meeting talks a bit general, but I noticed at the start of the talk a lot of students in the back who I thought were likely undergraduate students. So, I explained some of the background more carefully than usual, which was kind of interesting to adapt to with slides, but I think went okay.”

“A grid is a computer-friendly way to code a knot …”

For Gulati, everything went smoothly as a presenter: no slide mishaps and an engaged audience of perhaps two dozen.

At the end of Gulati’s talk, Miller raised her hand.

She asked Gulati what was technically difficult about producing a set of moves relating diagrams of Lagrangian-isotopic surfaces, or even just isotopic surfaces.

“The triple grid diagrams come from another system of diagrams (shadow diagrams) that do have a complete set of moves, so for them to not have proved the same thing for triple grid diagrams means there is probably a technical obstruction,” Miller said. “Devashi implied that the conditions for a triple grid diagram to be valid are very rigid, and the natural move you might guess to do isn’t actually an allowable move on these diagrams.”

After her talk, Gulati said, “I am happy I was able to share the math I have been thinking about recently,” confessing to having been a bit nervous, though it didn’t show in her presentation.

“Attending the JMM was a great experience,” Gulati added. “Usually at conferences, I end up meeting the people who work in only my field, in the USA. At the JMM, I was able to meet not only international mathematicians working in my field but also other mathematicians working in related fields. I was also able to reconnect with some other graduate students who I have met over the years at conferences, workshops.

“As doing math research can be a solitary endeavor, conferences are vital to not only refresh one’s perspective but also connect with others and feel a sense of belonging in the math community. I was able to talk with others not only about math, but also their personal journey doing math.”

Since midway through graduate school, Miller has traveled “a lot” for seminars, conferences, and research collaboration. “In-person meetings have been really influential to my career,” she said. “Most of my projects are joint research, and I can usually point at a specific trip that was the impetus of any given project. I don’t really enjoy brainstorming ideas over email or Zoom, and everything is much more efficient and interesting in person, for me at least.”

Among her conferences, JMM is unique, Miller said. “I enjoy how broad these meetings are, not just in terms of mathematical variety, but the teaching- and career-focused activities, panels on social topics or advice, etc. It’s completely different from any other conference I participate in during the year.”

Miller said that she saves various application deadlines to her calendar “just in case I had a student who would want to go, and will keep doing that in the future…As a faculty member, I would want to send future undergraduate or graduate students to JMM to give talks when possible, just like I did.”