# Moumanti Podder: A Rising Star in the Field of Mathematics

#### Moumanti Podder

Acting Assitant Professor, University of Washington

Moumanti Podder is a PIMS sponsored postdoc currently and an Acting Assistant Professor at the University of Washington with a research focus on probability theory, including statistical mechanics, and frequently combines combinatorial tools and mathematical logic with it.

She has been identified as an up-and-coming talent in the field of mathematics and has already distinguished herself at the Indian Statistical Institute, Kolkata; New York University, and now, the University of Washington.

It was obvious from speaking to Moumanti that she thoroughly enjoys what she does, which she speaks about in a cheerful and positive manner. It was a sincere pleasure to discuss her background and upbringing; the positive influences in her life; her work in the past, present and future; and the role of art and hobbies in her life.

This is an extract of the full interview with Moumanti.

*1.* *In the Acknowledgements section of your PhD, you thank teachers all the way back to primary school. How have the instructors that you’ve had in your life helped inspire you to become a mathematician?*

I would like to start with my parents. Both of them studied physics as their major, and this gave them a keen interest in mathematics. They would relentlessly inspire me to delve deeper into mathematical problems from a very tender age, but surprisingly, without the oft-mentioned pressure to perform flawlessly that many Indian kids experience at home. They somehow found the perfect balance between allowing me to take a sneak peek at lots of very interesting and fascinating problems of mathematics in high school, all the way up to the start of my undergraduate program, and advising me to always follow my heart.

I was also very fortunate to have a bunch of very caring, deeply insightful teachers in my high school years (by which, I mean from grade V through XII, because before that age, I do not believe I had enough consciousness to truly pursue knowledge). But these teachers, I have to say, were not limited to the discipline of mathematics. My teachers in every subject were equally passionate in their endeavour to motivate us students.

I think what I wish to stress here is that, whether it was a teacher in mathematics or physics, or whether it was one in the biological sciences, or another in Bengali or English literature — each of them played a crucial role in shaping and moulding my young and malleable brain to become enamoured in the beauty of learning — of asking questions and seeking answers.

In India, unlike in the US, you have to decide pretty early on which field you are going to study in. In other words, liberal arts is not really a thing in India (a system that has its fair share of advantages and disadvantages compared to the system in the US). So, I guess the credit for helping me have my heart set on studying mathematics goes to my parents and my high school teachers.

However, the truly amazing and brilliant professors who came into my life as my instructors and mentors during my undergraduate and master’s program years (I studied a 3-year B.Stat (Hons.) followed by a 2-year M.Stat at the Indian Statistical Institute, Kolkata) were instrumental in furthering my interests in mathematics. I would like to mention a few people in particular: my master’s thesis advisor Prof. Krishanu Maulik, and my two probability instructors, Prof. Parthanil Roy and Prof. Alok Goswami, along with the late Prof. Kamal Krishna Roy, were fundamentally responsible in opening up the immense scope and new horizons of probability theory to me.

These people still serve as my pillars of support. Their pedagogical styles were somehow perfect for motivating me to work very hard and actually apply for PhD programs in the US and Canada that were in mathematics instead of statistics, despite graduating with a statistics major.

By the time I arrived at Courant (NYU) to pursue my PhD in mathematics, I had already decided that probability would be my field. But until then, I was open to many possibilities within the realm of probability. A lot of credit goes to my beloved, fatherly doctoral advisor Prof. Joel Spencer for spiking in me the interest in focusing on discrete probability and combinatorics.

To this day, despite having dabbled a bit in continuous probability and hoping to know more about the continuous aspect in the near future, I know that discrete probability is my true love in academics.

*2.* *Why did you decide to write your PhD on Galton-Watson Trees?*

At first, it was Prof. Spencer’s idea. The reason he suggested this area was because, despite there being a wealth of literature on the study of logical properties on the Erdos-Renyi random graphs, very little was known or formally investigated on the premise of random trees. Moreover, the Galton-Watson trees are one of the most classically studied models of random trees, serving as models for population growth, ancestral or family trees, phylogenetic or evolutionary trees etc.

However, once I started working in this area, I soon realized that the Galton-Watson trees were absolutely beautiful objects to study. They presented with a very natural way of ordering edges in a graph, and so many logical relations, such as the parent-child relation, or ancestry, are naturally defined on these trees. I enjoyed working on this topic a lot and still continue to pursue this topic in my ongoing collaborations with Prof. Spencer and several other people.

In my work with Prof. Spencer, Dr. Alexander Holroyd and Dr. Avi Levy, which I did during my intermittent visits to Microsoft Redmond during 2016 and 2017, I went beyond the confines of Galton-Watson trees and focused on more general rooted random trees. In my work with Prof. Tobias Johnson and Dr. Fiona Skerman, I once again focus on the Galton-Watson trees with very general offspring distributions.

*3.* *Are there any real-world implications/uses for your research? If so, what are they?*

The Galton-Watson branching process that I have studied extensively from a logical-probabilistic perspective in my thesis, and continue to study it in my current research, was propounded by Francis Galton and Henry Watson in order to model/track the possible decline in the aristocratic family lines of the British empire, back in 1875. Since then, this stochastic process has been used to model not only family trees but also phylogenetic trees, such as gene trees and species trees, a fundamental object in understanding the changes in genetic or physical characteristics of biological species over millions of years. My work relates to the study of these objects.

In my work on existential monadic second-order logic on Galton-Watson and other random trees, I study *tree automata*, which are a kind of finite-state machines, i.e. an abstract mathematical model for computation. These are of interest to computer scientists in various algorithms.

In my work on the Potts, colouring and other statistical physical models, especially in the antiferromagnetic regime, on finite trees of bounded degree, we consider problems that are of interest to physicists. Physicists, through their very thorough experiments, have made several predictions/conjectures regarding these models, and we are trying to address rigorous proofs of a very small fraction of these problems.

In my ongoing work on interacting particles systems and Markov chains, we consider models similar to and related to the Fleming-Viot processes, which are crucial mathematical models for understanding allele drift in genetics, and also arise as limits of Moran processes in biology.

*4.* *If you were given an unlimited research budget, what would you like to work on and why?*

Ah, this question is rather hard to answer, since I would probably come up with a never-ending list of everything I have ever dreamed of working on. And moreover, I would not just need an unlimited budget, but also unlimited time… so let’s add the condition that I have been granted immortality to that question.

I would definitely continue my studies with Prof. Spencer and my collaborators on related topics, studying the novel and fascinating marriage of discrete probability and mathematical logic that has formed the basis of my PhD thesis, raising and trying to answer questions that dig deeper and deeper into this regime. This will not stay limited to Galton-Watson trees but would include research on much more general models of rooted random trees, and on random graphs such as the G(n, p) for various ranges of p = p(n), geometric random graphs etc.

I have ongoing collaborations with Prof. Prasad Tetali and Reza Gheissari on what I would loosely call “statistical mechanics”, though it is only a very focused part of the humongous field that claims that name. What we work on are the Potts and colouring models, among other well-known statistical theoretical models, on rooted finite trees of bounded degrees (especially truncations of the infinite regular trees).

This area proves to be quite a difficult field to maneuver through, especially because it is quite uncharted when it comes to investigating the behaviour of the associated Gibbs measures of these models in the *antiferromagnetic *case. I would like to* *continue investigating the numerous questions that plague the minds of scientists in this field.

Apart from these two definite fields, I would probably let my mind wander and pick out interesting topics on its own from among the other branches of probability. For example, a recently started, very nascent collaboration with Prof. Soumik Pal and Dr. Noah Forman is opening up the whole mesmerizing world of the study of Markov chains to me, and it would be worthwhile to pursue this area as well.

*5.* *What is your favourite aspect of teaching?*

Research, no matter how motivated you are, is a long-drawn, slow process, with triumphs and successes few and far between. I love my research, and I would never wish to switch the life I have with any other life where perhaps the work is less challenging but also a lot less engaging, a lot less rewarding and a lot less fun. However, I have realized that when I pair research with teaching in a good balance (and this balance will vary from one person to another), it gives me a very welcome sense of accomplishment.

To elucidate, most days, research in mathematics, given the very hard and very demanding job that it is, does not yield tons of cool results and publications. Most days, we sit down and with dogged determination, ponder one or perhaps two of the myriad research problems that are baffling our minds. Engrossed in this pursuit, it is very easy to berate and belittle yourself when success takes a long time to show up and to blame yourself for not being smart or diligent enough. Whereas criticizing yourself and urging yourself to do better is generally a good practice, too much of it can be disastrous and detrimental to your happiness.

But at the end of the day, if you have taught a class nicely, and perhaps helped students understand the intricacies of the homework problems in your office hours, and then perhaps industriously prepared your lecture notes for the next class, it gives you a very refreshing and much needed sense of having fruitfully completed something, of having some semblance of control on one of the things you do and are good at. It gives you the sense that what you do is important not just from a theoretical perspective, but also because you are helping younger people, and you are, in some sense, giving back to the society.

*6.* *How does your art compliment your work as a mathematician?*

It’s right to say that it “compliments” my mathematics. I think that there are several aspects of how being an amateur artist compliments my personality as a mathematician.

The first thing that I want to say is, part of becoming or growing into a mathematician is to discipline your mind, to train it to start thinking and analyzing problems that it encounters along certain avenues. Of course, innovation and novel thinking is very much needed and appreciated, but not before you have first explored and exhausted known routes and tools, and even then, there is a certain regime of discipline and rules that my mind has to follow.

This is not a feeling of confinement, mind you… there is nothing constricting about this. It is simply the demand of this subject — the subject that is the most rigorous and unfailingly logical and analytical. Painting, on the other hand, lets my mind, in some sense, break all rules and create something that need not even belong to this world. It need follow no rules, and it can have a whim of its own. Sure, if I don’t put the pencil strokes in just the right manner, I would end up creating something that is perhaps unrecognizable, but that is okay.

I suppose this is generally true for any hobby that a researcher pursues. Apart from painting, I engage in some singing, and once again, despite following rules set down by the Hindustani classical musical forms, it lets my mind create a melody in whatever manner it wishes to. I think pursuing these hobbies lets my mind maintain a very nice balance between the several, long hours that I spend ceaselessly musing on mathematical problems, and the time my mind goes on some sort of inward vacation.

*7.* *What’s next for you?*

Definitely trying to stay on in academia. I have never really imagined myself as anything but a young female professor who is passionate about her research and about teaching and helping younger, enthusiastic students. I understand that finding tenure-track positions in academia, especially in pure mathematics, has steadily been becoming more and more challenging and stressful, but I have always been known to be a very optimistic girl with a lot of hope. I am banking on that hope and working hard for now.

I have very few restrictions as to which countries I cannot settle in, and so I shall be applying to a wide range of places this coming fall, for both postdoctoral and tenure-track positions.

Other than that, I suppose I would want to continue pursuing my hobbies, read lots of books, travel, learn new languages and learn to cook new cuisines and adopt a cat (or two) :)

*Contact Moumanti **(As of January 2019)*

**Email:** mpodder3@uw.edu, moumantip3@gmail.com.**Office:** Department of Mathematics, University of Washington, Room C-524, Box 354350, Seattle, WA 98195**Website:** Visit the webpage

*Publications **(As of Sept 2018)*

- Johnson T., Podder M., Skerman F. “Random tree recursions: which fixed points correspond to tangible sets of trees?” — Submitted. Preprint available here.
- Podder M. “First order theory on G(n, cn−1 )” — Submitted. Preprint available here.
- Holroyd A., Levy A., Podder M. and Spencer J. “Existential monadic second order logic on random rooted trees” — Accepted for publication in Discrete Mathematics. Preprint available here.
- Austin T. and Podder M. “Gibbs measures over locally tree-like graphs and percolative entropy over infinite regular trees”. Journal of Statistical Physics, Volume 170(5), Pages 932–951, 2018. Springer US. Preprint available here.
- Podder M. and Spencer J. “Galton-Watson probability contraction”. Electronic Communications in Probability, Volume 22, Paper no. 20, 2017. The Institute of Mathematical Statistics and the Bernoulli Society. Preprint available here.
- Podder M. and Spencer J. “First order probabilities for Galton-Watson trees”. A Journey Through Discrete Mathematics: A Tribute to Jiˇr´ı Matouˇsek, Pages 711–734, 2017. DOI: 10.1007/978- 3–319–44479–6. Springer International Publishing. Preprint available here.
- Maulik K. and Podder M. “Ruin probabilities under Sarmanov dependence structure”. Statistics & Probability Letters, Volume 117, Pages 173–182, 2016. Elsevier. Preprint available here.
- Maulik K. and Podder M. “Inverse Problems under Sarmanov dependence structure” — Submitted. Preprint available here.

*Academic Awards & Achievements **(As of January 2019)*

**Degrees: **Bachelor of Statistics (Hons.) and Master of Statistics (Indian Statistical Institute, Kolkata, India). PhD (New York University, USA)

**Awarded the****NSF/AWM Travel Grant**, Association of Women in Mathematics, for the academic year 2018–2019**Winner of the****Harold Grad Memorial Prize**, awarded by the Courant Institute of Mathematical Sciences, for the academic year 2015–2016.**Henry MacCracken Fellowship**, Graduate School of Arts and Sciences, New York University, 2013–2018.**INSPIRE Scholarship for Higher Education (SHE)**, Department of Science and Technology (DST), Government of India, 2008–2013.- Successful in the
**Indian National Mathematical Olympiad (INMO)**, 2007 and 2008. Participated in the International Mathematical Olympiad Training Camp (IMOTC) conducted by the National Board for Higher Mathematics (NBHM).