Counting his blessings in math and nature, with PIMS PDF Venkata Pantangi
By Robyn Humphreys, PIMS Communications and Event Assistant
Venkata Pantangi arrived in Lethbridge, Alberta, last August. He notes that the view of the Oldman River from his office is the best thing at the University of Lethbridge. That said, there are many beautiful trails on the campus along the river as well. Venkata loves a hike. While in China, he made an effort to walk through the Lychee tree trails at the Southern University of Science and Technology (SUSTech). Immediately after settling in Lethbridge he travelled to Banff, visiting Lake Louise and Johnston Canyon, and he plans to return and explore more trails once the pandemic subsides.
“The best thing about hiking for me are the sights,” Venkata explains,“I am mesmerized by the view of water bodies from atop a hill or mountain. When time permits, I would love to do some hiking in the Himalayas in India. I visited them once in 2015, and haven’t found a prettier view.”
Seems poetic then, for one whose current work is on Movement and Symmetry on Graphs, to be so taken with the movement and symmetry found in nature.
Tell us about your research and what are you most interested in?
My research is in the area of algebraic combinatorics. I am interested in (a) applying representation theory and finite group theory to compute some numerical invariants of certain combinatorial objects; and (b) investigating group theoretic/linear algebraic analogues of some classical results in combinatorics.
My doctoral thesis at University of Florida, under the supervision of Prof. Peter Sin, was on computing the Smith normal forms (SNF) of combinatorial incidence matrices. The SNF of an incidence matrix is a powerful invariant that may help distinguish the underlying incidence structure. I computed the SNF’s of the adjacency and Laplacian matrices of graphs. The SNFs of Laplacian matrices of graphs arise in combinatorics in the context of chip firing games, as the abelian sandpile group in statistical mechanics, and also in arithmetic geometry. Representation theory of automorphism groups of these graphs proved useful in computing the SNFs.
What have you been working on and how did that lead to your connection to Professor Karen Meagher (University of Regina)?
During my first postdoc at SUSTech (Shenzhen, China), I worked on the permutation groups analogue of the classical Erdős-Ko-Rado (EKR) theorem from extremal set theory. There are many different analogues of the classical EKR theorem, all of which can be transferred to finding the independence number of certain graphs, and classifying the independent sets of maximum possible size. The permutation group analogue of EKR is about independent sets in the derangement graphs of permutation groups. Once again, representation theory and group theory provide important tools to find more about these independent sets. While at SUSTech, I wrote with Prof. Cai Heng Li (my supervisor at SUSTech) and Dr. Shu Jiao Song. After a few months, I found that Prof. Karen Meagher and her collaborators wrote a paper on a similar kind of problem. I corresponded with Prof. Meagher after reading her paper.
Prof. Meagher informed me about an opening for a Postdoc position with the PIMS CRG on Movement and Symmetry on Graphs. As part of the group, I am able to collaborate with Prof. Joy Morris, Prof. Karen Gunderson, and Prof. Meagher. We are currently working on an extremal graph theory problem closely related to the EKR problem.
This is your second postdoc. Do you feel there is a difference in your graduate research at UFlorida and PDF research?
I don’t find any difference to be honest. Both as a graduate student and as a postdoc, I had the freedom to choose my research problems. At the same time, I have been fortunate enough to have the safety net of my supervisor’s/PDFmentors’ excellent guidance.
Many postdoctoral researchers get the opportunity to teach some undergraduate and graduate courses. What has been your experience?
In fall of 2021, I was teaching an in-person class of Group and Ring Theory. This was one of my favourite topics as an undergraduate and so I was very excited to teach the course. I was fortunate to have some passionate and inquisitive students, whose questions made me look at the area through a different perspective. In China, I helped teach an advanced Combinatorics course. Having never taken one in my years as a student, it was a fantastic opportunity for me to learn the topic. This spring, our CRG is offering a PIMS course on extremal combinatorics (see syllabus). I am looking forward to gaining the experience of teaching an advanced graduate course.
Venkata Pantangi obtained a BS-MS dual degree from IISER Pune in 2012. In 2019 he obtained a doctorate from the University of Florida, under the supervision of Professor Peter Sin. From 2019–2021, he worked as a postdoc at the Southern University of Science and Technology in China, under the mentorship of Professor Cai-Heng Li. Currently, he is a PIMS CRG postdoc at the University of Lethbridge, under the supervision of Professor Joy Morris, and is a member of the CRG on Movement and Symmetry in Graphs.
Venkata will be speaking at the PIMS Emergent Research Seminar Series, on January 26, 2022, at 9:30 AM Pacific. Details on his talk, EKR-Module Property, can be found here.
