Oh yeah, sure. Arson. Go ahead.

Please start by introducing your professional journey in academia

So. I started my academic journey when I joined UH Sri Venkateswara College. And I did a BSc Honors mathematics from there.

UH Sri Venkateswara College for your undergrad — right. And did you go straight into graduate studies after that, or was there something else in between?

After that. That I was. I was appointed as integrated PhD. Right. Yeah. Actually, I think I directly went for that. Oh, so I completed my undergraduate in. 2000. Uh, 2015.

Okay, let’s shift gears a bit. Professor, when you’re teaching introductory mathematics to undergraduates, what’s one foundational concept you particularly enjoy introducing, and why?

So after that I was I joined as an integrated pH D at Aiser Mohali. So basically like when students come from. When they come for undergrad from school. One thing that they're curious about is. Where is maths being applied? Like whatever they learned? Suppose they learned. About uh. Derivatives and integrals and all of that. So where do they apply it in real life? So when I introduce a subject, I basically come up with real life applications so that they feel motivated to study that. Oh yeah, and that's my answer.

So you focus on connecting calculus concepts like derivatives and integrals to real-world applications to motivate students — that’s a strong approach. Can you give one concrete example of how you link a mathematical concept to something practical in your classroom?

All right, sure. So for example, there's this linear algebra concept where you use. Eigenvalues and eigenvectors.

Alright, so you use eigenvalues and eigenvectors from linear algebra as a practical example. Can you walk me through how you’d make that concept relatable for students—what’s the real-life application you highlight?

So nowadays like. Like everybody has a mobile phone and everybody uses Internet. So I basically tell. Yeah. So the example that I give is Google's Page Rank algorithm. So whenever. Would they search something? What happens is. That it comes in some order.

Right, so you use Google's PageRank algorithm as a real-life example to show how eigenvalues and eigenvectors come into play. When you walk students through that, do you ever run into misconceptions or confusion about how linear algebra connects to something like web search? How do you address those moments?

And for that? What algorithm is being used like it? The foundation lies. In concepts of linear algebra. Right. Try it.

Professor, I noticed your doctoral thesis was titled “Skeleton ideals of graphs and their associated invariants.” How did you approach simplifying that research for undergraduate students or non-specialist audiences?

All right. Firstly, I would like to say that's a great question. So I would like to. So I start with a very basic example. Suppose there is a parking lot. And. There are like end parking. Spaces. So suppose I consider a parking lot with, say, 3 parking spaces. And the three cars that are. Entering that parking lot. Now each driver has a preferred parking place. Suppose the 1st.

All right. Firstly, I would like to say that's a great question. So I would like to. So I start with a very basic example. Suppose there is a parking lot. And. There are like end parking. Spaces. So suppose I consider a parking lot with, say, 3 parking spaces.

You start with a parking lot example to make the structure of skeleton ideals more accessible — that's clever. When you use that analogy, do students ever struggle to connect the abstraction back to graph theory, or do they grasp the link pretty quickly?

Mm-hm.

So initially like. If you are introducing this concept to somebody who's not. Familiar with this? So it'll take some time to familiarize. Themselves with the concept, but once they understand this analogy, it becomes pretty easy. To see like. Where droughts come into picture?

Yeah, it becomes very easy to see where graphs come into picture.

Yeah, you mentioned it takes some time for students to get comfortable with the parking lot analogy, but once they do, the graph connections become clearer. That sounds effective.

Right, so once students grasp the analogy, making the jump to graphs is straightforward for them. Professor,

Right.

Alright, you’ve made clear how the analogy helps students bridge to graphs. Professor, let’s pivot a bit — when you’re guiding student projects or research, how do you encourage them to connect theory to practical outcomes?

So when a student is. Like working on a project I basically asked them to. You know, read whatever has been done in that aspect. Like what other researchers have done or how are these concepts related to? Anything else that? Exist in literature and then. Try to come up. Web things because in algebraic combinatorics what we generally do is. We relate to completely unrelated object. So yeah. That's my motivation.

Professor, given your experience in algebraic combinatorics and graph theory, where do you see the most fundable research directions over the next three years? What kinds of grants or external funding opportunities would you pursue to sustain your work and build a research group?

So let me like. Answer your first question. By an example. So I I recently proved a result where I showed that. Uh, if you consider. If you consider a connected graph and you look at its resistance Laplacian matrix. Then the the eigenvector corresponding to its largest eigenvalue it partitions the graph. It gives a partition of the graph such that the two components that we get, they are connected.

Okay, you just described a result where partitioning a graph by the eigenvector of its resistance Laplacian’s largest eigenvalue yields two connected components. If you wanted to turn this into a long-term research program at VIT, what would your strategy be for attracting external funding or building a research group around this direction?

So a similar result is also known for Laplacian matrix, but in terms of algebra. Uh, eigenvector corresponding to algebraic connectivity. I'm. Right. Yeah, so. Just a minute, I have not completed my answer yet for the first question. So for. When you look at Laplacian matrix. Using the. The eigenvector corresponding to algebraic connectivity. That has its applications in data science.

So, people. Use it for clustering and. Uh, dimensionality reduction.

Alright,

So you’re connecting the Laplacian matrix’s eigenvectors to clustering and dimensionality reduction in data science. If you were seeking external funding for this research, what’s your pitch for its broader impact or industry relevance?

So now like my focus is. All right, so this concept. Of this feedler vector partition given by of. This feed. It has been used in data science. Like for clustering basically.

I'm using my result. We have seen that. Even, uh. Resistant like even the eigenvector for the resistance Laplacian gives similar result.

You’re focusing on how the Fiedler vector is used for clustering in data science — that’s a solid link between theoretical math and applications. Now, Professor,

You’ve tied your research to clustering and connected partitions, which makes the applied angle clearer. Now, Professor, let’s shift to teaching for a moment. Suppose you’re running a large mathematics course at VIT University with students from diverse backgrounds — how would you design your sessions to actively engage everyone, rather than relying on traditional lectures?

So there's. There's this one, Uh. Thing that I particularly do, so when you teach a large classroom, there are many students who grasp the concepts really quickly. While there are some students who really struggle and. Like umm. They take comparatively more time. So what I do is. I basically. Give like. I give more questions to the group. That has already like. Who are able to learn at a faster pace so that they don't feel that they are being left out. And at the same time, the students who? Take more time to learn. Like they'll have. Basically more time to grasp things in the classroom.

Alright, so you differentiate by giving advanced questions to faster learners, while letting others take their time to absorb the basics. How do you assess whether this approach is actually working for the whole class, especially for those who might be struggling quietly or disengaged?

All right, in such a situation, what I would do is. I'll conduct tutorial sessions where I divide the entire class into groups. And I'll try to evaluate. How it is? Group is performing.

All right, in such a situation, what I would do is. I'll conduct tutorial sessions where I divide the entire class into groups. And I'll try to evaluate. How it is? Group is performing. And yeah, that'll be my strategy that I'll use.

Accreditation cycles can be demanding — if you joined our department and found that outcome assessment data was inconsistent across courses, how would you approach fixing that?

You described dividing the class into groups for tutorial sessions and monitoring their progress — that's a practical way to get direct feedback. Now, Professor, accreditation cycles can be demanding. If you joined our department and found that outcome assessment data was inconsistent across courses, how would you approach fixing that?

Could you rephrase this question?

Sure, let me rephrase. If you joined our department and noticed that the data collected for assessing student learning outcomes wasn’t consistent across different courses, what practical steps would you take to make sure the assessment process meets accreditation standards?

Firstly, I would like to. I would like to conduct a survey. Uh, like from the students?

To see like how much? They are able to understand and what according to them.

To see like how much? They are able to understand and what according to them. Yeah, umm.

Alright, so you’d start with a student survey to understand how outcomes are being measured. If that didn’t resolve the inconsistency,

You’d use the survey to gauge student understanding and see what they consider important. How would you ensure that your findings from the survey translate into actual improvements in how the department collects and reports outcome data for accreditation?

Alright, you’re using surveys to gauge student understanding and see what they value in their courses. How would you make sure those insights actually lead to real improvements in how the department tracks outcomes for accreditation?

All right, the. Observations that. I'll get from the survey. I would like to discuss it with other faculty members. And I would request them to do the same so that we can come up with a common solution.

All right, the. Observations that. I'll get from the survey. I would like to discuss it with other faculty members. And I would request them to do the same so that we can come up with a common solution. So that. Like this problem can be solved Right.

So you'd take the survey results and bring them to the faculty for a discussion, aiming for a unified solution. How would you handle disagreements among faculty if some are resistant to changing their assessment methods for accreditation?

You’d bring the survey findings to the faculty and try to reach consensus — that’s collaborative. If you faced pushback from colleagues who didn’t want to change their assessment practices, what strategies would you use to persuade them and ensure compliance with accreditation standards?

So one way I would see doing that is like. Listing down pros and cons for the methods that they're using for this. So like my method that I come up with and the. Practices they are already using. We can make a program list. Then see like which one is better and to. Which method? So being more responsive to. I think that'll work.

Imagine you’re teaching at VIT and a student files a formal complaint alleging your grading is biased. Meanwhile, your department head is pressuring you to improve pass rates. How would you handle this situation to protect both academic integrity and your professional relationships?

In that scenario. What I can do is. Uh, I can probably like. Hand out. Umm. Like hand out assignments to them or like give open book problems or open book test? And then? Increasing like on the basis of that I can give them grading In that case I would like to discuss it with the head. And also with the other faculty members. Like what? Approach their. In their class in order to do the same.

In that scenario. What I can do is. Uh, I can probably like. Hand out. Umm. Like hand out assignments to them or like give open book problems or open book test?

Okay, so you're considering more flexible assessments like assignments or open book tests to address the complaint and the department head’s pressure. But if the department head disagrees with your approach and insists on raising grades quickly, how would you respond?

In that case I would like to discuss it with the head. And also with the other faculty members. Like what? Approach their. In their class in order to do the same. By taking that into consideration, probably I'll inculcate something in my teaching.

Given your background in mathematics, do you have any connections with industry or prior collaborations that could help students at VIT University secure internships or placement opportunities?

So you'd consult the head and other faculty to see how they're handling grade inflation and complaints, then adapt your own methods based on that input. Switching gears a bit — have you ever brought real-world industry problems or case studies into your mathematics courses, maybe through consulting work or collaboration? If so, can you give a concrete example?

Not till now, but as I mentioned earlier, I'm working on this.

From where I'm looking at club. Castering given by uh. Real clustering given by resistance Laplacy matrix.

Alright, so you haven’t brought in industry case studies yet but you’re working toward it. If you had to start tomorrow,

Right.

Okay,

You mentioned resistance Laplacian matrix for real clustering — how would you present that concept so students see its relevance to practical industry data challenges, not just pure theory?

So for that I would like to use some data sets. Like this Half Moon. Set and other. Actually, uh. The result that I'm talking about it seems to work on these. Data. So I'll just give these basic examples to give them an idea that it works on these. Datasets and on the basis of that I'm trying to. You know, I'm trying to prove that it works for higher data sets as well.

So you'd use datasets like the Half Moon set to show students how resistance Laplacian clustering works on real data, then scale up the examples.

And that would be my answer. Right. Could you repeat the question please?

You were talking about collaborating with an industry partner—say, a company working with large-scale network data—and I asked how you’d adapt your classroom approach using resistance Laplacian clustering to help students tackle those kinds of practical challenges.

OK, so in that case I would like to. I would ask my students to firstly work with basic examples and then. See, like how it's being used in? Much more generalized data.

So you'd start students with basic examples, then gradually move toward more generalized data to bridge the gap with industry problems. Professor,

All right, so I'll. Give you one example of. So it's. Uh, I. Taught in a. Village near my home. I taught. In an orphanage. So there was this student. Whom I asked to. Learn the formula of A+B Holy. Right, so. I and I asked him to write it five times. So he learned that formula and he wrote it 5 And then once he showed it to me, I gave. Right And then once he showed it to me, I gave. Right. So actually 1 issue with them was. They the concepts that were taught to them, they were wrong. And moreover, their mode of instruction was Hindi And then once he showed it to me, I gave. Right. So actually 1 issue with them was. They the concepts that were taught to them, they were wrong. And moreover, their mode of instruction was Hindi. I and I have started. Late match in English, so firstly I had to. Like shift to like I had to learn. The naming of. Mathematical concepts in Hindi and then explain it to them.

And using that approach like maybe they can build up for. Real life data sets as well. Right. Right.

Alright, so you want students to build up from simple data sets to more complex, real-world examples using that clustering method. Thinking about teaching at VIT University, how do you adjust your approach for students with different learning styles—say, visual learners versus those who need hands-on practice? Can you give a specific example from your mathematics courses?

All right, so I'll. Give you one example of. So it's. Uh, I. Taught in a. Village near my home. I taught. In an orphanage. So there was this student. Whom I asked to. Learn the formula of A+B Holy.

You taught at an orphanage and gave a student the formula for A plus B squared — sounds like you were adapting to their environment. Can you share how you modified your explanation or teaching method to help that student understand, especially since they might not have had the same resources as others?

So. That was one of the things and also I prepared notes for them, like using sketch pens or colorful drawings. So that they would find it interesting.

Alright, so you had to learn mathematical terminology in Hindi to bridge the language gap for your students in the orphanage. When you join VIT University, how do you plan to balance teaching, research, and service duties so you’re still able to support both the institution’s academic goals and your students’ development?

Okay, so you used sketch pens and colorful notes to make things more engaging for students with fewer resources. Now, thinking about your experience with curriculum development—have you ever contributed to shaping or revising math courses to meet accreditation standards, and if so, how would you approach aligning that work with VIT’s academic programs and objectives?

All right, so. I served as a tutor for BSMS course at ISA Mohali. In Aiser Mohali, many students who came. For BSMS program after class 12th. They did not have any maths background in class 12th.

I took their extra lectures and I planned out like what all concepts to teach.

I took their extra lectures and I planned out like what all concepts to teach. From cloud. Past 11th.

So you worked as a tutor for BSMS students at IISER Mohali, where many had little math background.

Alright, so you planned out extra lectures for BSMS students who lacked math background. Can you share a concrete example of how you contributed to reshaping the curriculum or course materials to help those students meet accreditation or academic standards?

Okay, so you planned out extra lectures and started from grade eleven concepts to help BSMS students catch up. Can you give a concrete example of how you changed course materials or structure to better meet accreditation standards or VIT’s objectives?

So one thing that I did was. I firstly saw. What was being done in the class? In order to understand that. What concepts do they need? So that's how I started I. It's not like I did everything from class 11th and 12th. SIGMOD courses, but I saw whatever was. Being done in their BSMS codes and what all basics they need for that. So I prepared. That background, while there, they were also learning in the. So both. The things. Going hand, hand in hand.

At the same time.

So you reviewed what was happening in their BSMS classes and built just enough foundational material to support those concepts,

You mentioned preparing background material to help students catch up while they learned new concepts. Now, let’s talk about your expertise in supply chain management, advanced statistical methods, and applications of deep tech or AI in mathematics. Say you’re teaching a course where students have to analyze a real-world supply chain problem—how would you guide them to use advanced statistical techniques or AI to optimize it?

I have not yet used these concepts like. Uh, in the sense like I've not applied my research or my teaching to these concepts yet. But I would like to learn and see how.

You haven't applied those concepts yet, but you're open to learning and integrating them. Let's switch to student evaluation for a moment—when you're responsible for exam duties or grading, how do you ensure fairness and consistency, especially with subjective responses or open-ended mathematical proofs?