S Arjun.

Please start by introducing your professional journey in academia

So this is Sumaya from Chennai. So, I'm currently working as an assistant professor at Satiba Institute of Science and Technology, Chennai. I completed both my undergraduation and post graduation in Stella Morris College. And I obtained my. Degree from UH Assistant College of Engineering. So so my area of research is fixed point theory and applications. The teaching has always been a passion from my young age. But after joining for PhD. I had a strong interest in. Research. So I hope I would. I hope I. Our focus on both the teaching and. Research in my future.

You mentioned fixed point theory as your research area, Dr. When you're teaching a new class, how do you introduce a foundational concept—like fixed point theory—to students who've never encountered it before?

So fixed point theory is nothing but. A point that remains. Same even after the transformation. That is called the fixed point rate. So I can. Tell I can tell them. A real life scenario. So in an ATM machine. Enter RS500, I will get back the same favorite. I will not get any other values so we can say that. That is a fixed point. Or when I'm studying a coffee. So anyways. Finally end up. With the point I started. So in that way we can say or mathematically. I can say that we define a function. From as non empty. What was it so we?

So fixed point theory is nothing but. A point that remains. Same even after the transformation. That is called the fixed point rate. So I can. Tell I can tell them. A real life scenario. So in an ATM machine. Enter RS500, I will get back the same favorite. I will not get any other values so we can say that. That is a fixed point. Or when I'm studying a coffee. So anyways. Finally end up. With the point I started. So in that way we can say or mathematically. I can say that we define a function. From as non empty. What was it so we? The function is a fixed point. East X is equal to X itself. So we can give. So we can give some simple examples to let them understand the concepts.

So you use real-life analogies like the ATM and coffee to ground the abstract idea—nice approach. When you introduce a concept like that, how do you check if your students have really understood it, especially in the early weeks of the course?

Alright, so you give them simple examples and real-life analogies to help them grasp the core idea. When you present these examples, how do you check if students actually understand the fixed point concept, especially in those first few classes?

So I give a very simple example. I define a function as T of X is equal to X ^2 minus. So when they are answering back, we can easily find out. They have understood the concept. Or they will be very enthusiastic too. Answer the. Those questions As a teacher, we can find it. If the students are understanding the concepts or not.

So I give a very simple example. I define a function as T of X is equal to X ^2 minus. So when they are answering back, we can easily find out. They have understood the concept. Or they will be very enthusiastic too.

Dr.,

Okay, you mentioned that as a teacher, you can usually tell if students are understanding or not. Thinking about your own classroom, can you share an example where you realized students weren’t getting a concept, and what you did to help them grasp it?

Thinking out of doing.

Thinking out of doing. Can you please repeat the questions?

You were saying "thinking out of doing"—did you want to add more to that example, or is there a specific incident you had in mind where you realized students were struggling and you changed your approach?

Mm-hmm.

So if they're not understanding. I'll repeat it. Repeat the concept. Or I'll I'll teach them slowly so. Cannot go fast.

Until they understand it, I ex. Explain it once again.

Okay, so your usual strategy is to slow down and repeat the concept if students are struggling—makes sense.

Right, so you'll keep explaining until they really get it. Thinking back to your research on fixed point theory, have you ever found that your own research insights directly shaped or changed the way you teach a particular topic?

Set uh, my own receipt is fixed point. Get an application.

Okay, so you’re saying your own research in fixed point applications influences your teaching. Can you give me a concrete example of how you’ve brought a result or method from your research directly into an undergraduate lesson or assignment?

So I'm teaching for engineering students so. They will not have this topics in. So in uh. In the BSE mathematics there is a course called Real Analysis. Did we study about a fixed point and ban a fixed point theorem?

Dr., given your research focus in fixed point theory,

So my. Research is basically. Extension of. The benefit fixed point theorem. So fixed point theory. It always have a wide range of applications. Applied changes because. The existence of fixed point is always equivalent to finding the existence of. Solutions to many mathematical models. So it always have application that there will be no backdrop for it.

I can I can always find a new metric spaces or I can prove a fixed point.

You’re emphasizing the broad applicability of fixed point theory, especially for existence results in mathematical models.

You mentioned you can always find new metric spaces or prove a fixed point—so you're focusing on extensions and generalizations within fixed point theory. Given that, how do you plan to align your research agenda with VIT’s expectation for high-impact publications in reputed journals?

I collaborate with international researchers. So with fix those. While working on fixed point theory. So I can definitely go for high impact factor journals and prod.

I collaborate with international researchers.

You mentioned teaching engineering students and some exposure to fixed point theory in BSc mathematics. Suppose you’re running a large Real Analysis class where slides aren’t allowed—how would you design an in-class activity or exercise to get students actively engaging with the material instead of just listening to you lecture?

You brought up collaborating on research and targeting high-impact journals, which is great for institutional visibility. Let’s talk a bit about departmental service. Suppose you joined our department and found that outcome assessment data for accreditation was inconsistent across different mathematics courses. How would you approach fixing that?

I collaborate with international researchers. So with fix those. While working on fixed point theory. So I can definitely go for high impact factor journals and prod. Like before, but. So can you, can you repeat the question because. You're talking about students and collaboration. I'm getting done.

Right, you mentioned collaborating with international researchers and aiming for high-impact journals, but my question was more about departmental responsibilities. Let me repeat: suppose you joined our department and found that outcome assessment data for accreditation was inconsistent across mathematics courses—how would you approach fixing that?

So what do you mean by outcome assessment data for? Patient. Not confused with the research and teaching.

See here I one side. Duochen. Collaborative Research.

Sure, that's a fair question.

Okay,

And so. Grading on. Department is forcing for water. Closing floor The fixed point here is a pure Max paper, so we don't need. The labs for this one.

And so. Grading on. Department is forcing for water.

Alright, let’s talk about connecting your academic work to industry outcomes. Given your expertise in fixed point theory and its applications, have you built any relationships with industry or research labs that could help students land internships or see where this theory is used outside academia?

The only things I focus on. Publications with high imp. High-impact journals.

The only things I focus on. Publications with high imp. High-impact journals. Yeah.

Okay, Dr., let's shift focus.

Alright, so you’re focused on publishing in high-impact journals. When it comes to teaching, how do you make sure your communication style actually helps students understand complex topics—especially if some of them struggle with abstraction?

Alright.

It's all about explain, explain. Them with the language they are. Make them as a group and ask them to discuss something and then I'll ask questions. So it would be like a group discussion. It will make the class interesting.

So you make sure students are using their own language and encourage group discussion to keep things lively—sounds like you value interaction.

And we can go for flipped classrooms also. So the the post graduation students have. Project in the last semester. So, uh. When I I'll, uh, if I'm guiding them. I will ask them to go for the.

And we can go for flipped classrooms also. So the the post graduation students have. Project in the last semester. So, uh. When I I'll, uh, if I'm guiding them. I will ask them to go for the. Basics of fixed point theory? Definitely health ML. Explain them the basic. Yes, first I'll ask him to learn the basics.

So you mentioned the option of flipped classrooms and guiding postgrad students on their projects,

Alright,

And and and then there will be. For presentation. After that. And if they start presenting their work, they.

So you bring in presentations to check their understanding as they go—sounds like you prefer ongoing feedback, not just a final grade. When you’re evaluating those presentations, what kind of criteria do you focus on most?

And and and then there will be. For presentation. After that. And if they start presenting their work, they. He definitely asked him for presentation. So I focus. That they understood the con. Clearly so instead of justice. Learning equation something I want them to understand it. Understand. Present so when they are presenting I can guess. Their level of understanding.

And and and then there will be. For presentation. After that. And if they start presenting their work, they. He definitely asked him for presentation. So I focus. That they understood the con. Clearly so instead of justice. Learning equation something I want them to understand it. Understand. Present so when they are presenting I can guess. Their level of understanding. If if not I will help them. And then I will give them some problems to solve it. Grading for exempt duties or. The research presentation, Sir.

So you’re looking for true understanding in those presentations, not just memorized content.

Alright, so you look for real understanding in their presentations and help them if they're off track. When you're handling exam duties, like preparing or grading written exams, how do you make sure the process is unbiased and aligns with the department's standards?

So because. We when we are grading the. Exam answer sheets. We will be given an answer key and for that. Every step the step marks will be given so we have to follow them so it will. It will not be. Biased for sure. Follow the answer key. Sword.

Alright, so you're careful to follow the answer key for exams and step marking to keep things fair. Shifting focus a bit—when you've published your work, have you been able to get articles accepted in journals that are widely recognized in your field, and can you share which ones?

I have more articles which was widely recognized.

From the first one, the one which was published in Filomat.

Okay,

Filomat is definitely well known in the field. What was the core contribution of your paper published there, and how do you see that result impacting ongoing research or applications in mathematics?

So the work published in Filomat was controlled by. Ansari, metric spaces and fixed point theorems. So in that paper. I have defined a new metric called control DB. Brancieri Matrix. Control V Brancherometric spaces. And. A fixed point theorem. Have given an application for solving. Distance and uniqueness of. A solution for the inferom integral equation. So, uh, the result is. Is jointed result. I extended my result to the next paper. It was published. Uh, PSA Journal.

Alright, so your Filomat paper introduced a new metric space and applied it to fixed point theorems and integral equations, and you mentioned following that up with a publication in PSA Journal.

Dynamic systems and applications. So following that I publish an article in. So I I don't go for industry things because it is a pure mathematics.

Alright, Dr., so your focus has been on pure mathematics and theoretical research, not industry applications. Thinking about your teaching style—when you’re explaining really abstract mathematical concepts, what’s your go-to strategy to make sure students truly grasp the material, especially those who might struggle with advanced topics?

But I approached. Any year, researchers. In my. So we when we explain. Concept compare it with the real life scenarios so that the. That is the way we. Three students attention.

Alright, we're wrapping up. Is there anything you'd like to ask about the role or the team?

It's all about. Explaining the things that. Is that I feel that matters.