Yes.

Please start by introducing your professional journey in academia

Good morning. I am Doctor V Madan. I have. I completed my MSC. And PhD. In mathematics. I have. 10 years of experience. At both undergraduate. And postgraduate. Levels.

Good morning. I am Doctor V Madan. I have. I completed my MSC. And PhD. In mathematics. I have. 10 years of experience. At both undergraduate. And postgraduate. Levels. Currently I am working. As an assistant professor. In the Department of Mathematics. At Sri Krishna Arts and Science College.

Good morning. I am Doctor V Madan. I have. I completed my MSC. And PhD. In mathematics. I have. 10 years of experience. At both undergraduate. And postgraduate. Levels. Currently I am working. As an assistant professor. In the Department of Mathematics. At Sri Krishna Arts and Science College. My research interest. In functional analysis. Particularly. Hilbert manifolds.

Good morning. I am Doctor V Madan. I have. I completed my MSC. And PhD. In mathematics. I have. 10 years of experience. At both undergraduate. And postgraduate. Levels. Currently I am working. As an assistant professor. In the Department of Mathematics. At Sri Krishna Arts and Science College. My research interest. In functional analysis. Particularly. Hilbert manifolds. And my TK. The interest? Uh, currently I'm taking. Linear algebra. For BSE AIML students.

Alright, so you’ve spent a decade teaching both undergrads and postgrads after finishing your PhD in mathematics. Anything else you’d like to add about your academic journey before we move ahead?

Good morning. I am Doctor V Madan. I have. I completed my MSC. And PhD. In mathematics. I have. 10 years of experience. At both undergraduate. And postgraduate. Levels. Currently I am working. As an assistant professor. In the Department of Mathematics. At Sri Krishna Arts and Science College. My research interest. In functional analysis. Particularly. Hilbert manifolds. And my TK. The interest? Uh, currently I'm taking. Linear algebra. For BSE AIML students. Discrete Mathematics. For computer science students.

Good morning. I am Doctor V Madan. I have. I completed my MSC. And PhD. In mathematics. I have. 10 years of experience. At both undergraduate. And postgraduate. Levels. Currently I am working. As an assistant professor. In the Department of Mathematics. At Sri Krishna Arts and Science College. My research interest. In functional analysis. Particularly. Hilbert manifolds. And my TK. The interest? Uh, currently I'm taking. Linear algebra. For BSE AIML students. Discrete Mathematics. For computer science students. Real analysis for BSE mathematics students.

Good morning. I am Doctor V Madan. I have. I completed my MSC. And PhD. In mathematics. I have. 10 years of experience. At both undergraduate. And postgraduate. Levels. Currently I am working. As an assistant professor. In the Department of Mathematics. At Sri Krishna Arts and Science College. My research interest. In functional analysis. Particularly. Hilbert manifolds. And my TK. The interest? Uh, currently I'm taking. Linear algebra. For BSE AIML students. Discrete Mathematics. For computer science students. Real analysis for BSE mathematics students. And I have. UH-6 Publications. Over out of 6. Two or Scopus index. Thank you.

So, teaching at both levels for this long—what’s one foundational concept in mathematics you especially enjoy explaining to students, and why does it stand out for you?

Okay, so your research is in functional analysis, especially Hilbert manifolds, and you’re teaching at Sri Krishna. Out of all the undergraduate or postgraduate courses you’ve taught, is there a particular foundational topic you find most rewarding to teach, and what makes it stand out for you?

Alright, you’re currently teaching linear algebra to BSc AIML students while researching Hilbert manifolds. When you teach linear algebra, what’s one specific concept or theorem you find students struggle with most, and how do you help them grasp it?

Alright, so you’re teaching both linear algebra for AIML students and discrete mathematics for computer science students. When you’re explaining a tough topic—say, eigenvalues in linear algebra or induction in discrete math—how do you adapt your teaching style so students from different backgrounds actually connect with the material?

Alright, so you’re handling linear algebra for AIML, discrete math for CS, and real analysis for mathematics students. Since those groups have different backgrounds, can you give me a concrete example of how you tailor your explanation of a complex concept—maybe something like eigenvectors or countable sets—so it really lands with each audience?

You mentioned you have six publications, with two in Scopus-indexed journals, and you're handling quite a diverse teaching load right now. Out of all those areas—linear algebra, discrete math, real analysis—is there a particular method or tool you use that really helps students engage with tough material, especially when they seem disengaged or overwhelmed?

Yes, while teaching. First, I will convince the students. How the mathematical concept? They are related to. Uh, real life, uh. Examples of real life. Situations. And I I I using. Uh, suppose for example. While teaching linear algebra. I am using. Geogebra. To show. How? The vector additions are. Earned linear combinations. And everything. So I will explain the abstract concepts. Through the advanced software tools.

Alright, so you bring real-life examples in and use tools like GeoGebra to make abstract concepts more concrete for your students. When you've got a class that's still not responding—maybe they're struggling with the software or just not engaging—what's your fallback strategy to bring them back into the discussion?

First I will try to understand. Where are the students are struggling? It may be either. Basics mostly in. Most of the students, they are lacking. Basics and another possibility that is. They have doubts about why we are studying this concept. So that. I will give simple examples. And solve the problem step by step. And I will give more. Practice problems. And uh. Well, for the second one. I will give. I will connect every mathematical concepts into real world situations. So it will motivate the students to study mathematics more.

So you focus on diagnosing whether it's a gap in basics or motivation, and then you simplify with step-by-step examples and more practice. When you give those real-world connections or problems, do you let students work through examples in class, or is it mostly demonstration from your side?

Yes. I I'm always used. The diagrammatic and insulation. In my dirt using. Umm, many software. Tools like Geogebra. For example. I will convince the students. This mathematical concepts are very important to the realm of the situation. For example. I will give I will give an example that. How to introduce? The vectors. To the PSC AIML students. Suppose considering a robot. From the a. So we need to. Uh, suppose the. Robert moving from the position A to B. So we need at least 2 information in two-dimensional space. So any. A object requires more than one information. That is called. Vector, so scalar is not like. Uh, scalar means it's a temperature. And. Weight and everything they are called. Uh, scalars. Under scale also we consider scale also very recent. Information. So I will convince the students. The vectors are more important in. Scientific and technological. Lettered information. So the vectors. Underscale us. Are very important. For BCA ML. And especially.

Yes. I I'm always used. The diagrammatic and insulation. In my dirt using. Umm, many software. Tools like Geogebra. For example. I will convince the students. This mathematical concepts are very important to the realm of the situation. For example. I will give I will give an example that. How to introduce? The vectors. To the PSC AIML students. Suppose considering a robot. From the a. So we need to. Uh, suppose the. Robert moving from the position A to B. So we need at least 2 information in two-dimensional space. So any. A object requires more than one information. That is called. Vector, so scalar is not like. Uh, scalar means it's a temperature. And. Weight and everything they are called. Uh, scalars. Under scale also we consider scale also very recent. Information. So I will convince the students. The vectors are more important in. Scientific and technological. Lettered information. So the vectors. Underscale us. Are very important. For BCA ML. And especially. Data science students.

Dr. Madan, I noticed your recent publication with Jeyanthi Venkatapathy on "Diffeomorphic Embedding of Higher-Dimensional Hilbert Manifolds into Hilbert Spaces" in Creative Mathematics and Informatics. Can you share an example of how insights from that research have influenced the way you approach teaching advanced topics like functional analysis or topology to your students?

Okay, so you use robotics examples and break down vectors versus scalars with AIML students, connecting it right to data science. Let me pivot to your research for a moment—out of your six publications, can you pick one that you feel most influenced your classroom teaching, and walk me through a specific way that research changed how you approached a topic with your students?

Yes. I guided. Uh, many students. Uh, the mini and the major product. Projects.

Yes. I guided. Uh, many students. Uh, the mini and the major product. Projects. Umm and uh, I my research. Uh, we introduced a new. It's called a Navy space.

You mentioned you've guided students on both mini and major projects, but I was asking about your own research—can you pick one of your six publications that actually changed the way you approached teaching a topic, and walk me through that connection?

Yes. I guided. Uh, many students. Uh, the mini and the major product. Projects. Umm and uh, I my research. Uh, we introduced a new. It's called a Navy space. Uh uh, it is the study about. Uh, reboot between reboot manifolds and. And. The the method of research. He studying. Uh, the unknown spaces like manifolds. With the help of. Well known spaces. Hilbert spaces. So. That is a big application. On data science that is called. Dimensionality reduction.

So you’ve introduced a new “Navy space” in your research and have guided students on projects related to that work. Could you walk me through a time when you had to explain this new concept—Navy space—to students who had no prior exposure to it, and how you made it accessible for them?

Yes. I guided. Uh, many students. Uh, the mini and the major product. Projects. Umm and uh, I my research. Uh, we introduced a new. It's called a Navy space. Uh uh, it is the study about. Uh, reboot between reboot manifolds and. And. The the method of research. He studying. Uh, the unknown spaces like manifolds. With the help of. Well known spaces. Hilbert spaces. So. That is a big application. On data science that is called. Dimensionality reduction. The classical dimensionality reduction methods. They are applied on. Uh, finite dimensional spaces. But our navalogy. The Navy space on the naviological page. The dimensionality rejection. Is applicable on infinite dimensions. So our method. To find. Clusters. Clusters on the manifolds. And based on that. Uh, we using the smooth immersion.

Yes. I guided. Uh, many students. Uh, the mini and the major product. Projects. Umm and uh, I my research. Uh, we introduced a new. It's called a Navy space. Uh uh, it is the study about. Uh, reboot between reboot manifolds and. And. The the method of research. He studying. Uh, the unknown spaces like manifolds. With the help of. Well known spaces. Hilbert spaces. So. That is a big application. On data science that is called. Dimensionality reduction. The classical dimensionality reduction methods. They are applied on. Uh, finite dimensional spaces. But our navalogy. The Navy space on the naviological page. The dimensionality rejection. Is applicable on infinite dimensions. So our method. To find. Clusters. Clusters on the manifolds. And based on that. Uh, we using the smooth immersion. Retraction. And accumulations. Our research is very. Helpful in dimensionality reduction.

Alright, so your work on connecting Hilbert spaces and manifolds has applications in dimensionality reduction, which is a big deal in data science. Since you mentioned guiding students on related projects, can you give me one concrete example where you helped a student translate this advanced research idea into something practical they could present or build?

So, your research on Navy spaces looks at dimensionality reduction for infinite-dimensional manifolds, which goes beyond the classical methods most students see. When you had to explain this new idea to your students—especially those with only a basic understanding of Hilbert spaces—how did you break it down so they could grasp the core idea without getting lost in abstraction?

So your work on Navy spaces and infinite-dimensional manifolds led to methods for dimensionality reduction beyond classical techniques. When you first introduced this idea to your students or colleagues—especially those not specializing in functional analysis—how did you adapt your explanation to make the concept approachable for them?

Yes, it is. Where do you see? To study dimensionality reduction.

Yes, it is. Where do you see? To study dimensionality reduction. Emotional Analysis. Is not required. Much. It is uh. To study the. The definitions and the concepts in. Especially. The Bonox. And input space. So Bono space is nothing. It is about completeness. With norm. And Hilbert space. Is about completeness. It is arise. Uh, from inner product. So this is very. See what the definitions are. Very easy.

Alright, so you see the practical side of dimensionality reduction—makes sense, especially for students interested in data science. You've also mentioned guiding students on both mini and major projects. Can you give me a concrete example of a student project you supervised that drew directly from your own research, and tell me how you helped that student bridge the theory to a real application?

Alright, so you see the definitions as straightforward, but I’m curious—when you teach concepts like Banach and Hilbert spaces to undergraduates who might not have a strong background in analysis, how do you avoid overwhelming them with abstraction?

Yes, it is possible. To explain. Every abstract concept.

Yes, it is possible. To explain. Every abstract concept. With diagrammatic. And simple examples. So there are several real life connectivity between us. Track concepts. Earned real life situations. So first we need to clarify the students. Uh uh, these concepts are very important. So that is enough. Recreate the curiosity about the concept with a simple examples.

You’re confident you can explain abstract concepts at any level. Can you give a specific example of a time when a student struggled with an abstract topic—maybe Banach or Hilbert spaces—and describe how you broke it down so they finally understood?

Right, so you believe sparking curiosity and using simple, tangible examples goes a long way, even for abstract concepts like Banach and Hilbert spaces. Before we move ahead, is there a publication or research project from your list that you found especially challenging to communicate, either to students or peers? What did you do differently that time to make the core ideas accessible?

Basically, functional analysis is abstract. It is in your mathematics. However. The applications of. Functional Analysis. In applied mathematics. So that it is. PC to connect with. Deals might be. Peer group and. Uh, the students.

Dr. Madan, shifting gears to your research productivity and funding—given your experience in functional analysis and its applications, where do you see the most fundable research directions emerging over the next few years? If you were at VIT, what kinds of grants or funding sources would you target to build out your research group?

Yes, my target. I will extend my. PhD work.

Yes, my target. I will extend my. PhD work. Uh, I already told. That is a good application in data science. That is called dimensionality reduction. So I further I will extend my research.

Yes, my target. I will extend my. PhD work. Uh, I already told. That is a good application in data science. That is called dimensionality reduction. So I further I will extend my research. And I planned to publish. 2 corpus papers in the UP. Coming here.

So you'd plan to extend your PhD work on Navy spaces and infinite-dimensional analysis. What are some specific external funding agencies or industry partners you believe would be most interested in supporting that direction, and how would you tailor your proposal to align with their priorities?

So you’d plan to extend your PhD work on Navy spaces and infinite-dimensional analysis. What are some specific external funding agencies or industry partners you believe would be most interested in supporting this kind of research at VIT?

You mentioned aiming for two more Scopus papers in the coming year, building on your dimensionality reduction work. Beyond publications, how would you involve students directly in your research at VIT—say, through projects, lab work, or industry-linked collaborations?

OK for students. I will, uh, give. A real life problems. Where map the dimensionality reductions are used. In data science.

OK for students. I will, uh, give. A real life problems. Where map the dimensionality reductions are used. In data science. To develop a new. Systems. And new ideology.

OK for students. I will, uh, give. A real life problems. Where map the dimensionality reductions are used. In data science. To develop a new. Systems. And new ideology. Enhance the current. Uh, data science. And uh. Artificial intelligence. Because there are several. Clustering. In unstructured learning. So I hope. It will be very helpful. In data science and as well as.

Okay, you've had a lot of hands-on experience bridging theory and practice. Suppose you were running a large undergraduate mathematics class at VIT—say, 200 students—and you couldn’t use slides or typical lectures. How would you actually run a session that keeps students actively engaged and makes them wrestle with the material?

Alright. Accreditation cycles can get pretty demanding—say you joined our department and saw that outcome assessment data was inconsistent across courses. How would you approach fixing that problem?

You mentioned giving students real-life problems where dimensionality reduction is used in data science, especially for clustering and unstructured learning. Let’s talk about the institutional side—accreditation cycles can be demanding. If you joined our department and found that outcome assessment data was inconsistent across mathematics courses, how would you approach fixing that?

I have already uh. Experience Alo. Along with teaching and research. I contributed many areas. In my current college. I am the ums nodal officer.

I have already uh. Experience Alo. Along with teaching and research. I contributed many areas. In my current college. I am the ums nodal officer. And IIC number. And I, I I contributed. In Nat accreditation. And NRF. And et cetera.

Alright, so you've acted as a UMS nodal officer at your current college—so you know the administrative side well. In that role, when you came across data inconsistencies or gaps in outcome assessments, what concrete steps did you personally take to resolve them?

Okay, you've had a lot of hands-on experience bridging theory and practice. Suppose you were running a large undergraduate mathematics class at VIT—say, 200 students—and you couldn’t use slides or typed notes due to a technical outage, just the board and your voice. How would you adapt your approach to keep the session engaging and ensure students still grasp the key concepts?

1st in my teaching. I will. Encourage or empathize? Over a Rd. Teaching method.

1st in my teaching. I will. Encourage or empathize? Over a Rd. Teaching method. So I focus on understanding concept. Clarity.

1st in my teaching. I will. Encourage or empathize? Over a Rd. Teaching method. So I focus on understanding concept. Clarity. And it it not only chalk and. Boat typing. Type uh, I will do. The. And visualization.

Alright, you mentioned you’d encourage or empathize with the class, even in a tech outage. Let’s shift to something you might face at VIT—say a student formally complains that your grading was biased, but at the same time, your department head is pressuring you to increase pass rates. How would you handle that situation, balancing fairness with institutional expectations?

1st in my teaching. I will. Encourage or empathize? Over a Rd. Teaching method. So I focus on understanding concept. Clarity. And it it not only chalk and. Boat typing. Type uh, I will do. The. And visualization. And I have. The idea about several ICT.

Alright, you focus on concept clarity and try to empathize with students, even when resources are limited. Now, let's talk about a scenario you might face here. Imagine a student files a formal complaint alleging your grading is biased, but at the same time, your department head is pressuring you to improve pass rates. How would you navigate this situation while maintaining both academic integrity and institutional expectations?

You emphasized hands-on and empathetic teaching, even when resources are limited. Now, let's talk about a scenario you might face at VIT—imagine a student files a formal complaint that your grading was biased, but at the same time, your department head is urging you to increase the pass rates in your course. How would you handle that situation while maintaining both academic integrity and good relationships within the department?

You mentioned using ICT tools and focusing on concept clarity, even when teaching resources are limited. Now let’s talk about a real ethical dilemma you could face at VIT. Suppose a student files a formal complaint that your grading is biased, but at the same time, your department head is urging you to raise pass rates. How would you handle this situation, balancing fairness to the student, your own academic standards, and the pressure from your department?

So in the academic environment. Whatever the pressure or whatever the complaint. Uh, everything I will handle. As per the. Uh, university norms. First I will understand. What is the nature of the compliant? And I will try to. Uh, convey my. Uh, problems? And, uh, the problem. Uh, uh, it's true. I will try to. Change the environment. Hello, can you hear me?

You're drawing a clear line around academic standards, even under pressure—appreciate that clarity. Let's turn to something VIT values highly: industry alignment. Given your background in mathematics and data science, do you have any current or past industry connections that could help open up internship or placement opportunities for our students?

Yeah, I already mentioned that. I have. I am, uh, currently taking. Linear algebra. For uh, BSc. AI and ML students. And also data science students. I have a clarity about. How? Uh. The linear algebra is directly connected to. Data science area.

Yeah, I already mentioned that. I have. I am, uh, currently taking. Linear algebra. For uh, BSc. AI and ML students. And also data science students. I have a clarity about. How? Uh. The linear algebra is directly connected to. Data science area. So I have. Introduce. My life teaching. Several real life examples.

Yeah, I already mentioned that. I have. I am, uh, currently taking. Linear algebra. For uh, BSc. AI and ML students. And also data science students. I have a clarity about. How? Uh. The linear algebra is directly connected to. Data science area. So I have. Introduce. My life teaching. Several real life examples. They offer directly connected to. Data science and linear algebra.

Yeah, I already mentioned that. I have. I am, uh, currently taking. Linear algebra. For uh, BSc. AI and ML students. And also data science students. I have a clarity about. How? Uh. The linear algebra is directly connected to. Data science area. So I have. Introduce. My life teaching. Several real life examples. They offer directly connected to. Data science and linear algebra. For example. Uh, suppose life finding entertainment. Why the determined value is equal to? Bigg Boss, the Rose, or. Dependent. So which means. The system or the the data set contains. Duplicate informations.

Yeah, I already mentioned that. I have. I am, uh, currently taking. Linear algebra. For uh, BSc. AI and ML students. And also data science students. I have a clarity about. How? Uh. The linear algebra is directly connected to. Data science area. So I have. Introduce. My life teaching. Several real life examples. They offer directly connected to. Data science and linear algebra. For example. Uh, suppose life finding entertainment. Why the determined value is equal to? Bigg Boss, the Rose, or. Dependent. So which means. The system or the the data set contains. Duplicate informations. Then we're getting. The determined value equal to 0.

Yeah, I already mentioned that. I have. I am, uh, currently taking. Linear algebra. For uh, BSc. AI and ML students. And also data science students. I have a clarity about. How? Uh. The linear algebra is directly connected to. Data science area. So I have. Introduce. My life teaching. Several real life examples. They offer directly connected to. Data science and linear algebra. For example. Uh, suppose life finding entertainment. Why the determined value is equal to? Bigg Boss, the Rose, or. Dependent. So which means. The system or the the data set contains. Duplicate informations. Then we're getting. The determined value equal to 0. Force that determined value is not equal to 0. Dell Data. The rows are linearly independent. So determined. Is there very essential important tool? To identify. Uh, uh. But, uh, data set. Contains duplication.

You’re teaching linear algebra to AI and data science students and you see the direct connection to their future work. But I’m looking for something more concrete—have you actually partnered with any companies or industry professionals for guest lectures, projects, or internships, or is this more of a future goal for you?

Yeah, I already mentioned that. I have. I am, uh, currently taking. Linear algebra. For uh, BSc. AI and ML students. And also data science students. I have a clarity about. How? Uh. The linear algebra is directly connected to. Data science area. So I have. Introduce. My life teaching. Several real life examples. They offer directly connected to. Data science and linear algebra. For example. Uh, suppose life finding entertainment. Why the determined value is equal to? Bigg Boss, the Rose, or. Dependent. So which means. The system or the the data set contains. Duplicate informations. Then we're getting. The determined value equal to 0. Force that determined value is not equal to 0. Dell Data. The rows are linearly independent. So determined. Is there very essential important tool? To identify. Uh, uh. But, uh, data set. Contains duplication. So through the. I gave several mini projects and assignments to the students. In the real life examples. As as I told them. To solve. The problem? Problems based on. Real life examples. The real problem? Nowadays. The textbook contains the classical. Theoretical oriented problem. So it is very essential. It is our. Duty to convert every mathematical. And the theoretical problem. Into industry oriented problem. Then it will be. You see? Uh, to convey. The students. The abstract mathematics. Is important. In data science and AI. I am unable.

So, you’re teaching linear algebra to both AI and data science students, and you’re bringing in real-life examples. But I’m looking for something more concrete—have you actually partnered with any companies or industry groups, or brought in outside professionals, to give your students exposure to real-world math applications or potential internships?

Alright, Dr. Madan, I want to switch gears and touch on some core skills for this role. When it comes to supply chain management in a mathematical context—let’s say you’re asked to model inventory optimization under uncertain demand—how would you approach integrating advanced statistical methods or AI techniques to improve decision-making?

Okay, so you’re connecting linear algebra to data science for your students using real-life examples, like identifying duplicate information in datasets. But I’m looking for something more concrete—have you actually partnered with any companies or industry professionals to expose your students to real-world data or projects, or is it mostly classroom-based at this point?

Okay, so you’re teaching linear algebra to both AI and data science students, and you’re bringing in real-life examples tied to things like duplicate information in datasets. But I’m looking for something more concrete—have you actually partnered with any companies, or brought in any real-world projects or consultancy work for your students to engage with?

Alright, you’ve shown how you connect linear algebra concepts like determinants to detecting duplication in datasets—so students see the relevance for data science. Now, thinking about student evaluation, suppose you have a large mix of high performers and struggling students in a theory-heavy course. How do you design your exams or assignments to fairly assess both groups and minimize grade inflation?

Okay, so you've designed mini projects and real-world assignments to connect linear algebra with data science, which helps students see the relevance. Now, thinking about your overall teaching style—how do you make sure your lectures stay structured and clear, especially in advanced or abstract topics where students might get lost?

Yeah, in every lecture.

Yeah, in every lecture. The first. 5 minutes. I will explain. The upstart. Concept How? This topic is. Directly related to. Their core or real life situation?

Yeah, in every lecture. The first. 5 minutes. I will explain. The upstart. Concept How? This topic is. Directly related to. Their core or real life situation? First I will convince or explain. The topic is very.

Alright, so you emphasized turning theoretical problems into industry-oriented ones, and you’re using real-world assignments. Shifting to another key skill—can you walk me through a time you directly supervised or guided a student’s research project or thesis, especially where the topic was outside your immediate expertise? How did you make sure their work stayed rigorous and on track?

Yeah, in every lecture. The first. 5 minutes. I will explain. The upstart. Concept How? This topic is. Directly related to. Their core or real life situation? First I will convince or explain. The topic is very. Then I will. Go to. A small interaction. About two to three minutes. Then I will create. The curiosity. About that topic.

Yeah, in every lecture. The first. 5 minutes. I will explain. The upstart. Concept How? This topic is. Directly related to. Their core or real life situation? First I will convince or explain. The topic is very. Then I will. Go to. A small interaction. About two to three minutes. Then I will create. The curiosity. About that topic. I will give. They definition. Uh, the definitions. 2. Understand the definition. And I I also give sometimes. Counterexamples. Where the definition will not. Worked and I will go with. Yeah, regular problems. Uh, and I will give step by step, sorry.

So you kick off each lecture by connecting abstract concepts to real-world situations right away—that helps set the context for students. Now, thinking about your research publications, can you tell me about one of your papers published in a reputed journal where you had to revise your work based on challenging peer review feedback? What changed between the first and final versions?

So you always start by showing students how the topic links to real situations—that helps ground abstract ideas. Now, let’s talk about student evaluation and exam duties. When you’re designing a final exam for a theory-heavy course like functional analysis, how do you make sure your questions actually measure deep understanding rather than just memorization?

Alright, so you build curiosity at the start, tie topics to real life, then interact with students to make sure they're engaged. Thinking about guiding student projects, can you give a concrete example of a project you supervised—what was the student's role, and how did you steer them when they hit a roadblock?

So you structure each lecture to start with real-world context, short interactions, definitions, and counterexamples to guide students step by step—sounds like you put a lot of thought into keeping things clear. Earlier, you mentioned your involvement with accreditation and student evaluation—when you’re designing a final exam for a mathematics course, how do you ensure your questions fairly assess both theory and practical understanding?

Yes, I believe that. Suppose a student.

Alright, so you like to create curiosity at the start, use definitions, counterexamples, and step-by-step problems to keep your lectures structured. Let’s switch gears—can you talk about a specific project where you guided students through a research or industry-linked problem, and what your approach was to mentoring them through challenges?

Yes, I believe that. Suppose a student. Completely understand. A concept with real life situation. And rela applications. You can able to. Attend any. Uh, questions? And you can you can write. It won't so. It is not related to. The rote learning. Something we memorise and writing. So I believe that. It will help. To their understanding level and it will improve their understanding level. And so on. Hello, are you there?

Alright, so you emphasized that real understanding—not rote learning—lets students tackle any type of exam question, especially when you connect concepts to real-life applications. On student project guidance, can you give a concrete example of a research or industry-oriented project you’ve supervised, and how you supported the student in making it rigorous and relevant?

Yes.

Alright, but I need a bit more detail. Can you walk me through a specific student project you supervised—what was the topic, what was your role, and how did you help the student ensure the work met both academic and practical standards?

Yes. In every project. For assignment. I will help students. They are lagging. So I. I will explain clearly. The basic concepts. How to understand? The abstract definitions in. Mathematics.

Yes. In every project. For assignment. I will help students. They are lagging. So I. I will explain clearly. The basic concepts. How to understand? The abstract definitions in. Mathematics. And I will give you. The real life problems. Like. And weather condition. And and and so on. So first I will connect the abstract. Definitions into real life examples. Uh, then I will. Feed or. The curiosity. About their problems. And I will give you. The statements. Problem statements. With several object flows. And variety of technique. And how to explain?

Yes. In every project. For assignment. I will help students. They are lagging. So I. I will explain clearly. The basic concepts. How to understand? The abstract definitions in. Mathematics. And I will give you. The real life problems. Like. And weather condition. And and and so on. So first I will connect the abstract. Definitions into real life examples. Uh, then I will. Feed or. The curiosity. About their problems. And I will give you. The statements. Problem statements. With several object flows. And variety of technique. And how to explain? I will explain how to use. They're tools like. Algebra. Python.

Yes. In every project. For assignment. I will help students. They are lagging. So I. I will explain clearly. The basic concepts. How to understand? The abstract definitions in. Mathematics. And I will give you. The real life problems. Like. And weather condition. And and and so on. So first I will connect the abstract. Definitions into real life examples. Uh, then I will. Feed or. The curiosity. About their problems. And I will give you. The statements. Problem statements. With several object flows. And variety of technique. And how to explain? I will explain how to use. They're tools like. Algebra. Python. End song. So it will really helpful.

Okay, so you focus on making sure students understand the basics and abstract definitions, and help them when they struggle. Let’s switch gears—can you talk about one of your research publications in a reputed journal? What was the main mathematical contribution, and how did you decide where to publish it?

Yes. In every project. For assignment. I will help students. They are lagging. So I. I will explain clearly. The basic concepts. How to understand? The abstract definitions in. Mathematics. And I will give you. The real life problems. Like. And weather condition. And and and so on. So first I will connect the abstract. Definitions into real life examples. Uh, then I will. Feed or. The curiosity. About their problems. And I will give you. The statements. Problem statements. With several object flows. And variety of technique. And how to explain? I will explain how to use. They're tools like. Algebra. Python. End song. So it will really helpful. The core and. Their future research directions and career.

Right, so you connect abstract definitions to real-world problems—like weather conditions—to help students understand and get curious, then you guide them through problem statements and different techniques. Let's switch topics a bit. Can you tell me about one of your research publications in a reputed journal—what was the main result, and why do you think it was significant for the field?

Alright, so you guide students from abstract definitions to real-life examples and help them use the right tools, whether it's algebra or Python. Thinking about your own research, can you share details about a publication of yours in a reputed journal—what was the main result, and how did you position it to stand out in the field?

So you make a point of connecting abstract mathematics to real-world examples, and you guide students through both the conceptual and technical aspects of their projects—including using tools like Python. Switching gears, can you share a bit about your doctoral research—what was your primary area of specialization, and how does it inform your teaching and research today?

Alright, so you help students bridge the gap between abstract math and real-world problems, and guide them on tools like Python. Thinking about your own research publications—can you talk about one specific paper you published in a reputed journal, and explain what made the research novel or impactful?

Yes.

Yes. I published published. What is Navisa?

Alright, Dr., you mentioned earlier that you've worked with both advanced statistical methods and AI applications in mathematics. Imagine you're tasked with teaching a lab course where students need to implement a machine learning model from scratch—how would you structure that lab to make sure students really understand both the math and the coding?

You repeated "published" and then asked "What is Navisa?"—I want to clarify, are you referring to a specific paper or topic named Navisa, or was that a misstatement? If you meant a specific paper, can you walk me through the main idea and what made it stand out in your field?

Yes. I published published. What is Navisa? Through Navalogy. It is a framework. Between. Hilbert manifolds. Find Hilbert spaces. So we. Hilbert manifolds into input spaces. Through several. Embedding techniques. Like diffume morphic ability. Isometric embedding. Homotopic MPT. And so on. So there is a. Huge applic. That is called. Dimensionality reduction.

Yes. I published published. What is Navisa? Through Navalogy. It is a framework. Between. Hilbert manifolds. Find Hilbert spaces. So we. Hilbert manifolds into input spaces. Through several. Embedding techniques. Like diffume morphic ability. Isometric embedding. Homotopic MPT. And so on. So there is a. Huge applic. That is called. Dimensionality reduction. We are playing dimensionality reduction. On manifolds.

Yes. I published published. What is Navisa? Through Navalogy. It is a framework. Between. Hilbert manifolds. Find Hilbert spaces. So we. Hilbert manifolds into input spaces. Through several. Embedding techniques. Like diffume morphic ability. Isometric embedding. Homotopic MPT. And so on. So there is a. Huge applic. That is called. Dimensionality reduction. We are playing dimensionality reduction. On manifolds. We will convert. The unknown spaces into well known spaces. Because, uh. In generally the unknowns. Basis contains several. Clustering. So that it is directly related to unstructured learning.

Yes. I published published. What is Navisa? Through Navalogy. It is a framework. Between. Hilbert manifolds. Find Hilbert spaces. So we. Hilbert manifolds into input spaces. Through several. Embedding techniques. Like diffume morphic ability. Isometric embedding. Homotopic MPT. And so on. So there is a. Huge applic. That is called. Dimensionality reduction. We are playing dimensionality reduction. On manifolds. We will convert. The unknown spaces into well known spaces. Because, uh. In generally the unknowns. Basis contains several. Clustering. So that it is directly related to unstructured learning. So there is a direct application that. In data science. Uh, in data science also. They're converting and structured. Data. Infrastructure data. So this is the. Core idea about our research. I believe that. It will. Useful in data science. In future. We will. This concept. Into uh. Several applications of data science.

Alright, so your research on Hilbert manifolds and embedding techniques like diffeomorphic ability and isometric embedding really ties into dimensionality reduction. For your work in industry projects or consultancy—can you give a specific example where your mathematical expertise directly contributed to solving a real client or industry problem?

So your work with Hilbert manifolds and embedding techniques for dimensionality reduction clearly brings novelty to the field—especially since you’re connecting advanced mathematical frameworks to real applications. For your experience with industry projects or consultancy, can you describe a concrete example where you applied your mathematical expertise to solve an actual business or industry problem?

So your work embedding Hilbert manifolds into Hilbert spaces using techniques like diffeomorphic and isometric embeddings really shows depth in bridging advanced math with real-world applications like dimensionality reduction and unstructured learning. Now, for industry projects or consultancy—can you give one concrete example where you applied your mathematical expertise in an industry or consultancy context, and explain what your specific contribution was?

Okay, so your research bridges advanced mathematics and data science applications using things like isometric embedding and Hilbert manifolds. Switching gears, Professor, I'd like to hear about your experience with industry projects or consultancy—can you describe a time when you worked directly with an outside company or organization, and what your specific contribution was?

Yes, in my current institution. I already told that. I am the UM IS nodal officer. UM, specificity management. Information systems. So I will. I contributed several things. In such students scholarship. And, uh, distributing. Uh, free laptops? And so on and. About the several schemes. I'm I am, uh, a IAC. Member and I conducted. Several. Programs and. Contribution in. Several documentation works. And also I am serving as a residential warden. So here. I I. Motivating the students in. Many competitive examinations. And doubt clarification sessions. And uh. I contributed many things in student mentoring. In the house Yes, I am seeking A broader environment. Like I will grow. In both. Can't research. And uh. I already working in a well reputed college. That is called. Straight to snorts in science college. In Coimbatore. Over 10 years. We focus on. Uh, good teaching. And academic environment. However, I want to sip. Shift from. This college environment to. The university run.

Yes, in my current institution. I already told that. I am the UM IS nodal officer.

Yes, in my current institution. I already told that. I am the UM IS nodal officer. UM, specificity management. Information systems.

Okay, Professor, we're at the end of our interview. Is there anything you'd like to ask about the role or the mathematics department here at VIT?

So your role as the UMIS nodal officer had you working with management information systems at your current institution. Alright, Professor, as we wrap up—do you have any questions for me about the role or the team here at VIT?

Yes, in my current institution. I already told that. I am the UM IS nodal officer. UM, specificity management. Information systems. So I will. I contributed several things. In such students scholarship. And, uh, distributing. Uh, free laptops? And so on and. About the several schemes. I'm I am, uh, a IAC. Member and I conducted. Several. Programs and. Contribution in. Several documentation works.

So your work as the UMIS nodal officer included things like scholarship administration and running various programs, plus a fair bit of documentation. Alright, Professor, as we wrap up—is there anything you’d like to ask about the role or the mathematics department here at VIT?

Sounds like you've had a decade in a strong academic environment and now you're looking for the broader research and university experience VIT offers. If you have any specific questions about the role, our research culture, or the mathematics department here, I'm happy to answer them now.

Uh, yes, I have uh. Some several. So some important questions. Like. The research supervision. And associateship.

Uh, yes, I have uh. Some several. So some important questions. Like. The research supervision. And associateship. Uh, in the. For math department at Vit. And I also. Of a question that about. Uh, what are the subject? Teaching Nature. It is related to. Direct PhD. Mathematics and MSC. Committees or engineering based subject.

You'd like to know more about research supervision and associateship opportunities here at VIT. The mathematics department has a strong record in both doctoral supervision and collaborative research, and there are structured programs for guiding PhD and postgraduate research scholars. Faculty are also encouraged to seek associateships with other departments and research centers, both within VIT and through national funding schemes. Is there anything else you'd like to ask about the department or the role, Dr.?