On October 4, 2024, Department of Mathematics at SRM University-AP hosted its 10th Distinguished Lecture, featuring renowned mathematician and educator Prof. R Ramanujam. The event attracted a diverse audience, including BSc and BTech students, PhD candidates, and faculty members, all eager to engage with the critical topic of mathematics and science education for students from socially and economically marginalised backgrounds.

Prof. Ramanujam’s lecture posed a thought-provoking question: “What do mathematics and science education mean to a student from socially and economically marginalised sections?” Drawing from his extensive experience in various educational contexts, he provided valuable insights into the intersection of education and social equity. His work with the Tamil Nadu Science Forum, government curriculum bodies, and teacher education programs at Azim Premji University in Bengaluru informed his perspective on the necessity of aligning educational practices with the realities faced by marginalised communities.

During his talk, Prof. Ramanujam emphasised the importance of conducting educational research that is deeply rooted in social contexts. He argued that curriculum-making decisions should be informed by such research to ensure that education is socially inclusive and responsive to the unique challenges faced by disadvantaged students. His advocacy for an education system that addresses the needs of all learners resonated strongly with the audience, highlighting the potential for education to serve as a transformative force in society.

Prof. R Ramanujam is a distinguished figure in the fields of mathematics and education. He completed his PhD at the Tata Institute of Fundamental Research (TIFR) and pursued postdoctoral work at the City University of New York (CUNY), USA. His long-standing association with the Institute of Mathematical Sciences (IMSc) in Chennai and his current role as a visiting professor at Azim Premji University further underscore his commitment to advancing educational practices.

The lecture provided a stimulating exploration of how mathematics and science education can help address social inequalities. Prof. Ramanujam’s reflections on education, grounded in his experiences with marginalised communities, left a lasting impact on attendees. The event concluded with an engaging Q&A session, where participants raised questions about the challenges of implementing socially rooted educational reforms. This discussion reinforced the lecture’s key themes of inclusivity and the transformative potential of education when designed to meet the diverse needs of learners.

The 10th Distinguished Lecture at SRM University-AP not only highlighted the importance of educational equity but also inspired dialogue on how institutions can better serve all students, particularly those from marginalized backgrounds.

The Department of Mathematics, SRM University-AP, is pleased to announce that Assistant Professor Dr Subha Sandeep Repaka has published a significant research paper titled “On Reducibility of Induced Representations of Odd Unitary Groups: The Depth Zero Case.” This accomplishment reflects Dr Repaka’s expertise and dedication to advancing mathematical research, further enriching the academic contributions of the department and the university.

Abstract:

We study a problem concerning parabolic induction in certain $p$-adic unitary groups. More precisely, for $E/F$ a quadratic extension of $p$-adic fields the associated unitary group $G=\mathrm{U}(n,n+1)$ contains a parabolic subgroup $P$ with Levi component $L$ isomorphic to $\mathrm{GL}_n(E) \times \mathrm{U}_1(E)$. Let $\pi$ be an irreducible supercuspidal representation of $L$ of depth zero. We use Hecke algebra methods to determine when the parabolically induced representation $\iota_P^G \pi$ is reducible.

Future Research Plans:

We would like to solve the same problem which I had solved in this paper for the groups U(n,n) and U(n,n+1) over p-adic fields using L-Functions which is a very novel approach.

The link to the article:

http://nyjm.albany.edu/j/2024/30-50.html

Dr Shekhar Singh Negi from the Department of Mathematics has published a research paper titled “A note on Sugeno exponential function with respect to distortion.” Dr Negi’s research investigates the Sugeno exponential function. This research develops new mathematical tools and rules to work with a different way of measuring things, which can be useful in various fields like economics, biology, or any area where traditional measurements don’t quite fit the problem at hand.

Abstract:

This study explores the Sugeno exponential function, which is the solution to a first order differential equation with respect to nonadditive measures, specifically distorted Lebesgue measures. We define k-distorted semigroup property of the Sugeno exponential function, introduce a new addition operation on a set of distortion functions, and discuss some related results. Furthermore, m-Bernoulli inequality, a more general inequality than the well-known Bernoulli inequality on the real line, is established for the Sugeno exponential function. Additionally, the above concept is extended to a system of differential equations with respect to the distorted Lebesgue measure which gives rise to the study of a matrix m-exponential function.

Finally, we present an appropriate m-distorted logarithm function and describe its behaviour when applied to various functions, such as the sum, product, quotient, etc., while maintaining basic algebraic structures. The results are illustrated throughout the paper with a variety of examples.

Collaborations:

Prof. Vicenc Torra, Professor at the Department of Computing Science at Umea University. His area of research include artificial intelligence, data privacy, approximate reasoning, and decision making.

Future Research Plans:

To explore the aforementioned derivative and investigate results with applications in real life.

The link to the article

Dr Koyel Chakravarty, Assistant Professor in the Department of Mathematics, has made a significant contribution to the field of cancer research with her paper “Analysis and Regulation of Chaos Dynamics in a Cancer Model through Chemotherapeutic Intervention and Immune System Augmentation,” which was recently published in the International Journal of Dynamics and Control. In her paper, Dr Chakravarty delves into the intricate world of chaos dynamics within a cancer model and explores the potential for regulating these dynamics through the combined approach of chemotherapeutic intervention and immune system augmentation.

Her research offers insights into understanding the complex behaviour of cancer cells and how such insights can be leveraged to develop more effective treatment strategies. Dr Chakravarty’s work marks a crucial step forward in the ongoing efforts to combat cancer, shedding light on the dynamic interplay between therapeutic interventions and the body’s immune response.

The publication of this paper not only underscores Dr Koyel’s expertise in the field of mathematical analysis in cancer research but also signifies a promising advancement in the collective pursuit of understanding and addressing the challenges posed by cancer.

Abstract

The focus of the current investigation lies in the formulation and analysis of a dynamic model depicting cancer growth, incorporating the joint influences of chemotherapy and immune system augmentation. The primary emphasis of this study revolves around the analysis of the dynamic behaviour within a living-cell closed carcinoma system, specifically one devoid of external vitamin support, with a particular exploration of chaos dynamics. Subsequently, the authors aim to scrutinise the pivotal impact of infused vitamins in attaining stable system dynamics through the application of chaos control techniques.

The formulated model exhibits fundamental mathematical properties, revealing a spectrum of co-dimension one and co-dimension two bifurcations. The identification of specific bifurcation types relies on algebraic criteria techniques, where conditions necessary and sufficient for bifurcation types are developed. Notably, these criteria are distinct from traditional approaches based on the characteristics of the eigenvalues of the Jacobian matrix, instead relying on coefficients derived from characteristic equations. The accuracy of the analytical conclusions is validated through numerical findings, elucidating diverse bifurcation structures. The article enriches its contribution by delving into the control of chaos through the reinforcement of the internal immune system and the maintenance of the biological system’s stability. This work culminates in proposing future directions aimed at advancing a more realistic approach to eradicating cancer.

Research in Layperson’s Terms

This study focuses on developing and analysing a model that simulates how cancer grows, considering both chemotherapy and the immune system’s response. The main goal is to understand how cancer behaves over time in a system that doesn’t have external vitamin support, especially looking at how chaotic or unpredictable the growth can become. The researchers also investigate how adding vitamins might help stabilise this chaotic system using specific control techniques. The model they created has certain mathematical features that show different types of changes, called bifurcations, which can occur under specific conditions.
Additionally, the study explores how strengthening the immune system might help control this chaos and stabilise the biological system. The paper concludes by suggesting future research directions that could lead to more effective cancer treatment strategies.

Practical implementation

The practical implementation and social implications of analysing and regulating chaos dynamics in a cancer model through chemotherapeutic intervention and immune system augmentation can be profound. Insights gained from this research could be applied to optimize cancer treatment protocols, potentially leading to more effective therapies with reduced side effects. By understanding and controlling the chaotic behaviour in cancer systems, patient outcomes could be improved through personalized treatment strategies.
Socially, the adoption of these findings may lead to increased public confidence in advanced cancer treatments, as well as a broader acceptance of integrating immune system support with traditional therapies. The potential for more stable and predictable treatment outcomes may also reduce the emotional and financial burden on patients and healthcare systems. Additionally, this approach may encourage further interdisciplinary research, bridging gaps between Mathematics, Biology, and Medicine, thus fostering innovation in cancer therapy development.

Collaborations
Dr Lakshmi Narayan Guin, Associate Professor, Department of Mathematics, Siksha Bhavana, Visva-Bharati

Future research plans
Potential areas for further exploration include:

• Personalised Medicine: Developing patient-specific models that consider individual biological variations could lead to more tailored and effective cancer treatments, minimising side effects and improving outcomes.
• Integration with Advanced Therapies: Combining the insights from chaos dynamics with emerging therapies such as immunotherapy, targeted therapy, and gene editing could enhance the precision and efficacy of cancer treatments.

The Department of Mathematics at SRM University-AP successfully conducted a two-week summer programme “Chetna: Awakening Mathematical Minds” from June 17th to June 28th, 2024. This programme aimed to inspire and enhance mathematical understanding among participants from various parts of the country. The programme saw enthusiastic participation from 25 students hailing from different states across India, including West Bengal, Assam, Kerala, Karnataka, Tamil Nadu, Maharashtra, Gujarat, Delhi and Andhra Pradesh.

The programme featured a diverse curriculum, covering a wide range of mathematical topics. Eleven subjects were taught by eleven distinguished faculty members from the Department of Mathematics. The subjects provided a broad and enriching mathematical experience, designed to ignite a passion for mathematics in the participants.

Insights of the Two-Week Programme

First Week Highlights

1. Number Theory by Prof. Kalyan Chakraborty
The first week began with an in-depth exploration of Number Theory. Prof. Kalyan Chakraborty introduced participants to fundamental concepts such as divisibility, prime numbers, and modular arithmetic. The engaging sessions provided a strong foundation in understanding the properties and applications of numbers.

2. Abstract Algebra by Dr Anirban Bose
Dr Anirban Bose led the sessions on Abstract Algebra, diving into structures like groups, rings, and fields. The course covered essential algebraic concepts and their applications, enhancing the participants’ problem-solving skills and theoretical knowledge.

3. Linear Algebra and Basic Operators by Dr Animesh Bhandari
Dr Animesh’s lectures on Linear Algebra included topics such as vector spaces, linear transformations, and matrices. The sessions aimed to build a solid understanding of linear systems and the role of operators in mathematical computations.

4. Graph Theory by Dr Fouzul Atik
Graph Theory, taught by Dr Fouzul Atik, introduced participants to the study of graphs, which are mathematical structures used to model pairwise relations between objects. Topics included graph traversal, connectivity, and graph colouring, providing insights into the practical applications of graph theory.

5. Ordinary Differential Equation by Dr Nityananda Roy
The week concluded with Dr Nityananda Roy’s sessions on Ordinary Differential Equations (ODEs). This course covered methods of solving first-order and higher-order ODEs, along with real-world applications of differential equations in various fields.

Second Week Highlights

1. Advanced Algebra by Dr Kalyan Banerjee
Building on the first week, this subject delved deeper into algebraic structures, including advanced group theory and ring theory, preparing students for research-level problems.

2. Metric Spaces by Dr Choiti Bandyopadhyay
Dr Choiti’s sessions on Metric Spaces introduced participants to the concepts of distance and convergence in metric spaces. Topics included open and closed sets, continuity, and compactness, providing a deeper understanding of analysis.

3. Foundations of Probability and Statistics by Dr Vijayakrishna Rowthu
Dr. Vijayakrishna covered the Foundations of Probability and Statistics, focusing on probability theory, random variables, and statistical inference. The course aimed to equip participants with the skills needed to analyze and interpret data.

4. Mathematical Modelling by Dr Tapan Kumar Hota
Dr. Tapan’s lectures on Mathematical Modelling demonstrated how mathematics can be used to represent, analyse, and solve real-world problems. The course included case studies and practical applications in various disciplines.

5. Partial Differential Equation by Dr Ram Baran Verma
The sessions on Partial Differential Equations (PDEs) by Dr Ram Baran explored methods of solving PDEs and their applications in physics and engineering. Topics included separation of variables, Fourier series, and boundary value problems.

6. Math Education by Dr Jayasree Subramanian
The final course on Math Education, taught by Dr Jayasree, focused on pedagogical approaches and techniques for teaching mathematics effectively. The sessions aimed to inspire future educators and enhance their teaching methodologies.

Conclusion
The “Chetna: Awakening Mathematical Minds” summer programme was a resounding success, providing participants with valuable insights and knowledge in mathematics. The diverse backgrounds of the participants and the expertise of the faculty created a vibrant and stimulating learning environment, fostering a deeper appreciation for the subject. The Department of Mathematics at SRM University -AP looks forward to organising similar programmes in the future to continue inspiring young mathematical minds across the country.