### Prof Indranath Sengupta to illuminate on the unboundedness of Betti numbers

Department of Mathematics is organising the 17th Departmental Weekly Seminar on October 13, 2021, at 3 pm. Prof Indranath Sengupta from IIT Gandhinagar will be addressing the students on “Unboundedness of Betti numbers of some families of curves in affine and projective spaces”. Prof Indranath Sengupta will discuss some problems related to the unboundedness of Betti numbers of families of affine curves defined by Numerical semigroups. He will also indicate possible connections, with the help of examples, between the unboundedness of the last Betti number and the Cohen-Macaulayness of the projective closure of these affine curves. This work has been carried out in collaboration with Ranjana Mehta, Joydip Saha & Pranjal Srivastav.

Mathematics Departmental Seminar is widely popular among students and Mathematics enthusiasts. This seminar provides a homey environment where students can interact with renowned mathematicians. Eminent mathematicians and scholars have visited SRM University-AP and enjoyed conversations with students. Everyone is encouraged to take part in the exciting journey through the realms of Mathematics with Prof Indranath Sengupta on October 13, 2021, at 3 pm.

### Dr Tathagata Sengupta to speak on ‘Debt, Mathematics and Education’.

Department of Mathematics is organising the 16th edition of the “Departmental Weekly Seminar Series” on October 06, 2021, at 3 pm with Dr Tathagata Sengupta as the Chief Guest. Dr Tathagata Sengupta is from Homi Bhabha Centre for Science Education, Tata Institute of Fundamental Research and he is going to speak on ‘Debt, Mathematics and Education’.

The talk is based on the ongoing work of Dr Sengupta, where he and his collaborators deal with the sociological, emotional and intellectual impacts of mechanical reproduction of formal knowledge systems – such as those based on mathematical models – in the service of economies of endless repetition and mass reproduction. Symbols and formalisms can carry over across different paradigms of human existence, across both time and space, without the underlying meanings and subtleties necessarily being carried along. Such nominalisation of meanings only gets exacerbated under systems of massive mechanical reproduction. Mathematical models particularly are not just mere vehicles of computation but play a paradigmatic role in the very realisation of today’s political economy – being endlessly used to reproduce social relations that suit the interests of power and capital.

Specifically, Dr Sengupta and his team analyse a particular, basic microfinance model that aims to mathematise and thus aid in the management of micro-lending businesses. They describe how such a model not only tries to construct particular social realities and certain kinds of financial ‘common sense’ as such but also how pre-existing normative common sense is likewise codified into the model itself. They argue how such mathematical models have no independent truth value outside of specific historic processes, contexts and paradigms of public common sense – hoping that this allows us to fundamentally shift the culture of mathematical modelling in a way that respects such subtleties of human knowledge in their extremely rich, dynamic, plural, communistic wisdom and creativity.

Dr Sengupta’s main attempt is to push the discussion not only out of the binaries of ‘good/bad models’ but also beyond rule-based rationalist imaginations of ethics into the mundane and emotional – and yet creative, subtle and even magical – daily existence of ordinary people. Existence is marked by social relations of radical inequalities and radical unities. In particular, this also opens up possible directions to pursue intellectually and in practice, when it comes to the question of education.

Mathematics enthusiasts can avail this opportunity to listen to the captivating talk of Dr Tathagata Sengupta on October 06, 2021 at 3 pm.

### The Narasimhan-Seshadri theorem and some of its ramifications

The Department of Mathematics at SRM University-AP organises the first episode of the Distinguished Lecture Series on September 29, 2021, at 3:30 pm. Prof Vikraman Balaji, renowned Mathematician from Chennai Mathematical Institute, Chennai, India will deliver a lecture on the topic “The Narasimhan-Seshadri theorem and some of its ramifications

Abstract of the talk:

The Narasimhan-Seshadri theorem is one of the spectacular theorems from India in the past 50 years or so. The theorem is more than a deep result but is in a way philosophy or correspondences and symmetries. The theorem has had an impact on several aspects of mathematics. The theorem has also led to developments along lines that are similar but by themselves are also deep and central. Since the talk is for a general audience, I plan to give an overview of the theorem, a few of its big impacts in topology and geometry and a few of its ramifications in terms of generalizations.

Prof Vikraman Balaji is a renowned Indian Mathematician and currently a professor at the Chennai Mathematical Institute, India. He completed his doctorate in mathematics under the supervision of Prof C S Seshadri. His primary research area is algebraic geometry. He has made outstanding contributions to moduli problems over algebraic varieties. In particular, his work on ‘compactification of moduli of principal G-bundles over algebraic surfaces and his joint work with C.S Seshadri on ‘Parahoric torsors’ are very significant among his many other notable works. In 2006, he received the prestigious Shanti Swarup Bhatnagar Award in Mathematical Sciences and was awarded the J.C Bose fellowship in 2009. He was elected Fellow of the Indian Academy Of Sciences in 2007 and Fellow of the Indian National Science Academy (INSA) in 2015. He is presently an elected member of the National Academy Of Sciences, India (NASI).

Join this lecture on September 29, 2021, at 3.30 pm to understand the Narasimhan-Seshadri theorem and its impact on Mathematics.

### A session to explore novel areas of research

The Department of Mathematics at SRM University-AP is organising a webinar session on the topic “On non-vanishing of modular L-functions inside the critical strip” on September 08, 2021, at 3:30 pm. Mr E. M Sandeep, a senior researcher from the Kerala School of Mathematics will be the guest speaker at the event. All interested students and faculty are invited to join the session and gain insightful thoughts from the expert scholar.

### Flipping with the flow – Perspectives of puzzling fluid dynamics and human health

The Department of Mathematics is organising the first episode of the Distinguished Lecture Series on September 15, 2021, Wednesday, at 6.30 pm. Prof Suman Chakraborty from the Department of Mechanical Engineering, IIT Kharagpur, will deliver a lecture titled “Flipping with the Flow – Perspectives of Puzzling Fluid Dynamics and Human Health”.

Abstract of the Lecture:
Over the past century, advancements in fluid dynamics hallmarked deeper studies on complex fluids, though. Fluid dynamics of blood, possibly the most critical complex fluid impacting human lives, is primarily dictated by red blood cells (RBCs) that are flexible biconcave discs spending their lives suspended in blood plasma that is elusively more complex than simple water. Commonly, RBCs stack together to form structures called rouleaux like cylindrical packs of coins that reform continuously. Contrary to intuition, instead of clogging, such reforms result in the easier flow of blood as it passes through extremely narrow channels. An influential theoretical premise of blood flow has been rationalizing this by drawing analogies of RBCs with compound liquid droplets in which the cytoplasm is more viscous than the outer fluid that triggers a series of complex shape transitions. However, a stiffening of RBC membranes under certain conditions contradicts this analogy and may alter ATP release that happens due to shape deformation. This may signify specific diseased conditions and influence a plethora of ailments ranging from cardiovascular irregularities to cancer metastasis. The role of unique flexibility of microvasculature and morphology of the microenvironment, dynamical signals of pressure pulsation and disease-specific blood rheology make it extremely deceptive and patient-specific and difficult to model within the known territories of expertise of fluid dynamics.

Prof Suman Chakraborty will discuss here various computational, in-vitro and in-vivo studies conducted in his research group that have attempted to address some of the pertinent outstanding questions, unresolved paradoxes, and will present a deeper challenge that makes even ‘simple’ blood flow strikingly more complicated than its intuitive analogy of pipe flow in engineering fluid mechanics. He will also suggest a way forward with a convergence of physics-based modelling and data science, where blood flow is not merely perceived as an ‘inert’ physical phenomenon but recognized as an exclusive hallmark of ‘life’ with all individualism intrinsic to humans.

Prof Suman Chakraborty received the prestigious Santi Swaroop Bhatnagar Prize and became the youngest Fellow of the Indian National Academy of Engineering. He has also been a Fellow at the Indian National Science Academy (INSA), Indian Academy of Sciences (IAS), and Indian National Academy of Science (NASI), in addition to being the recipient of the Indo-US Research Fellowship. He is also a recipient of the Scopus Young Scientist Award given by Elsevier for high citations in his research publications, the Alexander von Humboldt Fellowship (2005), and the Young Scientist/Young Engineer Award from various National Academies. He has been bestowed with the Fellowship of the American Physical Society, the Fellowship of the Royal Society of Chemistry, and the Fellowship of the American Society of Mechanical Engineers.

Join this educational session on September 15, 2021, at 6.30 pm to gain insights from the field expert.

### “PDEs and Digital Images”- in discussion with Dr Vijayakrishna Rowthu

Department of Mathematics is back with another exciting version of the Departmental Seminars Series. This week, the Department of Mathematics invites the in-house mathematician Dr Vijayakrishna Rowthu to deliver a talk on “PDEs and Digital Images.” He is an Assistant Professor in the Department of Mathematics. The seminar has been scheduled for April 07, 2021, at 3 pm.

Digital images are discrete versions of 2D functions defined over a rectangular bounded domain. In the language of Partial Differential Equations(PDE), a digital Image Processing Method(IPM) appears as an Initial Value Problem (IVP) where the initial value is an image, and the PDE mimics the processing part of the method. Unlike the traditional IPMs, the final outcome is not subjective but majorly depends on the convergence of the evolving solution over the time axis.

In this talk, various PDE models will be illustrated to showcase the benefits and to infuse enough mathematical rigour into the field of image processing itself. Mathematics enthusiasts are requested to avail this opportunity to listen to our distinguished speaker on April 07, at 3 pm.

### Dr Chittaranjan Mishra to discuss “Fast pricing of multi-asset American options under jump-diffusion models”

In the next chapter of Departmental Seminars Series, Department of Mathematics, SRM University-AP, Andhra Pradesh welcomes Dr Chittaranjan Mishra, Department of Mathematics, Indian Institute of Technology Ropar, to deliver a lecture on “Fast pricing of multi-asset American options under jump-diffusion models” on March 24, 2021, at 3 pm.

Multi-asset American options are interesting in many ways, e.g., they give the holder the flexibility to exercise at any time up to maturity, allow for risk diversification and for us, these contracts are mathematically challenging to price due to the non-availability of a closed-form formula. When jumps are introduced to model underlying assets, one will be required to solve a partial integro-differential complementary problem (PIDCP) for pricing these contracts. In these cases, we find that computing sufficiently accurate option prices in real-time is extremely difficult. That is because the in hand PIDCP involves a multi-dimensional partial integro-differential equation with a non-local double integral term. Solving these multi-dimensional PIDCP by advanced numerical techniques, such as a customized finite difference method, is very time-consuming, as the corresponding discretization matrices are huge in size. More importantly, the integral approximation matrix is also dense, posing a serious challenge to handle storage memory. Many efficient techniques are proposed primarily to handle the double integral term. However, the required solving time is still not practicable for practitioners.

In our research, we exploit the amazing parallel architecture of modern graphics processing units (GPUs) to solve computationally expensive scientific problems. Nevertheless, resolving the problem at hand by employing a GPU is not straightforward. It requires one to overcome many bottlenecks, such as in. In this work, we have investigated these issues in order to achieve substantial speed-ups compared to a sequential FD implementation.

Mathematics enthusiasts are requested to avail this opportunity to listen to our distinguished speaker on March 24th, at 3 pm.

### Dr Gaurav Bhatnagar to interact on “The Partition-Frequency Enumeration Matrix”

Progressing with the series of Departmental Seminars, Department of Mathematics, SRM University-AP, Andhra Pradesh invites Dr Gaurav Bhatnagar, Visiting Associate Professor, Department of Mathematics, Ashoka University to deliver a lecture titled “The Partition-Frequency Enumeration Matrix” on March 10, 2021, at 3 PM.

The Partition-Frequency Enumeration (PFE) matrix is an infinite upper-triangular number-theoretic matrix that is used to enumerate partition-like objects as an elementary approach. This matrix unifies voluminous results connecting number-theoretic functions to partition-type functions. The calculus is extended to arbitrary generating functions and functions with Weierstrass products. As a by-product, some well-known recurrence relations for many number-theoretic functions are recovered. These include the sum of divisors function, Ramanujan’s $\tau$ function, sums of squares and triangular numbers, and $\zeta(2n)$, where $n$ is a positive integer. As an application, Ramanujan’s famous congruences $p(5n+4)\equiv 0$ (mod $5)$ and $\tau(5n+5)\equiv 0$ (mod $5)$ are embedded into an infinite family of such congruences. During the lecture, Dr Gaurav Bhatnagar will highlight two other congruence results concerning the sum of the divisor function.

### Dr Ravi Prakash to illustrate Homogenization Problem and Tartar’s Method

Department of Mathematics, SRM University-AP, Andhra Pradesh presents departmental seminar on “Introduction to Homogenization Problem and Tartar’s Method”. During the session on February 17, 2021, at 5.30 PM, Dr Ravi Prakash, Assistant Professor, Departamento de Matem ́atica, Universidad de Concepci ́on, Concepci ́on, Chile, will describe this mathematical theory that has been introduced to explicate the behaviour of composite materials used by the material scientists. He will illustrate this model by drawing example of a homogenized material.

The aim of ’Homogenization’ is precisely to give the macroscopic properties of the composite by taking into account the properties of its structure. For a good understanding of this area, one must have a definite knowledge of Distribution Theory, Functional Analysis, Measure Theory, and Differential Equations.

The theory of Homogenization has reaching applications in several areas (including composite materials) such as porous media, analysis of their structures, etc. During the session, the esteemed guest lecturer will enable the audience to comprehend how Tartar’s Method uses two scales for the characterization of the material – the microscopic one, describing the heterogeneities, and the macroscopic one, describing the global behavior of the composite.