## Past Events

• A session to explore novel areas of research September 6, 2021

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 August 23, 2021

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 April 7, 2021

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” March 24, 2021

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.

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.