**Speaker:** Mrs Anagha S, PhD Scholar, SRM University-*AP*

**Date:** March 01, 2023

**Abstract:** Soils, textiles, gels, and biological tissues are porous and very soft. In these materials, deformation and fluid flow are strongly coupled through rearrangements of the pore structure. The resulting flow fields, which are both heterogeneous and unsteady, can play a key role in the transport and mixing of solutes in practical problems such as groundwater contamination and tissue engineering. Here, we use a continuum model based on large-deformation poroelasticity to study the impact of periodic squeezing on solute transport and mixing in a soft porous medium. Transport occurs through advection, molecular diffusion, and hydrodynamic dispersion, each of which interacts differently with the deformation. We identify the key dimensionless control parameters, explore the resulting deformation and transport regimes.

**Speaker:** Dr Manish Kumar Pandey, Assistant Professor, SRM University-*AP*

**Date:** March 29, 2023

**Abstract:** In this talk, we will talk about the infinitude of zeros of the Koecher Maass series on the critical line.

**Speaker:** Dr Sazzad Ali Biswas, Assistant Professor, SRM University-*AP*

**Date:** April 12, 2023

**Speaker:** Dr Tapan Kumar Hota, Assistant Professor, Department of Mathematics, SRM University-*AP*

**Date:** May 10, 2023

**Abstract:** The essential concept of many scientific investigations in computational and experimental fluid

dynamics is to present an objective and quantitative representation of flow behavior. A thorough understanding of all key processes also lays the groundwork for the incorporation of fundamental fluid effects into technical applications and fluid-based devices. Experiments and numerical computations are the two pillars upon which this process relies. Almost all current techniques in quantitative fluid dynamics rely on a model equation, most often, say, the linearized Navier-Stokes equations and their variants. This model is implemented in the algorithms as a matrix-vector mul-application, which is critical for maintaining orthogonality or adding robustness to the corresponding approach. However, only the measured data are available in physical experiments. To reach the same level of quantitative description of fluid processes, popular algorithms must be adjusted to curtail their reliance on models and limit their input to data exclusively. In this context, we shall visit from elementary level to modern computational algorithm to accommodate the snapshot based process to understand the model reduction and explore the role of eigenmodes.

**Speaker:** Dr Narravula Harshvardhan Reddy, California Institute of Technology (Caltech), USA

**Date:** June 14, 2023

**Abstract:** Rotation-free finite element analysis While the majority of analytical analyses of plates and shells rely on Kirchhoff-Love (KL)formulations put forth for thin plates and shells, modern finite element formulations draw upon the Reissner-Mindlin (RM) theory for moderately thick shells. The finite element formulations based on RM theory treat translations and annotations as independent variables and are advantageous due to their demand foronly C0-continuity of the geometry between elements and the use of relatively simple shape functions. Nonetheless, RM elements suffer from various locking henomena such as shear locking and are inefficient in analysing very thin shells. With the emergence of stronger materials like carbon fibre-reinforced composites and the realization of lightweight structures with extremely small thicknesses, KLfinite element formulations utilizing only translations as the degrees of freedom are gaining prominence. This talk discusses two such rotation-free finite element formulations: Onate’s EBST [1] and NURBS-based isogeometric analysis [2] for thin-shell structures.

**Speaker:** Mr Faiz Imam, Guest Faculty

**Date:** June 21, 2023

**Abstract:** The classification of the sets of periodic points of a family of topological dynamical systems has been extensively studied. The study of periodicity helps us understand the other dynamical aspects in many cases. This talk is based on similar work for the family of automorphisms on a one-dimensional solenoid.

In this talk, we peek inside the world's tastiest doughnut, i.e., a dyadic solenoid. It is obtained as the intersection of the members of a nested system of embedded solid tori in R^3 (a solid torus wrapped twice inside another solid torus). Although it is a particular case, this gives an excellent geometric insight and dynamic aspect of what generally happens. We describe this solenoid in terms of inverse limits and Pontryagin duality. Later we characterize the periodic points of automorphisms of a one-dimensional solenoid, considering it as the inverse limit of a sequence of circle maps, followed by the description of the periodic points of automorphism of this solenoid. The last part of the talk will further continue this characterization for some higher-dimensional solenoids.

This work was done as a part of a SERB-DST Early Career Project and jointly co-authored with Prof. Sharan Gopal.

**Speaker:** Dr Arvind Kumar, IIT Jammu

**Date:** July 13, 2023

**Abstract:** Ramanujan made a series of influential conjectures in his 1916 paper &Quotron some arithmetical functions & quot; on what is now called the Ramanujan tau function. In the same paper he also proved a notable congruence mod 691 for the Ramanujan tau function. The existence of such congruences opened the door for many modern developments in the theory of modular forms. For newforms of prime level, some partial results about the existence of such congruences are known. In this talk, we discuss and refine some of those results.

**Speaker:** Dr Arvind Kumar, IIT Jammu

**Date:** July 13, 2023

**Abstract:** In the ever-evolving landscape of engineering design, structural optimization emerges as a key

discipline that empowers researchers and engineers to harness the full potential of materials and structures by automating the design process. This seminar delves into the realm of structural optimization aided by adjoint sensitivity analysis, elucidating its profound impact on contemporary engineering endeavors. The seminar commences by demystifying the core principles of optimization and describing structural optimization types such as topology, shape, and sizing optimization. Attendees will gain insights into the underlying mathematical formulations and algorithmic techniques that drive these optimization paradigms, fostering a comprehensive understanding of their applicability across different design challenges. Central to the seminar is the exploration of adjoint sensitivity analysis, a mathematical paradigm that enables structural design updates in response to performance criteria changes. Participants will delve into the mathematical foundations of adjoint methods, comprehending how they enable efficient calculation of gradient information crucial for design modifications. Enriching the discourse, the seminar interweaves theoretical concepts with interesting case studies, exemplifying the transformative potential of structural optimization. Through these illustrative examples, attendees will grasp how these techniques optimize designs across industries.

**Speaker:** Dr Satyajit Pramanik, IIT Guwahati

**Date:** September 13, 2023

**Abstract:** Soils, textiles, gels, and biological tissues are porous and very soft. In these materials, deformation and fluid flow are strongly coupled through rearrangements of the pore structure. The resulting flow fields, which are both heterogeneous and unsteady, can play a key role in the transport and mixing of solutes in practical problems such as groundwater contamination and tissue engineering. Here, we use a continuum model based on large deformation poroelasticity to study the impact of periodic squeezing on solute transport and mixing in a soft porous medium. Transport occurs through advection, molecular diffusion, and hydrodynamic dispersion, each of which interacts differently with deformation. We identify the key dimensionless control parameters, explore the resulting deformation and transport regimes.

**Speaker:** Dr Ram Baran Verma, Assistant Professor, SRM University-*AP*

**Date:** September 20, 2023

**Abstract:** I will be talking about the regular boundary point for the possession equations. If possible I will be talking about the necessary and sufficient conditions for a point to be regular

**Speaker:** Dr Repaka Subha Sandeep, Assistant Professor, SRM University-*AP*

**Date:** October 04, 2023

**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 $\mathrm{U}(n,n)$ contains a parabolic subgroup $P$ with Levi component $L$ isomorphic to $\mathrm{GL}_n(E)$. 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.

**Speaker:** Dr Narendra Singh Yadav, Assistant Professor, SRM University-*AP*

**Date:** October 11, 2023

**Abstract:** We consider the strong and weak maximum principles for partial differential equations. We also give some examples and an application to illustrate the usefulness of the discrete maximum principles. It is a very useful tool when analyzing the behavior of solutions to convection-diffusion problems.

**Speaker:** Dr Choiti Bandopadhyay, Assistant Professor, SRM University-*AP*

**Date:** November 09, 2023

**Abstract:** The study of different notions of amenability on a given category of objects, have been one of the most fundamental areas of research in abstract harmonic analysis. In this talk, we first provide a preliminary overview of the category of semihypergroups. As the name itself suggests, the category of semihypergroups can be regarded simply as a natural extension to the category of locally compact semigroups, with abundant examples in different areas of research. We then introduce the concept of amenability in this broader setting, and discuss several characterizations of the same in terms of certain ergodic, stationary, Banach algebraic and hereditary properties of the associated convolutive measure algebras.

**Speaker:** Prof V Kannan, SRM University AP

**Date:** February 23, 2022

**Abstract:** We discuss four classical theorems on roots of polynomials. They relate to four different branches of Mathematics, namely, Geometry, Topology, Complex Analysis and Functional Analysis. The theorems are stated below:

**Theorem 1 (Lucas)**. Every root of the derivative of a polynomial lies within the convex polygon formed by the roots of that polynomial.

**Theorem 2**: The roots of a polynomial vary continuously with its coefficients.

**Theorem 3 (Cauchy)**: If all the coefficients of a polynomial lie in the unit disc D, then all the roots lie in the disc 2D.

**Theorem 4 (Bernstein)**: The norm of the linear operator D (namely the differentiation) on (The space of polynomials of degree at most n on D) is exactly n.

**Speaker:** Prof Rajiv Lochan, SRM University-AP

**Date:** March 02, 2022

**Abstract:** Motivating the central ideas of quantum mechanics and quantum computation with trivial models. From there move on to a formal presentation of quantum mechanics that is needed for basic quantum computation. Central notions of quantum architecture (qubits and quantum gates) shall be described.

**Speaker:** Dr Sazzad Ali Biswas, SRM University-AP

**Date:** March 09, 2022

**Abstract:**This is an introductory level talk on p-adic numbers and p-adic analysis. Our primary goal is to give answers to the following questions:

(1) What is the p-adic number?

(2) How are they different from real numbers?

**Speaker:** Dr Manish Kumar Pandey, SRM University-AP

**Date:** March 16, 2022

**Abstract:** In this talk, we will talk about some portion of the Imai’s paper on Generalization of Hecke’s correspondence to Siegel modular forms. Our goal would be to define the Mellin transform on the Siegel space.

**Speaker:** Dr Rossi D'Souza, Homi Bhabha Centre for Science Education, TIFR

**Date:** March 28, 2022

**Abstract:**“Mathematics is hard!” has been a universal refrain among school children (and often their parents) for as long as we recall. But why do so many children dislike mathematics? Is it the way mathematics is taught – because math teachers follow a “rote-learning” approach instead of making sure students understand the basic concepts? Why are students from marginalized backgrounds/identities disproportionately lagging behind in & excluded from mathematics knowledge production? Or is mathematics really not for everybody?

In this talk, I draw from my PhD research with visually challenged students as well as from years of industry experience to highlight the importance of taking into account social factors in Mathematics Education Research to effectively address the challenges posed by STEM Education – and to work towards a world where mathematics really is for everybody!

**Speaker:** Mr Lokenath Kundu, SRM University-AP

**Date:** April 04, 2022

**Abstract:** This is a foundational talk on hyperbolic geometry. We will define the hyperbolic plane and geodesics for the hyperbolic plane model. The fundamental difference between Hyperbolic geometry and Euclidean geometry will be established in this talk. Our main focus will be to prove the Gauss-Bonet formula. As an immediate corollary of the Gauss-Bonet formula, we will find out the area of an n-polygon in the Hyperbolic plane model. The manifold theory is a prerequisite of this talk.

**Speaker: **Dr Anirban Bose, SRM University-AP

**Date:** April 18, 2022

**Abstract:** In this expository talk, we intend to discuss some basic notions related to linear algebraic groups and see some prototype examples.

**Speaker: **Dr suratno Basu, SRM University-AP

**Date:** May 02, 2022

**Abstract:** In this talk, we will give a brief survey of the theory of stable vector bundles

on smooth, irreducible projective curves (equivalently compact, connected Riemann surfaces).

**Speaker: **Dr Mohan Kumar Mallik, SRM University-AP

**Date:** May 09, 2022

**Abstract:** Habitat edges can have a number of effects on populations, including modifying their patterns of dispersal. Dispersal patterns can influence population dynamics. In this talk, we will explore the possible effects of a pattern of dispersal where the response of organisms to the boundary of a habitat patch depends on their local density. This talk will discuss some mathematical models for the population growth of organisms having diffusing and nonlinear per capita growth inside a patch, but with the likelihood of an individual crossing the patch boundary to leave the patch decreases as the local density of conspecifics within the patch increases. Such behaviour at patch boundaries has been observed among Glanville fritillary butterflies and has been proposed as a mechanism for generating an Allee effect at the patch level. These models predict that the behavior can indeed induce an Allee effect at the patch level even though there is no such effect built into the local population dynamics inside the patch. Also, we will discuss how per capita growth and boundary behaviours impact the Allee effects. The models are relatively simple and are not intended to give a complete description of any particular population but only to verify the idea that the mechanism of density-dependent dispersal behaviour at a patch boundary is capable of altering population dynamics within the patch.

**Speaker: **Dr Sazzad Ali Biswas, SRM University-AP

**Date:** May 16, 2022

**Abstract:** This is an introductory level talk on p-adic numbers and p-adic analysis. Our primary goal is to give answers to the following questions:

(1) What is the p-adic number?

(2) How are they different from real numbers?

**Speaker:** Dr RamBaran Verma, SRM University-AP

**Date:** May 23, 2022

**Speaker:** Mr Lokenath Kundu, PhD Scholar, SRM University-*AP*

**Date:** September 07, 2022

**Abstract:** We will first prove that isometries of upper half plane i.e. Isom(H) = P SL2(R). Using Bouwer’s fixed point theorem we will classify the elements of the group P SL2(R). The discrete subgroup of P SL2(R) is known as the Fuchsian group. At last, we will define the signature of the finitely generated Fuchsian group. If time permits then we will define the signature of finite groups.

**Speaker:** Dr Jayasree Subramanian, Associate Professor, SRM University-*AP*

**Date:** September 28, 2022

**Abstract:** The role language plays in teaching and learning of mathematics has been a matter of enquiry for more than 4 decades now. The first paper addressing this issue appeared in the year 1979 in Educational Studies in Mathematics. Some of the early studies on language and mathematics education examined bilingual/ language minority students’ performance in mathematics from a deficit perspective. However, recent classroom studies focusing on socio-cultural perspectives argue that minoritized languages rather than being a barrier can in fact be a resource for learning mathematics. Though there is very little research on mathematics education in India, the work of NGOs such as Eklavya have engaged with the language issue in the mid 80’s.

In my talk, I will give a broad overview of the issues addressed in the literature on Language and Mathematics Education and present what I think is different in the Indian context.

**Speaker:** Dr Rajkumar Nayak, Assistant Professor, SRM UNiversity-*AP*

**Date:** October 19, 2022

**Abstract:** Inequalities have existed in different branches of Mathematics since time long. In 1934, the first book “Inequalities” was written by G. H. Hardy, J. Littlewood and J. Polya. The second book on this topic was written by E. Bechanbach and R.Bellman in 1961. These books have revolutionized the field of inequalities into a well organized field and provide motivations, ideas, techniques and applications for new research. One such salient inequality is Numerical radius inequality.

The inequalities involving the bounds of numerical radius of a bounded linear operator on a Hilbert space has attracted the attention of many mathematicians all over the world for a long time. We have calculated new upper and lower bounds for the numerical radius of a bounded linear operator and 2 × 2 operator matrices defined on a complex Hilbert space, which improves on the existing bounds.

**Speaker:** Mr Swapnil, PhD Scholar, SRM University-*AP*

**Date:** November 16, 2022

**Abstract:** In this seminar, we will discuss the journey from the butterfly effect to the definitions of chaos through topological conjugacy, sensitive dependence on initial condition, Scrambled set, e.t.c. Also, the changes in the definition depending on the change in the phase space will be discussed. Unlike other topological spaces, topological transitivity is sufficient for a function on a real interval to behave chaotic.

**Speaker:** Mr Lokenadh Kundu, PhD Scholar, SRM University-*AP*

**Date:** November 30, 2022

**Abstract:** In this talk, we will define the growth of a group and the conjugacy growth ofa group. We will establish some interesting but contrasting phenomena betweenthe above two growth functions.

**Speaker:** Dr A Satyanarayan Reddy, Shiv Nadar University, New Delhi

**Date:** December 07, 2022

**Abstract:** Let $c(G)$ denotes the number of cyclic subgroups of a finite group $G.$ A group $G$is{\em $n$-cyclic} if $c(G)=n$. We review the work of $n$-cyclic groups for a few values of $n.$ In particular, we show that $c(G)=11$ if and only if$G\cong H,$ where $H\in \{\Z_{p^{10}}, \Z_{27}\times \Z_3, \Z_{27}\rtimes \Z_3, Dic_7,\Z_{7}\rtimes \Z_9, \Z_3\times S_3, \Z_{5}\rtimes \Z_8,\Z_{3}\rtimes \Z_{16}\}$ and $p$ is a prime number.

**Speaker:** Dr Ravi Prakash

**Date:** February 17, 2021

**Speaker:** Dr Gaurav Bhatnagar

**Date:** March 10, 2021

**Speaker:** Dr Vijay Krishna Rowthu

**Date:** April 07, 2021

**Speaker:** E M Sandeep

**Date:** September 08, 2021

**Abstract:** Holomorphic modular forms of (integral) weight *k* are analytic functions on the upper half-plane which are invariant under the action of certain discrete subgroups Γ of* SL2*(R) and holomorphic at the cusps of Γ. Hecke eigenforms are certain nice functions which span this finite-dimensional Hilbert Space and are simultaneous eigenfunctions corresponding to a class of nice operators on this space called Hecke Operators. The Fourier expansion of Hecke eigenforms around the cusps are arithmetically significant and demand the study of the Dirichlet L-series (and its analytic continuation) associated to it. Riemann Hypothesis in this context predicts that non-trivial zeros of their L function lie exactly on the line of symmetry <*(s)* = 1/2 and is a long-standing open problem in Mathematics. While Riemann Hypothesis is at present out of reach, one can of course ask simpler questions.

In this talk, we discuss certain partial results on the following related question: Given* s = σ + it,* a complex point inside the critical strip (outside the line of symmetry), can we quantify the number of Hecke eigenforms* f* in *S*_{k} whose* L*-value is non-vanishing at *s?* This is a joint work with Prof M Manickam and Prof V Kumar Murty. Here, Sk denotes the space of modular cusp forms of weight* k* with respect to *SL _{2}*(Z).

**Speaker:** Dr Tathagata Sengupta, Homi Bhabha Centre for Science Education, TIFR

**Date:** October 06, 2021

**Abstract:** This presentation is based on presently ongoing joint work, where we 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 carryied along. Such nominalization 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 realization of today's political economy - being endlessly used to reproduce social relations that suit the interests of power and capital.

Specifically, we analyze a particular, basic microfinance model that aims to mathematize, and thus aid in the management of, micro-lending businesses. We 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. We 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 modeling in a way that respects such subtleties of human knowledge in their extremely rich, dynamic, plural, communistic wisdom and creativity.

Our 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.

**Speaker:**Prof Indranath Sengupta, IIT Gandhinagar

**Date:** October 13, 2021

**Abstract:** We discuss some problems related to the unboundedness of Betti numbers of families of affine curves defined by Numerical semigroups. We 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. (Joint work with Ranjana Mehta, Joydip Saha & Pranjal Srivastav)

**Speaker:** Dr Sundar Sobers

**Date:** November 11, 2021

**Abstract:** In the late eighties, Powers initiated the study of 1-parameter semigroup of endomorphisms on B(H). This was further studied intensively by many others during the last three decades led by William Arveson. Although from the physics point of view, 1-parameter theory is the most important one, from the mathematical perspective it is not necessary to restrict oneself to 1-parameter, i.e. the half-line [0, ∞) and we could replace the half-line by any ‘reasonable semigroup’ like convex cones in higher dimensional Euclidean space. One of the nice features is that the basic theory stays intact while there are significant differences between the 1-parameter theory and the n-parameter theory. I will explain one such phenomenon. In particular, I will define the basic examples of E0-semi-groups, i.e. the CCR and CAR flows associated to isometric representations of the semigroup P. In the multi-parameter world, CCR flows need not be isomorphic to its opposite, a sharp contrast to the one parameter situation.

**Speaker:** Prof V Kannan

**Date:** January 08, 2020

**Speaker:** Prof Jesse Deutsch

**Date:** January 22, 2020

**Speaker:** Dr B Madhav Reddy

**Date:** Febuary 12, 2020

**Speaker:** Dr B Madhav Reddy

**Date:** Febuary 19, 2020

**Speaker:** Dr Atul Dixit

**Date:** March 11, 2020

**Speaker:**Prof Sukumar Das Adhikari

**Date:** September 23, 2020

**Speaker:**Dr Mithun Bhowmik

**Date:** October 14, 2020

**Speaker:** Dr Rajat S Hazra

**Date:** October 21, 2020

**Speaker:**Dr Madhu Raka

**Date:** November 04, 2020

**Speaker:**Dr Bittu Raja Raman

**Date:** November 24, 2020