- March 24, 2021
##### Unimodular rows

- Dr. Mrinal Das, ISI Kolkata

Dr. Mrinal Das first introduced some basic and classical results on unimodular rows and went on to present their recent research work and some of the open problems in the study.

- March 17, 2021
##### Prime-characteristic commutative algebra

- Dr. Manoj Kummini, CMI

This expository talk by Dr. Manoj Kummini focussed on the Ring theory and explained how every commutative ring of prime characteristic $p$ has the Frobenius endomorphism $F : r \mapsto r^p$. This, he said, can be used to study singularities of (the prime spectra of) such rings. In this session, Dr. Manoj described a class of such singularities, called F-rational rings, a notion closely related to rational singularities over complex numbers.

- March 10, 2021
##### $p^r$-Selmer companion modular forms

- Dr. Sudhanshu Shekhar, Department of Mathematics & Statistics, IIT Kanpur

Dr. Sudandhu Sekhar presented the joint work of Somanth Jha and Dipramit Majumdar, and it focussed on Selmer companion modular forms.

- February 24, 2021
##### Deep Learning for Automated Ocean Feature Extraction from Satellite Images

- Dr. Deepak Narayanan Subramani, Department of Computational and Data Sciences, IISc Bengaluru

Dr. Deepak Narayanan Subramani rationalized how digitization of synoptic ocean features could help in climate studies and forecasting ocean-atmosphere systems. He outlined how this was done through a time-consuming manual process by skilled human operators in the past. The dynamics-inspired deep learning system that Dr. Subramani’s research team has worked on and developed, extracts satellite images of sea surface temperatures and sea-surface heights and allows predictions with about 70-80% accuracy.

- February 10, 2021
##### Stabilized Variational Multiscale Sub-Grid Finite Element Analysis of Coupled Brinkman-Stokes-Transport Model

- Prof. B. V. Rathish Kumar, Department of Mathematics and Statistics, IIT Kanpur

Prof. Rathish Kumar began this lecture with an introduction to the concept of variational multiscale Sub-Grid Finite Element Method for fluid flow problems and went on to explain the notion of apriori and aposteriori error analysis for the Finite Element Method, in the context of transport models with variable diffusivity. He further explained the theory of stabilized Variational Multiscale Sub-Grid Finite Element Method (VMSGFEM) for transport equations, which is especially helpful to handle convection dominated fluid flows. Prof. Rathish Kumar ended the lecture with a discussion on the VMSGFEA for the unified Brinkman-Stokes/Transport Model, and the results from the numerical test cases.

- January 27, 2021
##### Mixed-precision subspace iteration algorithm for large-scale nonlinear eigenvalue problems towards quantum-mechanical modelling of materials

- Dr. Phani Motamarri, Dept. of Computational and Data Sciences, IISc Bangalore

Dr. Phani Motamarri’s research focus includes Computational Materials Physics, Computational algorithms for ab-initio material modelling at extreme-scale, Machine learning for materials design, High-performance computing, Computational solid mechanics, Finite-element methods, open-source code development using finite-elements for density functional theory (DFT-FE).

- December 02, 2020
##### Finite Element Computations of Free surface and Multiphase flows with Surfactants

- Dr. Sashikumaar Ganesan, Dept. of Computational and Data Sciences, IISc Bangalore

Dr. Sashikumaar Ganesan in this talk explained why computations of free surface and two-phase flows are very challenging, in particular, when surface-active agents (surfactants) are present in the fluid. He went on to describe how Marangoni forces are induced and how the existence of surfactants in fluids strongly influences the dynamics of the flow. Dr. Sashikumaar presented a finite-element scheme based on a coupled arbitrary Lagrangian-Eulerian and Lagrangian approach to compute free surface and interface flows with soluble surfactants.

- November 05, 2020
##### A study on Navier Stokes equations with Navier-slip boundary conditions

- Dr. Subha Pal, Tezpur University

Dr. Subha Pal started with a short overview of Navier-Stokes equations and different boundary conditions, and progressed to discuss the existence and uniqueness of solutions to the Navier-Stokes and damped Navier-Stokes equations subject to Navierslip boundary conditions in R3. He then went on to explain the Rothe method to prove the existence of weak solutions of the damped Navier-Stokes equations subject to Navierslip boundary condition with nonlinear source term in a bounded domain. The talk ended with a discussion on their future research plans.

- November 04, 2020
##### Central Limit Theorem, Moderate and Large Deviations for Nonlinear Stochastic Dynamical Systems

- Dr. A. Haseena, Government College Chittur, Palakkad

Dr. Haseena’s talk centred around the Large Deviation Theory, a branch of probability theory which studies the exponential decay of probabilities of rare events. In the first part of this talk, Dr. Haseena discussed the Freidlin-Wentzell type large deviation principle (LDP). The next part of her talk focussed on her future work - formulate a SIRI-PDE epidemic model and prove the global solvability results in both deterministic and stochastic framework. The main objective of this research is to predict the time to extinction of epidemics falling under SIRI category.

- November 03, 2020
##### HOC Approach to the Dynamics of Wave Patterns in Excitable Media

- Devanand, Ph.D. scholar at IIT, Guwahati

In this talk, Devanand briefly described a part of his thesis work where he has explored the dynamics of wave patterns of the excitable media. His work is mainly concerned with High Order Compact (HOC) simulation of spiral waves in excitable media, particularly the study of spiral wave dynamics.

- November 02, 2020
##### Complementarity problems and non-cooperatives games

- S. Gokulraj, CUTN

This talk was presented by Gokulraj, a research scholar at CUTN

- October 28, 2020
##### Differential quadrature parallel algorithms for solving system of convection-diffusion-reaction models

Numerical simulation of blood flow in the aorta- V. S. Aswin

V.S. Aswin presented two talks. The first one introduced three numerical schemes based on differential quadrature formulations for solving the system of convection-diffusion-reaction models.

The second talk described how Computational Hemodynamics, provides clinicians sufficiently accurate diagnosis of cardiovascular disease, and guides them in the choice of optimal treatment methodologies.

- October 22, 2020
##### Dynamics of Distal Actions on Certain Compact Spaces

- Alok Kumar Yadav, IISER-Mohali

- March 03, 2021
##### Semiglobal optimal Feedback stabilization of autonomous systems via deep neural network approximation

- Dr. Karl Kunisch (RICAM, Linz & Uni Graz, Austria)

The presentation explored the joint work of Dr.Karl Kunisch and his research team with Dr. Daniel Walker. This collaborative research analysed a learning approach for optimal feedback gains for nonlinear continuous time control systems. The goal of the study was to establish a rigorous framework for computing approximating optimal feedback gains using neural networks. Dr. Karl explained how the approach rests on two main ingredients. First, an optimal control formulation involving an ensemble of trajectories with 'control' variables given by the feedback gain functions. Second, an approximation to the feedback functions via realizations of neural networks. Based on universal approximation properties they proved the existence and convergence of optimal stabilizing neural network feedback controllers.

- November 11, 2020
##### First and second order shape optimization based on restricted mesh deformations

- Dr. Roland Herzog (TU Chemnitz, Germany)

Dr. Roland Herzog explained how in shape optimization problems involving partial differential equations, the domain is often represented by a computational mesh, and the optimization proceeds by repeatedly updating the mesh node positions. It is well known that such a procedure eventually may lead to a deterioration of mesh quality, or even an invalidation of the mesh, when interior nodes penetrate neighbouring cells. Dr. Roland examined this phenomenon, which can be traced back to the ineptness of the discretized objective when considered over the space of mesh node positions. As a remedy, they proposed a restriction in the admissible mesh deformations, inspired by the Hadamard structure theorem. First and second order methods were considered in this setting. Numerical results showed that mesh degeneracy can be overcome, avoiding the need for remeshing or other strategies.

- March 09, 2020
##### Challenges in Computational Calculus of Variations: 3 Examples in 1D.

- Prof. Carsten Carstensen, Humboldt-Universitat zu Berlin, Germany.

Prof. Carsten Carstensen explained the three examples in the calculus of variations that serve as master examples to illustrate what can go wrong in the minimization of a functional. He explained the three disaster problems and illustrated the direct method in the calculus of variations and the success or failure of the simplest finite element approximation.

- February 19, 2020
##### A Shape calculus approach for time harmonic solid -- fluid interaction problem in stochastic domains.

- Dr. Debopriya Mukherjee, Montanuniversitat Leoben, Austria.

In this talk, Dr. Debopriya Mukherjee presented the work that his team has been engaged in, in collaboration with Dr. Thanh Tran and his research team from the University of New South Wales, Australia. The talk focussed on the interior solid-fluid interaction problem in harmonic regime with randomly perturbed boundaries. He also provided an analysis of the shape derivative and shape Hessian of vector- and tensor-valued functions.

- February 08-23, 2020
##### Modelling of biochemical processes with randomness

- Lecture series by Prof. Erika Hausenblas, Montanuniversitst Leoben, Austria

Prof. Erika Hausenblas delivered a series of 4 lectures during her visit to IISER TVM. Dr. Erika has observed that chemical and biochemical reactions can exhibit surprisingly different behaviours, from multiple steady-state solutions to oscillatory solutions and chaotic behaviours. Such behaviours have been of great interest to researchers for many decades. The Briggs-Rauscher, Belousov-Zhabotinskii and Bray-Liebhafsky reactions, for which periodic variations in concentrations can be visualized by changes in colour, are experimental examples of oscillating behaviour in chemical systems. In the series of lectures, some systems of stochastic reaction-diffusion processes were introduced, the existence and uniqueness of solution were tackled, and finally some results related to numerical modelling were presented.

- November 01, 2019
##### Mini Symposium

- This Mini Symposium was held on the occasion of the Department Day and included talks by faculty from JNCASR, CMI, IISc, IISER TVM and Ph.D. scholars from IISER TVM. The event had 4 sessions with 2 talks in each session.

##### Speakers

- Prof K B Sinha, JNCASR Bangalore;
**Topic:**Introduction to Mathematical Aspects of Quantum Theory - Prof B V Rao, CMI Chennai;
**Topic:**Stochastic Modelling: Markov Chains - Dr. Viji Thomas, IISER TVM;
**Topic:**Schurs Exponent Conjecture - Prof S Gadgil, IISc Bangalore;
**Topic:**Free Groups, Lengths and Computer Proofs - Prof M Mukund, CMI Chennai;
**Topic:**Languages, Auromata and Logic - Mr. M C R Praphulla, IISER TVM;
**Topic:**Manifolds, Lie Groupoids and their Geometry - Mr. A Tiwari, IISER TVM;
**Topic:**The Rise and Fall of Lyapunov Exponents - Dr. P Devaraj, IISER TVM;
**Topic:**Reconstruction from Local Averages

- August 22, 2019
##### Half-day Symposium on Mathematics

- This half-day symposium was organized by the School of Mathematics and included talks by faculty from leading academic institutions

##### Speakers

- Prof. S. Sundar, IIT Madras
- Prof. J. K. Verma, IIT Bombay
- Prof. Mythily Ramaswamy, TIFR Centre for Applicable Mathematics
- Prof. B. Sury, ISI Bangalore

- August 16-17, 2021
##### International Workshop on High-Performance Computing in Science and Engineering

- The Center for HPC, IISER TVM organized an online "International workshop on High-Performance Computing in Science and Engineering” on 16th and 17th August 2021. The workshop brought together computational and life sciences research communities, enabling knowledge sharing on HPC technologies. Prof. J. N. Moorthy, Director, IISER TVM delivered the opening address which was followed by presentations from six globally renowned HPC specialists, who also explored the current challenges, and future opportunities for HPC applications in science and engineering. The second day of the workshop was completely devoted to a hands-on session organized by industry experts HPE and NVIDIA

##### Speakers

- Prof. David Keyes, Director, Extreme Computing Research Center, KAUST;
**Topic:**Scalable Solvers for CSE: Universals and Innovations - Prof. Peter Bastian, Head of Parallel computing group, University of Heidelberg, Germany;
**Topic:**Trends in High-performance Finite Element Simulations - Prof. Edoardo Di Napoli, Head of the SimLab Quantum Materials, Institute for Advanced Simulation (IAS) and Jülich Supercomputing Centre (JSC), Germany;
**Topic:**Chasing the hardware evolution: Goals, challenges and perspectives in high-performance and parallel computing - Prof. Martin HeadGordon, Department of Chemistry, University of California, Berkeley, USA;
**Topic:**Recent developments in density functional theory: From new functionals to the nature of the chemical bond - Prof. Bertrand Llorente, Cancer Research Center of Marseille (CRCM), CRNS, France;
**Topic:**Meiotic recombination in budding yeast and the importance of bioinformatics - Prof. Heather J. Kulik, Department of Chemical Engineering, MIT;
**Topic:**What can machine learning do to accelerate the design of catalysts and materials

- May 22, 2020
##### NCM Workshop on Complex Fluids and Liquid Crystals

- The mathematics of complex fluids and nematics is broad and rich, spanning multiple branches of mathematics such as calculus of variations, nonlinear PDEs, numerical analysis, topology, stochastic analysis and scientific computation. The training school was structured to be a set of introductory courses to the mathematics, modelling, analysis and applications of complex fluids and nematic liquid crystals.

- December 16-21, 2019
##### Winter School in Mathematics for Young Women

- This week-long event was organized by the Indian Women and Mathematics (IWM) – a collective of Indian mathematicians. The winter school provided women mathematicians a platform to network with one another and the motivation to pursue a career in mathematics.

- December 6-8, 2019
##### Higher Secondary Level Teachers’ Training Program

- The School of Mathematics, IISER TVM in collaboration with the Samagra Shiksha Kerala (SSK) of the Government of Kerala conducted a 3-day residential training program for Higher Secondary School Teachers. The main focus of the SSK is to improve the quality of education in schools, at all levels from pre-nursery to class 12 and improving systems level performance and schooling outcomes through appropriate interventions, infrastructure development and program management.

The training program was inaugurated by Prof. J N Moorthy, Director, IISER TVM, and the Guest of Honour for the inaugural day was Prof. Kuttykrishnan A. P., State Project Director, Sarva Shiksha Abhiyan. Each day had 5 sessions and included presentations by experts in the field of teacher training.

##### Speakers

- Prof. Inder K. Rana
- Prof. Raju K. George
- Prof. Kaushal Verma
- Prof. P. Balaram
- Prof. K. N. Raghavan
- Prof. Moosath
- Prof. Sreerup Raychaudhuri

- June 03 – 15, 2019
##### Instructional School for Teachers (IST)

- Representation Theory (of finite groups)

The National Centre for Mathematics is a joint centre of IIT Bombay and TIFR, Mumbai. They offer advanced training in Mathematics Schools. An Instructional School for Teachers was conducted at IISER TVM from June 03-15, 2019. The central theme of the IST program - Representation Theory (of finite groups). The participants in this workshop included Ph.D. scholars, Post-Doctoral Fellows and faculty from Higher Education Institutes, spread all across the country. The workshop consisted of 4 modules that had both lectures and tutorials conducted by faculty from IISER TVM, TIFR Mumbai and IMSc. At the end of the two-week long program, all participants received certificates from the Director of IISER TVM.

##### Speakers

- Viji Thomas, IISER TVM; Module A - Group action on sets: Permutation representations: the notion of action of a group
- Sandeep Varma, TIFR Mumbai; Module B - Ordinary representation theory of finite groups via characters: basic results
- Geetha Thangavelu, IISER TVM; Module C - Basics of the Wedderburn structure theorem for a finite dimensional semisimple algebra: application to ordinary representation theory of a finite group
- K N Raghavan, IMSc; Module D - Examples: especially the case of symmetric groups. Tabloid representations and their decomposition. Specht modules. Young tableaux and RSK correspondence

- May 20 – June 14, 2019
##### Mathematical Training and Talent Search Program (MTTS)

- One of the most popular undergraduate/graduate training programs in Mathematics is the MTTS program. These programs are conducted all through the year in different regions of the country by the MTTS Trust. The duration of these training programs ranges from one to 4 weeks. IISER TVM hosted a 4-week long MTTS program in May 2019 and students from across the region participated in this event.

- March 11-13, 2019
##### International Conference on Number Theory

- A 3-day international conference was hosted by IISER TVM in the second week of March 2019. The participants in the conference included several national and international experts from research institutes within the country, and from across its borders. There were several presentations covering a wide range of topics.

##### Speakers

- Vincent Sécherre;
**Topic:**Galois-self-dual cuspidal types and Asai local factors - Brundaban Sahu;
**Topic:**Rankin-Cohen brackets on modular forms and special values of certain Dirichlet series - Bibekananda Maji;
**Topic:**A generalization of Ramanujan’s formula for zeta(2m+1) - Atul Dixit;
**Topic:**On odd zeta values and analogues of Eisenstein series - Rahul Kumar;
**Topic:**Zeros of combinations of the Riemann Ξ-function and the confluent hypergeometric function on bounded vertical shifts - Soumya Das;
**Topic:**Fundamental Fourier coefficients of Siegel modular forms - Anuj Jakhar;
**Topic:**Charatcterization of primes dividing index of an algebraic integer - Garima Sood;
**Topic:**Recent Developments in the theory of Restricted partition function - Jaitra Chattopadhyay;
**Topic:**On the divisibility of class numbers of quadratic fields - Somnath Jha;
**Topic:**p^r-Selmer companion modular forms - Sudesh Kaur Khanduja;
**Topic:**On the ring of algebraic integers of the compositum of number fields - Shunsuke Yamana;
**Topic:**Towards the p-adic Gross-Zagier formula for triple product L-series - Takashi Nakamura;
**Topic:**Functional equations and zeros of the bilateral Hurwitz and periodic zeta functions - Rajneesh Kumar;
**Topic:**Large sieve inequality with power moduli for function fields - Ravindranathan Thangadurai;
**Topic:**On Prime k-tuple Conjecture - Debargha Banerjee;
**Topic:**Eisenstein cycles and Manin-Drinfeld properties - Neil Dummigan;
**Topic:**Automorphic forms on Feit's Hermitian lattices - Subha Sarkar;
**Topic:**Regularity of certain Diophantine equations - Bidisha Roy;
**Topic:**On Quadratic non residue non primitive roots - Rajat Gupta;
**Topic:**Generalized Lambert series, Raabe’s cosine transform and a two-parameter generalization of Ramanujan’s formula for ζ(2m + 1) - Kathiravan;
**Topic:**Ramanujan types of congruence for (5, t)-regular bipartition modulo t - Sunil Pasupulati;
**Topic:**On ramification indices of compositum of discrete valuation fields - AUBERT Anne Marie;
**Topic:**Variations of depths for Langlands parameters under local lifts. - Srinivas Kotyada;
**Topic:**Zeros of zeta-functions on the critical line - Soma Purkait;
**Topic:**Local Hecke algebra and minus space - Sampa Dey;
**Topic:**Staistics of the moduli space of vector bundles on hyperelliptic curves over finite fields - Abinash Sarma;
**Topic:**Congruence relations for 17-, 23-,65- regular partions - Amsuman Hegde;
**Topic:**Heuristics for the construction of counterexamples to the Agrawal Conjecture - Karthikesh;
- Umesh;
- Narasimha Kumar;

- December 05-08, 2018
##### Algebras, Combinatorics and Representation Theory

- This 4-day Conference had participants from top national institutes like the IITs, IISc, IMSc, IISERs, ISI, CMI, Satya Sai Institute of Higher Learning and from the University of Stuttgart, Germany and the NTNU Norway.

##### Speakers

- Apoorva Khare, IISc Bangalore;
**Topic:**On supercharacters of some pattern subgroups of Un(q) - Dilpreet Kaur, IISER-Pune;
**Topic:**Quadratic forms in characteristic 2 and a Wedderburn decomposition over rationals - Mohan. R , ISI Bangalore;
**Topic:**Leavitt path algebras of weighted Cayley graphs Cn(S, w) - Santosha Kumar Pattanayak, IIT Kanpur;
**Topic:**Torus quotients of Schubert varieties - Mrigendra Singh Kushwaha, IMSc Chennai;
**Topic:**A Path approach to Kostant-Kumar (KK) Modules - Arvind Ayyer, IISc, Bangalore;
**Topic:**The combinatorics of cyclic orders - Pooja Singla, IISc Bangalore;
**Topic:**Whittaker Model for Representations of General Linear Groups over complete DVR - Richard Dipper, University of Stuttgart, Germany;
**Topic:**On supercharacters of some pattern subgroups of Un(q) - C.P. Anil Kumar, IMSc Chennai;
**Topic:**Normal Representation of Hyperplane Arrangements and Convex Positive Bijections - G. Arunkumar, IISER Mohali;
**Topic:**Graph coloring and Free partially commutative Lie algebras - Tanusree Khandai, IISER Mohali;
**Topic:**Spectral Characters of a Integrable Representations of Toroidal Lie Algebras - Digjoy Paul, IMSc Chennai;
**Topic:**On the Centralizer Algebra of Symk (Fn) over Sn - Shripad Garge, IIT Bombay;
**Topic:**Z-classes of reductive groups - Clare D’Cruz, CMI, Chennai;
**Topic:**Symbolic powers of Monomial Curves in P3 and invariants associated to them. - Anuradha S. Garge, Mumbai University;
**Topic:**Generation of the special linear group over rings of integers - Uday Bhaskar Sharma, IISER Pune;
**Topic:**On Tuples of Commuting Unitary and Symplecti Groups over a Finite Field - M Hassain, IISc Bangalore;
**Topic:**Representation growth of Special Compact Linear Groups of Order Two. - Upendra Kulkarni, CMI Chennai;
**Topic:**Strict polynomial functors and Jantzens sum formula - Shraddha Srivastava, IMSc Chennai;
**Topic:**Schur Algebras for Alternating group and Koszul duality - B Ravinder, CMI Chennai;
**Topic:**Bases for local Weyl modules in type A and C - Venkatesh Rajendran, IISc Bangalore;
**Topic:**On tensor products of irreducible integrable representations - Sampath Lonka, Sri Sathya Sai Institute of Higher Learning;
**Topic:**Zero Weight Space for tori inside a division algebra - Mamta Balodi, IISc Bangalore;
**Topic:**Linear primitivity of interval of finite groups - Kamalakshya Mahatab, NTNU Norway;
**Topic:**Integer Stochastic Matrices - Sridhar Narayanan, IMSc Chennai;
**Topic:**Representation theory of 2-Sylow Subgroups of the Symmetric group

- November 04, 2020
##### The beautiful mathematics of H. Furstenberg and G. A. Margulis

- Prof. Anish Ghosh, School of Mathematics, Tata Institute of Fundamental Research (TIFR), Mumbai

This interactive session by Prof. Anish Ghosh was dedicated to the two living mathematical stalwarts who won the Abel Prize 2020. He described in detail the pioneering work of these mathematicians and their invaluable contributions to mathematics.

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