Title: The lens of complexity
Speaker: Maya Saran
Date: March 14, 2019 (Thursday)
Abstract: If two trigonometric series converge everywhere to the same function, must they be the same series? This (old) question leads, in harmonic analysis, to sets called "sets of uniqueness". In the problem of characterising, i.e., recognising, such sets, it turns out that looking through the lens of descriptive set theory is richly fruitful. In this talk I will describe what a result of Kechris-Louveau-Woodin says about the complexity of the collection of sets of uniqueness. While the talk will be mostly expository, time permitting I'll also touch upon some recent work in this area. If you know what the real line is, you should be able to follow most of the talk.

Title: Endomorphism Rings of Finite Drinfeld Modules
Speaker: Sumita Garai
Date: March 08, 2019 (Friday)

Title: Aspects of Pluralism in Mathematics
Speaker: Prof. Mihir Chakraborty
Date: March 06, 2019 (Wednesday)
Abstract: In recent times there has emerged the study of various pluralistic aspects of mathematics and mathematical practices. This has gone so far as the publication of a book named " Pluralism in mathematics : A new position in Philosophy of Mathematics", author, Michele Friend. I have been experiencing this phenomenon as a practicing mathematician for last 30 years or so. Pluralism arises from within mathematics and outside. As examples of 'from within' one can cite various Euclidean and non-Euclidean geometries, Cantorian and non-Cantorian Set theories, various foundations of mathematics, e.g. Logicism, Intuitionism, Formalism, Fictionalism and Pluralism (as mentioned above). These are not all about within. As regards influence from outside we can talk about mathematical practices in various cultures. Role of culture in the shaping of mathematical activity of a particular society, community or group has become an interest of studies of the current era.

Title: Performance Improvement in Adaptive Control:An Initial Excitation based Framework
Speaker: Dr. Sayan Basu Roy, IIIT-Delhi
Date: February 28, 2019 (Thursday)
Abstract: This talk would focus on performance issues in adaptive control, which is a class of nonlinear control technique used to tackle structured uncertain dynamical systems. Adaptive control can be visualized as a real-time uncertainty handling mechanism, which uses an online parameter estimator in conjunction with the controller to control a plant with parametric uncertainty.

It is well known that classical adaptive controllers typically guarantee Lyapunov stability in the extended state space (tracking error and parameter estimation error space), and asymptotic convergence of tracking error to zero, however, parameter convergence is only guaranteed if a restrictive condition of persistence of excitation (PE) is satisfied by the regressor signal. The PE condition is stringent since it demands sufficient energy/richness of information content for the entire time duration and, in general, conflicts with the tracking requirement.

The talk would emphasize on transient improvement of adaptive controllers through ensuring parameter convergence without requiring the stringent PE condition. We have developed new class of composite adaptive controllers, which build on two-layers of low-pass filters, and ensure parameter convergence using a milder condition of initial excitation (IE) on the regressor signal. The IE condition, which is shown to be online verifiable, is significantly less stringent than PE, since it demands sufficient energy/richness of the regressor only in the initial time window. The IE-based adaptive control guarantees exponential stability of the tracking and parameter estimation error once the online-verifiable IE condition is satisfied. Unlike conventional adaptive controllers, which only ensure asymptotic tracking, the proposed design is practically more significant due to its capability of exponentially fast tracking performance, which is especially crucial in safety-critical applications.