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4. Number Theory Seminar
Day, Date and Time : Wednesday, 25th September at 11:30 am
Venue: Room 215
Speaker: Aditi Savalia
Title: Spectral theory of automorphic forms
Abstract : We'll discuss Sections 2.2 and 2.3 of Iwaniec's Topics in
Classical Automorphic Forms.
APS Seminar
Date and Time: 11:30 AM - 12:30 PM on 25th September, Wednesday
Venue: Ramanujan Hall
Speaker: Surajit Pal
Title: Unique Continuation Principle and its applications
Abstract: This seminar explores the relationship between Hatus Lemma and
unique continuation principle, highlighting how UCP can be used to prove
the conditions for stabilizability in the Hautus Lemma. The Hautus Lemma
provides necessary and sufficient conditions for the stabilizability of
linear systems. The unique continuation which states that any solution of
an elliptic equation that vanishes in a small ball must be
identically zero.
Then we will try to give the argument how we can get unique continuation
principle for elliptic equation with constant, real-analytic coefficient
and later we will prove the unique continuation for little bit general
set-up using Carleman inequality.
Speaker: Unnati Nigam
Day, Date and Time: Wednesday, 25th September, 11.30 am
Online mode: join at https://meet.google.com/viw-jwsy-zdr
Title: Modelling of quasi-periodic data
Abstract: Quasi (pseudo/approximate) periodic signals often occur in natural settings, particularly when a periodic signal is recorded with noise. In this seminar, we will present a new dynamical equation system to construct a family of Quasi-Periodic Gaussian Processes (QPGP). We will describe a computationally inexpensive algorithm for the maximum likelihood estimation of parameters based on dynamic equations. This approach also simplifies the signal forecasting. We will illustrate via a simulation study that the proposed QPGP estimation strategy is faster as well and more accurate than existing constructions. Unlike these existing models, the proposed approach extends to multiple families of kernels, which we illustrate by modeling sunspot data, carbon dioxide emissions data and ECG data with both periodic Mat\'ern and MacKay's covariance kernel. This shows the exclusive advantage of the new QPGP family proposed in this work.
Debapriya Ojha will give her 2nd APS as follows.
25 September, 2-3 pm, Ramanujan Hall
Title: Hilbert's 17th Problem
Abstract: We will see the general concept of orderings of arbitrary
fields. We then establish relations between sums of squares in a field
and orderings of the same field. Next, we try to enlarge an ordered
field by extending the order to the new elements. Finally, we will
discuss Hilbert's 17th problem about the representation of forms by sums
of squares and its solution by Emil Artin . As an application of this
theorem we get the "sign change criterion".
Google Meet joining info
Video call link: https://meet.google.com/tgz-psxc-riq