April2021
Schedule for April 2021
Talk 14
Date: 06 April 2021, 16:00 Indian Standard Time (10:30AM GMT)
Speaker: Professor Amritanshu Prasad, IMSc, Chennai, India
Title: The Frobenius Characteristic of Character Polynomials.
Abstract: Many families of representations of symmetric groups exhibit stability properties. The characters of such families are often given by polynomials in variables that count the number of cycles of a given size in a permutation. We characterize such families in terms of symmetric polynomials that are associated to them via the Frobenius characteristic. We provide some examples and applications of this computational technique.
Talk 15
Date: 13 April 2021, 16:00 Indian Standard Time (10:30AM GMT)
Speaker: Dr Shripad M Garge, IIT Bombay, Mumbai, India
Title: Applying Galois cohomology in group theory
Abstract: I will give a brief account of Galois cohomology for the first half of the talk. In the second half, I will outline some old results and some recent results in group theory that were obtained using Galois cohomology.
Talk 16
Date: 20 April 2021, 16:00 Indian Standard Time (10:30AM GMT)
Speaker: Dr Sandip Singh, IIT Bombay, Mumbai India
Title: Arithmeticity and Thinness of Hypergeometric Groups
Abstract: The hypergeometric groups we will discuss in this talk are the subgroups of GL_n(C) generated by the companion matrices of two monic self-reciprocal coprime polynomials of degree n so that their Zariski closures (inside GL_n(C)) are either symplectic or orthogonal groups. In this talk, we will discuss the progress on the question to determine the arithmeticity and thinness of these hypergeometric groups.
Talk 17
Date: 27 April 2021, 16:00 Indian Standard Time (10:30AM GMT)
Speaker: Dr. Geetha Thangavelu, IISER Thiruvananthapuram, India
Title: Schur-Weyl duality and diagram algebras.
Abstract: Schur-Weyl duality is the foundational result in representation theory which connects the representation theory of general linear groups and the symmetric groups. Its classical version, due to Issai Schur (1901 and 1927), can be viewed as another formulation of the first and second fundamental theorem of the invariant theory of general linear group. After Schur's work, several attempts have been made to study the analogues of this duality. We will explore two important classes of algebras called "Schur algebras" and "diagram algebras" which arise from this duality in connection to other theories like Lie theory, quantum groups, statistical mechanics and mathematical physics. In this talk we will see an overview of these algebras, the theory of cellular algebras introduced by Graham and Lehrer (1996)) which provides a beautiful model to understand these classes of algebras and my recent work in this direction.
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