


Seminar on Linear Algebra Friday,18 November 2022 at 3.30 pm Venue: Ramanujan Hall Speaker: Rajesh Sharma, Himachal Pradesh University, Shimla Title: On some inequalities related to the CauchySchwarz inequality in matrix algebra Abstract: We focus on the noncommutative versions of some inequalities related to the CauchySchwarz inequality in matrix algebra. We discuss some inequalities involving positive unital linear maps on matrix algebra and demonstrate how positive linear maps can be used to obtain bounds for the spreads of matrices. The particular cases provide inequalities of statistical interest involving moments of discrete and continuous random variables.
Date: Friday, 18th November 2022 @4:35 pm
Venue: Ramanujan Hall
Speaker: T. N. Venkataramana, TIFR Mumbai
Title: Unipotent Generators for Higher Rank arithmetic Groups.
Abstract: Old results of Tits, Vaserstein, Raghunathan and myself say that the subgroup generated by elementary matrices, in any arithmetic higher rank group  namely the G(Z) of integer points of a simple algebraic group G defined over Q, is also arithmetic. The proofs rely on constructing a suitable completion of the group G(Q) of rational points and showing that this completion is a central extension of the (finite) adelic completion of G(Q). The other main ingredient of the proof relies on "Moore's uniqueness of reciprocity laws", which is used to deduce that
this extension is finite.
In this talk I describe a modification of the proof which shows that only the centrality is enough; the technically complicated second step may be avoided.
Virtual Commutative algebra seminar Date and Time: Friday, 18 November 2022, 5:30pm Gmeet link: meet.google.com/nrffugoxzp [1] Speaker: Mina Bigdeli, IPM, Tehran, Iran Title: Quadratic monomial ideals with almost linear free resolutions For more information and links to previous seminars, visit the website of VCAS: https://sites.google.com/view/virtualcommalgebraseminar [2]