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 Cauchy-Schwarz inequality in 
matrix algebra

Abstract: We focus on the non-commutative versions of some inequalities 
related to the Cauchy-Schwarz 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/nrf-fugo-xzp [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/virtual-comm-algebra-seminar [2]