Topology and Related Topics Seminar

Tuesday, 16  April 2024, 11:30 am-12:30 pm

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Venue: Ramanujan hall

Host: Rekha Santhanam

Speaker: Bittu Singh

Affiliation: IIT Bombay

Title:  Topological Hochschild homology

Abstract: This is the first of a series of two talks. We will discuss cyclic homology, Symmetric monoidal category of spectra and S^1 action on a cyclic set.

Algebraic Groups Seminar

Tuesday, April 16, 2024, 4 pm
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Venue: Ramanujan Hall

Host: Shripad M. Garge

Speaker: Akash Yadav

Affiliation: IIT Bombay, Mumbai

Title: Borel and parabolic subgroups

Abstract: We complete the 6th chapter of Springer's book with some important properties of Borel and parabolic subgroups of linear algebraic groups.

Commutative Algebra Seminar 

Speaker: Om Prakash
Affiliation: IIT Bombay
Host: Tony J. Puthenpurakal

Time: Tuesday, 16  April 2024, 4:00-5:00  pm
Venue: Room # 215 
Title:   Commutative Algebra Seminar

Title: Numerical Semigroups and associated Semigroup Rings-II.

Abstract: In this series of two lectures, we will study numerical
semigroups and their associated semigroup rings. Initially, we will define
numerical
semigroups, state their fundamental properties, and introduce relevant
invariants. Subsequently, we aim to prove the following fundamental
results: (i) The Frobenius number of a numerical semigroup S equals the
degree, viewed as a rational function, of the Hilbert series of the
numerical semigroup ring k[S]. (ii) The Cohen-Macaulay type of the
numerical semigroup ring k[S] corresponds to the number of
pseudo-Frobenius elements of S.  Consequently, we derive a well-known
result concerning Gorenstein numerical semigroup rings (credited to
Kunz) asserting that k[S] is Gorenstein if and only if S is symmetric.