


Topology and Related Topics Seminar
Tuesday, 16 April 2024, 11:30 am12:30 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, 4:005:00 pm
Venue: Room # 215
Title: Commutative Algebra Seminar
Title: Numerical Semigroups and associated Semigroup RingsII.
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 CohenMacaulay type of the
numerical semigroup ring k[S] corresponds to the number of
pseudoFrobenius elements of S. Consequently, we derive a wellknown
result concerning Gorenstein numerical semigroup rings (credited to
Kunz) asserting that k[S] is Gorenstein if and only if S is symmetric.