Name of the Speaker with their Affiliation

No. of Lectures

Detailed Syllabus

Debasis Sen

IIT Kanpur

4 (1 ½ hour lectures)

Power operations on E_\infty F_p algebras 
(Series1)
E_infinity -algebras are algebraic structures that capture the multiplicative structure present in certain homotopy types. They are closely related to spaces with an action of an infinite loop space, and their study provides insights into in stable homotopy theory. Power operations on E_infinity algebras are operations that arise naturally from the structure of the E_infinity -algebra. They generalize various classical constructions such as Steenrod operations and Adams operations.

Surojit Ghosh

IIT Roorkee

4 (1 ½ hour lectures)

A_\infty obstruction theory and application to Morava K- theories (Series 2)
Stasheff defined a sequence of polyhedra (aka Stasheff associahedra) that encodes higher homotopy associativity of ring spectra. Given a ring spectrum \(E\), we build an obstruction theory to find a strictly associative ring spectrum that is homotopy equivalent to \(E\). Under certain assumptions on the homotopy groups of \(E\), we prove that these obstruction classes lie in the normalized Hochschild chain complex of the algebra \(E_\ast E\) over the ring \(E_\ast\).

Furthermore, as an application of this obstruction theory, we prove that there are uncountably many different strict associative structures on the Morava K-theory \(K(n)\) for all \(n\) and primes.

Samik Basu

ISI Kolkata

4 (1 ½ hour lectures)

Strict models for homotopy coherent multiplications on spaces
(Series 3)

Homotopy coherent multiplications are described in terms of an action by a suitable operad. The higher coherences for associativity gives rise to the A_\infty operad, which those for commutativity give rise to the E_\infty operad. Another way to describe these objects are using functors from certain categories : \Delta for the associative case, and \Gamma for the commutative case. The latter leads to a K-theory construction.

Somnath Basu

IISER Kolkata

3 (1 ½ hour lectures)

Framed little 2-disk operad and BV algebras
(Series 4)
We shall study the (framed) little 2-disk operad and its properties. Following Getzler, we will uncover its relation to 

Batalin-Vilkovisky (BV) algebras. Along the way, we shall discuss (through relevant examples) what BV algebras are and how circle action plays a key role.

Rekha Santhanam

IIT Bombay

3 (1 ½ hour lectures)

Equivariant Operads and Homotopical combinatorics
(Series 5)

We shall talk about operads over G-spaces, equivariant E_infinity operads and N_\infinity operads and the role they play in equivariant stable homotopy theory. We will discuss the work for Balchi, Barnes, and Roitzheim and independent work of Rubin connecting N_\infinity operads to equivariant transfer systems. We will conclude with discussing some of the recent work in this subject.