NCMW  Operads in Topology (2024)
Speakers and Syllabus
Syllabus to be covered in terms of modules of 6 lectures each:
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 
Surojit Ghosh IIT Roorkee 
4 (1 ½ hour lectures) 
A_\infty obstruction theory and application to Morava K theories (Series 2) Furthermore, as an application of this obstruction theory, we prove that there are uncountably many different strict associative structures on the Morava Ktheory \(K(n)\) for all \(n\) and primes. 
Samik Basu ISI Kolkata 
4 (1 ½ hour lectures) 
Strict models for homotopy coherent multiplications on spaces 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 Ktheory construction. 
Somnath Basu IISER Kolkata 
3 (1 ½ hour lectures) 
Framed little 2disk operad and BV algebras BatalinVilkovisky (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 We shall talk about operads over Gspaces, 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. 
References (For each series of Lectures).
 Series 1:
a) Algebraic approach to Steenrod operations, Peter May.  Series 2:
a) Robinson, Alan. "Obstruction theory and the strict associativity of Morava Ktheories." Advances in homotopy theory (Cortona, 1988), 143–152, London Math. Soc. Lecture Note Ser., 139,
b) Lazarev, A. "Hochschild cohomology and moduli spaces of strongly homotopy associative algebras." Homology Homotopy Appl. 5 (2003), no. 1, 73–100.  Series 3 : 
a) May : The geometry of iterated loop spaces
b) Segal : Categories and cohomology theories.  Series 4:
a) BV algebras and 2dimensional topological field theories by E. Getzler (arxiv9212043)
b) The cohomology ring of the coloured braid group by V. I. Arnold (Mat. Zametki 5 ('69))  Series 5:
a) Lewis, May, Steinberger Equivariant Stable homotopy theory.
b) Balchin, Barnes, Roitzeihm : N_\infty operads and Associahedra
Names of the tutors with their affiliations:
1. Aprajita Karmakar, IIT Bombay (AK)
2. Bikramjit Kundu, IIT Roorkee (BK)
3. Sandip Samanta, IISER Kolkata (SS)
Time Table
Day 
Date 
Lecture 1 (9.30 
Tea (11.05 
Lecture 2 (11.30 
Lunch (1.05 
Lecture 3 (2.00 
Tea (3.35 
Discussion (4.005.00) 
Snacks (5:005:30) 


(Speaker) 

Speaker 

Speaker 

Speaker + Tutors 

Fri 
29/11/24 
DS 

SG 

SB1 

DS+AK+BK 

Sat 
30/11/24 
SB2 

RS 

DS 

SG+BK+SS 

Sun 
01/12/24 
SG 

SB1 

SB2 

SB1+AK+SS 

Mon 
02/12/24 
RS 

DS 

SG 

SB2+BK+SS 

Tue 
03/12/24 
SB1 

SB2 

RS 

RS+ AK+BK 

Wed 
04/12/24 
DS 

SG 

SB1 

SB1+SS+BK 

Full forms for the abbreviations of speakers and tutors:
DS : Debasis Sen
SB1 : Samik Basu
SG: Surojit Ghosh
SB2: Somnath Basu
RS: Rekha Santhanam