Postdoc extension talk
Speaker: Sucharita Biswas, IIT Bombay
Host: S Krishnan
Title: Classification of Wilf Equivalence and Shape Wilf Equivalence classes for POPs and Short Pattern Sets
Time, day and date: 10:30:00 AM - 11:30:00 AM, Monday, June 29
Venue: Ramanujan Hall
Abstract: Permutation pattern avoidance is a central topic in enumerative combinatorics. In this talk, I will discuss Wilf equivalence and shape Wilf equivalence for permutation patterns, with a particular focus on partially ordered patterns (POPs) and short pattern sets. Partially ordered patterns generalize the classical notion of permutation patterns by allowing certain entries of a pattern to be incomparable. I will present a complete Wilf equivalence classification of POPs of sizes $3$, $4$, and $5$ whose connected components are chains, thereby confirming a conjecture of Dimitrov posed during the problem session of the British Combinatorial Conference 2024 (BCC30). I will also describe recent results on shape Wilf equivalence for families of claw-shaped POPs. In particular, we prove that several such families are shape Wilf equivalent and obtain enumerative formulas for the corresponding avoidance classes.
Turning to short pattern sets, I will present a complete classification of shape Wilf equivalence classes for triples of patterns of length $3$. This work extends to a complete classification of quadruples and quintuples of patterns of length $3$, obtained in subsequent joint work. If time permits, I will conclude with a brief discussion of pattern avoidance in matchings, highlighting its rich connections with shape Wilf equivalence and related bijective phenomena.

Topology seminar
Speaker: Bittu Singh, IIT Bombay
Host: Rekha Santhanam
Title: Applications of Rational Homotopy Theory
Time, day and date: 4:00:00 PM – 4:40:00 PM, Monday, June 29
Venue: Room 215
Abstract: We now have all the tools from rational homotopy theory to algebraically model free loop spaces, which is key to its rational cohomology ring.
We continue the talk by presenting the solution to the closed geodesic problem due to Vigué-Poirrier and Sullivan. This solution relates the algebraic structure of the rational cohomology ring of a manifold to the existence of infinitely many closed geodesics.

Topology seminar
Speaker: Sudharshan Gurjar, IIT Bombay
Host: Rekha Santhanam
Title: Eilenberg MacLane and Moore spaces in algebraic geometry.
Time, day and date: 4:40:00 PM – 5:20:00 PM, Monday, June 29
Venue: Room 215
Abstract: I will make some comments about Eilenberg MacLane and Moore spaces in the setting of complex manifolds/complex algebraic geometry, with special focus on complex surfaces.

Algebra Seminar
Speaker: Neena Gupta, ISI Kolkata
Host: Manoj Kumar Keshari
Title: On Affine Forms
Time, day and date: 11:30:00 AM – 12:30:00 PM, Wednesday, July 01
Venue: Ramanujan Hall
Abstract: Let k be a field and A be a k-algebra.  A is said to be an A^n-form over k if there exists a field extension L of k such that A\otimes_k L is isomorphic to a polynomial ring in n indeterminates over L. A is said to be a separable A^n-form if L can be taken to be a separable extension over k. It is an important question when an A^n form over k is necesarily a polynomial ring. It is well known that separable A^1 and A^2 forms are necessarily polynomial rings, and that there exist examples of A^n-forms over non-perfect fields, which are not polynomial rings.

In this talk we shall discuss a few recent developments on this problem. It will be mainly based on joint works with A.K. Dutta, Animesh Lahiri and Parnashree Ghosh and an independent work of Debojyoti Saha.