Topology Student Seminar
Speaker: Advaith Nair, IIT Bombay
Host: Rekha Santhanam
Title: --
Time, day and date: 11:00:00 AM – 12:00:00 PM, Wednesday, September 24
Venue: Room 113
Abstract: Poincare duality is a result on an n-dimensional orientable manifold. It is an important tool useful in various calculations such as cohomology ring of several spaces and also in proving several other results in the subject. I will start by defining the fundamental class of a manifold and then eventually formulate and prove the main theorem

APS
Speaker: Lavanya V, IIT Bombay
Host: Rekha Santhanam
Title: Irreducible Representation of the Unitary Group
Time, day and date: 4:00:00 PM – 5:00:00 PM, Wednesday, September 24
Venue: Room 114
Abstract: In this seminar, we will characterize the irreducible representations of the unitary group U(n). First, we show that every finite dimensional representation of U(n) has a special vector called a highest weight vector. And we will derive Weyl Character Formula. By combining this formula with the Weyl Integration Formula, we show a one-to-one correspondence between irreducible representations and a set of dominant weights