8:00am 


9:00am 


10:00am 
[10:30am] Amritanshu Prasad (IMSc)
 Description:
 Title: The RobinsonSchenstedKnuth Algorithm for Real Matrices
Abstract: The RobinsonSchenstedKnuth (RSK) correspondence is a bijection
from the set of matrices with nonnegative integer entries onto the set of
pairs of semistandard Young tableaux (SSYT) of the same shape. SSYT can be
expressed as integral GelfandTsetlin patterns. We will show how Viennot's
lightandshadows algorithm for computing the RSK correspondence can be
extended from matrices with nonnegative integer entries to matrices with
nonnegative real entries, giving rise to real GelfandTsetlin patterns.
This real version of the RSK correspondence is piecewiselinear. Indeed,
interesting combinatorial problems count lattice points in polyhedra, and
interesting bijections are induced by volumepreserving piecewiselinear
maps.


11:00am 


12:00pm 


1:00pm 


2:00pm 


3:00pm 
[3:30pm] Dr. Neeraj Kumar
 Description:
 Title: Koszul algebras V
Abstract: In the first half of the talk, we shall recall Koszul filtation
and Grobner flag. Let R be a standard graded algebra. If R has a Koszul
filtation, then R is Koszul. If R has a Grobner flag, then R is
Gquadratic. I will mention an important result of Conca, Rossi, and
Valla: Let R be a quadratic Gorenstein algebra with Hilbert series 1 + nz
+ nz^2 + n^3. Then for n=3 and n=4, R is Koszul.
In the second half of the talk, we shall focus on class of strongly Koszul
algebras. If time permits, I will prove that Koszul algebras are preserved
under various classical constructions, in particular, under taking tensor
products, Segre products, fibre products and Veronese subrings.


4:00pm 

5:00pm 


6:00pm 

