Abstract: In this second lecture we will continue with the material in
Chapter 1 in Cassels and Frohlich.
Time:
9:30am-10:30am
Location:
Ramanujan Hall
Description:
Title: Herzog-Kuhl Equations and its Applications - II
Abstract: In these talks, we will see relations between Hilbert series of
a module and its graded Betti numbers. This gives relations between the
graded Betti numbers of a modules which are known as Herzog-Kuhl
equations. As an application, we show that the property of R being
Cohen-Macaulay is characterized by the existence of a pure Cohen-Macaulay
R-module of finite projective dimension.
Time:
10:30am-11:30am
Location:
Ramanujan Hall
Description:
Title: Tate Resolutions - II
Abstract: Let S be a Noetherian ring, and R = S/I. It is always possible
to construct a differential graded algebra (DG-algebra) resolution of R
over S due to a result of Tate. If R is the residue field of S, then
Gulliksen proved that such a DG-algebra resolution is minimal. We shall
discuss the construction of the Tate resolution in our talk.
Time:
4:00pm-6:30pm
Location:
Room 216, Department of Mathematics
Description:
Speaker: Arghya Mondal
Title: Local Langlands Correspondence in the Archimedean case
Abstract: In this lecture, we will understand the statement of the local
Langlands correspondence in the Archimedean case. This lecture will be
based on the article available here https://www.math.stonybrook.ed
u/~aknapp/pdf-files/motives.pdf
Time:
11:00am-12:30pm
Location:
Ramanujan Hall
Description:
Title: The Szemeredi-Trotter Theorem (postponed from last week)
Speaker: Venkitesh S.I. (IITB)
Abstract:
Given a finite set of points P in R^2 and a finite family of lines L
in R^2, an incidence is a pair (p,l), where p\in P, l\in L and p is a
point in l.
The Szemeredi-Trotter Theorem states that the number of incidences is
atmost a constant multiple of (|L||P|)^{2/3} + |L| + |P|. We give a
proof by Tao, which uses the method of cell partitions.
Time:
3:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Name: Dr Nigel Calder
Title: Using mobile technologies to enhance the learning of
mathematics
Time:
3:30pm
Location:
Room 215, Department of Mathematics
Description:
Title: Homotopy theory
Abstract: I will give introduce the basic ideas in homotopy theory, along the way
state some classical theorems and if time permits some recent results. The talk
will be expository and will have few or no proofs possibly.