Title: Mixed multiplicities and the number of generators of ideals
Abstract: Using Minkowski inequality for mixed multiplicities of
ideals we derive an upper bound on the number of generators of
m-primary ideals in Cohen-Macaulay local rings. This upper bound
implies results of S.S. Abhyankar, E. Becker-D. Eisenbud-D. Rees,
I.S. Cohen, D. Rees and J. D. Sally.
Time:
4:00pm-5:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Mathematics Colloquium
Time: 4.00-5.00 pm, Wednesday, 21 November , 2018.
Venue: Ramanujan Hall
Speaker: Hema Srinivasan
Affiliation: University of Missouri, Columbia, MO, USA
Title: Resolutions of Semigroup Rings
Abstract: We consider the semigroup rings $S = k[t^{a_i}| 1\le i\le n]
\subset k[t]$ of embedding dimension $n$ over a field $k$. We write $S =
k[x_1, \ldots, x_n]/I_{a_1, \ldots, a_n}$ and explicitly construct the
minimal free resolutions of $S$ over $k[x_1, \ldots, x_n]$ when ${a_1,
\ldots, a_n}$ are special and derive formulae for the invariants such as
Betti Numbers, Cohen-Macaulay type, Frobenius numbers, Hilbert Series and
Regularity.
Time:
2:30pm-3:30pm
Location:
Room No. 215, Department of Mathematics
Description:
Time: 22 Nov, Thursday, 2.30-3.30pm.
Venue: Room 215.
Speaker : Tony J. Puthenpurakal.
Title: On p_g ideals.
Abstract: Let $(A,\m)$ be an excellent normal domain of dimension two.
We define an $\m$-primary ideal $I$ to be a $p_g$-ideal if the Rees algebra
$A[It]$ is a \CM \ normal domain. When $A$ contains an algebraically
closed field $k \cong A/\m$ then Okuma, Watanabe and Yoshida proved that
$A$ has
$p_g$-ideals and furthermore product of two $p_g$-ideals is a $p_g$ ideal.
In this talk we show that if $A$ is an excellent normal domain of
dimension two containing a field $k \cong A/\m$ of characteristic zero
then also $A$ as $p_g$-ideals. Furthermore product of two $p_g$-ideals is
$p_g$.
Time:
4:00pm-5:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
PDE seminar on Control and homogenization:
Title: Control of wave equation.
Time: Thursday, 22-11-18, 4p.m.-5p.m.
Venue: Ramanujan Hall, Department of Mathematics, IIT Bombay.
Speaker: Debanjana Mitra.
Abstract: In this talk, we will discuss the controllability of wave
equation with variable coefficients. The main objectives are to understand
the proof of the observability inequality and how the constants in the
inequality depend on the coefficients of the wave equation.
Time:
10:30am
Location:
Ramanujan Hall, Department of Mathematics
Description:
Analysis Seminar.
Time:Friday, 23 November, 10:30 am.
Venue: Ramanujan Hall.
Speaker: Soumalya Joardar.
Title: Quantum Symmetry and graph C*-algebra.
Abstract: is attached.
Time:
4:30pm-5:30pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
CACAAG seminar.
Time: Friday, 23 November, 4:30pm-5:30pm. (Note the unusual time).
Venue: Ramanujan Hall.
Speaker: Madhusudan Manjunath.
Title: Combinatorial Brill-Noether Theory, Stanley Theory,
Castelnuovo-Mumford Regularity.
Abstract: We discuss ongoing work where we relate Brill-Noether theory on
a finite graph to
homological invariants of certain modules associated to it. Our approach
resembles Stanley's commutative algebraic approach to enumeration of magic
squares.