February 26, 2018 - March 2, 2018
Public Access Category: All |
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- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: G. Arunkumar
Date & Time : Monday Feb 26, at 11:30am
Venue: Ramanujan Hall
Title: Chromatic polynomials and Lie algebras
Abstract: In this talk, I will prove a connection between root
multiplicities for Borcherds-Kac-Moody
algebras and graph coloring. I will show that the generalized
chromatic polynomial of the graph
associated to a given Borcherds algebra can be used to give a closed
formula for certain root
multiplicities. As an application, using the combinatorics of Lyndon
words, we construct a basis for the root spaces corresponding to these
roots and determine
the Hilbert series in the case when all simple roots are imaginary.
In last ten minutes, We will talk about chromatic discriminant of a graph:
The absolute value of the coefficient of q in the chromatic polynomial
of a graph
G is known as the chromatic discriminant of G and is denoted
$\alpha(G)$. We start with a brief survey on many interesting
algebraic and combinatorial interpretations of $\alpha(G)$. We use two
of these interpretations (in terms of
acyclic orientations and spanning trees) to give two bijective proofs
for a recurrence formula
of $\alpha(G)$ which comes from the Peterson recurrence formula for
root multiplicities of Kac-Moody algebras.
- Time:
- 2:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG (Combinatorial Aspects of Commutative Algebra and Algebraic
Geometry) seminar
Speaker: Ronnie Sebastian
Date & Time : 26th February, 2pm
Venue : Ramanujan Hall
Abstract: This talk will be based on the following elementary and nice
exposition
http://www.math.stonybrook.edu/~roblaz/Reprints/Green.Laz.Simple.Pf.Petri.pdf
Using some simple facts about projective space, cohomology, cohomology of
line bundles on projective space, we shall prove the following theorems:
1. Noether's theorem - Projective normality of the canonical embedding of
non-hyperelliptic curves.
2. Petri's -theorem - Let X be a smooth and projective curve of genus g
\geq 5. Assume that X carries a line bundle A of degree g-1 with h^0(A)=2.
Further assume that both A and \Omega_X\otimes A^* are generated by their
global sections. Then the homogeneous ideal of X in its canonical embedding
is generated by degree 2 elements.
- Time:
- 2:00pm-3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Title: A function field analogue of a theorem of Sarkozy, due to B Green.
Speaker: Niranjan Balachandran
Date-Time: Wednesday, February 28 2018, 2 PM to 3.30 PM
Venue: Ramanujan Hall
Abstract: In the late 70s Sarkozy proved the following theorem: Given a
polynomial f(T) over the integers with f(0)=0, there exists a constant c_f
such that for any set $A\subset [n]$ of size at least $n/(log n)^{c_f}$
there exist distinct $a,b\in A$ such that $a-b=f(x)$ for some $x$. In
2016, Ben Green proved a function field analog of the same result but with
a much better bound for $|A|$: Given a polynomial $F\in\bF_q[T]$ of degree
$k$ with $F(0)=0$, there exists $0
- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Time and Date: 28th Feb 2018, 4-5 pm
Venue: Ramanujan Hall
Speaker : Prof. Ujjwal Das, IIM Udaipur
Title: Modeling Interval Censored Competing Risks Data with Missing
Causes of Failure
Missing causes of failure are quite frequent in survival and
reliability studies. Surprisingly for interval censored data, this
problem has not been investigated much, albeit in
lifetime studies such data occur frequently. In this article, interval
censored competing risks data are analyzed when some of the causes of
failure are missing. The proposed technique uses vertical modeling, an
approach that utilizes the data to extract information to the maximum
possible extent, especially when some causes of failure are missing.
The maximum likelihood estimates of the model parameters are obtained.
Through a Monte Carlo simulation study, the performance of the point
and interval estimators are assessed. It is observed through the
simulation study that the proposed analysis performs better than the
complete case analysis. Such analysis is particularly relevant for
smaller sample sizes, as carrying out a complete case analysis in
those cases may have a significant impact on the inferential
procedures. Through Monte Carlo simulations, the effect of a possible
model misspecification is also assessed on the cumulative incidence
function which is an important statistic in the framework of competing
risks. The proposed method has been illustrated on a real data set.