CACAAG (Combinatorial Aspects of Commutative Algebra and Algebraic
Geometry) seminar
Speaker: Dr. Ashwin Deopurkar, TIFR Mumbai
Date & Time: 12th February, 2018, 2-3:15pm
Venue: Ramanujan Hall
Title: Divisor theory on tropical curves: Riemann-Roch and Brill-Noether.
Time:
4:00pm-5:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
TITLE OF THE TALK: Ethical and Responsible Conduct of Research
SPEAKER : Professor Graeme Fairweather
Distinguished Visiting Professor, Department of Mathematics, IIT Bombay and
Former Head, Mathematical and Computer Sciences, Colorado School of Mines,
Golden, USA.
Date: Monday, February 12, 2018
Time: 4.00 pm - 05.00 pm
Venue: Ramanujan Hall, Department of Mathematics
Abstract: Research ethics involves the application of moral rules and
professional codes of conduct to a variety of topics involving scientific
research. The importance of adherence to ethical norms in research will be
discussed, with emphasis on the key issues of scientific misconduct,
publishing practices and responsible authorship. Numerous examples of
plagiarism, self-plagiarism and questionable publishing practices from the
current mathematics literature will be presented.
Time:
11:45am-1:00pm
Description:
Commutative algebra seminar
Speaker: Madhusudan Manjunath
Date and time :
Tuesday 13 Feb, 11.45-1.00
Venue: Room 215
Title: Groebner bases of Toric Ideals.
Abstract: This is the first of two lectures where we'll cover Groebner
bases of toric ideals. We start with an introduction to toric ideals and
then study their Grobener bases. Our main goal will be a theorem of Bernd
Sturmfels from 1991 that relates (certain) initial ideals of toric ideals
to regular triangulations of an associated point configuration. The
lectures are based on Chapters 4 and 8 of the book ``Groebner Bases and
Convex Polytopes'' by Strumfels.
Time:
2:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Combinatorics Seminar
Title: Lift of Reed-Solomon code with an application to Nikodym sets
Speaker: S. Venkitesh (IITB)
Date and Time: Feb 14, 2018, 2PM
Venue: Ramanujan Hall, Dept. of Mathematics
Abstract:
We will work over the finite field F_q, q = p^k. The Reed-Solomon code
with parameters (q,d), denoted as RS(q,d), is the linear space of all
polynomial functions from F_q to F_q with degree atmost d. The
Reed-Muller code with parameters (q,m,d), denoted as RM(q,m,d), is the
m-variable analog of RS(q,d), defined to be the linear space of all
polynomial functions from F_q^m to F_q with total degree atmost d.
A nonempty set N in F_q^m is called a Nikodym set if for every point p
in F_q^m, there is a line L passing through p such that all points on
L, except possibly p, are contained in N. Using the polynomial method
and the code RM(q,m,q-2), we can prove the lower bound |N| >= q^m /
m!. We will outline this proof.
We will then define a new linear code called the m-lift of RS(q,d),
denoted as L_m(RS(q,d)), and show that RM(q,m,d) is a proper subspace
of L_m(RS(q,d)). We will use this fact crucially, in a proof very
similar to the earlier one, to obtain the improved lower bound |N| >=
(1 - o(1)) * q^m, when we fix p and allow q to tend to infinity. This
result is due to Guo, Kopparty and Sudan.
Time:
4:00pm-5:30pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Coding Theory and Cryptography Seminar
Speaker: Tovohery Randrianarisoa, University of Zurich, Switzerland
Date & Time: 15th February (Thursday), 4-5:30pm
Venue: Ramanujan Hall
Title: On a metric using the linear complexity on finite sequences.
Abstract: Using the linear complexity on finite sequences over a finite
field F,
I will define a metric on F^n. We will develop a coding theory using the
new
metric. I will also give the exact expression of number of finite sequences
of
length n with a fixed linear complexity l. A possible application is a new
cryptosystem similar to the McEliece cryptosystem but with a different
metric
on the code.
Time:
10:30am-11:30am
Location:
Ramanujan Hall, Department of Mathematics
Description:
Speaker: K. N. Raghavan
Affiliation: The Institute of Mathematical Sciences
Date & Time: Friday, 16th February, 10:30-11:30am
Venue: Ramanujan Hall
Title: The KPRV theorem via paths
Abstract: Let V and V' be irreducible representations of a complex
semisimple Lie algebra g with highest weight vectors v and v' of weights m
and m' respectively. For w in the Weyl group, let M(m,m',w) denote the
cyclic g-submodule of V tensor V' generated by the vector v tensor wv'
(where wv' denotes a non-zero vector in V' of weight wm'). It was
conjectured by Kostant and proved by Kumar that the irreducible
representation V(m,m',w) whose highest weight is the unique dominant Weyl
conjugate of m+wm' occurs with multiplicity exactly one in the
decomposition of M(m,m',w) into irreducibles. Since M(m,m',w0) equals
V tensor V', where w0 denotes the longest element of the Weyl group, it
follows from this that V(m,m',w) occurs in the decomposition of V tensor
V'. This corollary was conjectured earlier by Parthasarathy, Ranga Rao,
and Varadarajan (PRV) and proved by Mathieu independently of Kumar.
There's a subsequent proof by Littelmann of the PRV conjecture using his
theory of Lakshmibai-Seshadri paths. I will talk about joint work with
Mrigendra Kushwaha and Sankaran Viswanath where we consider such a path
approach to Kostant's refinement of the PRV.
Time:
4:00pm-5:00pm
Location:
Room No. 105, Department of Mathematics
Description:
Speaker: Dr. Rajeev Gupta , IIT Kanpur
Date: Friday, February 16, 2018
Time: 4:00 pm - 5:00 pm
Venue: Room 105
Title: On a question N. Th. Varopoulos
The abstract of the talk is attached.
Time:
4:00pm-5:00pm
Location:
Conference Room, Department of Mathematics
Description:
Title : On the distance between two weighted sums of random variables.
Speaker : Professor Vydas Cekanavicius
Vilnius University
Lithuania.
Date: Friday, February 16, 2018
Time: 4.00 pm - 05.00 pm
Venue: Conference Room, Department of Mathematics
Abstract: We discuss the approximation problems between two weighted sums
of the form $w_1X_1+ \ldots +wn_Xn$, where the weights are fixed and the
$Xi$'s are independent or weakly dependent random variables. The Kolmogorov
metric is used to obtain the estimates which, in general, are of the order
$O(n^{-1/2}$.