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- Time:
- 2:00pm-3:15pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- 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

$O(n^{-1/2}$.