4:30pm» Dr. Siddhartha Mandal- Time:
- 4:30pm - 5:30pm
- Location:
- Ramanujan Hall
- Description:
- Title: Statistical approaches for studies of human microbiome
Speaker: Dr. Siddhartha Mandal
Research Scientist (Biostatistics)
Public Health Foundation of India
Gurgaon, India
Venue: Ramanujan Hall
Date: 01/02/2018
Time: 4:30 p.m. -- 5:30 p.m.
abstract is attached.
The speaker is a faculty candidate, and the talk is over Skype.
- Time:
- 12:00pm
- Location:
- Ramanujan Hall Department of Mathematics
- Description:
- Speaker: Dr. Mahendra Verma (Ben-Gurion University, Israel)
Time & Date: 12:00 noon, Monday, 05th February 2018
Venue: Ramanujan Hall
Title: Disjointness of models.
Abstract: attached
- Time:
- 2:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar
Date & Time : 5th February, 2pm
Venue : Ramanujan Hall
Speaker: Ashwin Deopurkar
Title: Riemann-Roch and Brill-Noether theory for tropical curves
- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall Department of Mathematics
- Description:
- Statistics seminar
Date & Time : 5th February, 4 p.m.-- 5 p.m.
Venue: Ramanujan Hall
Speaker: Monika Bhattacharjee, Post Doctoral Fellow
Information Institute, University of Florida, USA.
Title: Change point estimation in dynamic stochastic block model
Abstract: We shall consider a dynamic stochastic block model with single
change point. An easily implementable algorithm based on maximum
pseudo-likelihood method and spectral clustering will be proposed for
estimating the change point. We shall also estimate the edge-probability
matrices and community structures before and after the change point. The
convergence rate and asymptotic distribution for these estimators will be
discussed and compared with other existing works in the literature. This is
joint work with Moulinath Banerjee and George Michailidis.
- Time:
- 11:45am - 1:00pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- Commutative Algebra Seminar
Speaker: Rajiv Garg
Date & Time: 6th February, 11:45am-13:00pm
Venue: Room 215
Title: Boij-S\ddot{\text{o}}derberg Theory over Standard Graded Rings
Abstract: In 2009, Eisenbud and Schreyer prove that extremal rays of Betti
cone over
a polynomial ring are spanned by Betti diagrams of pure Cohen-Macaulay
S-modules,
where S={\sf k}[X_1,\dots, X_n]. In this talk, we discuss
Boij-S\ddot{\text{o}}derberg theory for standard
graded {\sf k}-algebras. We note the obstacles in using their techniques in
the general situation
and identify classes of rings where we can prove some of these results.
- Time:
- 3:00pm
- Description:
- Speaker: Pranav Pandit
Date & Time: 6 February, 3pm
Venue: Room 215
Title: Categorical Kähler Geometry: from derived categories to dynamical
systems
Abstract:Mirror symmetry is a phenomenon predicted by string theory in
physics.
It allows one to translate questions in symplectic geometry to questions
in complex geometry, and vice versa. The homological mirror symmetry
program interprets mirror symmetry within the unifying categorical
framework of derived noncommutative geometry. After introducing these
ideas, I will describe an approach to a theory of Kähler metrics in
derived noncommutative geometry. We will see how this leads to (i) a
non-Archimedean categorical analogue of the Donaldson-Uhlenbeck-Yau
theorem, inspired by symplectic geometry, and (ii) the discovery of a
refinement of the Harder-Narasimhan filtration which controls the
asymptotic behavior of certain geometric flows. This talk is based on
joint work with Fabian Haiden, Ludmil Katzarkov, and Maxim Kontsevich.
- Time:
- 4:15pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium
Speaker: Prof. Michael J. Barany from
Dartmouth College
Date & Time: 7th February, 4-5pm
Venue: Ramanujan Hall
Title: A Synthesis and a Simplification: Difficulty and differentiation in
the intercontinental history of the theory of distributions.
Abstract: Between 1945 and 1960, French mathematician Laurent Schwartz’s
theory of distributions became one of the first of a new kind of
mathematical theory: one shared and studied almost from the start across
multiple continents. Today, distributions have mostly settled into a
comfortable niche in the basic graduate (or in some cases advanced
undergraduate) mathematics curriculum, as a theory many researchers use
routinely as a basic tool while many others safely ignore it. But in those
early years the theory’s leading expositors came to many different answers
about how difficult the theory was, who should study it, and what that
meant for the theory’s place in modern mathematics. My talk will explain
the early history of Schwartz’s theory with special attention to the
question of how difficult the theory was understood to be in different
contexts across five continents. The fact that there were so many different
answers to the question of distributions’ difficulty, I argue, can explain
how the theory was able to spread so far and so quickly. This, in turn,
calls attention to the changing nature of mathematical theories themselves
in the mid-twentieth century.
- Time:
- 4:00pm
- Description:
- Speaker: Dr. Nishant Chandgotia, Tel Aviv university
Date & Time - 8-2-18, Thursday, 4 PM
Title: Universal models in ergodic theory
Abstract: In 1970, Krieger proved that any free ergodic probability
preserving invertible transformation of finite entropy can be modelled by
A^Z, the set of unconstrained bi-infinite sequences in some finite alphabet
A. This result has seen many generalisations for more constrained systems
and for actions of other groups. Along with Tom Meyerovitch, we prove that
under certain general mixing conditions $Z^d$-topological dynamical systems
can model all free ergodic probability preserving Z^d actions of lower
entropy. In particular, we show that these mixing conditions are satisfied
by proper colourings of the Z^d lattice (colourings of the Z^d lattice
where adjacent colours are distinct) and the domino tilings of Z^2 lattice,
thus answering a question by Şahin and Robinson. The talk will begin with
an introduction to the terms mentioned in the abstract and should be
accessible to a general audience.
- 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
$O(n^{-1/2}$.
- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Commutative algebra seminar
Speaker: Sara Faridi, Dalhousie University
Day: Saturday, 17th February.
Time: 04:00 - 05:00 p.m.,
Venue: Ramanujan Hall
Title: Monomial Ideals with Linear Resolution
This talk is about various generalizations that have been made of
the concept of a chordal graph to hypergraphs and simplicial
complexes, with a view toward generalizing a theorem of Froeberg
in 1990 which characterized ideals generated by degree 2
monomials with linear resolution in terms of chordal graphs.
Some of the higher dimensional counterparts of chordal graphs are
constructed from a topological point of view, and some from a
purely combinatorial one.
We will discuss older and newer work in this area, based partly
on joint work with Emma Connon and recent work with Mina Bigdeli.
- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Title: Stochastic Modelling and Simulation of Neuronal System with
Distributed Delay
Speaker: Prof. Karmeshu, JNU, Delhi
Day & Date: Monday, 19th February 2018
Time: 2.30 pm
Venue: Ramanujan Hall
Brief Bio: Professor Karmeshu has been with the School of Computer and
Systems
Sciences (SC&SS) at the Jawaharlal Nehru University, New Delhi since 1986.
He is
a recipient of the Shanti Swarup Bhatnagar Award in Mathematical Sciences
for the
year 1993, a Fellow of the National Academy of Sciences (India) and several
other
organisations. His primary research interests are in Mathematical Modelling
and
Computer Simulation.
Abstract: Modelling of neuronal dynamics aims to capture the mechanisms
that generate empirically observed
inter-spike interval (ISI) patterns. The time-interval between spikes gives
ISI distribution which requires
solution of the first passage time problem of the stochastic differential
equation governing the dynamics
of membrane potential when it reaches the threshold for the first time. The
empirical spiking patterns
exhibit both unimodal and bimodal/multimodal patterns. A theoretical model
based on generalized
neuronal model with distributed delay (GNMDD) is proposed to generate
multimodal/ bimodal inter
spike interval (ISI) distribution. Further the effect of external damped
oscillatory current in neuronal
model is investigated. It is found that with increasing amplitude of damped
oscillatory current, the
multimodal ISI distribution changes to unimodal ISI distribution when the
magnitude of external current
reaches some critical value. It is noted that the entropy also shows a
sudden transition around the
critical point. This phenomenon is akin to phase transition. This work is
done jointly with Sudheer
Sharma and Sanjeev Yadav.
- Time:
- 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG (Combinatorial Aspects of Commutative Algebra and Algebraic
Geometry) seminar
Speaker: Ronnie Sebastian
Date & Time : 19th February, 3:30pm
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:
- 11:45am
- Location:
- Room No 215, Department of Mathematics
- Description:
- Commutative algebra seminar
Speaker: Madhusudan Manjunath
Date and time : Tuesday 20 Feb, 11.30am-1.00pm
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 Sturmfels.
- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Department Colloquium
Speaker: CS Dalawat, Harish Chandra research Institute
Date & Time: Tuesday, February 20, 2018, 16:00-17:00.
Venue: Ramanujan Hall
Title : Some footnotes to Galois's memoirs
Abstract : In his first memoir, Galois gave a criterion for an irreducible
equation of prime degree to be solvable by radicals. In the second memoir,
he defined primitive equations and showed that if a primitive equation is
solvable by radicals, then its degree is the power of a prime. His results
can be reformulated in terms of extensions of fields. We will show how to
extend this reformulation and parametrise all primitive solvable extensions
of an arbitrary field. (An extension is called primitive if there are no
intermediate extensions, and it is called solvable if the Galois group of
its Galois closure is a solvable group). All these concepts will be
recalled and illustrated through examples. If time permits, we will
discuss an arithmetic application. The talk should be accessible to a wide
audience, including students.
- Time:
- 1:45pm - 2:45pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- POPULAR LECTURE
Date and Time: 21st February, Wednesday
1.45-2.45pm
Title:The Cartan-Dieudonne' Theorem
Speaker: Prof.J.K.Verma
Venue: Ramanujan Hall
Abstract: We shall discuss the Cartan-Dieudonne theorem which
establishes that every orthogonal transformation of the n-dimensional
Euclidean space is a composition of at most n reflections. We shall
show how to construct these n reflections using the Householder
matrices.
- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Mikhail Borovoi, Tel Aviv University, currently at TIFR
Date: Thursday, February 22, 2018
Time: 4:00 pm -- 5:00 pm
Venue: Ramanujan Hall
Title: Cayley groups
Abstract
:
I will start the talk from the classical "Cayley transform" for the special
orthogonal group SO(n) defined by Arthur Cayley in 1846. A connected linear
algebraic group G over C is called a *Cayley group* if it admits a *Cayley
map*, that is, a G-equivariant birational isomorphism between the group
variety G and its Lie algebra Lie(G). For example, SO(n) is a Cayley
group. A linear algebraic group G is called *stably Cayley* if G x S is
Cayley for some torus S. I will consider semisimple algebraic groups, in
particular, simple algebraic groups. I will describe classification of
Cayley simple groups and of stably Cayley semisimple groups. (Based on
joint works with Boris Kunyavskii and others.)
- 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.