2pm» Dr. Vivek Mukundan- Time:
- 2:00pm - 3:30pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Speaker : Dr. Vivek Mukundan
Title : Implicitization problem and the defining ideal of the Rees algebra.
When : Thursday, 2 Aug 2.00-3.30 pm
Venue: Room 215
=============
Abstract: Consider a rational map from P^{n-1}—>P^n parametrized by homogeneous polynomials f_0,\dots,f_n of degree d. We study the equations defining the graph of the map whose coordinate ring is the Rees algebra of the ideal generated by f_0, .., f_n. We provide new methods to construct these equations using work of Buchsbaum and Eisenbud. Furthermore, for certain classes of ideals, we show that our construction is general. These classes of examples are interesting, in that, there are no known methods to compute the defining ideal of the Rees
algebra of such ideals. These new methods also give rise to effective criteria to check that φ is birational onto its image.
- Time:
- 3:00pm - 4:00pm
- Location:
- Ramanujan Hall
- Description:
- Title: General Glivenko- Cantelli. Theorem.
Speaker: Prof. K.B. Athreya
Venue: Ramanujan Hall
Time: 3:00 pm to 4:00 pm
Abstract:
The classical version of Glivenko Cantelli theorem says: let X sub I , i = 1, 2, 3, ..be real valued r.v. with cdf F(x) then the empirical cdf based on X sub i , i = 1,2,3,....n converges wp1 as n goes to infinity to F uniformly over R.
In this talk this theorm is generalised to cover Markov chains, exchangeable sequences and regenerative sequences.
Some open problems will also be posed.
- Time:
- 4:00pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Speaker: Prof. Sudarshan Gurjar
Title: Introduction to Symplectic Geometry
Abstract: I will begin by introducing the class of symplectic manifolds
and explain their connections to other well known geometric objects. In
the second part of the talk, I will introduce symplectic reduction whereby
one constructs symplectic quotients of symplectic manifolds under suitable
actions of lie groups.
- Time:
- 5:30pm
- Location:
- Ramanujan Hall
- Description:
- Popular Lecture
We will begin our Popular Lecture series in Mathematics for this semester on Monday, 6 August, 2018.
Sudarshan Gurjar will be speaking at Ramanujan Hall at 5:15 PM on the following topic.
Title: Applications of Analysis and Topology to Commutative Algebra
Abstract: In this talk, I will discuss two applications of analysis and
topology in constructing counterexamples to certain questions in
commutative algebra. The talk will be fairly elementary and accessible to
M.Sc students.
- Time:
- 5:00pm - 6:30pm
- Location:
- Ramanujan Hall
- Description:
- Seminar: CACAAG.
Time: 5-6:30 pm, Tuesday, August 07, 2018.
Venue: Ramanujan Hall.
Speaker: Dr. Samir Shukla.
Title: An introduction to some graph coloring complexes
Abstract: Graph complexes are simplicial complexes arising from graphs. In
this talk we mainly focus on two types of complexes: Neighborhood
complexes and Hom complexes. The topology of these complexes are closely
related to the chromatic number of the underlying graphs. We give a brief
survey of the research have been done with respect to them in recent
years. We also discuss some open problems related to them.
- Time:
- 2:00pm - 3:30pm
- Location:
- Room. 215
- Description:
- Commutative algebra seminar
Thursday 09 August, 2.00-3.30 pm
Venue: Room 215
Speaker: Sudhir R Ghorpade
Title:
A Finite Field Nullstellensatz and the Number of Zeros of Polynomials over Finite Fields.
Abstract:
In this series of two talks, we will begin by discussing some Nullstellensatz-like results when the base field is finite, and outline the proofs. Next, we will discuss a combinatorial approach to determining or estimating the number of common zeros of a system of multivariate polynomials with coefficients in a finite field. Here
we will outline a remarkable result of Heijnen and Pellikaan about the maximum number of zeros
that a given number of linearly independent multivariate polynomials of a given degree can have
over a finite field. A projective analogue of this result about multivariate homogeneous polynomials
has been open for quite some time, although there has been considerable progress in the last two
decades, and especially in the last few years. We will outline some results and conjectures here,
including a recent joint work with Peter Beelen and Mrinmoy Datta.
- Time:
- 4:00pm
- Location:
- Room No. 215 Department of Mathematics
- Description:
- Title: Introduction to Symplectic Geometry
Abstract: In this second talk of the series I will continue the discussion
on symplectic manifolds. I will introduce the moment map and use it to
construct quotients of symplectic manifolds under certain actions of lie
groups.
- Time:
- 3:30pm - 5:00pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- Lie Theory Seminar
Speaker: Atharva Korde
Title: Cartan's theory of the highest weight and Verma modules
Day and Date: Monday, August 13
Time: 15:30 - 17:00
Venue: Room 215, 2nd floor, Department of Mathematics
- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Combinatorics Seminar
Speaker: Vaidy Sivaraman (University of Central Florida)
Venue: Ramanujan Hall
Date & Time: Monday 13th August, 4-5 PM.
Title: Detecting odd holes
Abstract: The complexity of determining whether a graph has an induced odd
cycle of length at least 5 (odd hole) is unknown. In this talk, I will
describe a polynomial-time algorithm to do this if the input graph does
not contain the bull (a particular 5-vertex graph that turns out to be
important in the theory of induced subgraphs) as an induced subgraph.
This is joint work with Maria Chudnovsky.
- Time:
- 5:00pm - 6:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Seminar: CACAAG.
Time: 5-6:30 pm, Tuesday, August 14, 2018.
Venue: Ramanujan Hall.
Speaker: J. K. Verma
Title: Richard Stanley's solution of Anand-Dumir-Gupta conjecture about
enumeration of magic squares
Abstract: In 1973 Richard Stanley solved several conjectures about magic
squares
proposed by Harsh Anand, V. C. Dumir and Hans Raj Gupta. In his "Green
Book"
Stanley used the theory of Cohen-Macaulay and Gorenstein rings to solve
these
conjectures. I will sketch his solution assuming only basic commutative
algebra.
- Time:
- 2:00pm - 3:30pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- Commutative algebra seminar
Thursday 16 August, 2.00-3.30 pm
Venue: Room 215
Speaker: Sudhir R Ghorpade
Title:
A Finite Field Nullstellensatz and the Number of Zeros of Polynomials over
Finite Fields.
Abstract:
In this series of two talks, we will begin by discussing some
Nullstellensatz-like results when the base field is finite, and outline the
proofs. Next, we will discuss a combinatorial approach to determining or
estimating the number of common zeros of a system of multivariate
polynomials with coefficients in a finite field. Here
we will outline a remarkable result of Heijnen and Pellikaan about the
maximum number of zeros
that a given number of linearly independent multivariate polynomials of a
given degree can have
over a finite field. A projective analogue of this result about
multivariate homogeneous polynomials
has been open for quite some time, although there has been considerable
progress in the last two
decades, and especially in the last few years. We will outline some results
and conjectures here,
including a recent joint work with Peter Beelen and Mrinmoy Datta.
- Time:
- 3:30pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Lie Theory Seminar
Speaker: Atharva Korde
Title: Cartan's theory of the highest weight and Verma modules
Day and Date: Monday, August 20
Time: 15:30 - 17:00
Venue: Room Ramanujan Hall, 2nd floor, Department of Mathematics
Abstract: Finite dimensionality of Verma modules and the Weyl character
formula.
- Time:
- 5:15pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Popular Lecture in Mathematics
Date & Time: Monday 20th August 2018 at 5:15 PM.
Venue: Ramanujan Hall
Speaker: Venkitesh Iyer
Title: A Fixed Point Theorem and a Coloring Lemma
Abstract: The Sperner Lemma is a combinatorial lemma that talks about a
certain type of coloring (called the Sperner coloring) of a triangulation
of a simplex. It has applications in several root-finding and
fair-division algorithms.
The Brouwer Fixed Point Theorem is a classical theorem that asserts the
existence of a fixed point for a continuous function from the unit disc in
Euclidean space to itself.
There are several proofs for each of these results. In this talk, we will
show that both these results are equivalent. We will look at the proof in
the case of two dimensions. The general case is similar modulo some more
careful book-keeping.
[We encourage all MSc, Ph.D and UG students to attend. Note tea and
snacks will be served before the talk at 5:00 PM.]
- Time:
- 3:30pm - 4:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium
Date & Time : Tuesday 3:30-4:30pm
Venue: Ramanujan Hall
Speaker: Saurabh Kumar Singh
Title: Sub-convexity problems: Some history and recent developments
Abstract : attached.
- Time:
- 5:00pm - 6:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Seminar: CACAAG.
Lecture 1: Time: 5-6 pm, Tuesday, August 21, 2018.
Venue: Ramanujan Hall.
Speaker: J. K. Verma
Title: Richard Stanley's solution of Anand-Dumir-Gupta conjecture about
enumeration of magic squares
Abstract: In 1973 Richard Stanley solved several conjectures about magic
squares
proposed by Harsh Anand, V. C. Dumir and Hans Raj Gupta. In his "Green
Book"
Stanley used the theory of Cohen-Macaulay and Gorenstein rings to solve
these
conjectures. I will sketch his solution assuming only basic commutative
algebra.
- Time:
- 6:00pm - 7:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Lecture 2: Time: 6-7 pm, Tuesday, August 21, 2018.
Venue: Ramanujan Hall.
Speaker: Suchita Goyal
Title: Neighborhood Complexes of Graphs
- Time:
- 2:00pm - 3:30pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- Commutative algebra seminar
Speaker: Sudeshna Roy
Title: Equations of multi-Rees algebra of a family of monomial ideals
Venue: Room 215
Date and Day: Thursday, 23 August, 2018
Time: 2-3.30 PM
Abstract: Consider the the multi-Rees algebra \R_R(I_1 \oplus \cdots \oplus
I_r)
of monomial ideals I_1, . . . , I_r. In this talk, the defining ideal of
\R_R(I_1 \oplus \cdots \oplus I_r)
will be described explicitly. We will cover Section 1 and Section 2 of the
recent paper
"Multi-Rees Algebras and Toric Dynamic Systems" (
https://arxiv.org/pdf/1806.08184.pdf)
of Cox, Lin and Sosa. We will also see that for any homogeneous ideals J_1,
. . . , J_s,
the defining ideal of \R_R(J_1 \oplus \cdots \oplus J_s) can be expressed
as a contraction
of the defining ideal of \R_R(I_1 \oplus \cdots \oplus I_r) for some
monomial ideals I_1, . . . , I_r.
- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Date & Time: Friday, 24th August, 4pm
Venue: Ramanujan Hall
Speaker: Dr Richard Clarke, Associate Dean Post Graduate Research,
Engineering department from the University of Auckland
Title: Active Matter: A smart material for the 21st Century
Abstract: The theories of fluid dynamics and solid mechanics are a
cornerstone of Engineering, enabling us to make predictions about the way
in which materials and structures behave. The continuum-level mathematical
formulations which were developed over a century ago allow us to overcome
the impracticalities of considering every microscopic particle within the
system, and instead consider the material’s macroscopic bulk behaviour. The
type of substances usually described in this way are passive, meaning that
the drivers of the system are usually externally-applied forces or energy.
However, there exist more exotic types of active matter, where the
constituent components themselves contain a source of energy. Suspensions
of swimming microbes provide an important example. The innumerable cells
within the mixture are capable of self-propelling themselves through the
suspending medium. Modern micro- and nano-fabrication methods also allow
for the creation of artificial microswimmers. The flows generated by
self-motile cells leads to fluid-mediated coupling between the swimmers,
which can lead to highly-organised collective bulk motions, sometimes
referred to as bacterial turbulence or slow turbulence. This
self-organisation has also be seen to change the bulk rheology of the
suspension, leading to plastic and superfluidic behaviours, some of which
may have technological applications. Continuum models developed for passive
materials do not perform well for active matter, and so there has been a
great deal of interest and interdisciplinary activity in recent years to
derive an effective continuum-level description for such systems. In this
talk I will outline some of the current challenges, as well as ideas and
progress made to-date in this area.
- Time:
- 4:00pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- Geometry and Topology seminar
Speaker: Reebhu Bhattacharya
Date & Time : 24th August at 4: 00 PM
Venue: Room 215
Title: Towards Jones Isomorphism Theorem: Preliminaries(Intersection theory, Morse theory and Hochschild Complex)
Abstract:
I will be talking about three distinct topics which will serve as preliminaries for the Jones isomorphism theorem which we will discuss in a later talk. Firstly we will talk about some intersection theory and prove the Thom isomorphism theorem. Finally we will define the Hochschild complex for differential graded algebras and it's Hochschild (co) homology.
- Time:
- 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Lie theory seminar
Speaker: Ravi Raghunathan
Title: The Peter-Weyl Theorem
Time: 3:30 p.m., Monday, August 27, 2018
Venue:
Abstract; I will prove the Peter-Weyl theorem for compact topological
groups. This talk will be independent of the talks given earlier in the
seminar. In particular, no Lie theory is necessary (and nor will it be
assumed).
- Time:
- 3:30pm - 5:00pm
- Location:
- Room No.215 Department of Mathemaics
- Description:
- Commutative algebra seminars
Monday, 27 August 2018
Room 215, 3.30-5.00
Speaker: Sudeshna Roy
Title: Equations of multi-Rees algebras
Abstract: We shall present a recent result of Davi Cox, K.-N. Lin and G.
Sosa
which explores the defining equations of multi-Rees algebras of monomial
ideals
in a polynomial ring over a field.
- Time:
- 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar
Speaker: Madhusudan Manjunath
Time & Date: 5pm Tuesday.
Venue: Ramanujan Hall
Title: Triangulations of Root Polytopes.
Abstract: We will discuss recent work on triangulations of the root
polytope associated to a subgraph of the complete bipartite graph.
- Time:
- 2:00pm - 3:30pm
- Location:
- Room No.215, Department of Mathematics
- Description:
- Thursday, 30 August 2018
Room 215, 2.00-3.30
Speaker: Kriti Goel
Title: Mixed multiplicities of ideals
Abstract: The concept of Hilbert-Samuel polynomial for an m-primary ideal
was extended for two m-primary ideals by P. B. Bhattacharya. In other
words, the function l(R/I^rJ^s) is given by a polynomial for r, s large.
The coefficients appearing in the highest total degree terms in the
polynomial are called the mixed multiplicities. These were investigated by
B. Teissier (and J. J. Risler) in his Cargese paper.
In a series of two talks, we will look at some properties of mixed
multiplicities, using superficial elements. These talks aim to cover the
preliminaries required for reading the paper 'A generalization of an
inequality of Lech relating multiplicity and colength' by C. Huneke, I.
Smirnov and J. Validashti.
- Time:
- 3:00pm - 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Dr. Iker Perez, Assistant Professor in Statistics at the
University of Nottingham, UK
Date: 30th Aug 2018
Time 3-4 pm
Venue: Ramanujan Hall
Title: Approximate Uncertainty Quantification with Jump Processes
Abstract:
This talk will discuss foundational statistical challenges and
probabilistic considerations associated with families of stochastic jump
models, which often find applications in domains such as genetics,
epidemiology, mathematical biology or operations research. I will review
Markov jump processes, and by means of common accessible examples, discuss
the strong impediments posed by real-world application scenarios to inverse
uncertainty quantification tasks.
Next, I will discuss current statistical advances linked to structured jump
systems along with relevant literature. Through a model exemplar borrowed
from queueing theory, I will finally present an approximate and scalable
variational Bayesian framework, suitable for uncertainty quantification
tasks with a large class of structured processes. The talk will further
include examples with applications of the methods introduced.
- Time:
- 4:00pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- Reebhu Bhattacharya will be speaking in the Geometry and Topology Seminar in 215 at 4:00 PM on 31st August 2018.
Title: Jones Isomorphism Theorem
Abstract: We will continue our discussion of Hochschild homology from the last talk, defining it for dga's and proceeding to calculate the Hochschild homology of $k[X]/X^2$, the cohomology ring of the sphere. Then we will outline a proof of Jones Isomorphism Theorem using simplicial sets and hence obtain the homology of the loop space of spheres.