- 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.