September 2018
Public Access Category: All |

- Time:
- 3:30pm - 5:00pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- Date & Time: Monday, 3rd Sept 2018, 3:30 - 5:00 p.m.

Venue: Room 215

Speaker: Kriti Goel

Title: Mixed multiplicities of ideals (Lectures II )

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:
- 5:00pm
- Location:
- Room No.215
- Description:
- CACAAG seminar.

Speaker: Madhusudan Manjunath

Time & Date: 5pm Tuesday, September 04.

Venue: Room 215

Title: Triangulations of the Root Polytopes.

Abstract: The root polytope associated to a subgraph of the complete

bipartite graph generalizes the Cartesian product of two simplices.

Triangulations of such polytopes is a well studied topic with connections

to algebraic geometry and computational algebra. We discuss recent work in

characterizing these triangulations.

The talk will not assume any background beyond linear algebra.

- Time:
- 2:00pm - 3:30pm
- Location:
- Room 215
- Description:
- Date & Time:

Thursday, 6th Sept 2018, 2:00 - 3:30 p.m.

Venue: Room 215

Speaker: Kriti Goel

Title: Mixed multiplicities of ideals (Lectures III )

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:
- 4:00pm
- Location:
- Ramanujan Hall
- Description:
- Prof. A.J. Parameswaran from TIFR, Mumbai will give a seminar this

Friday at 4:00 pm in Ramanujan Hall.

Title: Topology by Bundles.

Abstract: Beginning with Wyle's theorem that a bundle induced by the

Universal cover is finite (satisfies a polynomial) and its converse by

Nori that finite/essentially finite bundles are induced from

"coverings/finite principal bundles". We will revisit the etale

fundamental group of Grothendieck and the fundamental group scheme by

Nori.

Later we will glance through other associated group constructions using

Tannakian techniques using bundles.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Analysis Seminar

Speaker: Sayani Bera, Ramakrishna Mission Vivekanada Educational and

Research Institute.

Date and Time: 4:00 pm, Tuesday, 18th September.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Non-autonomous basins of attraction and short Ck's.

Abstract: In this talk, we first define the dynamical setting of a

non-autonomous system and its relation to Bedford conjecture. Further, we

will discuss about Short Ck's that arises as basins of attraction of a

fixed point in the non-autonomous setting. Lastly, we will see some

methods to construct short Ck's with pathological properties and discuss

some related problems.

- Time:
- 5:00pm
- Location:
- Room 215, Department of Mathematics
- Description:
- CACAAG seminar.

Speaker: Dhruv Ranganathan

Time & Date: 5pm Tuesday, September 18.

Venue: Room 215

Title and abstract:

Curves, maps, and singularities in genus one

I will outline a new framework based on tropical geometry to study genus

one curve singularities and discuss its relationship with the geometry of

moduli spaces. I will focus on the application of this framework to

construct new nonsingular compact moduli spaces parameterizing elliptic

curves in projective space. This also reveals a modular interpretation for

Vakil and Zinger’s famous desingularization of the space of elliptic curves

in projective space, as well as a short and conceptual proof of that

result. If time permits, I will discuss applications to some questions in

the classical enumerative geometry of surfaces. This is based on joint work

with Keli Santos-Parker and Jonathan Wise, building on prior work of

Speyer, Smyth, Viscardi, Vakil, and Zinger.

- Time:
- 4:00pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Department Colloquium

Speaker: Dhruv Ranganathan

Time & Date: 4pm Wednesday, September 19

Venue : Room 215

Title and abstract:

The space of equations for an algebraic curve

The geometry of a Riemann surface is captured by the ways in which it can

manifest as a projective variety, or more precisely, by the geometry of

spaces parameterizing embeddings of the curve into projective space. These

“Brill-Noether varieties” of a curve are well understood in two cases. On

one end, work of Clifford gives a complete understanding of hyperelliptic

curves. On the other end, a curve that is general in moduli exhibits

expected behaviour. In recent joint work with Dave Jensen, building on

previous work of Nathan Pflueger, we determine formulas for the dimensions

of the Brill-Noether varieties for the intermediate cases, i.e. general

curves of a fixed gonality. Our methods blend the combinatorics of the

sandpile model on graphs with methods from non-archimedean analysis and

deformation theory. I will give an overview of ideas surrounding the

theorem and its proof, and try to give a sense of the link between

algebraic and combinatorial geometry.

- Time:
- 2:00pm - 3:30pm
- Description:
- Commutative algebra seminar

Who: Ananthnarayan H.

Where: Room 215, Maths Building

When: Thursday, 20th Sept, 2:00 - 3:30 p.m.

What: On generalizations of an inequality of Lech - I

In recent work (see https://arxiv.org/abs/1711.06951), Craig Huneke, Ilya

Smirnov, and Javid Validashti study conjectured generalisations of an

inequality of Lech, relating the multiplicity and the colength of an ideal

I of finite colength in a Noetherian local ring (R,m,k). Using mixed

multiplicities, they show that one of these conjectures regarding the

multiplicity of mI is true.

In this series of talks, we will discuss some of the results in t

- Time:
- 4:00pm - 5:00pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- Topology and Geometry Seminar

Date & Time: Tuesday at 4:00-5:00 PM

Venue: Room 215

Speaker: Reebhu Bhattacharya

Title: Jones Isomorphism Theorem

Abstract: Then we will outline a proof of Jones Isomorphism Theorem using

simplicial sets and hence obtain the homology of the loop space of spheres.

- Time:
- 5:00pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- CACAAG seminar.

Speaker: Prof. Trygve Johnsen, The Arctic University of Norway.

Time & Date: 5pm Tuesday, September 25.

Venue: Room 215

Title: Coding theory and algebraic properties of matroids

Abstract:

We will show how one can determine properties of linear codes, by

studying algebraic properties of matroids,

which in a natural way are associated to the codes. Concretely, one studies

resolutions of Stanley-Reisner rings associated

to the simplicial independence complexes of the matroids involved. From

these resolutions one may extract generalized Hamming weights and higher

weight spectra, of the codes in question.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall
- Description:
- Mathematics Colloquium

Date & Time: 26th September 2018, 4-5pm

Venue: Ramanujan Hall

Speaker: Prof.Carlos Conca, University of Chile, Santiago.

Title: Modeling our sense of smell

Abstract

In this lecture, we are interested in the study of an inverse problem for an

integral equation arising from the biology of the human olfaction system.

The transduction of an odour into an electrical signal is accomplished by

a depolarising influx of ions through cyclic-nucleotide-gated (CNG for

short) channels on the cilium membrane. The inverse problem studied is to

determine the spatial distribution of these ion channels from measurements

of the electrical current at the ends of the cilium. The Mellin

transform will allow us to write an explicit formula for its solution, so

obtaining observability or continuity results will then amounts

to punctual estimates of the kernel of this integral equation on vertical

lines of the complex plane. These will be accomplished using arguments in

the spirit of the stationary phase method.

- Time:
- 2:00pm - 3:30pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- Commutative algebra seminar

Who: Ananthnarayan H.

Where: Room 215, Maths Building

When: Thursday, 27th Sept, 2:00 - 3:30 p.m.

What: On generalizations of an inequality of Lech - II

In recent work (see https://arxiv.org/abs/1711.06951), Craig Huneke, Ilya

Smirnov, and Javid Validashti study conjectured generalisations of an

inequality of Lech, relating the multiplicity and the colength of an ideal

I of finite colength in a Noetherian local ring (R,m,k). Using mixed

multiplicities, they show that one of these conjectures regarding the

multiplicity of mI is true.

In this series of talks, we will discuss some of the results in their paper.

- Time:
- 11:00am - 12:00pm
- Location:
- Ramanujan Hall
- Description:
- Time & Date : 11am-12pm, Friday 28th September

Venue: Ramanujan Hall

Speaker: Arunava Mandal

Title: Images of the power maps on Lie groups

Abstract: Let G be a Lie group. For a natural number k, we denote by P_k,

the k-th power map, defined by g\to g^k for all g\in G. In this talk, we

discuss the question as to when the individual power map P_k has a dense

image or a surjective image in a Lie group. The problem is

closely related to the study of exponentiality of Lie group.

- Time:
- 2:30pm - 3:30pm
- Description:
- Probability-Statistics seminar

Speaker: Dr. Dootika Vats

NSF Postdoctoral Fellow

Department of Statistics

University of Warwick

Venue: Ramanujan Hall

Time: 2:30 p.m. -- 3:30 p.m.

Date: 28th September, 2018

Title*: *Lugsail lag windows and their application to Markov chain Monte

Carlo

Abstract*: *

Lag windows are commonly used in the time series, steady state simulation,

and Markov chain Monte Carlo (MCMC) literature to estimate the long range

variances of ergodic averages. We propose a new lugsail lag window

specifically designed for improved finite sample performance. We use this

lag window for batch means and spectral variance estimators in MCMC

simulations to obtain strongly consistent estimators that are biased from

above in finite samples and asymptotically unbiased. This quality is

particularly useful when calculating effective sample size and using

sequential stopping rules where they help avoid premature termination.

Further, we calculate the bias and variance of lugsail estimators and

demonstrate that there is little loss compared to other estimators. We also

show mean square consistency of these estimators under weak conditions. Our

results hold for processes that satisfy a strong invariance principle,

providing a wide range of practical applications of the lag windows outside

of MCMC. Finally, we study the finite sample properties of lugsail

estimators in various examples.

- Time:
- 4:00pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- Topology and Geometry seminar

Speaker: Manoj Gopalkrishnan, EE Department

Time and Date: at 4:00 PM on 28th September 2018

Venue: Room 215

Title: Classical Mechanics and Symplectic Geometry

Abstract: Many of the historical motivations for symplectic geometry come from classical mechanics. Conversely, classical mechanics can be treated elegantly with the tools of symplectic geometry. We will present a "dictionary" between classical mechanics and symplectic geometry that is well-known to practitioners in both fields, but is often not explicitly taught in beginning courses in either subject, but left to the mathematical maturity of the student to pick up. The dictionary may be of pedagogic value to students embarking on a study of symplectic geometry, allowing them to ground their understanding of notions like Lagrangian submanifolds in concrete physical situations. Our presentation will be broadly based on notes by John Baez which can be found here: http://www.math.ucr.edu/home/baez/classical/texfiles/2005/book/classical.pdf . We will assume familiarity with basic notions of differential geometry, and some previous exposure to both classical mechanics and symplectic geometry.