September 2018
Public Access Category: All |
3:30pm» Kriti Goel- 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.