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.