Fri, September 28, 2018
Public Access Category: All |
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- 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.