Fri, September 28, 2018
Public Access

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September 2018
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11:00am [11:00am] Arunava Mandal
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.

2:00pm [2:30pm] Dr. Dootika Vats NSF Postdoctoral Fellow Department of Statistics University of Warwick
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.

4:00pm [4:00pm] Manoj Gopalkrishnan, EE Department
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: . We will assume familiarity with basic notions of differential geometry, and some previous exposure to both classical mechanics and symplectic geometry.