Seminars in Mathematical Sciences

One of the most fundamental tools in statistics is the central limit theorem. Under very general conditions, the asymptotic fluctuation of vector-valued statistical estimators around their true (unknown) value, based on increasing sample sizes n, tends to a normal distribution rescaled by the square root of n. A typical nonparametric estimator is the expected value of a random variable. Fréchet has generalized this concept to metric spaces and subsequently strong laws, of potentially set valued so-called Fréchet means have been established. On manifolds, or spaces stratified by manifolds, in local coordinates, also central limit theorems have been derived. Their asymptotic rates, however, may deviate from those of their Euclidean kin. For instance, faster rates let the sample mean "stick" to the population mean, whereas slower rates let it appear to be "smearily" spread out. In this talk we illustrate some relationships between Geometry and Statistics via dirty (sticky, smeary) asymptotic rates of Fréchet means. In this context there seem to be more problems open than solved.

Venue: MCS2068

May 01 14:00 Raphael Zentner (Durham): SL(2,C)-representations of 2-torsion homology spheres, and applications to the Kauffman skein module

In recent joined work with Sudipta Ghosh and Steven Sivek we prove that any rational homology 3-sphere whose first homology group is 2-torsion, and which is not a connected sum of RP^3s, admits irreducible representations to SL(2,C) of its fundamental group. This has applications to the question of torsion in the Kauffman skein module. We will explain elements of the proof of our result, and how the application to the skein module is derived.

Venue: MCS2068

Jun 12 14:00 Ilka Agricola (Marburg): TBD

Venue: MCS2068

Usual Venue: MCS3070

Contact: andrea.grigoletto@durham.ac.uk,nakarin.lohitsiri@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

Usual Venue: MCS0001

Contact: silvia.nagy@durham.ac.uk,enrico.andriolo@durham.ac.uk,tobias.p.hansen@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

Usual Venue: MCS2068

Contact: kohei.suzuki@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

Usual Venue: MCS0001

Contact: raphael.zentner@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

Usual Venue: MCS3070

Contact: irving.d.calderon-camacho@durham.ac.uk,joe.thomas@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

Usual Venue: MCS2068

Contact: hyeyoung.maeng@durham.ac.uk,andrew.iskauskas@durham.ac.uk

Apr 02 14:00 Stephan Huckemann (University of Göttingen): Dirty Limit Theorems and Applications

This is a joint meeting of the Geometry & Topology and Statistics seminars.

One of the most fundamental tools in statistics is the central limit theorem. Under very general conditions, the asymptotic fluctuation of vector-valued statistical estimators around their true (unknown) value, based on increasing sample sizes n, tends to a normal distribution rescaled by the square root of n. A typical nonparametric estimator is the expected value of a random variable. Fréchet has generalized this concept to metric spaces and subsequently strong laws, of potentially set valued so-called Fréchet means have been established. On manifolds, or spaces stratified by manifolds, in local coordinates, also central limit theorems have been derived. Their asymptotic rates, however, may deviate from those of their Euclidean kin. For instance, faster rates let the sample mean "stick" to the population mean, whereas slower rates let it appear to be "smearily" spread out. In this talk we illustrate some relationships between Geometry and Statistics via dirty (sticky, smeary) asymptotic rates of Fréchet means. In this context there seem to be more problems open than solved.

Venue: MCS2068

Contact: adam.stone2@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).