2014 Past Seminar Talks

Tuesday, November 18
Title: Group Action of SL_2(Z) on the Hyperbolic Plane (Part 2)
Speaker:
Robert Kelvey, BGSU
Abstract:
We will continue our discussion from a few weeks ago. The main goal will be to try and explain why SL_2(Z) can be decomposed as an amalgamated free product of Z_4 and Z_6 over Z_2.

Thursday, November 13
Title: An Introduction to Modern Portfolio Theory
Speaker:
Matthew Wascher, BGSU
Abstract:
Introduced in 1952 by Harry Markowitz, Modern Portfolio Theory is considered an important development in the field of mathematical finance and is still used in modified forms in the industry today. Markowitz showed mathematically that under certain assumptions, it is possible to reduce the risk of a portfolio of risky assets by diversifying. In particular, risky assets are not uncorrelated and so given any projected return, it is possible to choose a portfolio that minimizes risk, generating what is known as the efficient frontier of portfolios. We can then incorporate a risk-free asset and borrowing into the model using capital allocation lines. Finally, we will more closely examine the assumptions behind Modern Portfolio Theory, some criticisms that have been made of these assumptions, and potential modifications to address these criticisms. The mathematics required for Modern Portfolio Theory are very accessible. Including only multivariable calculus, linear algebra, and elementary statistics, and no prior knowledge of economics or finance is presumed.

Tuesday, November 4
Title:
Group Action of SL_2(Z) on the hyperbolic plane

Speaker:
Robert Kelvey, BGSU

Thursday, October 30
Title:
Pure Math Comprehensive Exam Workshop (II)
Speaker:  John Maddrey, Sam Carolus, Mike Hughes, BGSU10:30AM-11:20AM, RM: MSC 459
Abstract:
We will continue to discuss some analysis problems in preparation for the upcoming pure math comprehensive exams.

Tuesday October 21
Title:
Pure Math Comprehensive Exam Workshop
Speaker: 
Sam Carolus and Mike Hughes, BGSU
Abstract:

We will discuss some problems in preparation for the upcoming pure math comprehensive exams.

Thursday, October 16
Title: A Kleinian Exercise in Hyperbolic Isometrics
Speaker:
Jeffrey Norton, BGSU
Abstract:
We will discuss what geometry is, how we study it and particulars of hyperbolic geometry. There will be pretty pictures and examples of hyperbolic geometry in the real world. There will also be proofs about the Riemann sphere, isometries of the hyperbolic plane and its metric.

Tuesday, October 7
Title:
Change Point detection of Mean Residual Life Functions
Speaker: Ying-Ju Chen, BGSU
Abstract:
In this talk, I will introduce the mean residual life functions in the survival analysis. The nonparametric method based on Jackknife empirical likelihood through U-statistic to test the change point of mean residual life functions of independent random variables will be studied. The test statistic and its asymptotic distribution are investigated. Monte Carlo simulations under different lifetime settings are carried out to show the power performance of the test.

Thursday, October 2
Title:
Introduction to Uniformly Most Powerful Unbiased Tests

Speaker:
John Haman, BGSU
Abstract:
We will show that the uniformly most powerful tests do not exist in a certain scenario and consider a wider class of tests. We present a few theorems and examples regarding UMPU tests.

Tuesday, September 23
Title:
The Chabauty Topology
Speaker:
Robert Kelvey

Abstract:
Given any topological space X, we can consider the collection F(X) of all closed subsets of X. There is a natural topology that can be placed on F(X), called the Chabauty topology. This topology is always compact, and has many other cool and wonderful properties. We will try and discuss/prove as much about this interesting topology as we can. A good introduction can be found here: http://arxiv.org/abs/0807.2030 .

Tuesday, September 18
Title: Information on Graded Lie Algebras
Speaker: Jake Laubacher
Abstract: We journey through a brief introduction to Graded Lie Algebras, consisting of mostly definitions and examples aplenty.

Tuesday, September 9
Title:
Brief Introduction to CAT(0) Spaces
Speaker: Mark Medwid, BGSU
AbstractIn this talk we will cover some basic facts about CAT(0) spaces including definitions, examples and elementary properties.
                (References: Metric Spaces of Non-Positive Curvature, M. Bridson and A. Haefliger)

Notes

Tuesday, June 2

Title: Differential Geometry -- Contact, osculating sphere
Speaker: Samuel Carolus, BGSU


Tuesday, May 27
Title: Differential Geometry -- Contact, osculating sphere
Speaker: Samuel Carolus, BGSU

Thursday, May 29

Title: Differential Geometry -- Natural equations of a curve
Speaker: Mark Medwid, BGSU   

Tuesday
, May 22

Title: Differential Geometry -- Spherical Image of a curve / Canonical Representation
Speaker: Jacob Laubacher, BGSU
Notes
  
Thursday, April 3
2:30PM, MSC 459  

Thursday, March 27

Noon, MSC 459

Wednesday, February 19
Title:
Differential Geometry
Speaker:
Abstract:
We continue working through Differential Geometry by Erwin Kreyszig.


Thursday, February 13
Title: Differential Geometry
Speaker: Rob Kelvey, BGSU
Abstract
:
We continue working through Differential Geometry by Erwin Kreyszig.


Thursday, February 6

Title:
Differential Geometry
Speaker:
Jake Laubacher, BGSU
Abstract
:

We continue working through Differential Geometry by Erwin Kreyszig.

Thursday, January 23
Title: Welcome to Grad Student Seminar!
Speaker: Mark Medwid, BGSU
Abstract:
This is an organizational meeting, but with luck we can give motivations of Differential Geometry and get down some notation.