Tuesday, November 18Title: Group Action of SL_2(Z) on the Hyperbolic Plane (Part 2)Robert Kelvey, BGSUSpeaker:
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 13Title: An Introduction to Modern Portfolio TheoryMatthew Wascher, BGSUSpeaker:
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 4Group Action of SL_2(Z) on the hyperbolic planeTitle: Robert Kelvey, BGSUSpeaker:Thursday, October 30Title: 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 21Pure Math Comprehensive Exam WorkshopTitle: Sam Carolus and Mike Hughes, BGSUSpeaker: Abstract: We will discuss some problems in preparation for the upcoming pure math comprehensive exams. Thursday, October 16Title: A Kleinian Exercise in Hyperbolic IsometricsJeffrey Norton, BGSUSpeaker: 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.Abstract: Tuesday, October 7Change Point detection of Mean Residual Life FunctionsTitle: 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 2Title: Introduction to Uniformly Most Powerful Unbiased TestsJohn Haman, BGSUSpeaker: 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 23The Chabauty TopologyTitle: Robert KelveySpeaker: 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 18Title: Information on Graded Lie AlgebrasSpeaker: Jake LaubacherAbstract: We journey through a brief introduction to Graded Lie Algebras, consisting of mostly definitions and examples aplenty.Tuesday, September 9Brief Introduction to CAT(0) SpacesTitle: Speaker: Mark Medwid, BGSUAbstract: In
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)NotesTuesday, June 2 Title: Differential Geometry -- Contact, osculating sphereSpeaker: Samuel Carolus, BGSUTuesday, May 27Title: Differential Geometry -- Contact, osculating sphereSpeaker: Samuel Carolus, BGSUThursday, May 29 Title: Differential Geometry -- Natural equations of a curveSpeaker: Mark Medwid, BGSU Tuesday, May 22 Title: Differential Geometry -- Spherical Image of a curve / Canonical RepresentationSpeaker: Jacob Laubacher, BGSUNotes Thursday, April 3 2:30PM, MSC 459 Thursday, March 27 Noon, MSC 459 Wednesday, February 19 Differential GeometryTitle: Speaker: Abstract: We continue working through Differential Geometry by Erwin Kreyszig. Thursday, February 13Title: Differential GeometrySpeaker: Rob Kelvey, BGSUAbstract: We continue working through Differential Geometry by Erwin Kreyszig. Thursday, February 6 Differential GeometryTitle: Jake Laubacher, BGSUSpeaker: Abstract: We continue working through Differential Geometry by Erwin Kreyszig. Thursday, January 23Title: Welcome to Grad Student Seminar!Speaker: Mark Medwid, BGSUAbstract: This is an organizational meeting, but with luck we can give motivations of Differential Geometry and get down some notation. |