Address:  Mathematics | University of Alabama at Birmingham 
1300 University  Blvd | Birmingham, AL 35294-1170 
Phone:  943 2154 | Fax: 934 9025 

• Wednesday, February 23, 2005
  No seminar this week

• Wednesday, February 16, 2005
  No seminar this week

• Wednesday, February 9, 2005
  James R Ward (UAB)
  Topological Degree and Stability of Periodic Solutions; Part 2
  10:45 AM in Room CH 402

Abstract.  This lecture will continue the series on connections between the local topological degree of a solution and its stability.

• Wednesday, February 2, 2005
  James R Ward (UAB)
  Topological Degree and Stability of Periodic Solutions
  10:45 AM in Room CH 402

Abstract.  Topological and Leray-Schauder degrees are well known for their usefulness in studying the existence, multiplicity, and bifurcation of periodic solutions to differential equations. Usually little or nothing can then be deduced about stability. In recent years Rafael Ortega has found connections between the index (local degree) of periodic solutions and their Lyapunov stability, for both ordinary differential equations and some partial differential equations. I will talk about some of this work, which will take more than one lecture. There are also some interesting recent results by Ortega and by Urena on the instability of periodic solutions which are minimizers of action functionals; this problem was earlier considered by Carathèodory and by Moser. This could be a topic for later talks.

• Tuesday, November 30, 2004
  James R Ward (UAB)
  Global Bifurcation in Systems of Ordinary Differential Equations
  2:00 PM in Room CH 402

Abstract.  In this talk I will explain how rotation numbers can be used to describe the structure of global bifurcation in boundary value problems for systems of ordinary differential equations. The bifurcation results can in turn be applied to show the existence of infinitely many distinct solutions to some classes of boundary value problems.

• Tuesday, October 12, 2004
  Joytsna Prajapat (UAB)
  Some problems related to CR Geometry
  2:00 PM in Room CH 402

Abstract.  This lecture continues the series of talk on CR geometry.

• Tuesday, October 5, 2004
  Joytsna Prajapat (UAB)
  Some problems related to CR Geometry, Part II
  2:00 PM in Room CH 402

Abstract.  This lecture continues the series of talk on CR geometry.

• Tuesday, September 28, 2004
  Joytsna Prajapat (UAB)
  Some problems related to CR Geometry
  2:00 PM in Room CH 402

Abstract.  This begins a series of three to four lectures on CR geometry.  I plan to begin by giving a brief introduction to CR Geometry with the reduction to a nonlinear PDE (subelliptic) on Heisenberg group, and  to indicate proofs of some symmetry results on Heisenberg group, and more generally, nilpotent, stratified Lie groups.

• Tuesday, September 21, 2004
  Gilbert Weinstein (UAB)
  A Counter-Example to a Penrose Inequality with Charge, Part IV
  2:00 PM in Room CH 402

Abstract.  In this fourth and last talk in the series, I will discuss some of the technical details involved in proving the proof outlined in Part III.  I will then discuss the connection of this work with cosmic censorship, and discuss some of the open questions.

• Tuesday, September 14, 2004
  Gilbert Weinstein (UAB)
  A Counter-Example to a Penrose Inequality with Charge, Part III
  2:00 PM in Room CH 402

Abstract.  In this third talk in the series, I will discuss the conformal gluing method and its use in constructing a counter example to a Penrose inequality with charge.

• Tuesday, September 7, 2004
  Gilbert Weinstein (UAB)
  A Counter-Example to a Penrose Inequality with Charge, Part II
  2:00 PM in Room CH 402

Abstract.  This talk continues the series started last week.  After completing the introductory material, I will state our result and outline the proof.   Additional technical details on the analysis will be given in the next talk.

Please note the time change.

• Tuesday, August 31, 2004
  Gilbert Weinstein (UAB)
  A Counter-Example to a Penrose Inequality with Charge, Part I
  2:15 PM in Room CH 402

Abstract. This begins a series of two, perhaps three, lectures on a joint work with Sumio Yamada.  In this introductory lecture, some background will be given on the constraint equations in general relativity, the conformal method for solving the constraints, the Penrose inequality and the two methods known for its proof, the Huisken-Ilmanen inverse mean curvature flow, and Bray's conformal flow.

• Tuesday, August 24, 2004
  Organizational Meeting
  3:30 PM in Room CH 458

  This research level seminar will include three types of activities:

  • presentations by UAB faculty on their research;
  • presentations by guests;
  • presentations by UAB faculty and students of current research of interest to participants.

  If you cannot attend the first organizational meeting, please email me.