University of Georgia

Department of Mathematics

 

Seminar Schedule

August 30 – September 3, 2004

 

All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.

 

MONDAY, August 30, 2004

 

Algebra

2:30-3:30p.m., Room 410

No Meeting this week

 

Topology
2:30-3:30p.m., Room 322
Speaker:
Will Kazez, University of Georgia
Title
of talk: An introduction to Ozsvath-Szabo's 3-manifold invariants

Abstract: Ozsvath and Szabo have introduced new invariants of 3-manifolds that are

being used to settle some of the oldest questions in 3-dimensional topology.  I hope

 this talk will serve as a starting point for reading seminar on their work.

 

Probability Theory

2:45-3:45pm Room 302
Speaker: Q. Zhang, University of Georgia
Title
of talk: Market Models: From Real Data to Geometric Brownian Motions and Beyond

 

Faculty and Graduate Social

3:00p.m., Room 409

Coffee, Cookies, Tea

 

 

TUESDAY, August 31, 2004

 

VIGRE Graduate Student Seminar

2:00p.m., Room 304

Speaker: Der-Chen Chang , Georgetown University
Title of talk: On the $\bar\partial$-Neumann Problem
Abstract: The $\bar\partial$-Neumann problem is a important problem in the field of

several complex variables. It has connection with the theory of PDE, Harmonic Analysis

and the Heisenberg group. The speaker will start from the Cauchy-Riemann operator in

 the complex plane and introduce the problem and its solution.

 

 

Dynamics on Berkovich Space

3:30-5:30p.m., Room 326

No Meeting this week

 

 

WEDNESDAY, September 1, 2004

 

Algebraic Geometry

2:30-3:45 p.m., Room 303

Speaker: Jiayuan Lin, University of Georgia
Title
of talk: Birational Unboundedness of $\Bbb Q$-Fano threefolds
Abstract: (Q-)Fano varieties appear naturally as one of the final results in
the (log) Minimal Model Program. V. Alexeev and A.Borisov conjecture that
the family of all Q-Fano varieties of a given dimension with log discrepancy
greater than a fixed positive number is bounded. A lot work has been done on
this motivating conjecture.  Naturally people wonder whether we can replace the

fixed positive number by  zero in the Alexeev and Borisov conjecture if we consider

the families up to birational equivalence. The answer is yes in dimension 1 or 2.

However, it is false in higher dimension. In my talk, we will show that the family of $\Bbb
Q$-Fano threefolds with Picard number one is birationally unbounded.


VIGRE – Cardiac Physiology
2:30p.m., Room 323

VIGRE – Clifford Algebras
2:30p.m., Room 322

Faculty and Graduate Social

3:00 p.m., Room 409

Coffee, Cookies, Tea

 

Number Theory

3:45 p.m., Room 304

Speaker: Robert Rumely, University of Georgia

Title of talk: A survey of the dynamics of rational functions, continued

 

THURSDAY, September 2, 2004

 

VIGRE - Rational points on curves
2:00p.m., Room 304

 

VIGRE Algebraic Geometry Group
3:00p.m., Room 410

 

Faculty  Meeting
3:30p.m., Room 304

 

FRIDAY, September 3, 2004

 

Student Arithmetic/Algebraic Geometry Seminar

2:15p.m., Room 323
Speaker: Peter Petrov, University of Georgia
Title
: Cyclic quotient singularities and continued fractions.

Abstract: I am going to discuss a down-to-earth case of resolution of singularities

of dimension 2, which plays important role and could be represented by combinatorial

geometry (as toric variety). Another representation will be using Hirzebruch - Jung

continued fractions. Some relations with other areas and further development of the

topic will be sketched briefly.

 

VIGRE-Algebra

2:30p.m., Room 302

Speaker: David Benson, University of Georgia
Title
of talk: Introduction to Complexity and Support Varieties  for Finite Groups II

 

Spline Analysis

2:30-3:30p.m., Room 303

Speaker:  Taytana Sorokina, University of Georgia
Title
of talk:  Construction of 3D splines, cont.

Geometry

2:30 p.m., Room 323

Speaker:  Jason Parsley, University of Georgia
Title
of talk:  The Biot-Savart operator and linking integrals on S^3
Abstract:  We extend the Biot-Savart law from physics to an operator BS acting on all

vector fields on S^3, a geometric setting for electrodynamics in positive curvature.  We

 show that Maxwell's equations hold and that BS acts as a right inverse to curl.  We then

 discuss its application to energy-minimization problems in geometry and physics that

depend on curl eigenvalues.  Also, BS allows us to construct linking integrals on S^3. 

As one further application, we can express the helicity of a vector field, a measure of

 how much it coils around itself, as H(V) = <V, BS(V)>. We find upper bounds for

 helicity on the three-sphere; our bounds are not sharp but within an order of magnitude.

 

Wavelet  Analysis

3:30-4:30 p.m., Room 303

Speaker:  O. Cho, University of Georgia

Title of talk:  A class of orthonormal refinable functions, cont.