Department of Mathematics
Seminar Schedule
August 30 –
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
Algebra
No Meeting this week
Topology
Speaker: Will Kazez,
Title
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
Speaker: Q. Zhang,
Title
Faculty and Graduate
Social
Coffee, Cookies, Tea
VIGRE Graduate
Student Seminar
Speaker: Der-Chen Chang ,
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
No Meeting this week
Algebraic Geometry
Speaker: Jiayuan Lin,
Title
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
VIGRE – Clifford
Algebras
Faculty and Graduate
Social
Coffee, Cookies, Tea
Number Theory
Speaker: Robert
Rumely,
Title of talk: A survey of the dynamics of rational functions, continued
VIGRE - Rational
points on curves
VIGRE Algebraic
Geometry Group
Faculty
Meeting
Student Arithmetic/Algebraic
Geometry Seminar
Speaker: Peter Petrov,
Title
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
Speaker: David
Benson,
Title
Spline Analysis
Speaker: Taytana Sorokina,
Title
Geometry
Speaker:
Jason Parsley,
Title
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
Speaker: O.
Cho,
Title of talk:
A class of orthonormal
refinable functions, cont.