Department of Mathematics
Seminar Schedule
September 7 –
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
Algebra
No Meeting this week
Topology
Please see
Probability Theory
No
Meeting this week
VIGRE Graduate
Student Seminar
Speaker: Mukul Patel, on leave from UGA Graduate Program in Mathematics
Title of talk: Overcoming Goedel's Incompleteness Theorem
Abstract: (I will review the basic notions of a 'first order formal theory', so that the talk should be accessible to all. )
Goedel's Incompleteness theorem implies that a complete axiomatic formal "foundation" of mathematics a la Hilbert is not possible---or so it seems. Although this hardly affects the work of any mathematician, one does feel a sense of apprehension regarding the problem with the touchstone of mathematical truth---deducibility from first principles.
We adopt a different viewpoint which lets us by-pass Goedel's theorem and provides a means to better understand the deductive structure of mathematics. If we call a 'nice' (formal) theory an aristotelian system, then Goedel says that the deductive structure of mathematics is not aristotelian. However, it is trivially a LOCALLY aristotelian, meaning it can be covered by more than one separate aristotelian systems, which agree wherever they overlap. (This is somewhat similar to saying that a sphere is not euclidean, but is locally euclidean.) The crucial result of our investigation is a 'compactness theorem' which says that FINITELY MANY such aristotelian systems are sufficient to 'cover' mathematics. Thus, Hilbert's purely finitary formal foundation is, in principle, possible. Finally, it can be shown that TWO such patches are sufficient to cover mathematics----first order theory of sets (say ZFC), and a first order theory of categories. This is very satisfactory, because set-theoretic and categoric viewpoints are also conceptually complementary---the former being introverted and the latter being extroverted viewpoint on mathematical structures.
Topology
3:
Speaker: Paolo Lisca,
Title of talk: Ozsvath-Szabo invariants and tight contact structures, I
Abstract: This is the first of two
talks in which I will describe recent joint work with Andras
Stipsicz on the existence of tight contact structures
on closed oriented 3-manifolds. I will state our results and then describe the
two main tools needed to prove them, namely contact surgery and the Ozsvath-Szabo invariants for contact structures.
Dynamics on Berkovich Space
No Meeting this week
VIGRE Algebraic
Geometry Group
12:
Algebraic Geometry
Speaker: Jiayuan Lin,
Title
VIGRE – Cardiac
Physiology
VIGRE – Clifford
Algebras
Faculty and Graduate
Social
Coffee, Cookies, Tea
Number Theory
No meeting this week
VIGRE - Rational
points on curves
Faculty and Graduate Social
Coffee, Cookies, Tea
Colloquium
Speaker: Peter Greiner,
Title of talk: Subelliptic PDE's and SubRiemannian
Geometry
Abstract: I propose a structure for inverse
kernels - fundamental solutions, heat kernels, etc. - of second order partial
differential operators given as sums of squares of vector fields. The formulas
are built from invariants of the underlying geometry induced by the given vectorfields. I shall assume that brackets of these vectorfields yield a basis for the tangent space, thus
Chow's theorem gives a distance function and a subRiemannian geometry. The main object of interest
is a "complex distance", parametrized by
the characteristic variety, whose critical points along the characteristic
variety give all geodesic distances. I shall illustrate these ideas by
examples.
Student Arithmetic/Algebraic
Geometry Seminar
Speaker: Peter Petrov, University of
Title: Resolution of singularities and continued fractions, Part II.
VIGRE-Algebra
Speaker: David
Benson,
Title
Spline Analysis
Speaker: Taytana Sorokina,
Title
Geometry
Speaker: Jason
Parsley,
Title
Wavelet Analysis
Speaker: O.
Cho,
Title of talk:
A class of orthonormal
refinable functions, cont.