University of Georgia
Department of Mathematics

Seminar Schedule
November 29 –December 3, 2004

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

MONDAY, November 29, 2004

Algebra
2:30-3:30p.m., Room 410
No Meeting this week

Probability Theory
2:45-4:00pm, Room 302
No Meeting this week

Faculty and Graduate Social
3:00 p.m., Room 409
Coffee, Cookies, Tea

VIGRE Algebraic Geometry Group
3:30-4:30 p.m., Room 304

Topology
3:30-4:30pm, Room 326
Speaker: Ken Baker, University of Georgia
Title of talk: On thin position of knots in lens spaces.
Abstract: John Berge has a conjectured classification of knots in $S^3$ that admit Dehn surgeries yielding lens spaces. The corresponding knots in the lens spaces are $0$- or $1$-bridge braids with respect to the Heegaard torus of the lens space. Given a knot $K'$ in $S^3$ of genus $g$ with a Dehn surgery yielding a lens space $Y$ of order $r$, if $r \geq 4g-1$ then we will sketch the key points of a proof that the corresponding knot $K$ (which is the core of the surgery solid torus) in $Y$ has bridge number at most $3$ with respect to the Heegard torus of $Y$. This is a work in progress.

Lie Theory
3:30p.m., Room 303
No meeting this week

TUESDAY, November 30, 2004

VIGRE Graduate Student Seminar
2:00p.m., Room 304
Speaker: Mukul Patel (on leave from UGA Graduate Program in Mathematics)
Title of talk: Noncommutative Gelfand-Naimark Duality
Abstract: C^*-algberas are a special class of norm-closed algerbas of operators on Hilbert space that have special connections with in topology, geometry, harmonic analysis, etc. Any COMMUTATIVE C*-algebra is naturally isomorphic to the algebra of complex functions on a compact Hausdorff space naturally associated with it. This "Gelfand-Naimark duality" sets up an equivalence between the category of commutative C*-algebras on one hand, and compact Hausdorff spaces on the other. This fact constitutes the heavenly gateway to practically everything we know about commutative C*-algebras. Furthermore, it leads to spectral theorem for normal operators on Hilbert space, Pontryagin duality for locally compact abelian groups, etc.

We extend this (commutative) Gelfand-Naimark duality to the general (possibly noncommutative) C^*-algebras, by identifying the noncommutative analog of compact Hausdorff spaces. This analog turns out to be simply a quotient of a compact Hausdorff space. Again, this extends the equivalence of categories mentioned above to: (C*-algebras <----> Quotients of Compact Hausdorff spaces). We can only hope that this can open some heavenly doors to the study of general C*-algebras.

We mention couple of applications---
1) A nonabelian Pontryagin duality, applicable to noncommutative harmonic analysis.
2) A simultaneous gneralization of finite-dimensional Jordan canonical form on one hand, and Spectral theorem for normal operators on a (possibly infinite dimensional) Hilbert space.

Dynamics on Berkovich Space
3:30-5:30p.m., Room 326
Speaker: Robert Rumely, University of Georgia
Title of talk: The Structure of the Domain of Quais-Periodicity

WEDNESDAY, December 1, 2004

Algebraic Geometry
2:30-3:45 p.m., Room 410
Speaker: JongHae Keum (Korean Institute for Advanced Study and Michigan)
Title of talk: Finite groups acting on K3 surfaces
Abstract: A remarkable work of S. Mukai [1988 Invent. Math.] gives a classification of finite groups which can act on a complex K3 surface leaving invariant its holomorphic 2-form (symplectic automorphism groups). Any such group turns out to be isomorphic to a subgroup of the Mathieu group $M_{23}$ which has at least 5 orbits in its natural action on the set of 24 elements. A list of maximal subgroups with this property consists of 11 groups, each of these can be realized on an explicitly given K3 surface. Different proofs of Mukai's result were given by S. Kondo [1998 Duke Math. J.] and G. Xiao [1996 Ann. Inst. Fourier]. None of the 3 proofs extends to the case of K3 surfaces over algebraically closed fields of positive characteristic $p$.

In this talk I will outline a recent joint work with I. Dolgachev, showing that Mukai's proof can be extended to positive characteristic $p > 11$.

For $p=2,3,5, 11$, we give examples of K3 surfaces over a field of characteristic $p$ whose automorphism group contains a finite symplectic subgroup not contained in Mukai's list.

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
3:45-5:15pm, Room 304
Speaker: TBA
Title of talk: TBA

THURSDAY, December 2, 2004

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

FRIDAY, December 3, 2004

Student Arithmetic/Algebraic Geometry Seminar
12:20p.m., Room 326
Speaker: TBA
Title of talk: TBA

Geometry
2:30p.m., Room 323
No Meeting this week

VIGRE – Algebra
2:30p.m., Room 410
Speaker: Dave Benson, University of Georgia
Title of talk: Computation of the support varieties of Specht modules

Spline Analysis
2:30p.m., Room 303
Speaker: T. Sorokina, University of Georgia
Title of talk: Construction of 3D macro-elements

Wavelet Analysis
3:30p.m., Room 303
Speaker: Jie Zhou, University of Georgia
Title of talk: Construction of nonseparable wavelets in 3D