University of Georgia
Department of Mathematics

Seminar Schedule
September 15, - September 19, 2003

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

MONDAY, September 15, 2003

Numerical Analysis
1:30p.m., Room 524
Speaker: Ming-Jun Lai, University of Georgia
Title of talk: Analysis of Ginzburg-Landau equation

Geometry
1:30p.m., Room 410
Speaker: Joe Fu, University of Georgia
Title of talk: Unitary kinematic formulas and Alesker multiplication

Topology
2:30p.m., Room 323
Speaker: Will Kazez, University of Georgia
Title of talk: Knot theory, dynamics, and some recent work of Ghrist and Kin
Abstract: This will be a pretty elementary talk that relates knot theory, fibred knots, and flows on S^3.

VIGRE - Algebra Seminar
2:30p.m., Room 410
Speaker: Daniel Nakano, University of Georgia
Title of talk: Partitions, Weighted Dynkin Diagrams, and the Jacobson-Morozov Theorem

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

Lie Theory
3:30p.m., Room 303
Speaker: Joseph Landsberg, Georgia Tech
Title of talk: Secant varieties, shadows and a universal dimension formula for complex simple Lie algebras
Abstract: I will describe a generalization of some of the dimension formulas Vogel derived in the context of his universal Lie algebra and their relation to elementary algebraic geometry.

TUESDAY, September 16, 2003

VIGRE Graduate Student Seminar
2:00-3:15pm, Room 304
Speaker: Mukul Patel, University of Georgia
Title of talk: The Unity of Mathematics
Abstract: Bringing concentrated doses of liquid mathematical pearls from the Gelfand 90th birthday conference "The Unity of Mathematics'' held at the beginning of September 2003. The theme of the conference is said to be the same as that of Gelfand's life work (which is still not finished, it seems!). Most amazing connections between various "branches'' of mathematics were expounded upon. The most amazing being that of Sir Michael Atiyah.

The topics of the conference:
# 1) noncommutative geometry and modular forms. (Connes)
# 2) quantum field theories and algebraic geometry
# 3) unity of quantum field theories (and/or string theories)
# 4) noncommutative geometry and number theory (Selberg like traces, and the Riemann hypothesis) (a la Connes)
# 5) Gelfand's own lecture that attempted to bring in several threads together, and proposed directions to future mathematics.
# 6) lots and lots of culture.

Also will mention various "organizational principles'' proposed by various mathematicians recently at the turn of the millenium.
# 1) Michael Atiyah's is vision of the past and future of mathematics (from today's vantage point)
# 2) A stunning vision of Arnol'd, in a very similar sense..
# 3) Gelfand's vision on replacing categories with something he calls ``heredetaries'' , which in his opinion, is a better, more relevant way of organizing mathematical fields...
# 4) a brief mention of ancient (and mainly superficial) organizal principles such as set theory, category theory, "the first year graduate courses at American universities''.

Analysis
3:30pm, Room 326
Speaker: Robert Varley, University of Georgia
Title of talk: Definition of the free field in Euclidean field theory.

WEDNESDAY, September 17, 2003

Group Representation & Cohomology
2:30p.m., Room 410
Speaker: Dave Benson, University of Georgia
Title: Stable and derived categories of kG-modules, continued

Algebraic Geometry
2:30pm, Room 303
Speaker: Ivan Cheltsov, University of Georgia
Title of talk: Non-rational complete intersections
Abstract: This will be the continuation of the talk form September 2, the technical part with details of the proof.

Faculty and Graduate Social
3:00pm, Room 409
Coffee, Cookies, Tea

Number Theory/Arithmetic Geometry
3:30pm, Room 304
Speaker: Su-Ion Ih, University of Georgia
Title of talk: Rational points on varieties
Abstract: We will talk about some issues concerning rational points on varieites --- what topics are at issue these days and why they are important in number theory.

THURSDAY, September 18, 2003

VIGRE Quantum Mechanics Seminar
2:00p.m., Room 303
Speaker: Cal Burgoyne, University of Georgia
Title of talk: Quantum Harmonic Oscillator

VIGRE - Contact Topology
2:00p.m., Room 326

Student Number Theory
3:30p.m., Room 304
Speaker: Sungkon Chang, University of Georgia
Title of talk: A practically computable algorithm for finding the $p$-Selmer group for an elliptic curve
Abstract: I shall discuss about some basics of elliptic curves to introduce the well-known unsolved problem: finding the rank of an elliptic curve, and the descent method, which has been the standard way to attack the notorious problem.

FRIDAY, September 19, 2003

Wavelet Analysis
2:30p.m., Room 524
Speaker: Ming-Jun Lai, University of Georgia
Title of talk: Box Spline Theory for Wavelet Analysis, continued

CATS
1:25p.m., Room 306
Speaker: Michael Geller, Computer Science, University of Georgia
Title of talk: Quantum Computing with Superconductors
Abstract: There is currently tremendous interest in exploiting the quantum mechanical behavior of matter to process, encrypt, transfer, and store information in ways impossible, or at least practically impossible, by classical or conventional means. Unfortunately, the lack of a scalable architecture with sufficient quantum coherence has prevented this from happening. Last year, however, exciting experiments have demonstrated that certain superconducting devices called Josephson junctions have all the properties required to be used as building blocks of a large-scale quantum computer. These results have produced an explosion of interest in this architecture and a worldwide race to build a quantum computer out of superconductors.

I will give a series of three lectures on these developments. The talks will be geared toward nonspecialists with some exposure to quantum mechanics and quantum computing. The topics to be covered are as follows:

Part I (9/19). Superconductivity and the Josephson effect. Here I will introduce the basics of Bose-Einstein condensation, superconductivity, and the Josephson effect.

Part II (9/26). Superconducting qubits. Here I will explain how to make a qubit, the most basic element of a quantum computer, out of a Josephson junction.

Part III (10/3). Superconducting qubit storage and entanglement. In the final lecture I will describe an architecture we have proposed to couple qubits together to make a viable quantum computer. The architecture makes use of high-frequency mechanical resonators as "bus" qubits to store and transfer the quantum state or wave function of a Josephson junction, and to carry out quantum logic operations.