University of Georgia
Department of Mathematics

Seminar Schedule
February 26 – March 2, 2007

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

MONDAY, February 26, 2007

Topology
2:30pm, Room 304
No Meeting this week

Algebra
2:30pm, Room 410
Speaker: Dorte Feichtenschlager, Braunschweig
Title of talk: On the construction of CF pro-$p$-groups by coclass
Abstract: The classification of finite $p$-groups is an often examined area of group theory. In this talk the classification by coclass is investigated for the special class of CF groups. These groups were introduced by Norman Blackburn as a generalisation of groups of maximal class.

The coclass-project will be established for background knowledge. It was initialised by Charles Leedham-Green and Mike Newman. Most important for this theory is the definition of coclass and the coclass-graph. Guided by this CF pro-$p$-groups will be investigated, as these arise from the inverse limit of the infinite branches of this coclass-graph.

The main result is the construction of a special class of CF pro-$p$-groups. This construction yields at least $p^{p^{s-1}-(s+2)}$ different CF pro-$p$-groups of coclass $s$. It is known that there exists up to isomorphism only one pro-$p$-group of maximal class for each prime $p$.

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

TUESDAY, February 27, 2007

VIGRE-Graduate Student Seminar
2:00pm, Room 304
Speaker: Carrie Wright, University of Georgia
Title of talk: The Singled Out Game
Abstract: Do you remember the game show "Singled Out" on MTV from the late 90's? Is there a strategy to winning the game? I will explain the basic premise of the game and then talk about whether there is a strategy to win the game of the 3 finalists. I will first break it down to what happens if there were only 2 finalists and then talk about the case when there are 3 finalists. Is the strategy the same as in the 2 person case?

WEDNESDAY, February 28, 2007

Algebraic Geometry
2:30pm, Room 410
Speaker: Peter Petrov, University of Georgia
Title of talk: Combinatorial Structure of the Dual Complex
Abstract: The talk is based on results of Stepanov. The dual complex associated with a good resolution of singularities is defined. It is shown that its homotopy type is independent of the resolution. How the topology of the complex reflects the type of the singularity is demonstrated in the cases of isolated rational singularities, isolated hypersurface singularities, 3-dim terminal singularities, and others.


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

Number Theory/Arithmetic Geometry
3:30pm, Room 304
Speaker: Konstantin Oskolkov, University of South Carolina
Title of talk: Gauss' sums game played by a Schroedinger particle, continued

VIGRE – Quantum Mechanics
4:00pm, Room 302

Math Club Special Lecture
7:00pm, Life Sciences, Room C127
Refreshments will be provided following the talk.
Speaker: Michael Spivak
Title of talk: How Newton Analyzed Planetary Motion (Why It's Dangerous to be Smarter Than Every One Else)
Abstract: The proof that bodies moving under an inverse square law must have conic sections as orbits surely ranks not only as a major achievement of Newton, but as one of the pivotal points in the history both of physics and mathematics.

Hardly a soul nowadays has any idea how Newton's proof proceeds, a situation usually regarded as a consequence of our modern-day unfamiliarity with the myriad properties of conic sections. But the real problem is that nowadays it's too hard to read what Newton actually wrote. Newton's proof is not only extremely ingenious, but it has led to debates and misunderstandings from the very beginning (Bernoulli seemed to think that Newton had confused a proposition with its converse) to the current time (Arnol'd has given a defense of Newton that is quite ingenious, but totally irrelevant).

In this lecture we will see what Newton actually said, and you won't have to worry overmuch about the properties of conic sections; you will need to have a bit of familiarity with ideas of calculus, but nothing very fancy.

THURSDAY, March 1, 2007

VIGRE – ODE
2:00pm, Room 326

VIGRE – Moduli spaces
2:00pm, Room 304

VIGRE – Geometry
2:00pm, Room 410

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

Colloquium
3:30pm, Room 328
Speaker: Michael Spivak
Title of talk: Physicists’ Rigid Bodies With Mathematician’s (Being Lesson 1 of Physics Without Tears)
Abstract: Newton's laws apply to "particles" or "point masses," which can also be considered to apply to the objects of astronomical problems, but you can't do most other physics problems without considering larger (rigid) bodies.

Newton never discussed rigid bodies (smart man). Euler's pioneering treatment, the basis for the elementary undergraduate hocus-pocus, regards solid bodies as continuous expanses of matter, a rather disconcerting view in the atomic age, whereas the advanced graduate hocus-pocus considers a collection of particles bound by "constraints" in a manner sufficiently abstract to hide all the difficulties in a haze of generalities.

This lecture attempts to give a coherent exposition of the subject, essentially explaining and giving meaning to some of the strange things that physics textbooks contain.

FRIDAY, March 2, 2007

Applied Math Seminar
12:20pm-1:10pm, Room 326
(Pizza at 12:10pm)
Speaker: Haomin Zhou, Georgia Institute of Technology
Title of talk: Variation Models and PDE Techniques in Wavelet Inpainting
Abstract: In this talk, I will present our work (collaborated with Tony Chan (UCLA) and Jackie Shen (Minnesota)) on image inpainting in wavelet domain. The problem is closely related to the classical image inpainting, with the difference being that the inpainting regions are in the wavelet domain, that brings new challenges to the reconstructions, as there is no geometrically well defined inpainting region in the pixel domain, and the damage is inhomogeneous. We propose new variational models, especially total variation minimization in conjunction with wavelets for the wavelet inpainting problems. The models lead to PDE's, which are Euler-Lagrange equations of the variational formulations, in the wavelet domain and can be solved numerically. The proposed models can have effective and automatic control over geometric features of the inpainted images including sharp edges, even in the presence of substantial loss of wavelet coefficients, including in the low frequencies.

Geometry
2:30pm, Room 410
Speaker: Sa’ar Hersonsky, University of Georgia
Title of talk: More on tilings and triangulations
Abstract: In this talk, Dr. Hersonsky will follow up on his excellent and accessible introduction to the seminar that he gave in a joint meeting of the geometry and topology seminars on Feburary 5.

VIGRE–Algebra
3:30pm, Room 304

VIGRE - Hodge Theoretic questions in Algebraic Geometry
3:30pm, Room 303