Seminar Schedule
February 18 - February 22, 2008
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, February 18, 2008
VIGRE – Algebraic Geometry
2:15pm, Room 222
Topology
2:30pm, Room 303
No meeting this week
Algebra
2:30pm, Room 410
No meething this week
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
TUESDAY, February 19, 2008
Mathematical Physics
3:30pm, Room 303
Speaker: Robert Varley, University of Georgia
Title of talk: The definition and properties of pressure in ergodic theory
WEDNESDAY, February 20, 2008
Algebraic Geometry - Please see Friday, Feb. 22, 2008
2:30pm, Room 410
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
Number Theory/Arithmetic Geometry
3:30pm, Room 304
No meeting this week
THURSDAY, February 21, 2008
VIGRE – Tropical Geometry
2:00pm, Room 304
VIGRE – Circle Packing
2:00pm, Room 326
VIGRE – Number Theory
3:30pm, Room 303
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
Colloquium
3:30pm, Room 304
Speaker: Christopher Hacon, University of Utah
Title of talk: Finite generation of canonical rings
Abstract: Let X be a smooth projective algebraic variety. A pluri-canonical form is an section of a power of the canonical linear bundle on X. The canonical ring formed by the pluri-canonical forms is an invariant that is of fundamental importance in the study of the birational geometry of X.
In dimension 2, its properties were understood by the Italian school of Algebraic Geometry at the beginning of the 20th century. The 3 dimensional case was understood in the 1980's by celebrated work of Mori and others. In this talk I will discuss joint work with Birkar, Cascini and McKernan towards understanding the geometry of algebraic varieties of arbitrary dimension. In particular I will discuss the following theorem:
Theorem. The canonical ring of any smooth projective algebraic variety X is finitely generated.
(Note that this Theorem was independently proven by Siu.)
FRIDAY, February 22, 2008
VIGRE-Algebra
2:30pm, Room 322
Applied Math
2:30pm, Room 302
Speaker: David Prager, University of Georgia
Title of talk: Stock Loan Pricing Under Geometric Brownian Motion and Mean-Reverting Stock Models
Abstract: A stock loan is a debt instrument in which the borrower uses a share of stock as collateral. When the loan matures, the borrower may regain the share of stock by repaying the loan principle plus interest, or if the borrower fails to repay the loan, the lender may retain the collateral. Unlike traditional debt instruments, the collateral of a stock loan is subject to wide and frequent price fluctuations, creating difficulties in determining a fair price, interest rate, or service fee for the loan. This talk will introduce stock loans and give some examples to illustrate why such instruments are desirable. We will explore some of the difficulties associated with pricing these instruments. Closed-form solutions will be given for the cases when 1) the loan is American, perpetual, and the price of the stock behaves a geometric Brownian motion and 2) the loan is European and the price of the stock behaves a mean-reverting price model.
Geometry
2:30pm, Room 410
Speaker: Rob Kusner, University of Massachusetts, Amherst
Title of talk: Coplanar Constant Mean curvature Surfaces
Algebraic Geometry – note the special day
3:30pm, Room 410
Speaker: Christopher Hacon, University of Utah
Title of talk: Deformations of canonical pairs
Abstract: It is known that results concerning the extension of pluricanonical forms from a divisor to the ambient variety (such as Siu's celebrated theorem on the deformation invariance of plurigenera) have important consequences on the deformations of singularities of algebraic varieties. For example, by work of Kawamata and Nakayama, it is known that deformations of canonical/terminal singularities are also canonical/terminal.
In this talk we will discuss the problem of deformation invariance for canonical/klt log pairs (X,D) and for the sections of the corresponding pluricanonical ring. Using these results we will also study deformations of Fano varieties with terminal singularities.
This is joint work with T. de Fernex.