Un of Tenn | Math Department

Seminars and Colloquiums
for the week of March 31, 2008

Speakers:

Professor Jan Rosinski , Monday
Mr. John LaGrange, Monday
Professor Haijin Wu, Monday
Mr. Drew Schmidt, Wednesday
Dr. Felipe Voloch, Thursday
Dr. Vladimir Chernov, Friday
Dr. Felipe Voloch, Friday

Monday, March 31

PROBABILITY SEMINAR - continued
TIME: 10:10 -- 11:00 a.m.
ROOM: Ayres 309A

SPEAKER: Professor Jan Rosinski
TITLE: "On a cancellation property of sigma-finite measures with applications to inverse problems for regular variation, linear filters, and identification of stable laws.
ABSTRACT: A group of problems leads to consideration of a multiplicative convolution equation for sigma-finite measures. That includes inverse problems for regular variation of linear filters and of products of independent random variables, as well as identification of stable random measures from their stochastic integrals. Our problem is related to the existence of nontrivial unbounded solutions of the Deny-Choquet equation and is solved by methods of generalized functions. We also develop techniques to resolve problems in applications mentioned above. This is based on a joint work with M. Jacobsen, T. Mikosch, and G. Samorodnitsky.

DOCTORAL DEFENSE
TIME: 1:30 p.m.
ROOM: Ayres 218

SPEAKER: Mr. John LaGrange
TITLE: "Zero-Divisor Graphs, Commutative Rings of Quotients, and Boolean Algebras"

His committee consists of Professors Anderson (chair), Mulay, Tzermias and Langston (CS).

DE/APPLIED AND COMPUTATIONAL MATH SEMINAR
TIME: 3:35 -- 4:25 p.m.
ROOM: Ayres 104

SPEAKER: Professor Haijin Wu, UTK and Nanjing University of China
TITLE: "Adaptive finite element methods for diffraction gratings"

Wednesday, April 2

ALGEBRA SEMINAR
TIME: 3:35 -- 4:25 p.m.
ROOM: Ayres 309A

SPEAKER: Mr. Drew Schmidt

Thursday, April 3

COLLOQUIUM
TIME: 3:40 p.m.
ROOM: Ayres 214

SPEAKER: Dr. Felipe Voloch, University of Texas, Austin
TITLE: "Local-global principles for curves, old and new"
ABSTRACT: In Number Theory, congruences modulo prime powers provide local information and sometimes (e.g. for equations of degree two), everywhere local solvability is enough to imply global solvability. It's been known for some time that this does not hold for more general curves.

Some recent conjectures say that a modified local-global principle for curves holds if we consider unramified covers. This talk will explain these topics.

Friday, April 4

TOPOLOGY SEMINAR
TIME: 2:30 - 3:20 p.m.
ROOM: Ayres 209A

SPEAKER: Dr. Vladimir Chernov, Dartmouth College
TITLE: "Linking of skies and causality in globally hyperbolic spacetimes" (Based on joint work with Yuli Rudyak, from the University of Florida, Gainesville) ABSTRACT: To $x$ in a space-time $X$ one associates the sphere of all null-geodesics through $x$ called the sky $S_x$ of $x.$ Low observed that if the link $(S_x, S_y)$ in the space of all null geodesics of a globally hyperbolic spacetime is nontrivial, then $x,y$ are causally related. The link components in this case are not zero homologous so the classical linking number is undefined. We define the generalized linking number $alk$ for such links. We show that when the Cauchy surface is not an odd-dimensional rational-homology sphere with finite $\pi_1$ and all the timelike sectional curvatures are nonnegative, then $x$ and $y\in X$ are causally related if and only if $alk(S_x,S_y)\neq 0.$ For $y$ in the future of $x$ we interpret $alk(S_x,S_y)$ as the algebraic number of times an observer travelling to $x$ along a timelike curve intersects the null geodesics through $x.$ We show that $x,y$ in a nonrefocussing globally hyperbolic spacetime are causally unrelated if and only if $(S_x, S_y)$ can be unlinked by an isotopy through skies. Low showed that if a globally hyperbolic $(X^{m+1}, g)$ is nonrefocussing then its Cauchy surface $M$ is compact, we show that the universal cover of $M$ is also compact.**

SPECIAL ALGEBRA SEMINAR
TIME: 3:35 p.m.
ROOM: Ayres 209A

SPEAKER: Dr. Felipe Voloch, University of Texas, Austin
TITLE: "Local-global principles for curves over function fields"
SUBJECT: We will sketch a proof of the conjecture from the colloquium talk in the function field case and discuss related issues.

Interested in giving or arranging a talk? Check out our calendar.

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