Un of Tenn | Math Department

Seminars and Colloquiums
for 2010-2011

Week of February 14, 2011

Speaker:
Mr. Matt Turner, Monday
Dr. Mike Gilchrist, Tuesday
Professor James Conant, Tuesday
Professor Ohannes Karakashiann, Wednesday
Dr. Valera Berestovskii, OMSK, Friday

If you are interested in giving or arranging a talk for one of our seminars or colloquiums,
please review our calendar.

If you have questions, or a date you would like to confirm, please contact Dr. Fernando Schwartz.

Monday, February 14

PROBABILITY SEMINAR - POSTPONED - DATE TBA
TIME: 3:35 – 4:25 p.m.
ROOM: Ayres 114
SPEAKER: Mr. Matt Turner
TITLE: “Ito isomorphisms for stochastic integrals driven by Levy processes with applications. Part II continued.”
ABSTRACT: “In this talk we will use results presented last semester on moments of infinitely divisible random variables to develop Ito isomorphisms for stochastic integrals driven by Levy processes.”

Tuesday, February 15

MATH BIOLOGY SEMINAR
TIME: 9:45 – 10;35 AM
ROOM: NIMBioS Classroom
SPEAKER: Dr. Mike Gilchrist
TOPIC: “Continuous Markov processes”

TOPOLOGY SEMINAR
TIME: 3:40 – 4:30 p.m.
ROOM: Ayres Hall 406
SPEAKER: Professor James Conant
TITLE: “Concordance of Links, an Introduction”
ABSTRACT: Two knots in the 3-sphere are said to be isotopic if there is a smooth 1 parameter deformation from one to the other. This can be thought of as a movie, which is a level-preserving embedding of S^1 x 1 into S^3 x 1, with the second parameter representing time. On the other hand, if one relaxes the condition that the embedding is level preserving, much more subtle phenomena happen. In this case, the equivalence relation on knots is called “concordance.” In this talk, we will introduce this notion, give several examples, and define some algebraic invariants of link concordance introduced by Milnor, called mu invariants. This talk is intended to be accessible to graduate students.

Wednesday, February 16

APPLIED/COMPUTATIONAL MATH SEMINAR
TIME: 3:35 - 4:30 p.m.
ROOM: Ayres 111
SPEAKER: Professor Ohannes Karakashian
TITLE: “Adaptive Methods for Elliptic PDEs”, Part II

Friday, February 18

COLLOQUIUM
TIME: 3:35 pm
ROOM: Ayres 405
SPEAKER: Dr. Valera Berestovskii, OMSK
TITLE: "LOCALLY G-HOMOGENEOUS BUSEMANN G-SPACES"
ABSTRACT: I'll discuss the content of our joint submitted paper on Busemann G-spaces. Any such space M could be roughly described as a locally compact geodesic metric space with local condition of extendibility of metric segments without ramification.
The paper is directed to the Busemann conjecture, divided in two steps:
1) Every space M has a finite topological dimension;
2) Every n-dimensional space M is a topological n-manifold.
These conjectures have been proved affirmatively only in special cases (the first one for M with metrically convex small balls by Berestovskii, the second by Busemann (n = 1; 2), Krakus (n = 3), P.Thurston (n = 4).

The second conjecture, as well as the famous Poincare conjecture (which was proved earlier by G.Perelman), would be a direct corollary of (unsolved) Bing-Borsuk conjecture which states that all finite-dimensional topologically homogeneous ANR-spaces are manifolds.

In this paper we give brief proofs of topological properties of general (sometimes finite-dimensional) Busemann G-spaces; no other property is known at present without above mentioned specifications of their dimension; the new result is that small metric spheres in any M with n ? 3 are simply connected.

Then we add some additional conditions like
1) the visibility of metric sphere with arbitrary center x for some radius r(x) > 0
from all points sufficiently close to x;
2) more stronger locally uniform version of this condition.
These conditions are weaker than the mentioned condition of metric convexity of small spheres and possibly are true for every Busemann G-space M.

We prove that in the situation 1), all small spheres in M are (strongly) topologically homogeneous and mutually homeomorphic, while for 2), the space M is finite-dimensional.

Also I'll show computer pictures (created by Denise) demonstrating a two-dimensional metrically homogeneous Busemann G-space (so-called Stadium space) with no metrically convex sphere which satisfies both conditions 1) and 2) above.

Refreshments available in Ayres 401 at 3:15 p.m.

Past notices:

winter break