University of Georgia
Department of Mathematics
Seminar Schedule
April 16 – April 20, 2007
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, April 16, 2007
Special Applied Math Seminar
12:20pm-1:10pm, Room 304
Speaker: Louis Tao, Dept of Mathematical Sciences, NJIT
Title of talk: Orientation Selectivity in Visual Cortex
Abstract: In the mammalian visual pathway, orientation selectivity
is first observed in the primary visual cortex (area V1). The LGN cells that
comprise the input to V1 are not orientation selective, but most V1 neurons
are quite selective. In this talk, we summarize the two main classes of theoretical
models that have been offered to explain orientation selectivity. We present
results from a large-scale computational model of V1 that is consistent with
most of the extant data. To understand the network mechanisms behind orientation
selectivity, we construct idealized models which can be analyzed using population
density and kinetic theoretical methods. Within such reduced models, we examine
how intrinsic dynamic fluctuations modify the effect of strong recurrent network
excitation and allow for the emergence of orientation selectivity.
Algebra
2:30pm, Room 410
Speaker: Kelly McKinnie, Emory University
Title of talk: Noncyclic and indecomposable p-algebras
Abstract: In this talk we will discuss questions about finite
dimensional central simple p-algebras. In particular we will discuss the first
construction of a noncyclic p-algebra due to Amitsur and Saltman. From there
we will talk about the structure of these algebras under prime to p extensions
and the conditions under which they are indecomposable.
Topology Seminar
2:30pm, Room 304
Speaker: Will Kazez, University of Georgia
Title of talk: Products, open book decompositions, and
partial open book decompositions
Abstract: I will talk about the above topics in the context
of a contact structure on a 3-manifolds. These are the basic objects of interest
in recent joint work with Ko Honda and Gordana Matic.
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea and Cookies
TUESDAY, April 17, 2007
VIGRE-Graduate Student Seminar
2:00pm, Room 304
Speaker: Ed Azoff, University of Georgia
Title of talk: Measurable Dynamics
Abstract: Let E be an equivalence relation on a set X. A _uniformization_
of E is a subset of X which meets each equivalence class determined by E in
precisely one point. Finding "nice" uniformizations is a common mathematical
goal. For example, Jordan canonical forms solve the uniformization problem for
the relation of similarity on complex matrices.
After some general remarks, we will specialize to the following setting. Given a bijection f on the interval [0,1), define x~y if and only if some (forward, backward, or neutral) iterate of f sends x to y. We will discuss classical work of Poincare, Denjoy and Glimm Effros to the effect that the resulting equivalence relation is either very good or very bad. We will also examine some concrete examples illustrating how hard it can be to decide which alternative holds for a specific f. Along the way, we will catch glimpses into descriptive set theory (deining what "nice" means), ergodic theory (measures on [0,1) which are invariant under f), and dynamics (examining limit sets of orbits).
My interest in this topic arose from joint work with Eugen Ionascu on a question from wavelet theory.
WEDNESDAY, April 18, 2007
Algebraic Geometry
2:30pm, Room 410
No meeting this week
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
Number Theory/Arithmetic Geometry
3:30pm, Room 304
Speaker: Neil Lyall, University of Georgia
Title of talk: Polynomial configurations in sum/difference
sets
Abstract: We will discuss results relating to the beautiful
observation (made independently by Sarkozy and Furstenberg) that subsets of
the integers with positive upper density necessarily contain square differences.
VIGRE – Quantum Mechanics
4:00pm, Room 302
THURSDAY, April 19, 2007
VIGRE – ODE
2:00pm, Room 326
VIGRE – Geometry
2:00pm, Room 410
FRIDAY, April 20, 2007
Applied Math Seminar
12:20pm-1:10pm, Room 304
(pizza at 12:10pm)
Speaker: Serge Guillas
Title of talk: Approximation of functional regression models
with bivariate splines
Abstract: We consider the functional linear regression model
where the explanatory variable is a random surface and the response is a real
random variable, with no noise. Bivariate splines over triangulations represent
the random surfaces. We use this representation to construct least squares estimators
of the regression function with or without a penalization term. Under the assumptions
that the regressors in the sample are bounded and span a large enough space
of functions, bivariate splines approximation properties yield the consistency
of the estimators. Simulations illustrate the quality of the asymptotic properties
in various situations.
Geometry
2:30pm, Room 410
Speaker: Yang Liu, University of Georgia
Title of talk: The Thickness and Crossing Number of Knots
Abstract: It is known that the ropelength of a knot is bounded
below by the (3/4)-power of the crossing number of the knot. In this talk, we
follow Buck and Simon's proof of this result.
VIGRE–Algebra
3:30pm, Room 304
VIGRE - Hodge Theoretic questions in Algebraic Geometry
3:30pm, Room 303
**********************************
MONDAY, April 23, 2007
Colloquium
3:30pm. Room 323
Speaker: Professor R. Parthasarathy of the Tata Institute
THURSDAY, April 26, 2007
Special Math Education Seminar
3:30pm, Room 304
Speaker: Emilie Wiesner, University of Georgia