Seminar Schedule
April 7 - April 11, 2008
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, April 7, 2008
VIGRE – Algebraic Geometry
2:15pm, Room 222
Topology
2:30-3:30, Room 303
Speaker: Gordana Matic, University of Georgia
Title of talk: Arcs, surfaces, contact topology, etc, etc.
Abstract: This is a follow up to the previous talk on "Arcs, surfaces, contact topology, etc" The focus will be implications of the invariants of dividing sets on surfaces defined previously to the well definedness of sutured Floer homology over the integers.
Algebra
2:30pm, Room 410
Please see Thursday, April 10, 2008
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
TUESDAY, April 8, 2008
VIGRE - Graduate Student Seminar
2:00pm, Room 304
Speaker: Bree Ettinger, University of Georgia
Title of talk: Ozone Prediction using Bivariate Splines to Approximate
Functional Regression Models
Abstract: Functional linear regression models are models where the explanatory variable is a random surface and the response is a real random variable. We will discuss the recent results for bounded or normal real random responses. We use bivariate splines to represent the random surfaces then we use this representation to construct least squares estimators of the regression function. We will discuss the two cases of the least squares estimators, one with a penalty term and one without. Finally we will explore the functional regression model's application to predicting ground level ozone from 2006 EPA data over the continental United States.
Mathematical Physics
3:30pm, Room 303
Speaker: Robert Varley, University of Georgia
Title of talk: Examples and properties of equilibrium states
WEDNESDAY, April 9 2008
Algebraic Geometry
2:30pm, Room 410
Speaker: Valery Alexeev, University of Georgia
Title of talk: Weighted hyperplane arrangements
Abstract: We give a common generalization of (1) Hasset's weighted stable curves and (2) Hacking-Keel-Tevelev's stable hyperplane arrangements.
Faculty and Graduate Social
3:00pm, Room 309
Coffee, Tea, Cookies
Number Theory
3:30pm, Room 304
Speaker: John Voight, of the University of Vermont
Title of talk: "Quadratic forms that represent almost the same primes"
Abstract: The quadratic forms x2 + 9y2 and x2 + 12y2 represent the same primes, namely, those of the form p = 1 (mod 12). What other such pairs of forms exist? We give a complete answer to this question using the tools of class field theory, proving a conjecture of Jagy and Kaplansky.
THURSDAY, April 10, 2008
VIGRE – Tropical Geometry
2:00pm, Room 304
VIGRE – Circle Packing
2:00pm, Room 410
VIGRE – Number Theory
3:30pm, Room 303
Algebra
2:30pm, Room 410
Speaker: Pramod Achar (LSU)
Title: Staggered sheaves
Abstract: Perverse sheaves have been a very important and powerful tool in representation theory since their discovery 30 years ago. Their usefulness comes from the fact that in many ways, they have better properties than ordinary constructible sheaves (e.g., they have finite length; they are self-dual; they are subject to the "Decomposition Theorem"), and that makes them easier to work with.
A natural question is whether there is an analogue of this category in the world of vector bundles (or, more generally, coherent sheaves). In this talk, I will describe one possible candidate, the category of "staggered sheaves." These sheaves are to vector bundles as perverse sheaves are to local systems. Under some assumptions, staggered sheaves have finite length, they are self-dual, and they obey a Decomposition Theorem. I will also mention some potential applications in equivariant K-theory. This work is partly joint with D. Treumann.
FRIDAY, April 11, 2008
VIGRE-Algebra
2:30pm, Room 322
Applied Math
2:30pm, Room 302
No meeting this week
Geometry
2:30pm, Room 410
Speaker: Joe Fu, UGA
Title of talk: Hermitian Integral Geometry II
Abstract: This is the final version of joint work with A. Bernig on the integral geometry of C^n under the action of the affine unitary group. I'll describe several canonical bases for the space of unitary-invariant convex valuations \mu on C^n, and characterize in these terms the cones of nonnegative (\mu(K) >= 0 for all convex K) and monotone (K \subset L => \mu(K) \le \mu(L)) valuations. Then I'll state explicitly the principal kinematic formula in this setting, and show how it leads to a simple calculus for a variety of problems in the geometric probability of the unitary group. To illustrate, I'll compute explicitly the expected length of the curve of intersection of two real submanifolds of dimensions 4 and 5 placed in random positions in CP4. A transform of this last formula also gives an expression for the expected 7-dimensional volume of the Minkowski sum of a 3-disk and a 4-disk placed in random (unitary) positions in C4.