| ← November 2009 |
| January 2010 → |
| Monday | Tuesday | Wednesday | Thursday | Friday |
| November 30 |
- Representation Theory
Representation theory of hyperplane arrangements
Tom Braden, UMass
We study the algebra of polynomial differential operators on affine space invariant under a torus action. This turns out to have many of the properties of the universal enveloping algebra of a reductive Lie algebra. In particular, we define an analogue of the Bernstein-Gelfand-Gelfand "category O", and show that our category is highest weight and Koszul. We give an explicit decription of our category in terms of the combinatorics of a hyperplane arrangement which encodes the torus action, and we show that the Koszul dual category is given by the same construction for the Gale dual hyperplane arrangement.
This is the algebraic counterpart to the geometric talk I gave in the VGS, but you don't need to have seen that talk to understand this one.
Joint work with A. Licata, N. Proudfoot, and B. Webster
4:00pm–5:00pm, Monday, November 30, 2009 in LGRT 1322
Printable Announcement
- Statistics and Probability Seminar
MS projects
Presentations of the MS projects, Department of Mathematics and Statistics, University of Massachusetts
There will be two presentations, each 30 minutes.
The first project concern cortisol levels in pregnant women.
Cortisol is a hormone related to stress. We report on a study of 354 pregnant women, for whom cortisol was measured several times per day, on multiple days, both before and after delivery. We show the typical pattern by which cortisol fluctuates over the course of the day, and how the pattern varies before and after delivery.
The topic of the second project is ozone damage to forests.
Ground-level ozone is a pollutant, and one of the major ingredients in smog. Ozone is thought to affect plants when it is taken in through the stomates. But plants' stomates open only when the plants have sufficient moisture; so the effect of ozone depends on the amount of moisture. The US Forest Service collects data from around the country to assess how ozone affects the health of our forests. We report on those data, and the interplay between ozone, moisture, and damage to forests.
Refreshments at 3:45
4:00pm–5:00pm, Monday, November 30, 2009 in LGRT 1634
Printable Announcement
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| December 1 |
- Applied Mathematics and Computation Seminar
Hyperbolic systems: geometric structure and entropies
Kris Jenssen, Penn State
We study the problem of constructing nxn-systems of hyperbolic
conservation laws in one space dimension with prescribed eigencurves: the
eigenvector fields of the Jacobian of the flux are given.
We formulate this as an overdetermined system for the eigenvalues-to-be.
The resulting equations are analyzed with techniques from exterior
differential
systems.
Further constraints may be added and the cases of rich systems and systems
with associated entropies can be analyzed within the same setup.
This is joint work with Irina Kogan (North Carolina State University).
Refreshments at 3:45
4:00pm–5:00pm, Tuesday, December 1, 2009 in LGRT 1634
Printable Announcement
- Five College Number Theory Seminar
Abelian surfaces with extra endomorphims
Reinier Broker, Brown University
For elliptic curves, the modular polynomial Phi_p(X,Y) parametrizes elliptic
curves together with a p-isogeny. The polynomial Phi_p(X,X) parametrizes
elliptic curves together with an endomorphism of degree p. Kronecker
discovered
already that the irreducible factors of Phi_p(X,X) are Hilbert class
polynomials.
In this talk we will consider abelian surfaces with extra endomorphisms. We
will show which factors occur when you factor the 2-dimensional analogue
of the univariate polynomial Phi_p(X,X). In the case p = 2, everything can be
explicitly computed and we will give a complete classification of abelian
surfaces admitting a (2,2)-endomorphism.
Refreshments at 3:30pm in Seeley-Mudd 208
4:00pm–5:00pm, Tuesday, December 1, 2009 in Seeley-Mudd 207, Amherst College
Printable Announcement
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| December 2 |
- Geometry and Topology Seminar
Double Point Surgery and Configurations of Surfaces in 4-manifolds
Hee Jung Kim, Max Planck-Bonn
In this talk, we introduce "double point surgery", a variation of
the Fintushel-Stern rim surgery, and use it to create configurations that
are smoothly knotted, without changing the topological type, or the smooth
isotopy type of the individual components of the configuration. As an
application of knotting a configuration, we show that double point surgery
gives rise to
interesting exotic group actions with somewhat more complicated singular
sets consisting of a configuration of surfaces.
2:30pm–3:45pm, Wednesday, December 2, 2009 in LGRT 1535
Printable Announcement
- Mathematical Physics Seminar
On generalized monopole spherical harmonics and the wave equation of a charged massive Kerr black hole
Floyd Williams, University of Massachusetts at Amherst
We find linearly independent solutions of the Goncharov-Firsova wave equation (solutions these author were unable to find) for a massive complex scalar field on a charged Kerr black hole.These solutions generalize the classical monopole spherical harmonic solutions known in the massless case.This is joint work with one of my former students,Dr.Shabnam Beheshti.
2:30pm–3:30pm, Wednesday, December 2, 2009 in LGRT 1033
Note special time and room
Printable Announcement
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| December 4 |
- TWIGS
What is a hypergeometric function?
Eduardo Cattani
1:30pm–2:30pm, Friday, December 4, 2009 in LGRT 1634
Printable Announcement
- Valley Geometry Seminar
Rees algebras and singularities of rational plane curves
David Cox, Amherst College
Geometric modelers study parameterized curves and surfaces in the plane and 3-space. Their method of "moving curves" and "moving surfaces" led them to discover the polynomial relations defining the Rees algebra of the ideal generated by the polynomials that give the parametrization. At the time they did this, they had no idea what a Rees algebra was. Meanwhile, the commutative algebra community had studied for many years the Rees algebras of various types of ideals, though not those that arise from geometric modeling. Recently, the interests of these groups have converged, leading to new results and new hard problems to think about. My lecture will describe joint work with Kustin, Polini and Ulrich on the test case of rational plane sextics and the special role played by double and triple points. K3 surfaces will make a brief appearance toward the end of the talk in connection with my fantasy that they might help distinguish between certain types of Rees algebras.
Refreshments at 3:45
4:00pm–5:00pm, Friday, December 4, 2009 in LGRT 1634
Printable Announcement
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| December 7 |
- Statistics and Probability Seminar
Developing Statistical Perception
Cliff Konold , Scientific Reasoning Research Institute at University of Massachusetts Amherst
Statistics is too often portrayed as a set of methods for collecting and analyzing data. More fundamentally, it is a way of seeing the world. I describe our efforts to understand the perceptions and ideas young students bring to bear on data and how we work to shape students’ perceptions to make them more expert like. To facilitate learning, we have built into the data visualization software, TinkerPlots, tools that support and then build on novice perceptions. More recently, we have added modeling capabilities which students use to create and explore “worlds” of their own making. In this way, we hope to develop the crucial understanding that statistics is not only about seeing, but also about questioning what we see.
Refreshments at 3:45
4:00pm–5:00pm, Monday, December 7, 2009 in LGRT 1634
Printable Announcement
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| December 8 |
- Applied Mathematics and Computation Seminar
Some theoretical and practical aspects of information flow in complex dynamical systems
Richard Kleeman, Courant Institute of the Mathematical Sciences, NYU
The flow of uncertainty within a complex dynamical system is a problem of significant practical interest. For example in the problem of prediction, uncertainty in the initial
conditions of the appropriate dynamical system flows through the system as time increases and governs the uncertainty in any particular prediction.
In this talk we review various empirical measures of this flow which have been proposed in the context of simple dynamical systems. In addition we discuss a new formalism of flow introduced by the speaker and co-workers. This latter formalism involves the interpretation of entropy evolution equations in the context of dynamical systems which have a natural decomposition into two components.
In the last part of the talk we will discuss the practical application of these ideas to a problem that is as yet unsolved: The optimal design of observing networks to reduce the error in "important" atmospheric predictions.
Refreshments at 3:45
4:00pm–5:00pm, Tuesday, December 8, 2009 in LGRT 1634
Printable Announcement
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| December 9 |
- Geometry and Topology Seminar
David Shea Vela-Vick, Columbia University
2:30pm–3:45pm, Wednesday, December 9, 2009 in LGRT 1535
Printable Announcement
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| December 10 |
- TWIGS
What is Tumor Angiogenesis and how might one model it?
Nathaniel Whitaker
1:30pm–2:30pm, Thursday, December 10, 2009 in LGRT 1634
Printable Announcement
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| December 11: Last Day of Classes |
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| December 21: End of Semester |
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