| ← April 2008 |
| June 2008 → |
| Monday | Tuesday | Wednesday | Thursday | Friday |
| April 28 |
- Geometry and Topology Seminar
Symplectic duality for Hypertoric varieties, Part II
Tom Braden, University of Massachusetts
Continuation.
1:00pm–2:15pm, Monday, April 28, 2008 in LGRT 1535
Printable Announcement
- Representation Theory
Cohomology of Cotangent Bundles of Flag Varieties and the BK-Filtration
Charles Hague, Tufts
Let G be a complex algebraic group and let P be a parabolic subgroup of G. Let
T(G/P ) denote the cotangent bundle of the flag variety G/P . In this talk I will describe
results connecting cohomology of bundles on T(G/P ) to purely combinatorial objects such as filtrations on irreducible G-modules and generalizations of Lusztig's q-analog of weight multiplicity.
4:00pm–5:00pm, Monday, April 28, 2008 in LGRT 1234
Printable Announcement
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| April 29 |
- Applied Mathematics and Computation Seminar
Discontinuous Galerin Methods for the Modeling of Free Surface Flows Using High-Order Boussinesq Approximations
Jan Hesthaven, Division of Applied Mathematics, Brown University
We shall discuss the modeling of free surface flows and fluid-structure
interactions using high-order Boussinesq approximations. These sets of
equations are characterized by being purely dispersive and strongly non-linear, with
additional complications introduced by high-order spatial derivatives and
cross-derivatives.
The key elements of the formulation and some of the properties of the Boussinesq system will be discussed in some detail. This shall be used to argue why discontinuous Galerkin methods may be a suitable approach for the solution of these equations.
We shall develop the basic elements required for solving this system, discuss a number of subtleties and address practical concerns of performance and efficient solvers.
The computational approach will be extensively validated with both benchmark tests and experimental data.
This is work done in collaboration with A.P. Engsig-Karup (DTU, Denmark),
P. Madsen (DTU, Denmark), H. Bingham (DTU, Denmark) and T. Warburton
(Rice).
Refreshments at 3:45
4:00pm–5:00pm, Tuesday, April 29, 2008 in LGRT 1634
Printable Announcement
- Five College Number Theory Seminar
Michael Broshi , University of Chicago
We report on recent work to understand deformations of Galois
representations into reductive groups.
Refreshments at 3:30pm in Seeley-Mudd 208
4:00pm–5:00pm, Tuesday, April 29, 2008 in Seeley-Mudd 207, Amherst College
Printable Announcement
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| May 1 |
- Colloquium
New and old rectangular mixed finite elements for elasticity
Gerard Awanou, Northern Illinois University
The theory of elasticity is used to predict the response of a material body to applied forces. Recent years have seen tremendous progress in the understanding of how to construct finite elements which approximate directly the stress field using tools from algebraic topology, e.g. differential complexes. I will discuss rectangular mixed finite elements which may be viewed as analogues of the triangular elements developed for triangular meshes. Part of this work is joint with D. Arnold.
Refreshments at 3:45
4:00pm–5:00pm, Thursday, May 1, 2008 in LGRT 1634
Printable Announcement
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| May 2 |
- Reading Seminar in Algebraic Geometry
The Bertini Theorem / The Petri Theorem
Jason Brunson / Adam Gamzon
2:35pm–3:35pm, Friday, May 2, 2008 in LGRT 1634
Printable Announcement
- Valley Geometry Seminar
Hypergraphic divisors, curves, and morphisms
Jenia Tevelev, University of Massachusetts, Amherst
We construct myriads of extremal divisors, rigid curves, and
birational morphisms with unexpected exceptional loci for the
Grothendieck-Knudson moduli space of stable rational curves. The basic tool
is
an isomorphism between this moduli space and a Brill-Noether locus of a
very special reducible curve corresponding to a hypergraph
(like a graph but "edges" are triples of vertices and not pairs). This
hypergraph will actually have to be both a hypertree and
a sticky figure. Joint work with Ana-Maria Castravet.
Refreshments at 3:45
4:00pm–5:00pm, Friday, May 2, 2008 in LGRT 1634
Printable Announcement
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| May 5 |
- Special Colloquium
Qualitative/Quantitative Analysis of Biomolecular Network Dynamics
Eduardo Sontag, Rutgers University
Biomolecular networks, while exhibiting a rich variety of behaviors in
signaling and regulation, would appear to be fairly well behaved as dynamical
systems. Their (mathematical) models have solutions that tend to settle into
well-defined steady states or periodic, but not "chaotic", behavior. This
presents one major challenge to theoreticians: what is special about such
networks, vis a vis general dynamical systems? A second challenge arises in
the mathematical analysis itself: while on the one hand good qualitative,
graph-theoretic, knowledge is frequently available, on the other hand it is
often hard to experimentally validate the form of the nonlinearities used in
reaction terms, and even when such forms are known, to accurately estimate
coefficients (parameters, such as kinetic constants). This
"data-rich/data-poor" dichotomy seems to be pervasive in systems biology.
This theory talk is concerned with both challenges. We approach the problem
through the standard paradigm in control theory and signal processing, that of
viewing larger systems as interconnections of input/output subsystems:
provided that these subsystems are individually well-behaved, more complex
behaviors arise from the global interconnection structure. This brings up a
host of issues, from basic issues of modularity, retroactivity, and input and
output "impedance", to the characterization of classes of appropriately
"simple" components, to the question of what type of quantitative information
suffices for obtaining precise conclusions regarding dynamics (such as the
existence of multiple stable steady states, or oscillations).
As one specific example, we consider order-preserving (monotone) components,
which enjoy particularly nice dynamical properties as well as robust responses
to perturbations. Their interconnections may be, in principle, studied
through a blend of qualitative and (relatively sparse) quantitative
information, allowing one to draw conclusions about global dynamical behavior
and the location of steady states. The talk will also present evidence
suggesting that natural signaling and transcriptional regulation networks may
be close to monotone, and that networks that are close to monotone are
statistically better behaved than more arbitrary ones.
Refreshments at 3:45 PM
4:00pm–5:00pm, Monday, May 5, 2008 in LGRT 1634
Printable Announcement
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| May 6 |
- Applied Mathematics and Computation Seminar
Spectral stability of ideal-gas shock layers
Greg Lyng, University of Wyoming
In this talk, I'll describe how a combination of asymptotic
ODE estimates and numerical Evans-function computations can be used
to study the spectral stability of shock-wave solutions of the
compressible Navier--Stokes equations with ideal gas equation of
state. The main results are that, in appropriately rescaled
coordinates, the Evans function associated with the linearized
operator about the wave (i) converges in the large-amplitude limit to
the Evans function for a limiting shock profile of the same
equations, for which internal energy vanishes at one endstate; and
(ii) has no unstable (positive real part) zeros outside a uniform
ball. Thus, the rescaled eigenvalue ODE for the set of all shock
waves, augmented with the (nonphysical) limiting case, form a compact
family of boundary-value problems that can be conveniently
investigated numerically. An extensive numerical Evans-function study
yields one-dimensional spectral stability, independent of amplitude,
for the parameter range considered. This is joint work with J.
Humpherys (BYU) and K. Zumbrun (Indiana).
Refreshments at 3:45
4:00pm–5:00pm, Tuesday, May 6, 2008 in LGRT 1634
Printable Announcement
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| May 8 |
- Distinguished Lecture
String Topology and Algebra
Dennis Sullivan, Stony Brook
We will illustrate string topology of curves on surfaces, the geometry, the algebra and some related questions.
Then we can discuss generalizations to dimension three and to higher dimensions.
Refreshments at 3:30 PM
4:00pm–5:00pm, Thursday, May 8, 2008 in LGRT 1634
Printable Announcement
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| May 9 |
- Reading Seminar in Algebraic Geometry
Syzygy, gonality, and K3
Jenia Tevelev
The last installment of the Claire Voisin saga.
2:35pm–3:35pm, Friday, May 9, 2008 in LGRT 1634
Printable Announcement
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| May 12 |
- Geometry and Topology Seminar
4-manifolds with torus actions
Alvaro Pelayo, MIT
After reviewing the definition of symplectic manifold, symplectic
action and some basic results on Hamiltonian torus actions, I will present a
classification of symplectic actions of tori on (compact, connected)
four-manifolds. The classification is in terms of a collection of invariants
of the topology of the manifold, of the torus action and of the symplectic
form. I will present explicit models of such symplectic manifolds with torus
actions, defined in terms of these invariants. A stepping stone for this
classification is the previous classification of symplectic torus actions
with coisotropic principal orbits due to JJ Duistermaat and the speaker.
1:00pm–2:15pm, Monday, May 12, 2008 in LGRT 1535
Printable Announcement
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| May 13: Last Day of Classes |
- Applied Mathematics and Computation Seminar
Fluctuation results for some models of random environments and interactions
Timo Seppalainen, University of Wisconsin
This talk is a survey of some recent fluctuation
results for three stochastic models: ballistic random
walk in random environment, the random average process, and the
asymmetric simple exclusion process. We will see
fluctuations of different magnitudes, expressed as
powers of the ratio between macroscopic and microscopic
space and time scales.
Refreshments at 3:45
4:00pm–5:00pm, Tuesday, May 13, 2008 in LGRT 1634
Printable Announcement
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