| ← October 2009 |
| December 2009 → |
| Monday | Tuesday | Wednesday | Thursday | Friday |
|
|
| November 3 |
- Applied Mathematics and Computation Seminar
Fokker-Planck Description for Noisy Neuronal Network Dynamics
Gregor Kovacic, Rensselaer Polytechnic Institute
Kinetic theory provides a coarse-grained alternative to
the integrate-and-fire neuronal network description. In the limit of
infinitely short conductance responses, a Boltzmann-type differential-
difference equation can be derived for the probability density
function of the neuronal voltage. A Fokker-Planck equation can be
derived in the limit of small conductance fluctuations,. The talk
will present detailed solutions to this equation, describing both the
steady asynchronous and synchronously-oscillating states of the
network. The steady asynchronous state is described by asymptotic
solutions of the Fokker-Planck equation, using the size of the
neuronal conductance fluctuations as the small parameter. In
addition, the Fokker-Planck equation can also be used to describe the
likelihood and temporal period of synchronous network oscillations,
in which all the neurons fire in unison. The likelihood of
synchrony is computed combinatorially using the network oscillation
period and the voltage probability distribution. The oscillation
period is found from a first-passage-time problem described by a
Fokker-Planck equation, which is solved analyticaly via an
eigenfunction expansion. The voltage probability distribution is
found using a Central-Limit-Theorem-type argument via a calculation
of the voltage cumulants.
Refreshments at 3:45
4:00pm–5:00pm, Tuesday, November 3, 2009 in LGRT 1634
Printable Announcement
- Five College Number Theory Seminar
Finite conductor models for zeros near the central point of elliptic curve L-functions
Steven J. Miller, Williams College
Random Matrix Theory has successfully modeled the behavior of
zeros of elliptic curve L-functions in the limit of large conductors. In
this talk we explore the behavior of zeros near the central point for
one-parameter families of elliptic curves with rank over Q(T) and small
conductors. Zeros of L-functions are conjectured to be simple except
possibly at the central point for deep arithmetic reasons; these families
provide a fascinating laboratory to explore the effect of multiple zeros on
nearby zeros. Though theory suggests the family zeros (those we believe
exist due to the Birch and Swinnerton-Dyer Conjecture) should not interact
with the remaining zeros, numerical calculations show this is not the case;
however, the discrepency is likely due to small conductors, and unlike
excess rank is observed to noticeably decrease as we increase the
conductors. We shall mix theory and experiment and see some surprisingly
results, which lead us to conjecture that a new random matrix ensemble
correctly models the small conductor behavior.
Refreshments at 3:30pm in Seeley-Mudd 208
4:00pm–5:00pm, Tuesday, November 3, 2009 in Seeley-Mudd 207, Amherst College
Printable Announcement
|
|
| November 4 |
- Geometry and Topology Seminar
Monodromy factorizations and filling of contact structures
Olga Plamenevskaya, SUNY Stony Brook
A famous theorem of Giroux establishes a correspondence between open book
decompositions and contact structures on 3-manifolds; a contact structure
can arise on the boundary of Stein manifods iff it has an open books with
positive monodromy (in this case a Stein fillings can be constructed as a
Lefschetz fibration). Although in general one needs to study all
stabilizations of open books to understand all Stein fillings, in the genus
zero case it suffices to analyze the monofromy of a single open book (due to
a recent result of Wendl). I will review the basics on open books, contact
structures, and Stein fillings in some detail, and then explain how
factorizations of monodromy lead to classification of fillings of certain
lens spaces, and to some non-fillability results.
(Joint with J. Van Horn-Morris.)
2:30pm–3:45pm, Wednesday, November 4, 2009 in LGRT 1535
Printable Announcement
|
|
| November 5 |
- TWIGS
What is a Galois representation?
Tom Weston
1:30pm–2:30pm, Thursday, November 5, 2009 in LGRT 1634
Printable Announcement
|
|
| November 6 |
- Reading Seminar in Algebraic Geometry
Reconstruction problem in mirror symmetry
Jenia Tevelev, UMass
I will try to explain how to reconstruct a Calabi-Yau from a singular affine manifold,
following Gross-Siebert and Kontsevich-Soibelman. The talk will be much more elementary
than previous talks in the series. If you know what a polytope is, you are all set to understand it
(and it is actually enough to know what a triangle is). We will reload the matrix:
no knowledge of SYZ fibrations or Kahler geometry will be required.
We will also turn en masse to the dark side (aka B-side) of Mirror Symmetry.
2:50pm–3:45pm, Friday, November 6, 2009 in LGRT 1634
Printable Announcement
- Valley Geometry Seminar
The moduli space of stable quotients
Alina Marian, University of Illinois, Chicago
I will discuss features of a moduli space of stable quotients of the
rank n trivial sheaf on curves. This gives a compactification of the
moduli of maps from smooth curves to Grassmann varieties, distinct
from the Kontsevich-Manin space. The construction connects with
Gromov-Witten theory on the one hand, and leads to new relations in
the tautological ring of the moduli space of curves on the other. This
is joint work with Dragos Oprea and Rahul Pandharipande.
Refreshments at 3:45
4:00pm–5:00pm, Friday, November 6, 2009 in LGRT 1634
Printable Announcement
|
|
| November 9 |
- Representation Theory
Nilpotent orbits in characteristic 2 and Springer correspondence
Ting Xue, MIT
Let k and F_q be an algebraically closed and
a finite field of characteristic 2 respectively. Let G be an
adjoint (resp. simply connected) algebraic group of type B,C or
D over k, g the Lie algebra of G and
g^* the dual vector space of g. We
construct the Springer correspondence for g (resp.
g^*) following Lusztig's method. The correspondence is
a bijective map from the set A_g (resp.
A_g^*) to the set of irreducible
characters of the Weyl group of G, where
A_g (resp.
A_g^*) is the set of all pairs
(c,F) with c a nilpotent G-orbit
in g (resp. g^*) and F an
irreducible G-equivariant local system on c (up to
isomorphism). In particular, we obtain classifications of nilpotent
orbits in orthogonal Lie algebras over F_q and in the
duals of classical Lie algebras over k and
F_q. Finally, we describe the explicit correspondence
using similar combinatorics that appears in the description of
generalized Springer correspondence (defined by Lusztig) for
classical groups in the case of characteristic not equal 2 and
unipotent case in characteristic 2.
4:00pm–5:00pm, Monday, November 9, 2009 in LGRT 1322
Printable Announcement
- Statistics and Probability Seminar
Challenges in studying food insecurity in US using complex survey samples
Ryung S. Kim , Department of Epidemiology and Population Health, Albert Einstein College of Medicine
Food insecurity is a status of "limited or uncertain availability of
nutritionally adequate and safe foods or limited or uncertain ability to
acquire acceptable foods in socially acceptable ways" (USDA 1990). And a
number of national surveys include questionnaires to measure food
insecurity: the Current Population Survey, the Panel Study of Income
Dynamics, the National Health and Nutrition Survey, the Early Childhood
Longitudinal Survey, and more.
I will briefly describe important concepts to understand food insecurity
in US and current research progress in the area. Then I will discuss
several statistical challenges in studying food insecurity in US using
complex survey samples. These challenges include 1) ambiguity in what food
insecurity measures compared to more traditional measures in poverty,
hunger, or malnutrition, 2) selection bias by neglecting transitional
housings or emergency shelters in household surveys, 3) lack of
generalization of inference theories for statistical models to complex
survey settings. For example, inference results of mixed effects model is
not well established for complex surveys.
I will then present ideas to address these challenges. I will demonstrate
these ideas using aforementioned survey data sets.
Except for some parts, the talk is for general audience and is not
intended to be technical.
Refreshments at 3:45
4:00pm–5:00pm, Monday, November 9, 2009 in LGRT 1634
Printable Announcement
|
|
| November 10 |
- Applied Mathematics and Computation Seminar
On Sobolev spaces with weights strongly degenerated on the boundary of a domain
Mahmud (Max) Ahmadov, Holyoke Community College
It is well know that differential equations and corresponding boundary value problems generate natural spaces where the problem should be considered. In this context Sobolev spaces and their properties (embedding, compactness, traces and etc. results) play an important role. However, if the equations have coefficients with degenerations or singularities Sobolev type spaces with weights are more suitable for them. Moreover, if weights have weak degenerations on the boundary of the domain the functions from weighted Sobolev spaces have traces. However, for strongly degenerated weights the functions from the corresponding Sobolev type spaces may have no boundary values in classic sense. In this talk we are going to discuss our vision of boundary values for functions from such type of spaces. We introduce the notion of a weighted boundary value and discuss its properties. Also, we consider an application of our results to one class of boundary value problems.
Refreshments at 3:45
4:00pm–5:00pm, Tuesday, November 10, 2009 in LGRT 1634
Printable Announcement
- Five College Number Theory Seminar
A Complete Arithmetic-Geometric Mean for E(C)
Eleanor Farrington, Boston University
The relation between elliptic curves and the arithmetic-geometric
mean (AGM) was discovered Lagrange and Gauss as a method of calculating
elliptic integrals. This classical approach is limited to cases where the elliptic
curve is given by a cubic equation with three real roots. We define an arithmetic-
geometric mean for all elliptic curves over the complex numbers and detail the
choices implicit in the classical construction. As time allows, we will look at how these
results translate into an AGM for Klein's Quartic Curve, a genus three curve
with split Jacobian.
Refreshments at 3:30pm in Seeley-Mudd 208
4:00pm–5:00pm, Tuesday, November 10, 2009 in Seeley-Mudd 207, Amherst College
Printable Announcement
|
|
| November 11: Veterans Day |
|
|
| November 13 |
- TWIGS
What is a modular form?
Paul Gunnells
1:30pm–2:30pm, Friday, November 13, 2009 in LGRT 1634
Printable Announcement
- Reading Seminar in Algebraic Geometry
Reconstruction problem in mirror symmetry, II
Jenia Tevelev, UMass
2:50pm–3:45pm, Friday, November 13, 2009 in LGRT 1634
Printable Announcement
- Valley Geometry Seminar
Spaces of hyperelliptic curves with simple singularities
Maksym Fedorchuk, Columbia
The space of n-pointed smooth rational curves can be compactified to
Hassett's space of weighted pointed stable curves. Different choices
of weights lead to different compactifications related by
well-understood birational morphisms. In this work in progress, we
study an analogous picture for a certain space of (pointed) smooth
hyperelliptic curves.
Refreshments at 3:45
4:00pm–5:00pm, Friday, November 13, 2009 in LGRT 1634
Printable Announcement
|
|
| November 16 |
- Representation Theory
Faces of polytopes and Koszul algebras
Apoorva Khare, Yale University
Given a simple Lie algebra g and a finite-dimensional simple g-module
V, we study the category G of graded finite-dimensional modules of the
corresponding semidirect product Lie algebra. This framework includes
the truncated current Lie algebras as well as those associated to folding of
complex simple Lie algebras.
Given a face of the polytope formed by the weights of V, we introduce a
partial order on the simple objects in G. For certain finite subsets of the
affine weight lattice, we produce Koszul algebras of finite global dimension
equal to the number of weights of V which are on the face. This is joint work
with Vyjayanthi Chari and Tim Ridenour.
4:00pm–5:00pm, Monday, November 16, 2009 in LGRT 1322
Printable Announcement
|
|
| November 17 |
- Applied Mathematics and Computation Seminar
Reactant conversion for a simple reaction-diffusion system
Professor Renato Feres, Washington University, St. Louis
In the study of processes used in industrial catalysis,
a new type of chemical reactor, referred to as T.A.P devices
(for Temporal Analysis of Products), is gaining interest among
engineers. In T.A.P. experiments, chemical reactions
involving gases and metal catalysts are studied under
conditions of well-controled gas injection and transport.
The resulting system can be modeled by a very tractable reaction-diffusion
equation involving first order reaction,
which may be analyzed by analytic and stochastic methods.
The main problems posed are: how to determine
the yield of the reaction from information about the distribution
of catalyst inside the reactor; and how to extricate from the combined
effect of gas transport and reaction any useful information about
chemical kinetics, such as reaction constants.
I will present a number of results from undergraduate
research by two recent math graduates at Washington University.
Refreshments at 3:45
4:00pm–5:00pm, Tuesday, November 17, 2009 in LGRT 1634
Printable Announcement
- Five College Number Theory Seminar
Vojta's conjecture on some rational varieties
Yu Yasufuku, CUNY
Vojta's conjecture is a deep conjecture in Diophantine geometry, implying
for example the Mordell conjecture (Faltings' theorem) and the Bombieri-Lang
conjecture. In this talk, I will show some cases of the conjecture and
discuss their arithmetic consequences (such as to properties of GCD's). Moreover, I
will talk about some connections with the abc conjecture and arithmetic
dynamics.
Refreshments at 3:30pm in Seeley-Mudd 208
4:00pm–5:00pm, Tuesday, November 17, 2009 in Seeley-Mudd 207, Amherst College
Printable Announcement
|
|
| November 18 |
- Mathematical Physics Seminar
Elliptic functions in cosmology
Jennie D'Ambroise, University of Massachusetts at Amherst
In general, Einstein's gravitational field equations of the theory of general relativity cannot be solved exactly. One case in which exact solutions are possible is the Friedmann-Lema^itre-Robertson-Walker (FLRW) model, in which one assumes that on large scales our current universe is homogeneous and isotropic. We will show that the resulting equations have solutions in terms of elliptic functions, which are the simplest of non-elementary functions and are known to appear in many branches of physics. In particular we will write these solutions in terms of Jacobi or Weierstrass elliptic functions, and in some cases also show an equivalent expression in terms of theta functions.
2:30pm–3:30pm, Wednesday, November 18, 2009 in LGRT 1033
Printable Announcement
|
|
| November 19 |
- TWIGS
What is a billiard?
HongKun Zhang
1:30pm–2:30pm, Thursday, November 19, 2009 in LGRT 1634
Printable Announcement
- Colloquium
Effective divisors on moduli spaces of curves
Jenia Tevelev, UMass-Amherst
The main theme will be an interplay between global birational geometry of moduli spaces of curves
and existence of special line bundles on individual curves, the so-called "Brill-Noether loci".
I will review the classical Harris-Mumford story in high genus and then explain my recent results
(joint with Ana-Maria Castravet) which turn this theory on its head for curves of genus zero with punctures.
The talk is intended for a general audience and will be accessible to graduate students.
Refreshments at 3:45
4:00pm–5:00pm, Thursday, November 19, 2009 in LGRT 1634
Printable Announcement
|
|
| November 20 |
- Reading Seminar in Algebraic Geometry
How to glue a K3 surface from flat pieces
Paul Hacking, UMass
We describe the Gross-Siebert construction of a K3 surface from a
integral affine structure on the 2-sphere using a combination of toric
methods and gluing corrections coming from the singularities via an
amazing "scattering" procedure.
2:50pm–3:45pm, Friday, November 20, 2009 in LGRT 1634
Printable Announcement
- Valley Geometry Seminar
Maps of toric varieties in homogeneous coordinates
Jarek Buczynski, Texas A&M University
The Cox ring provides a coordinate system on a toric variety analogous
to the homogeneous coordinate ring of projective space. This allows to
relatively easily construct and describe subvarieties in toric varieties
by giving equations (analogously to homogeneous equations in projective
space), or to describe sheaves by giving graded modules. Rational maps
between projective spaces are described using polynomials in the
coordinate ring. In our work we generalise the description of maps to
toric varieties and we provide a unified description of maps between
toric varieties in terms of their homogeneous coordinates. The maps in
consideration do not necessarily preserve the toric structure.
Introducing roots of polynomials is necessary even in the simplest examples.
(Joint work with Gavin Brown.)
Refreshments at 3:45
4:00pm–5:00pm, Friday, November 20, 2009 in LGRT 1634
Printable Announcement
|
|
| November 23 |
- Representation Theory
Twisted geometric Satake correspondence
Ryan Reich, Harvard
Geometric Satake correspondence is a way to construct from a reductive group
G its Langlands dual group G*.
(One can think of it as a deep generalization of duality of vector spaces.)
This is a bases of the geometric approach to ``Langlands program'' which is
a unifying view on much of
Number Theory, Representation Theory, Algebraic Geometry and more recently
also some Quantum Field Theory.
The ``twisted'' version is a recent development which extends the scope of
Langlands program.
4:00pm–5:00pm, Monday, November 23, 2009 in LGRT 1234
Note special room
Printable Announcement
- Statistics and Probability Seminar
Forecasting with Hidden Markov Models
Daniel W. Chambers , Mathematics Department, Boston College
A hidden Markov model (HMM) consists of two random processes: a state sequence X_1, X_2, . . . and an observation sequence Y_1, Y_2 , . . . The state sequence is unknown (hidden), while the observation sequence is seen. The state sequence is a Markov chain and, at each time t, the observation Y_t depends on the state of the system- that is, the value of X_t . Hidden Markov models saw early use in speech recognition, but have seen applications in many other settings, including modeling ion channels, genetic sequences, and seismological activity.
We will review HMM’s, including parameter estimation algorithms, and then give a straightforward extension that allows us to forecast future observations, given past observations. That is, we will give the (calculable) density of Y_t+k, conditional on the values of Y_1 , . . . , Y_t for any k ≥ 1. We will give two examples: (1) the “occasionally dishonest casino” of Durbin
et al. (Biological Sequence Analysis), and (2) forecasting mainshock earthquake activity in
southern California (joint work with John Ebel, Alan Kafka, and Jenny Baglivo).
Refreshments at 3:45
4:00pm–5:00pm, Monday, November 23, 2009 in LGRT 1634
Printable Announcement
|
|
| November 24 |
- Five College Number Theory Seminar
On the low-lying zeros of Dedekind zeta functions attached to cubic number fields
Andrew Yang, Dartmouth College
We study the distribution of low-lying zeros of Dedekind zeta
functions attached to cubic number fields, in the sense of the Katz-Sarnak
philosophy, using the work of Davenport and Heilbronn on counting cubic
number fields, as well as recent work of Belabas, Bhargava, and Pomerance,
on error terms in Davenport and Heilbronn's counts. In accordance with the
predictions of the Katz-Sarnak philosophy, we find that the distribution of
low-lying zeros predicts a symplectic symmetry type for the family of
Dedekind zeta functions of cubic number fields.
Refreshments at 3:30pm in Seeley-Mudd 208
4:00pm–5:00pm, Tuesday, November 24, 2009 in Seeley-Mudd 207, Amherst College
Printable Announcement
|
|
|
| November 26: Thanksgiving |
|
| November 27: Thanksgiving |
|
| 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
|
|
| 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
|
|
| 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
|
|
|
| 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
Geometer 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
|
|
