|
|
Spring 2007
Colloquium
Speaker: Yanqiu Wang (Purdue University)
Time: Tuesday, January 16, 2007 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Different from the displacement/velocity-pressure formulation,
the mixed formulation for elasticity and Navier-Stokes problems
involves stress as a fundamental unknown. In this talk, we will
discuss the stress-displacement formulation for elasticity problems
and the pseudostress-velocity formulation for Navier-Stokes equations.
We shall cover the following subjects: the advantages and
disadvantages of the mixed formulation, the finite element
discretization, the error estimate and fast iterative solvers.
One essential step in developing efficient numerical methods based
on the mixed formulation is to construct fast iterative solvers.
Two types of preconditioners, the multigrid method and the
domain decomposition method, are considered. Theoretical analysis
of their convergence rates, which depends on the understanding
of the H(div) problem, will be presented.
This talk covers the work supervised by my Ph.D. advisor,
Prof. Joseph E. Pasciak, and the work done in collaboration
with Prof. Zhiqiang Cai.
|
Colloquium
Speaker: X. San Liang (Courant Institute)
Time: Thursday, January 18, 2007 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We put the concept of information transfer on a rigorous footing and establish
for it a formalism with causality faithfully represented. In a dynamical system
with many components,information transfer is a mechanism controlling
the marginal entropy evolution of the target component. It is
measured by the rate of entropy thus transferred, which is obtained
through freezing the source component instantaneously, and comparing
the entropy increases between the original system and the so modified
system. The resulting transfer measure possesses a property of
unidirectionalism or transfer asymmetry as emphasized by Scrheiber
(2000). Connections to classical formalisms are explored and
applications presented. We find that, in the context of the baker
transformation, there is always information
flowing from the stretching direction to the folding direction, while
no transfer occurs in the opposite direction; we also find that,
within the Henon map system, the transfer from the quadratic
component to the linear component is of a simple form as expected on
physical grounds. Application to a two-mode (four-dimensional)
truncated Burgers-Hopf system reveals more interesting results. No
significant information exchange is identified between the four
components, save for a transfer from the cosine direction of mode 2
to the sine direction of mode 1. This transfer occurs continuously
and at a nearly constant rate. The present work is expected to have
applications in many applied fields, such as neuroscience and
atmosphere-ocean science.
Key words: information transfer, causality, entropy evolution, baker
transformation,
Henon map, truncated Burgers-Hopf system
|
Colloquium
Speaker: Ulrike Riemenschneider (Physical Oceanography Department, Woods Hole Oceanographic Institution)
Time: Tuesday, January 23, 2007 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Topographically controlled flows (also referred to as
'hydraulically controlled') occur where ocean basins are separated by
shallow and narrow channels, which limit the exchange of water masses
between the basins. Two-layer rotating exchange flows through
channels of rectangular cross-section are modeled using
semi-geostrophic, zero potential vorticity theory. For a given
channel cross-section the full range of possible flow states is
considered. The interface always has a uniform slope across the
channel, but may separate from one or both of the side walls to
attach to the upper or lower boundary. The flow may be subcritical,
critical or supercritical. These different states are identified in
a pseudo-Froude number plane analogous to that developed by Armi
(1986) for non-rotating flows. An example of a sub-maximal exchange
is considered. The exchange flux is determined as a function of the
channel geometry, the strength of rotation and the difference in
Bernoulli potential between the two layers.
Riemenschneider, U., Smeed, D. A. and Killworth, P. D., 2005, Theory
of Two-Layer Hydraulic Exchange Flows with Rotation, Journal of Fluid
Mechanics, 545, 373-395.
|
Logic Seminar
Speaker: Carl Jockusch (University of Illinois)
Time: Wednesday, January 24, 2007 at 3:00 pm
Place: MSB 118 (University of Connecticut)
Abstract: This is joint work with John Chisholm, Jennifer Chubb,
Valentina Harizanov, Denis Hirschfeldt, Timothy McNicholl, and Sarah
Pingrey. We study the weak truth-table spectra of relations on
computable models. A basic result is that $K$ is not wtt-reducible to
the $omega$-part of any computable linear ordering of order-type
$omega + omega^*$. Further, we show that there is a low c.e. set
$C$ which is not wtt-reducible to any element of any countable
$Pi^0_1$ subset of $2^omega$, and hence is not wtt-reducible to any
initial segment of any scattered computable linear order. Kolmogorov
complexity is used to greatly simplify the original proof of this
result.
Comments: Note unusual time and location!
|
S.I.G.M.A. Seminar
Speaker: Keith Conrad (University of Connecticut)
Time: Wednesday, January 24, 2007 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Elliptic Curves are basic objects of interest in complex analysis,
algebraic geometry, and number theory.
We will explain what they are, some of their basic properties, and
how they arise in studying
some questions that don't even appear to be about elliptic curves
directly.
|
UConn Math Club
Speaker: Keith Conrad (University of Connecticut)
Time: Wednesday, January 24, 2007 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: The standard trigonometric functions are connected with
the geometry of the unit circle and are periodic.
We will look at functions which play a similar
role for a lemniscate (the sideways figure 8).
There are some similarities between circular and lemniscatic
trig functions, and also some important differences, especially
when we try to make sense of things using complex numbers.
Comments: Free Refreshments
|
Colloquium
Speaker: Dmitriy Leykekhman (Department of Computational and Applied Mathematics, Rice University)
Time: Thursday, January 25, 2007 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The Finite Element Method (FEM) is a popular technique to solve partial
differential equations (PDEs) numerically. In this talk, I will briefly
introduce the FEM for a model problem and review basic energy norm
estimates
for the error between the exact solution of the PDE and its FEM
approximation.
For many applications and for the development of adaptive FEMs
these energy norm error estimates are of limited use, however.
Instead, one often needs pointwise error estimates, which are much more
difficult to obtain. In the second part of this talk, I will describe
how pointwise error estimates are constructed for the model problem
as well as for some more complex problems, and I will outline a few
applications of pointwise error estimates.
|
Colloquium
Speaker: Xia Chen (University of Tennesee, Knoxville)
Time: Monday, January 29, 2007 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Moment method has been used to establish the weak convergence among the local
and intersection local times since the remarkable work by Darling and Kac (1957). In this
case the power of the moment is often fixed. However, much less has been explored on the
high moment asymptotics, where the power of the moment tends to infinity. The study
in this direction is motivated by the needs in investigating large deviations. In this talk,
I will speak on some recent development in the high moment method for the local times
and intersection local times related to Brownian motions and random walks.
|
Logic Seminar
Speaker: Rehana Patel (St. John's University)
Time: Monday, January 29, 2007 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: I will discuss a family of countable graphs with a forbidden subgraph: the family of existentially complete countably universal (K_l+K_3)--free graphs U_l, l > 2, K_l+K_3 being the graph on l+2 vertices consisting of a K_l and a triangle that share exactly one vertex. This family was first described by Cherlin, Shelah and Shi. I will locate the positions of the theories of the graphs U_l in Shelah's SOP_n hierarchy, showing that they each have SOP_3 but not SOP_4. In doing so, I will give a general condition on a complete first order theory T in a finite relational language that links the failure of SOP_4 for T with local finiteness and free amalgamation properties of algebraic closure in models of T.
|
Colloquium
Speaker: Luke Rogers (Cornell University)
Time: Tuesday, January 30, 2007 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: An elementary but surprisingly useful tool for investigating and
understanding the structure of signals (functions) is a phase-plane
portrait, which is the mathematical analogue of a musical score. I will
survey some features and applications of this representation and explain
why the Fourier multipliers corresponding to the wave and Schroedinger
operators preserve certain phase-space properties.
|
S.I.G.M.A. Seminar
Speaker: Reed Solomon (University of Connecticut)
Time: Wednesday, January 31, 2007 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Ramsey's Theorem for countable graphs says that any
countably infinite graph contains an infinite subgraph which is
either completely connected or completely disconnected. In this
talk, we will look at this theorem (and other "regularity" results)
as well as some simple applications of it. (Except for some brief
side remarks, there will be no logic in this talk!)
|
UConn Math Club
Speaker: Audrey Giesler (Teach for America)
Time: Wednesday, January 31, 2007 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: While the U.S. ranks first in gross domestic product,
it ranks 21st among the 25 top industrialized nations in the world in
eighth grade math scores.
Half of the high school seniors from low-income communities
won't graduate from high school.
Those who do graduate will, on average, read and do math at the level of
eighth graders from high-income communities.
This is our nation's most pressing problem.
But it doesn't have to be this way. Math students taught by a teacher who
majored in math outperform their peers by one full grade level.
We will talk about how recent college graduates can help solve this
problem both in the short and long-term, while continuing to pursue their
long-term career goals. More specifically, we'll talk about how math
and science majors are uniquely positioned to make an even greater impact
than most.
Comments: Free Refreshments
Additional Comments: USG funded
|
Colloquium
Speaker: Ionel Popescu (Northwestern)
Time: Thursday, February 1, 2007 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We discuss the interplay between differential geometry and probability. From the probabilistic standpoint one of the most important constructions on manifolds is the Brownian motion. Using this, one can represent heat kernels and analyze them via Feynman-Kac type formulae. This combined with an idea of Witten leads to a proof of Morse inequalities and some extensions. We also discuss the so called Witten-Helffer-Sjostrand theory from the probabilistic perspective.
|
Colloquium
Speaker: Lea Popovic (Cornell University)
Time: Tuesday, February 6, 2007 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: A reaction network is a chemical system involving multiple reactions and
chemical species. The simplest stochastic model for a network treats the
system as a continuous time Markov chain whose state is a vector giving
the number of molecules of each species present with each reaction modeled
as a possible transition for the state. In classical chemistry, systems
are so large that stochastic fluctuations are irrelevant and reaction
networks are modeled with systems of ordinary differential equations.
Interest in modeling chemical reactions within biological cells has led to
renewed interest in stochastic models, since the number of molecules
involved, at least for some of the species, may be sufficiently small that
the deterministic model does not provide a good representation of the
behavior of the system. Modeling is complicated by the fact that some
species may be present in much greater abundance than others. In addition,
the rate constants may vary over several orders of magnitude. With these
two issues in mind, we consider approaches to the approximation of the
stochastic models that take the multiscale nature of the system into
account.
|
UConn Math Club
Speaker: Masha Gordina (University of Connecticut)
Time: Wednesday, February 7, 2007 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Brownian motion was originally observed by Robert Brown, who
was examining pollen grains suspended in water under a microscope.
This is an example of a random or stochastic process, which has found many
applications: from describing the random erratic movement of molecules
to the behavior of financial markets. In 1905,
Einstein made a detailed study of Brownian motion in which he
postulated certain properties (axioms) that should hold. In 1923,
Norbert Wiener showed how to construct mathematically
a random function W(t)
giving the “position” of the molecules at time t
which satisfied Einstein's axioms.
We will talk about the fascinating history of Brownian motion and
its applications.
Comments: Free Refreshments
|
Colloquium
Speaker: Wei Zhu (Courant Institute)
Time: Thursday, February 8, 2007 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: In this talk, I will discuss two related pieces of work. In the first, I study "contour
completion" --- a task performed with relative ease by our visual system --- as a feature extraction problem in image processing. I will discuss a level set method based variational model, its analytical structure and then present our simulational results. I will also discuss my current work in visual neuroscience, in which I have constructed a neuronal network model of primary visual cortex, and used this model to study important functions in visual perception such as orientation and spatial frequency tuning.
|
Colloquium
UConn Math Club
Speaker: Matt Cecil (University of Connecticut)
Time: Monday, February 12, 2007 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: A stochastic matrix is a matrix whose columns represent the probability
that a given system will change from one state to another. Associated to
each stochastic matrix is a steady-state vector, which indicates the
system's behavior “in the long run.”
A nice application of these concepts
is Google’s innovative page rank algorithm. I’ll introduce the
mathematics of stochastic matrices and show how they can be applied in
this example and others. A basic knowledge of linear algebra would be
helpful.
Comments: Free Refreshments
|
Colloquium
Speaker: Kai Chen (University of Waterloo, Department of Statistics and Actuarial Science)
Time: Tuesday, February 13, 2007 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The Defined Benefit (DB) underpin Defined Contribution hybrid pension plan offers an attractive combination of benefit security and upside potential for pension plan members, and offers cost containment for employers, whilst still ensuring the provision of adequate equitable benefits. In this paper the DB underpin guarantee is valued as a financial option, within the traditional funding paradigms ofactuarial science. Assuming fixed interest rates, and assuming that salaries can be treated as a tradable asset, contribution rates are developed for the Entry Age Normal, Projected Unit Credit and Traditional Unit Credit funding methods. In addition, for the accruals methods, we demonstrate the implied hedging strategy. The traditional unit credit approach shows promise as a funding method in terms of average costs and in the incidence of costs, on average. However, the volatility in the resulting contribution rate is substantial.
|
Colloquium
Colloquium
Speaker: Yvonne Chueh (Central Washington University)
Time: Thursday, February 15, 2007 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Efficient stochastic modeling for insurance business can be achieved by effective sampling of the stochastic economic (risk) scenarios to reduce run time. There are several techniques to select representative scenarios for such purposes, but the Relative Present Value method and the Significance method are two of the most effective and used by the actuarial practitioners (and they were developed at UConn!!). To more effectively capture the tail distribution and to allow advanced model outcome analysis, we propose to apply continuously mixed parametric probability density curves to fit the tails produced by a small sample-run distribution. The idea, although simple, involves repeated use of optimizations and improper integrals. This presentation will introduce ALM (asset/liability model) and use representative scenarios to model variable annuities. Furthermore, ASEM model outcome distribution is used to test MLE parametric fittings. Due to the time-consuming computations, we offer two software engineering products SALMS (for representative scenarios) and AMOOF (mixed parametric density fitting) to implement algorithms that run 1024 times faster than spreadsheet visual basic programs. The value of the programs lies both in the originality of the development, and in actuarial or insurance modeling applications for the purposes of capital determination, reserve setting, risk analysis, and pricing.
|
PDE and Image Analysis Seminar
Speaker: Feng Zhou (East China Normal University)
Time: Monday, February 19, 2007 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
|
Logic Seminar
Speaker: Russell Miller (Queens College CUNY)
Time: Monday, February 19, 2007 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: The functions on omega computable in finite time have been well studied, and their computations can be represented either by Turing machines or by register machines. We consider a related question: what happens when we extend the computation time and/or the available memory to allow infinite ordinals as well? This topic has attracted increasing interest in recent years, particularly from set theorists. Different definitions of the infinite-time machines are possible, and it is not obvious, for instance, whether the functions computable in time alpha by a Turing machine are the same as those computable in time alpha by a register machine. We will offer several natural models of infinite-time computation, comparing them and examining basic questions about what sort of degree structure arises from them. We will also consider the complexity of functions on omega computable by such machines.
|
Mathematics Education
Speaker: Michelle Manes (Brown University)
Time: Wednesday, February 21, 2007 at 3:00 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Teachers know the dreaded question, "when will I ever need to know
this?" Many adults claim they never use the algebra they learned in
high school, and they are probably right. These problems stem from
seeing mathematics as a bag of facts. For most students, the real
utility of mathematics lies in developing the habits of mind that
allow one to look at the world through a mathematical lens. This view
has implications for curriculum design, both in the choice of
curricular topics and in how they are treated in the classroom. I will
discuss the background of this habits of mind perspective in my own
work on middle and secondary mathematics curricula. The talk will
include explication of these mathematical habits of mind, as well as
examples from curricula and stories from my own teaching to explore
how the idea plays out in classrooms.
|
S.I.G.M.A. Seminar
Speaker: Tom Peters (University of Connecticut)
Time: Wednesday, February 21, 2007 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The talk will consider these questions and present my answers:
What is computational topology?
Why is it of contemporary interest? (specifically for animation)
How do `pure' topology & `applied' computation mix?
How will this appear in a Fall07 graduate course?
No specific mathematical background is presumed -- just interest.
The talk will be self-contained and any `proof' will be `by picture'.
|
UConn Math Club
Speaker: Michelle Manes (Brown)
Time: Wednesday, February 21, 2007 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: In this talk, we'll define what a dynamical system is, and what it means for a dynamical system to behave chaotically. We'll look in detail at what seems at first like a silly example of a chaotic dynamical system. Then we'll see why it's not such a silly example after all, because it allows us to prove many other dynamical systems are chaotic.
“Chaos theory says two things. First, that complex systems like weather have an underlying order. Second, the reverse of that ? that simple systems can produce complex behavior”. - Ian Malcolm from Jurassic Park
Comments: Free Refreshments
Additional Comments: USG funded
|
Analysis and Probability Seminar
Speaker: Sasha Teplyaev (University of Connecticut)
Time: Friday, February 23, 2007 at 3:00 pm
Place: MSB 403 (UConn - Storrs)
Abstract: We define and study intrinsic first order derivatives on post critically finite fractals and prove differentiability almost everywhere for certain classes of smooth functions. We apply our results to extend the "geography is destiny" principle of Strichartz to these cases. Our main tool is the Furstenberg-Kesten theory of products of random matrices. This is a joint work with Anders Pelander of Uppsala University (Sweden).
Comments: The talk will be accessible to graduate students.
|
Algebra Seminar
Speaker: Brian Conrad (Michigan/Columbia)
Time: Monday, February 26, 2007 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: It is an old theorem of Tate that an abelian variety over a finite field
admits a CM lifting to characteristic 0 if we permit a finite extension of the finite
field followed by an isogeny. It is natural to ask if extension of the base field
and an isogeny are necessary. Oort showed that isogeny cannot be avoided,
even if we allow extension of the field. But if we fix the finite field and permit
isogenies (over that field) then it turns out that there are two natural
ways to formulate the lifting question. Under one formulation
a lift is always possible (with no isogeny), but under the other we exhibit
an obstruction to lifting even with isogeny permitted.
Interestingly, this
obstruction turns out to be the only one.
After discussing the formulation of the basic definitions and questions, we state the main results
and illustrate them with some concrete examples. If time permits we will say a bit
about the proofs.
|
UConn Math Club
Speaker: Brian Conrad (Michigan/Columbia)
Time: Monday, February 26, 2007 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: A famous theorem of Lagrange says that every positive integer is a sum of 4
perfect squares (some may be 0). More subtle is sums of 3
squares, because not every positive integer has that form.
For example, 7, 15, and more generally numbers of the form
8k+7 are not a sum of 3 squares (of integers).
Often in number theory, the problem of studying integer solutions to an
equation lies much deeper than the study of rational solutions
(because rational solutions are more susceptible to geometric methods).
Amazingly, the 3 square problem is the same
for rational numbers as it is for integers:
if an integer is a sum of 3 rational squares
then it is automatically also a sum of 3 integral squares! After
discussing a little history, we will show the nifty argument that proves this
fact.
Comments: Free Refreshments
Additional Comments: Partially funded by USG
|
Algebra Seminar
Speaker: Daniel Davis (Wesleyan University)
Time: Tuesday, February 27, 2007 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Given a topological group G and a topological
G-module M, the continuous cohomology of
G is computed from a cochain complex
defined, for example, by Tate. Closely related to
this cohomology group is the cohomology
of another complex that arises naturally in chromatic
homotopy theory. If G is an automorphism group
of a certain formal group law and the G-module is
a point-set Morava module (a type of spectrum),
then this second complex is of particular interest.
|
Geometry Seminar
Speaker: Ed Taylor (Weslyan University)
Time: Tuesday, February 27, 2007 at 4:30 pm
Place: MSB 219 (UConn - Storrs)
Abstract: We describe an analytic form of symmetry that many,
but not all, hyperbolic manifolds possess. Owing to rigidity
in dimensions three and above there is a fairly complete topological
and analytic picture that we can describe. The situation in
dimension two is more mysterious.
|
Analysis and Probability Seminar
UConn Math Club
Speaker: Many Speakers
Time: Saturday, March 3, 2007 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: On March 3rd, the first Saturday of our spring break,
the UConn Math Club is chartering a bus to
Providence to attend the Symposium for Undergraduates in
the Mathematical Sciences at Brown.
Speakers will come from Brown, CUNY, Harvard, Princeton, Tufts, UConn,
and UMass.
Our bus will leave UConn at 7:30 AM on Mar. 3 and will return
that evening no later than 10:30 PM. If you are interested in
joining us, please register at http://www.math.brown.edu/sums/,
where there is further information about the
talks, and also send an email to uconnmathclub@gmail.com
by February 26th, providing your name and a phone number.
(Students in the residence halls have to vacate on Mar. 2,
so if you are in the residence halls and do not have
alternate local housing,
please indicate this in your email and we will try to
find temporary accommodations near UConn on the night before and
after the symposium.)
Comments: Banquet Dinner
Additional Comments: USG funded
|
PDE and Image Analysis Seminar
Speaker: Sarah Frey (University of Connecticut)
Time: Monday, March 12, 2007 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract:
TITLE: Nonlinear Elastic Deformations of a Sphere (under
Self-Gravitational and Rotational Forces)
ABSTRACT: A derivation for the equations governing the nonlinear elastic
deformation of a homogeneous isotropic sphere will be presented. The
resulting system of PDEs can be reduced to a highly nonlinear system of
ODEs with nonlocal integral terms. A numerical scheme for solving these
equations under self-gravitational and rotational body forces will be
described.
|
Analysis and Probability Seminar
Speaker: Vladimir Koltchinskii (Georgia Institute of Technology)
Time: Tuesday, March 13, 2007 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The Dantzig Selector is a new method of estimation of
regression function
based on its representation as (or approximation by) a linear
combination
of given functions from a large dictionary. The method was recently
introduced by Emmanuel Candes and Terry Tao and it consists of
minimizing
the ell_1-norm of the vector of coefficients subject to constraints that
the gradient of the L_2 empirical loss belongs to the ell_{infty}-ball
around 0 of certain radius, which can be solved using linear
programming.
We will discuss several inequalities that go further than initial results
of Candes and Tao in showing (in the case of models with random design)
that this method performs in a nearly optimal way when the regression
function has a reasonably good sparse approximation in the dictionary.
Comments: UNUSUAL DAY, TIME, AND ROOM
Additional Comments: Analysis and Probability Seminar/Stochastic Seminar
|
Geometry Seminar
Speaker: Christina Sormani (CUNY)
Time: Tuesday, March 13, 2007 at 4:30 pm
Place: MSB 219 (UConn - Storrs)
Abstract: The covering spectrum of a Riemannian manifold was first defined
by Sormani-Wei in 2004. We will review the definition of this spectrum which roughly measures the sizes of holes in the space using a special sequence of covering spaces called delta covers. On compact spaces, we proved the covering spectrum is a subset of the (1/2) length spectrum and is determined by the marked length spectrum. This is not true on complete noncompact manifolds. In recent work with Wei, we have begun to prove related weaker theorems. To capture more information about complete manifolds we have defined two other spectra: the cut-off covering
spectrum and the rescaled covering spectrum. The rescaled covering
spectrum has some interesting properties on spaces like the one sheeted hyperboloid which are asymptotic to cones.
|
Analysis and Probability Seminar
Speaker: Richard Dudley (MIT)
Time: Tuesday, March 13, 2007 at 4:35 pm
Place: MSB 118 (UConn - Storrs)
Abstract: ``Fast speed'' will mean that the empirical process converges to
its Gaussian limit at a rate of $(log n)^k/sqrt{n}$ for some
$k$. Koml'os, Major and Tusn'ady (KMT) in 1975 gave such a rate
for the classical empirical process based on 1-dimensional
distribution functions, with $k=1$. Some years later, detailed
proofs were published. This talk will be mainly about a paper
of Tusn'ady (1977) stating a fast rate with $k=2$ for the
process based on the two-dimensional empirical distribution function for
the uniform distribution on the unit square. Tusn'ady
only briefly sketches a proof, based on adapting parts of the
KMT paper which itself is sketchy. Part of the talk will be
to begin an effort to fill in the proof of Tusn'ady's statement.
Another part will consider classes of functions, for
example, functions with uniformly bounded second derivatives.
Comments: UNUSUAL DAY, TIME, AND ROOM
Additional Comments: Stochastic Seminar: this talk continues a previous talk given at MIT on this subject and is unrelated to V. Koltchinskii's talk.
|
Mathematics Education
Speaker: Megan Staples (University of Connecticut)
Time: Wednesday, March 14, 2007 at 3:00 pm
Place: MSB 319 (UConn - Storrs)
Abstract: One important goal of the mathematics education research community is improving K-12 mathematics teaching and learning. In this talk, I’ll offer an overview of 7 “unsolved problems” in K-12 mathematics education in an effort to represent the current state of the field. I will then briefly discuss three research projects in which I have participated to demonstrate some of the approaches and methodologies being used to make progress on these issues. Finally, I point to possible avenues for future research, including those that might productively be undertaken at UConn.
|
UConn Math Club
Speaker: David Pollack (Wesleyan)
Time: Wednesday, March 14, 2007 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Given any real number, we can find rational numbers that
approximate it as closely as we might like. For example, if we want to
approximate ? to within 1/10000 we might take the rational
number
3.1415 = 31415/10000, which we get from the decimal expansion.
This uses a fairly large numerator and denominator.
Interestingly, there are better approximations to ? with much
smaller
denominators: 333/106 ? 3.1415904... approximates ? to better
than 1/12000 and 355/113 ? 3.1415929... approximates ? to better
than 1/350000.
We'll talk about how to find such unexpectedly good
approximations (using continued fractions), and about how well we can hope to
do this (theorems of Dirichlet, Thue, Siegel, and Roth).
Comments: Free Refreshments
Additional Comments: USG funded
|
Colloquium
Speaker: Andrew Sommese (Notre Dame)
Time: Thursday, March 15, 2007 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Numerical methods based on homotopy continuation have for
thirty years been an efficient method to find isolated solutions of
systems of polynomials arising in applications. In recent years the
methods for computing isolated solutions, enriched by ideas from
complex variable theory and algebraic geometry, have progressed into
an robust methods for ``computing and manipulating'' positive
dimensional components of the solution set of a polynomial system.
In this talk, aimed at a general audience of engineers and
scientists, an overview of this work (starting with a discussion of
the classical work on isolated solutions) will be given. Some
motivating examples of polynomial systems from applications will be
presented.
Additional Comments: Joint colloquium with CSE, tea at 3:30 in faculty lounge MSB
|
Logic Seminar
Speaker: Rodrigo Pelaez (University of Barcelona)
Time: Monday, March 19, 2007 at 4:00 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: I will introduce the notion of G-compactness and present some of the main results
obtained in [1], [2] and [3]. Then I'll show a new G-compact theory T such that
for a specific set of parameters A, T(A) is not G-compact. This givies a negative
answer to the question of wether G-compactness is preserved when enlarging the
language by constant symbols, contrary to the case of such other properties like
stability and simplicity. Finally, I will leave an open question related to the existence
of a non G-compact theory without the strict order property.
[1] E. Casanovas, D. Lascar, A. Pillay, M. Ziegler. Galois Groups of first order theories. JML 1 (2001).
[2] D. Lascar, A. Pillay. Hyperimaginaries and automorphisms groups. JSL 66 (2001).
[3] L. Newelski. The diameter of a Lascar strong type. Fundamenta Mathematicae 176 (2003).
Additional Comments: Note early starting time!
|
Algebra Seminar
Speaker: David Hayes (University of Massachusetts, Amherst)
Time: Tuesday, March 20, 2007 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: In 1935, Carlitz published "On certain functions connected with
polynomials over a finite field." This is the inauspicious title he
chose
for a paper that gave the first explicit construction of the maximal
abelian
extension of Fq(x). Actually, he constructed all but the part of the
class field theory attached to the infinite place of Fq(x). He showed
in
essence that the class field theory of Fq(x) could be generated by a
Drinfeld module (!) long before the 1974 paper of Drinfeld. This first
Drinfeld module is now called the Carlitz module. I will explain how he
developed this theory. I will also mention some recent applications of
quantum theory to algebraic function fields over Fq(x).
|
S.I.G.M.A. Seminar
Speaker: Keith Conrad (University of Connecticut)
Time: Wednesday, March 21, 2007 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The ergodic theorem describes situations where "the time average equals the space average" in a dynamical system. After defining ergodicity and stating the ergodic theorem, we will look at
some examples of ergodic dynamical systems. The talk is meant to be accessible to students currently taking Math 303.
|
UConn Math Club
Speaker: Changfeng Gui (University of Connecticut)
Time: Wednesday, March 21, 2007 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Nowadays imaging techniques such as MRI and CT are commonly used
for medical procedures and research. The huge amount of medical images
of different modalities demand the development of
automatic or semi-automatic, accurate and efficient processing techniques.
The digitalization of information and the easy access of fast computers
make the task of image processing widely possible.
Among many image
processing procedures, image denoising, image deblurring and
image segmentation
are fundamental tasks.
The goal of image denoising is to get rid of certain noises, image debluring
is to restored sharpness of image boundaries, and image segmentation is
to decompose an image into regions of
special interest.
In this talk the basic mathematics used for image processing tasks
will be discussed.
In particular, modern level set methods using partial differential equations
for
medical image processing will be introduced. These methods have been
successfully applied to
synthetic and real images of different modalities, including
optical, MR, and ultrasound images.
Comments: Free Refreshments
|
Analysis and Probability Seminar
Speaker: Jim Bridgeman (University of Connecticut)
Time: Friday, March 23, 2007 at 3:00 pm
Place: MSB 411 (UConn - Storrs)
Abstract: In a talk to the seminar last spring I described a stochastic interest rate
model developed on pragmatic grounds in my actuarial practice for Monte
Carlo stress testing of financial institution stability. This talk will
report on subsequent work resulting in a closed form integration of the
stochastic process involved for both the continuous and the discrete cases.
Exposure of partial results to actuaries and financial engineers last summer
suggests that the process has desireable features not seen before in
applications. I'll be looking for feedback on where the process might fit in
the theoretical landscape.
Comments: The talk will be accessible to graduate students.
|
Logic Seminar
Speaker: Chris Hardin (Smith College)
Time: Monday, March 26, 2007 at 5:15 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: Suppose that there are infinitely many people in a room. Colored hats are placed on their heads, such that everyone can see the hats of the other players. The players must attempt to guess the colors of their own hats. If they are allowed to strategize in advance, but cannot communicate after the hats are placed, how well can they do? It turns out that there is a finite-error strategy (a strategy guaranteeing that only finitely many players guess wrong); this is essentially due to Yuval Gabay and Michael O'Connor. More generally, one can put an arbitrary binary relation on the set of players that specifies which players can see which hats, leading to a harder question: For which of these binary relations does a finite-error strategy exist? We will present an answer to this question in the case of countably many players, and a partial solution in the case of uncountably many players. We will also look at a closely related result: There is a strategy which, given an arbitary function f from the reals into the reals, attempts to guess f(t) from the values of f(x) for x < t, and these guesses are only wrong countably often. This raises interesting questions regarding the philosophical problem of induction. (Joint work with Alan Taylor of Union College.)
Comments: NOTE LATE STARTING TIME
|
Analysis and Probability Seminar
Colloquium
Speaker: Bruce Driver (UCSD)
Time: Tuesday, March 27, 2007 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: This talk will start with a review of how the quantum mechanical
harmonic
oscillator leads to the "Segal - Bargmann" and "Fock space" transforms.
These transforms involve spaces of square integrable (relative to a
certain Gaussian measures) holomorphic functions on $mathbb{C}^{N}.$
We will then go on to explain a number of the more recent extensions
of this theory to the situation where $mathbb{C}^{N}$ is replaced by
a general complex Lie group, G. Ultimately, we will give a local
characterization of the spaces of (hypoelliptic)
heat kernel" square integrable holomorphic
functions on G. Much of the recent material described in this talk
is joint work with Leonard Gross and Laurent Saloff-Coste. (No prior
knowledge of the Segal - Bargmann or Fock space isomorphism will be
assumed.)
click for pdf-file of abstract
Comments: Special Colloquium
|
Mathematics Education
Speaker: Chuck Vinsonhaler (University of Connecticut)
Time: Wednesday, March 28, 2007 at 3:00 pm
Place: MSB 319 (UConn - Storrs)
Abstract: I will begin by discussing a fascinating study by DeFranco on the problem-solving expertise of PhD mathematicians. I will then add some observations, anecdotes and musings of my own. We will solve some problems, no calculators allowed.
|
S.I.G.M.A. Seminar
Speaker: Richard Brualdi (University of Wisconsin at Madison)
Time: Wednesday, March 28, 2007 at 5:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: I graduated with a Bachelor's degree from UConn in 1960. After
receiving a PhD from Syracuse University in 1964, I have spent 42 years as a mathematics professor at the University of Wisconsin in Madison. I will tell you something about (1) my professional life as a faculty member and mathematician, (2) my PhD students, and (3) my recent mathematics specifically, a Bruhat order on matrices of 0's and 1's.
|
UConn Math Club
Speaker: Nick Proudfoot (Columbia)
Time: Wednesday, March 28, 2007 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: I will give an introduction to the combinatorics associated with collections
of hyperplanes in a vector space. Along the way I'll talk about braids,
colorings of graphs, and infinite wedges of cheese
Comments: Free Refreshments
Additional Comments: USG funded
|
Colloquium
Speaker: Richard Brualdi (University of Wisconsin)
Time: Thursday, March 29, 2007 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: I will discuss certain ideas related to the diagonals and diagonal structure of a square matrix, with connections to the polytope of doubly stochastic matrices, its simplex faces, ray-nonsingularity, determinantal regions, digraphs, and bipartite graphs.
|
S.I.G.M.A. Seminar
Speaker: Keith Conrad (University of Connecticut)
Time: Thursday, March 29, 2007 at 12:30 am
Place: MSB 118 (UConn - Storrs)
Abstract: The set of complex numbers with positive imaginary part
plays a central role in
several areas of mathematics, both historically and today. Some
examples will be
provided to indicate why the upper half-plane shows up all over the
place.
|
Logic Seminar
Speaker: Barbara Csima (University of Waterloo)
Time: Monday, April 2, 2007 at 4:45 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We examine the effectiveness of classical theorems on Fraisse
limits, and also analyze the Turing degrees of relations on
computable Fraisse limits. As an application, we show that
the countable atomless Boolean algebra is spectrally universal
(roughly speaking, the degree spectra of each countable BA is the
same as the degree spectra of it's relation as embedded into the
countable atomless BA). Joint work with V. S. Harizanov, R. G.
Miller, and A. Montalban.
|
Mathematics Education
Speaker: Thomas Judson (Harvard University)
Time: Wednesday, April 4, 2007 at 3:00 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Is high school calculus in Japan different than high school calculus
in the U.S? How do high school calculus students from both countries
compare? We examined and interviewed above average high school
calculus students from Japan and the United States in order to
determine any differences in their conceptual understanding of
calculus and their ability to use algebra to solve traditional
calculus problems. We will discuss the Japanese high school
curriculum, some of our findings from the study, and the problems
that we encountered in doing a cross-cultural investigation of
Japanese and American calculus students.
|
S.I.G.M.A. Seminar
Speaker: Tom Roby (University of Connecticut)
Time: Wednesday, April 4, 2007 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Partially ordered sets (posets) arise naturally in a variety
of mathematical contexts. We will discuss some classical examples from
combinatorics whose Down and Up operators satisfy particularly nice
relations. This will allow us to give simple proofs of interesting
enumerative identities (many of which also have representation theoretic
interpretations) involving totally ordered subsets in these posets. We
assume no background, so this talk will be accessible to all graduate
students.
|
UConn Math Club
Speaker: Rich Schwartz (Brown)
Time: Wednesday, April 4, 2007 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Outer billiards is a simple dynamical system in which a
point “orbits” around a convex shape in the plane. This system was
introduced by B.H. Neumann in the 1950s and then popularized by
J. Moser in the 1970s as a toy model for celestial mechanics. All
along, one of the central questions has been whether or not one
can find a shape and a starting point, so that this point “escapes
to infinity” as it orbits around. This question is vaguely related
to the question of whether or not the orbit of the Earth around
the sun is stable: will the Earth eventually wander away from
the sun?
In this talk I will explain how outer billiards works.
I will also explain my recent solution to the basic problem I
mentioned. My solution relates the problem to certain kinds of
self-similar tilings. During the talk I will demonstrate my
program, Billiard King, the graphical user interface I built
and used to solve the problem of unbounded orbits.
Comments: Free Refreshments
Additional Comments: USG funded
|
Colloquium
Speaker: Xiuxiong Chen (University of Wisconsin, Madison)
Time: Thursday, April 5, 2007 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The critical points of Energy functional E_1 is the so called Kahler Einstein metric. The Kahler Einstein equation can be reduced to a 2nd order Monge Ampere equation. In this talk, we
want to prove a small energy lemma for this functional E_1: The gradient flow of E_1 is
a second order parabolic flow and we proved that if E_1 is sufficiently small, with some
other topological assumption, then this second order parabolic flow converges to a KE metric.
|
Analysis and Probability Seminar
Speaker: Tai Melcher (University of Virginia)
Time: Friday, April 6, 2007 at 3:00 pm
Place: MSB 411 (UConn - Storrs)
Abstract:
We will discuss the existence of ``$L^p$-type'' gradient estimates for second order differential operators. For certain values of $p$, these estimates imply logarithmic Sobolev and Poincar'e inequalities for the associated heat kernel. These inequalities have broad application and
have been studied and used extensively in the fields of mathematical physics, global analysis, and geometry. ``$L^p$-type'' gradient estimates are known for elliptic operators, but the method for obtaining them fails when the operator is not elliptic. In particular, such estimates have been unknown for hypoelliptic operators.
Malliavin calculus methods transfer the problem to one of determining certain infinite dimensional estimates. Malliavin calculus is a differential calculus on infinite-dimensional path space. In this talk, I will give a brief introduction to Malliavin calculus, and use it to show that ``$L^p$-type'' gradient estimates hold under some conditions.
|
UConn Math Club
Speaker: Keith Conrad (University of Connecticut)
Time: Monday, April 9, 2007 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: The formula
is one of the most important improper integral calculations
in mathematics.
It is usually first met in probability theory, where
it leads to the normal distribution.
I have collected eight different proofs of this basic result
and we'll see how many I can get through before time runs out.
Comments: Free Refreshments
|
Algebra Seminar
Speaker: Bill Wickless (University of Connecticut)
Time: Tuesday, April 10, 2007 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: A left R-module A is faithful if M tensored over R with A is nonzero for all finitely generated right R-modules M. A is fully faithful if the same claim holds without the finitely generated restriction on the right module M. Using simple ring theory, I'll show that, if R is Artinian, faithful implies fully faithful. Then I'll give an application to abelian groups. The application involves the standard trick of going from the endomorphism ring R = E(A) of an abelian group A to the finite dimensional rational algebra QR.
|
Geometry Seminar
Speaker: Kristen Selke (University of Connecticut)
Time: Tuesday, April 10, 2007 at 4:30 pm
Place: MSB 219 (UConn - Storrs)
Abstract: The Kauffman skein module is a 3-manifold
invariant. We will give an overview of its computation for the
complement of certain torus knots. Then, we will use the skein
module to show that the noncommutative A-ideal (a generalization
of the A-polynomial) is non-trivial.
|
Analysis and Probability Seminar
Speaker: Steffen Winter (University of Karlsruhe)
Time: Friday, April 13, 2007 at 3:00 pm
Place: MSB 411 (UConn - Storrs)
Abstract: Curvature measures have been used in convex geometry and differential geometry to describe certain geometric properties of a set with respect to different dimensions. For example: volume, surface area, mean width, and Euler characteristic are all quantities that can be ascribed to a set, and can also be localized to neighbourhoods of a set by means of an interpretation as measures. In my talk, I will describe these ideas and how they may be extended to a broad class of self-similar fractal sets by using the correct scaling exponent. As a result, we obtain a notion of fractal Euler characteristic and other fractal curvature measures.
Comments: The talk will be accessible for graduate students.
|
Analysis and Probability Seminar
Speaker: Erin Pearse (Cornell University)
Time: Friday, April 13, 2007 at 3:30 pm
Place: MSB 411 (UConn - Storrs)
Abstract: Complex dimensions are a generalization of the real-valued notions of dimension introduced by Hausdorff and Minkowski. I will discuss basic aspects of the theory as it has been introduced by Lapidus and van Frankenhuijsen for fractal subsets of the line. Additional, I will describe how certain tilings may be used to extend the theory of complex dimensions to higher dimensional self-similar sets. As time permits, we'll see some connections with convex geometry; in particular, curvature measures and the Steiner polynomial for the volume of an epsilon-neighbourhood.
Comments: The talk will be accessible for graduate students.
|
Logic Seminar
Speaker: Yun Lu (Wesleyan University)
Time: Monday, April 16, 2007 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: Let M be a countably categorical structure, homogeneous for a
finite relational language. A reduct of M corresponds, up to
bi-interpretability, to a closed subgroup of Sym(M) containing
Aut(M). In this talk, I will describe classifications of reducts given
by Higman, Thomas and Bennett. I will also present my own results
classifying reducts of the random bipartite graph and the random
bipartite graph having more than two cross types.
|
Algebra Seminar
Speaker: Keith Conrad (University of Connecticut)
Time: Tuesday, April 17, 2007 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We will continue the theme from the seminar talk on March 20 and indicate some additional
applications.
|
Geometry Seminar
Speaker: Ning Khamsemanan (University of Connecticut)
Time: Tuesday, April 17, 2007 at 4:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Nielsen theory is concerned with finding the minimum number of
solutions to certain equations involving maps, minimized among all the
maps in a given homotopy class. The classical setting for the subject is
Nielsen fixed point theory which studies a map f: X --> X on a compact ANR
and seeks to find the minimum number MF[f] of solutions to the fixed point
equation g(x) = x among all maps g homotopic to f.
Comments: Note: special room
|
Colloquium
Speaker: William Dunham (Muhlenberg College (Koehler Professor of Mathematics))
Time: Wednesday, April 18, 2007 at 4:00 pm
Place: IMS 20 (UConn - Storrs)
Abstract: This year we celebrate the 300th birthday of Leonhard Euler (1707-1783), one of history’s greatest mathematicians. The remarkable quality of his achievement is matched only by the equally remarkable quantity of his achievement – indeed, Euler’s collected works contain over 25,000 pages of pure and applied mathematics!
In this talk, we sketch his life and mention a few of his contributions to the various branches of mathematics. Then we examine a pair of Eulerian results: one evaluating a particularly difficult integral and the other establishing what is now known as “Euler’s identity.” Such clever arguments should give a sense of this towering mathematical genius
NOTE: This talk should be accessible to any student of calculus or beyond.
Comments: Awards Day. Tea 3:00 MSB 120, Ceremony 3:30 IMS 20, Talk 4:00 IMS 20
|
UConn Math Club
Speaker: Bill Dunham (Muhlenberg College)
Time: Wednesday, April 18, 2007 at 4:00 pm
Place: IMS 20 (UConn - Storrs)
Abstract: This year is the 300th birthday of Leonhard Euler (1707-1783),
one of history's greatest mathematicians. The remarkable quality of his
achievements is matched only by the equally remarkable quantity of his
achievements — Euler's collected works contain over 25,000 pages of
pure and applied mathematics!
We will sketch Euler's life, mention a few of his contributions,
and then examine a pair of Eulerian
results: evaluating a particularly difficult integral and
establishing what is now known as “Euler's identity.”
Such clever arguments
should give a sense of this towering mathematical genius
NOTE: This talk should be accessible to any student of calculus or beyond.
Comments: Free Refreshments at 3 PM in MSB 120
|
S.I.G.M.A. Seminar
Speaker: Birgit Kaufmann (University of Connecticut)
Time: Wednesday, April 18, 2007 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: In this talk, I will explain the mathematics of a particular type of
quantum spin chains. They can
be written in terms of generators of Hecke algebras whose representation
theory can be used
to gain insight into the spectrum of the corresponding Hamiltonian.
Furthermore, there is an interesting connection between quantum spin
chains and
reaction-diffusion models which are one-dimensional models describing a
system
of hopping and interacting particles.
This connection allows to compute non-equilibrium properties
of reaction-diffusion models in terms of eigenvalues of the quantum spin
chain.
There are many other connections to different areas of mathematics and
physics,
like random walks, directed percolation, surface growth, etc.
|
Analysis and Probability Seminar
Speaker: Adam Bowers (University of Connecticut)
Time: Friday, April 20, 2007 at 3:00 pm
Place: MSB 411 (UConn - Storrs)
Abstract:
In 1956 Alexandre Grothendieck published "Resume de la theorie
metrique des produits tensoriels topologiques," in which his
"theoreme fondamental de la theorie metrique des produits tensoriels"
first appeared. In 1968 Lindenstrauss and Pelczynski reformulated
it as a matrix inequality. We will generalize the inequality to a
continuous version by means of bimeasures and multidimensional
measure theory.
|
Colloquium
Speaker: De Witt Sumners (Florida State University)
Time: Monday, April 23, 2007 at 4:00 pm
Place: ITEB 336 (UConn - Storrs)
Abstract: Cellular DNA is a long, thread-like molecule with remarkably complex topology. Enzymes that manipulate the geometry and topology of cellular DNA perform many important cellular processes (including segregation of daughter chromosomes, gene regulation, DNA repair, and generation of antibody diversity). Some enzymes pass DNA through itself via enzyme-bridged transient breaks in the DNA; other enzymes break the DNA apart and reconnect it to different ends. In the topological approach to enzymology, circular DNA is incubated with an enzyme, producing an enzyme signature in the form of DNA knots and links. By observing the changes in DNA geometry (supercoiling) and topology (knotting and linking) due to enzyme action, the enzyme binding and mechanism can often be characterized. This talk will discuss topological models for DNA strand passage and exchange, introducing the tangle model for analysis of DNA site-specific recombination experiments.
Comments: Special joint seminar with Computer Science. Special Day, Special Room!
Additional Comments: Poster pdf abstract
|
UConn Math Club
Speaker: Greg Huber (University of Connecticut)
Time: Monday, April 23, 2007 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: At a low level, the human brain is a bubbling soup of particles, and
yet on a loftier level, it houses complex networks of abstractions, the
most central being the one called
“I”. To understand the mysterious
emergence of an “I”
out of mere matter, a recent book by Hofstadter employs
the idea of strange loops.
I will explore this and related concepts, using
a wide range of analogies and examples.
Comments: Free Refreshments
|
Algebra Seminar
Speaker: Keir Lockridge (Wesleyan University)
Time: Tuesday, April 24, 2007 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: This is a report on joint work with Mark Hovey. The stable category of spectra, arising in algebraic topology via a weakening of the homotopy equivalence relation, is an example of a more general phenomenon known as a triangulated category. Algebraic examples of triangulated categories include the derived category of a ring (a setting for homological algebra) and the stable category of modules over a group ring (arising in representation theory). In this talk, I will introduce triangulated categories and discuss when the category of projective modules over a graded ring admits a triangulation. The existence of such triangulations is related to whether certain functors on triangulated categories act faithfully.
|
Geometry Seminar
Speaker: Andy Haas (University of Connecticut)
Time: Tuesday, April 24, 2007 at 4:30 pm
Place: MSB 219 (UConn - Storrs)
Abstract: In this talk we shall derive several results that
describe the rate at which a geodesic makes excusions into and
out of a cusp on a finite area hyperbolic surface and relate them
to approximation with respect to the orbit of infinity for an
associated Fuchsian group. This provides proofs of several important
theorems from metric diophantine approximation in the context of
Fuchsian groups. It also illuminates the classical theory and
produces new estimates on the rate of growth of the partial quotients
in the continued fraction expansion of a generic real number.
|
Analysis and Probability Seminar
Speaker: Hannes Leeb (Yale University)
Time: Friday, April 27, 2007 at 3:00 pm
Place: MSB 411 (UConn - Storrs)
Abstract: We study the problem of selecting a model that performs well for out-of-sample prediction. We do not assume that any of the candidate models under consideration is correct.
Our analysis is based on explicit finite-sample results. Our analysis is non-standard because we consider a situation where the sample size is small relative to the complexity of the data-generating process. Also, we allow for the case where the number of candidate models is (much) larger than sample size.
For Gaussian data, we show under minimal assumptions that model selection based on generalized cross validation or the S_p criterion performs well in such situations, uniformly over large regions in parameter space.
We also show that the performance of other model selectors, including AIC and BIC, can be anything from satisfactory or mildly suboptimal to completely unreasonable, depending on unknown parameters.
|
Analysis and Probability Seminar
Speaker: Evarist Gine (University of Connecticut)
Time: Thursday, May 3, 2007 at 3:30 pm
Place: MSB 117 (UConn - Storrs)
Abstract: A very simple way of optimally estimating the integrated square of a density with unknown but relatively
weak smoothness properties is proposed. Lepski's method is adapted to the situation at hand. The treatment of the bias with elementary Fourier analytic techniques, and that of the variance with sharp U-statistic bounds are the main features. This is joint work with Richard Nickl.
Comments: UNUSUAL DAY, TIME, AND ROOM
Additional Comments: Analysis and Probability Seminar/Stochastic Seminar
|
Analysis and Probability Seminar
Speaker: Richard Dudley (MIT)
Time: Thursday, May 3, 2007 at 4:30 pm
Place: MSB 117 (UConn - Storrs)
Abstract: A note by Tusnady (1977) states a theorem on fast speed of
convergence in the uniform central limit theorem for two-dimensional
empirical distribution functions for the uniform measure on the unit
square. In the proof, a section of the paper by KMT (1975) is referred
to in what seems to be a crucial way, so that section will be considered.
Comments: UNUSUAL DAY, TIME, AND ROOM
Additional Comments: Stochastic Seminar
|
|
|
University of Connecticut | 
