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Spring 2006
Colloquium
Speaker: Seok-Jin Kang (Seoul National University)
Time: Tuesday, January 24, 2006 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: In this talk, we review some of the recent developments in combinatorial representation theory in connection with combinatorics of Young walls. The main theme will be the crystal basis theory for quantum affine algebras.
Comments: The colloquium is in conjunction with the Algebra Seminar.
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Algebra Seminar
Speaker: Seok-Jin Kang (Seoul National University)
Time: Tuesday, January 24, 2006 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: In this talk, we review some of the recent developments in combinatorial representation theory in connection with combinatorics of Young walls. The main theme will be the crystal basis theory for quantum affine algebras.
Comments: This is actually a colloquium, but is in conjunction with the algebra seminar.
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Geometry Seminar
Speaker: Tara Holm (University of Connecticut)
Time: Tuesday, January 24, 2006 at 4:00 pm
Place: MSB 117 (UConn - Storrs)
Abstract: After a brief introduction to symplectic geometry, I will focus on group actions, moment maps and localization. These techniques can be used to understand the topology of projective space, Grassmannians and flag varieties. This lecture will assume no background in symplectic geometry, and will be driven by examples.
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UConn Math Club
Speaker: Keith Conrad (University of Connecticut)
Time: Wednesday, January 25, 2006 at 5:30 pm
Place: MSB 315 (UConn - Storrs)
Abstract: The polygon below has vertices on an integer grid: it is a “lattice polygon”. What is its area? One approach is to add and subtract areas of rectangles and triangles surrounding the polygon. Pick’s theorem is another method, based on counting lattice points inside the polygon and on its boundary. The polygon has 5 lattice points inside it and 13 lattice points on its boundary. From these numbers alone, Pick’s theorem says that the area is 10 ½.
We will discuss Pick’s theorem and some applications. This is a good enrichment activity for future teachers.
Comments: Free Refreshments
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Colloquium
Speaker: Matthew Leingang (Harvard University)
Time: Thursday, January 26, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: I. Symmetric Space Valued Moment Maps:
For a compact Lie group G, we discuss three examples of G-spaces which can
serve as the target of a moment map. Abstracting the work of Alekseev,
Meinrenken, and Malkin, we cast these theories into a unified framework.
II. Advantages, Challenges, and Dividends of Online Placement:
Harvard first-year students come from very diverse mathematical backgrounds,
and determining the proper first course for each student can be difficult.
The placement recommendations determined by our current pencil-and-paper
placement exam often do a poor job of predicting student success in a course
(as determined by final course grades). To better achieve this and other
placement objectives, we developed the Mathematical Online Placement Exam
(MOPE). Key features include a flexible database of questions to build
exams; detailed, topic-specific feedback; and the opportunity to take each
exam more than once. We will discuss the extensions of such a project in
determining how best to place students and maintain student satisfaction.
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Colloquium
Speaker: Sarah Frey (California State University, East Bay)
Time: Tuesday, January 31, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: I. Planetary tides and Europa: In 1911, A.E.H. Love published a linear elastic model for the tidal
amplitude of a uniform, compressible, self-gravitating body. Recent
numerical evaluations of the solution to his governing equations reveal
the surprising result that there exists material parameter values
(density, rigidity, and compressibility) for which infinitesimal tide
raisers can raise tides of arbitrary height. We investigate these
singularities and discuss how planetary tidal models can help predict
the presence of life on Europa, one of the moons of Jupiter.
II. Tutor training case study: California State University, East Bay has recently begun an
innovative, interdisciplinary tutor training course requirement for its
tutors at the university's Student Center for Academic
Achievement. Tutors from across disciplines take a quarter long course
with topics ranging from learning styles to special needs students to
tutoring session outlines. We discuss content presented in this course
and present a preliminary assesment of the impact of this training on
tutoring quality.
Comments: Tuesday talk
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S.I.G.M.A. Seminar
Speaker: Reed Solomon (University of Connecticut)
Time: Wednesday, February 1, 2006 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: In mathematics, it is often useful to view algebraic
objects from a number of different viewpoints. In this talk, I will
use boolean algebras as an example of this phenomenon. It is not
hard to show that a boolean algebra is a subalgebra of a power set
algebra and that it is also the algebra of clopen subsets of a
boolean topological space. (This correspondence is called the Stone
Representation Theorem and we will sketch a proof of it.) Using the
Stone Representation Theorem, we will show that for any countable
boolean algebra, there is an associated tree such that the paths
through the tree are exactly the ultrafilters on the boolean algebra
(and vice versa). This correspondence leads to a number of nice
results about the difficulty of computing an ultrafilter on a boolean
algebra. You do not need any background in boolean algebras or logic
for this talk.
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UConn Math Club
Speaker: Stu Sidney (University of Connecticut)
Time: Wednesday, February 1, 2006 at 5:30 pm
Place: MSB 315 (UConn - Storrs)
Abstract: Two points determine a line and three points determine a circle.
How many points determine a square? a 3-4-5 right triangle? your
favorite plane curve or figure?
In fact, what do we mean by the question? While a circle
is determined by any three points on it,
it is not the case that any
set of (say) 100 points on a square determines it;
all the points could lie on one side, and then there would be
infinitely many squares passing through all of them. Our basic question,
carefully formulated, is this: given a simple closed plane curve C
(or other
plane figure), does it contain a finite point set E
such that if C? is any
curve similar to C
that passes through every point of E, then necessarily
C? = C?
Comments: Free Refreshments
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Colloquium
Speaker: Gustaff Jacobs (Brown University)
Time: Thursday, February 2, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: In the last decade high-order discontinuous Galerkin (DG) methods
have established themselves as effective methods for long time
integration of complex high-frequency wave-dominated continuum
problems. DG methods secure their geometric flexibility by using
fully unstructured grids, they can have arbitrary order of accuracy,
have inherent high frequency dissipation and have excellent stability
properties, while having virtually no dispersion errors.
I will present the development of DG methods for the simulation of
problems in the continuum/discrete or Eulerian/Lagrangian framework.
In this framework the governing continuum equations are solved on a
static grid, while individual particles are tracked using a
Lagrangian formulation. The focus is to carry over the favorable
aspects of the Eulerian DG method to the Eulerian/Lagrangian
framework, i.e. to develop efficient, high-order space and time
methods for moving particles, complex particle-boundary interactions,
and for coupled discrete phase and continuum phases. I will discuss
simulations with relevance to plasma dynamics and multi-phase flow
physics. In particular, I will present simulations of the Weibel
instability, magnetic reconnection, and the particle-laden turbulent
flow over a backward-facing step.
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Analysis and Probability Seminar
Speaker: Richard Bass (University of Connecticut)
Time: Friday, February 3, 2006 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Consider a symmetric Markov chain on the integer lattice in $d$ dimensions.
The chain has unbounded range if arbitrarily large jumps are possible.
I will discuss transition probability estimates, Harnack inequalities,
and central limit theorems. The central limit theorems involve
convergence of a sequence of symmetric Markov chains to diffusions
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Geometry Seminar
Speaker: Tara Holm (University of Connecticut)
Time: Tuesday, February 7, 2006 at 4:00 pm
Place: MSB 117 (UConn - Storrs)
Abstract: Continuing our foray into symplectic geometry, I will talk about quotients in this setting. This is an important way to construct new examples. We will explore the relationship between a symplectic manifold and its quotients in a variety of settings. This talk will be more or less independent from the first, and as before will be driven by examples.
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Colloquium
Speaker: Jung-Han Kimn (Louisiana State University)
Time: Tuesday, February 7, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Many important problems from current industrial and academic research,
including the numerical solution of partial differential equations,
generate extremely large data sets beyond the capacity of single-
processor
computers. Parallel computation on multiple-processor super computers is
therefore the key to increasing performance but efficient parallel
algorithms for
multiple-processor super computers with huge number of processors are
still needed.
Domain decomposition methods provide general flexible iterative
methods for solving such problems and are designed to take advantage of
parallel computers.
This talk gives a brief introduction to domain decomposition methods and
some of our theoretical and numerical results including their
applications
in interdisciplinary research.
Comments: Tuesday talk
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S.I.G.M.A. Seminar
Speaker: Joe Miller (University of Connecticut)
Time: Wednesday, February 8, 2006 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Consider two puzzles:
(1) Find periodic functions f(x) and g(x) on the reals such that f(x)
+ g(x) = x. (Of course, they cannot have the same period.)
(2) Find a two-coloring of the plane such that no arc is monochromatic.
Each puzzle has an easy solution using (an appropriate form of) the
axiom of choice (AC). But there is a difference: one of the puzzles
can be solved without AC while the other provably requires it. Our
discussion of these examples will lead us to consider -- in various
levels of detail -- set theory, independence results, and Baire
category. No previous knowledge of these topics will be assumed.
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Colloquium
Speaker: Jason Howald (John Carroll University)
Time: Thursday, February 9, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: I. Discovering whether the improper integral
∫f(x,y,z)-pdxdydz
is (locally) finite or infinite can be extremely difficult, depending on
the features of f and value of p. Using this question, we
will introduce multiplier ideals, and see two
cases (monomial ideals, and nondegenerate principal ideals) in which
the multiplier ideal can be directly calculated. We will briefly
discuss applications to optics, provided we can procure a wine glass.
II. This half of the talk will be much less scripted to encourage
two-way conversation. I will begin with a brief overview of my
experience in administration of teaching, tutoring, testing, and
placement efforts. Then I'll discuss how the Q-center can
strengthen its service to the greater learning network by improving
communication among faculty, tutors, and students, and producing
innovative tools of value to all three.
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Analysis and Probability Seminar
Speaker: Alexander Teplyaev (University of Connecticut)
Time: Friday, February 10, 2006 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We define sets with finitely ramified (but possibly post-critically
infinite) cell structures, which are generalizations of p.c.f.
self-similar sets introduced by Kigami and of fractafolds introduced by
Strichartz. In general, we do not assume even local self-similarity, and
allow countably many cells connected at each junction point. We prove that
for a resistance form that satisfies certain assumptions there exists a
weak Riemannian metric such that the energy can be expressed as the
integral of the norm squared of a weak gradient with respect to an energy
measure. Furthermore, we prove that if such a set can be homeomorphically
represented in harmonic coordinates, then for smooth functions the weak
gradient can be replaced by the usual gradient. We also prove a simple
formula for the energy measure Laplacian in harmonic coordinates.
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UConn Math Club
Speaker: Many Speakers
Time: Saturday, February 11, 2006 at 5:30 pm
Place: MSB 319 (Brown Univ.)
Abstract: On February 11th the UConn Math Club is chartering a bus to
Providence so we can attend the Symposium for Undergraduates in
the Mathematical Sciences (SUMS) at Brown University.
The talks at SUMS are targeted to undergraduates.
The speakers are
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Jeff Brock (Brown), mathematics
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Keith Conrad (UConn), mathematics
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Ian Dell’Antonio (Brown), astronomy
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Wendy Hagen-Bauer (Wellesley), astronomy
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Peter Schultz (Brown), geology
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Richard Schwartz (Brown), mathematics
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Maria Zuber (MIT), geophysics
There will be a conference banquet after the talks. The bus ride, the
conference, and the banquet are free, but you must
register in advance at the conference website
http://www.math.brown.edu/SUMS/index.html,
where you can find further information about the
talks.
The bus will be leaving UConn at 7:00 AM on Feb. 11 and will return to
campus that evening by 10:30 PM. If you are interested in
joining us, please send an email to uconnmathclub@gmail.com
by February 6th, providing your name and a phone number.
Comments: Free Refreshments
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Logic Seminar
Speaker: Carol Wood (Wesleyan University)
Time: Monday, February 13, 2006 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: We start with a brief introduction to the model theory of partial differential fields (with finitely many commuting derivations) of characteristic zero. Using results in a 1995 paper by Johnson, Reinhart and Rubel, we see that, unlike the one variable case, it is not possible in general to approximate solutions to certain partial differential equations via finite transcendence degree extensions.
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S.I.G.M.A. Seminar
Speaker: Lance Miller (University of Connecticut)
Time: Wednesday, February 15, 2006 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: This talk will be a review some recent resutls by Lauren Rose on determining the algebraic structure of modules of splines over polyhedral subdivision of regions in euclidean space. This determination was carried out by looking at a related module over the dual graph of the complex; called the Syzygy module, and determining its algebraic structure based on a decomposition of this graph into marked cycles. Definitions and concepts from algebra necessary for the talk will be reviewed.
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UConn Math Club
Speaker: Eric Sommers (UMass Amherst)
Time: Wednesday, February 15, 2006 at 5:30 pm
Place: MSB 315 (UConn - Storrs)
Abstract: The cube is an example of a regular solid in dimension three. There are 5
regular solids in dimension three, often called Platonic solids.
In four dimensions the situation becomes a little stranger.
In this talk, we show how to find the regular solids in dimensions three,
four, and five. We will also discuss the symmetry groups of
these solids, an idea which is valuable both in chemistry and throughout
mathematics.
Comments: Free Refreshments
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Analysis and Probability Seminar
Speaker: Jerry Neuwirth (University of Connecticut)
Time: Friday, February 17, 2006 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Some 250 years ago Euler found that the values of the Riemann Zeta function at the positive even integers are rational multiples of even powers of π. Euler was unable to evaluate the Zeta function at the positive odd integers, and conjectured that these should be irrational. Only a few years ago it was shown that ζ(3) is irrational.
In this talk I will present a method that gives a partial solution to Euler's problem, which strongly suggests that ζ(2n+1) = q(π)2n+1, where q is a rational number.
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Logic Seminar
Speaker: Russell Miller (Queens College)
Time: Monday, February 20, 2006 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: We present a survey of results and open questions on various
different notions of a emph{spectrum} which have been
investigated by computable model theorists. The two
best-known notions are the spectrum of a structure and
the spectrum of a relation on a computable structure.
In both cases, the idea is to use Turing degrees to
measure the complexity intrinsic to the structure or
the relation. We will review how model theory has
yielded new insights into computability theory, and
vice versa, by means of these concepts.
We also introduce a third notion, the automorphism
spectrum, which is the set of all Turing degrees of
nontrivial automorphisms of a fixed computable structure.
The intention is to measure the complexity of the
symmetries of the structure. This more recent concept is
the subject of current work by Harizanov, Morozov, and
the speaker, and we present certain early results.
An extra dimension to this investigation
lies in the possibility of composing two automorphisms
to get another; for structures and relations there is
no analogous operation. In some cases results on
automorphism spectra follow from or give rise to
results on other spectra. As an example, we will
show how our study of single-degree automorphism
spectra led to the first known example of
a structure whose spectrum contains exactly the high-n
Turing degrees (those degrees whose n-th jump
computes the (n+1)-st jump of the empty set).
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Colloquium
Colloquium
Speaker: Professor James Murray FRS (Membre de l'Institut de France, Oxford (em.), Univ. of Washington (em.))
Time: Wednesday, February 22, 2006 at 4:00 pm
Place: BSP 130 (UConn - Storrs)
Abstract: The prognosis for patients with brain tumours (gliomas) is grim.
Treatment protocols usually rely on general factors such as the type of
tumour, the grade, the position and so on. Besides these qualitative
features it would also seem important to base the prognosis on a
quantitative evaluation of the spatio-temporal infiltration of the
tumour, taking into account the anatomic site of the tumour as well as
the specificity of the treatment involved, such as radio- or
chemo-therapy or surgical intervention. I shall describe a simple
practical model, based on patient data and CT (computer tomography)
scans, to quantify the spatio-temporal growth of brain tumours. Even
with very early diagnosis, only those tumours with a low diffusion
coefficient and a rapid growth rate benefit (marginally) from a wide
resection (surgical removal). Surgical removals generally fail and we
suggest reasons why. We also suggest why tumour regrowth is often
multi-focal.
Using area measurements from CT scans, we estimate the parameters of the
model for individual patients. By including some of the detailed
anatomy of the brain, such as the white and grey matter distribution and
the relative cancer cell dispersal in each, we can show how the tumour
position is crucial for estimating survival times; these compare
remarkably closely to patient data. The model can also include the
effects of chemotherapy and resection therapy and I shall compare some
of the results with patient data. Among other things the spatio-temporal simulations
graphically show how difficult it is to decide on the volume to be treated
and suggest why such treatments have so little success.
Although still in the early stages, the modelling shows how it might be
possible to use a patient's past record to suggest specific treatment
protocols and calculate an index of treatment efficacy - predicted as
opposed to actual.
Comments: Joint with Dept of Molecular and Cellular Biology and Dept of Physiology and Neurobiology. Special Time and Special Place.
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S.I.G.M.A. Seminar
Speaker: Bjørn Kjos-Hanssen (University of Connecticut)
Time: Wednesday, February 22, 2006 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Can a robot use Google to boost its artificial intelligence? Paul Vitanyi
and others have developed a theory which explores this idea.
For example, by googling the words "horse", "whisperer", "telephone",
"horse whisperer" and "horse telephone" and counting the number of hits,
the robot could conclude: "A horse is more closely related to a whisperer
than to a telephone".
Their theory involves the mathematics of probability and computability, and
was recently reported on in New Scientist.
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UConn Math Club
Speaker: Mira Bernstein (Wellseley)
Time: Wednesday, February 22, 2006 at 5:30 pm
Place: MSB 315 (UConn - Storrs)
Abstract: Consider two games:
- (For two players) Start with several piles of pebbles. On her
turn, a player removes any number of pebbles from any one pile. Whoever
removes the last pebble wins. (This is a very famous game, called
Nim.)
-
(For N players) Each player is given a black or white hat,
randomly and with equal probability. Each player can see his teammates'
hats but not his own. At a signal from the judge, all the players
simultaneously guess their own hat colors; they are also allowed to pass
and guess nothing. If there is at least one correct guess and no incorrect
guesses among the players, the whole team gets a prize. Is there a
strategy the players can decide on in advance to maximize their chances of
winning? (Try it with N=3.)
The strategies for these games are closely
related to each other and to the theory of error-correcting codes.
We will see how the first game can be used to derive an optimal strategy
for the second one, and then discuss how game strategies in
general can lead to good codes.
Comments: Free Refreshments
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Colloquium
Speaker: Leonid Bunimovich (Georgia Tech)
Time: Friday, February 24, 2006 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The theory of open dynamical systems where orbits may disappear upon
reaching some region ("hole") in a phase space started to attract attention of mathematicians just recently. A natural reason for this is because it is harder in general to study open systems in comparison with closed dynamical systems, where a theory is rather well developed.
One of possible paths to explore in studies of open systems was recently suggested. Consider an open system with several "holes" and compare its behavior with the corresponding single hole system. The idea is that such comparison may shed a light on understanding dynamics of a closed system one gets by "patching" all the holes in the open system. This idea has also a lot of potential applications for the real world systems. Indeed,
in experimental studies researchers perform measurements outside a region of interest ("container") by e.g. measuring fluxes out the container.
It occured that already seemingly the simplest problem of this type,
namely the comparison of escape rates from a circle uniformly filled with particles with one and with two opposite holes, is equivalent to Riemann hypotheses (RH). There are several well known equivalent formulations of RH but this one seems to be the most unexpected
coming directly from a question arising in real experiments.
Despite this "experimental" flavour, the talk is going to be purely
mathematical with all necessary definitions provided.
Comments: This talk is on a FRIDAY at 3pm.
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Analysis and Probability Seminar
Speaker: Leonid Bunimovich (Georgia Tech)
Time: Friday, February 24, 2006 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The theory of open dynamical systems where orbits may disappear upon
reaching some region ("hole") in a phase space started to attract attention of mathematicians just recently. A natural reason for this is because it is harder in general to study open systems in comparison with closed dynamical systems, where a theory is rather well developed.
One of possible paths to explore in studies of open systems was recently suggested. Consider an open system with several "holes" and compare its behavior with the corresponding single hole system. The idea is that such comparison may shed a light on understanding dynamics of a closed system one gets by "patching" all the holes in the open system. This idea has also a lot of potential applications for the read world systems. Indeed,
in experimental studies researchers perform measurements outside a region of interest ("container") by e.g. measuring fluxes out the container.
It occured that already seemingly the simplest problem of this type,
namely the comparison of escape rates from a uniformly filled with particles circle with one and with two opposite holes is equivalent to Riemann hypotheses (RH). There are several well known equivalent formulations of RH but this one seems to be the most unexpected
coming directly from a question arised in real experiments.
Despite this "experimental" flavour, the talk is going to be purely
mathematical with all necessary definitions provided.
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Logic Seminar
Speaker: Walker White (Cornell University)
Time: Monday, February 27, 2006 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: Event systems are query processing systems applied to streaming data, and have a wide number of applications from protocol enforcement to XML processing. Event systems are able to process primitive events and compose them together to form new events, which are then added to the stream. To add them to the stream, we need some model for assigning time stamps to this new events. This is surprisingly difficult and most of the existing solutions result in bizarre and undesirable query behavior.
In this talk we will axiomatize the fundamental properties of event systems in attempt to identify an ideal time stamp model. We will discover that there is exactly one acceptable model (up to isomorphism), but that this model is difficult to implement in real time systems. By weakening one of our axioms, we will discover one additional model (up to isomorphism) which is possible to implement, and which is being incorporated into the streaming XML system developed at Cornell.
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Algebra Seminar
Geometry Seminar
Colloquium
Speaker: Friedrich Goetze (Universitaet Bielefeld)
Time: Wednesday, March 1, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract:
We shall describe an analytic approach to the so-called free
convolution of two (spectral)
measures, which can be viewed as the limiting spectrum of sums of two
random matrices of growing dimension whose spectra approximate these
measures, after they are rotated to a generic relative position.
The classical theory of convolution of probability measures and their
limit behavior by Gnedenko, Khintchin, Kolmogorov will be compared
to analogous results for free convolution.
Although there are many analogies, the decomposition of
measures exhibits surprising differences. Furthermore, we shall
discuss rates of convergence in the CLT for free convolutions.
This is joint work with G. Chistyakov.
Comments: This talk is on a Wednesday
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UConn Math Club
Speaker: Tom Weston (UMass Amherst)
Time: Wednesday, March 1, 2006 at 5:30 pm
Place: MSB 315 (UConn - Storrs)
Abstract: It is an old result of Euclid that there are infinitely many primes.
One way to refine this is to ask how the primes
are distributed in arithmetic progressions.
For example, there are three arithmetic progressions with
common difference 3:
1, 4, 7, 10, 13, 16, 19, 22, 25, …
2, 5, 8, 11, 14, 17, 20, 23, 26, …
3, 6, 9, 12, 15, 18, 21, 24, 27, …
Among the first 1,000,000 primes excluding 3,
the first progression contains
499829 primes and the second progression contains 500171 primes.
The primes are trying to be “equally distributed”.
The proof of results like this is quite different from
Euclid's relatively simple proof; it involves analytic techniques. In
this talk we will illustrate the ideas for arithmetic progressions
having common difference 3 (as above) and 5.
No background beyond second semester calculus will be required.
Comments: Free Refreshments
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Colloquium
Speaker: Dan Abramovich (Brown University)
Time: Thursday, March 2, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: This lecture is about combinatorial geometry inspired by
algebraic geometry.
A cornerstone of the classification of algebraic surfaces is:
"Every birational map of smooth projective surfaces is composed of a
sequence of blowings up followed by a sequence of blowings down."
What about higher dimensions?
I will present and discuss an embarrassingly simple and explicit
conjecture about stellar subdivisions of simplicial complexes. This
conjecture would imply the strongest relevant result for three-dimensional
algebraic manifolds in characteristic 0.
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Algebra Seminar
S.I.G.M.A. Seminar
Speaker: Eugene Spiegel (University of Connecticut)
Time: Wednesday, March 15, 2006 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The integral group ring isomorphism problem asks whether
two non-isomorphic finite groups can have isomorphic integral group
rings. The solution of this problem resisted the efforts of
researchers for over 60 years before it was solved in 2001. This
expository talk will present some of the main results obtained from
attempts at solving the problem. No mathematical background in this
area is necessary
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UConn Math Club
Speaker: David Pollack (Wesleyan)
Time: Wednesday, March 15, 2006 at 5:30 pm
Place: MSB 315 (UConn - Storrs)
Abstract: Factoring numbers, which was once a mathematical problem without
practical importance, is now recognized as a very
significant problem: it is closely connected to
the security of encrypted messages on the internet.
So how does one factor a number?
If it is small, say 119, you might proceed by
simply trying to divide by all the small primes in the hope of stumbling on
a divisor. This method becomes hopelessly inefficient if you are trying to
factor a larger number, such as 42680447189985041129249.
We will discuss several algorithms that allow one to factor large
numbers quickly,
culminating with the quadratic sieve which can factor numbers with
as many as 100 digits.
Comments: Free Refreshments
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Algebra Seminar
Geometry Seminar
Speaker: Marina Ville (Paris 7)
Time: Tuesday, March 21, 2006 at 4:00 pm
Place: MSB 117 (UConn - Storrs)
Abstract: There is a type of singularity of (real) surfaces in smooth manifolds which is more general than the branch points of complex curves and yet is far from being generic: the real branch points. In particulr these are the singular points of minimal surfaces.
We would like to describe some questions pertaining to these points: their relatons to knots, what happens when a sequence of smooth surfaces degenrates into a dsurface with a branch point?
We will focus exclusively on the case where the ambiant manifold is 4-dimansional: there is a partial simlarity with complex curves in complex surfaces and it is interesting to ask how far this similarity goes.
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S.I.G.M.A. Seminar
Speaker: Keith Conrad (University of Connecticut)
Time: Wednesday, March 22, 2006 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We will explain how Fourier series generalize to the
setting of functions on certain topological groups. It is an
interesting mixture of algebra, analysis, and topology. The audience should be familiar with concepts like dual spaces in linear algebra, integration with respect to a measure, and local compactness, but prior experience with classical Fourier analysis is not required. If time permits, we will explain how Fourier analysis on rather non-classical groups leads to a striking insight about the Riemann zeta-function.
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UConn Math Club
Speaker: Alexander Russell (University of Connecticut)
Time: Wednesday, March 22, 2006 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Ramsey theory formalizes the intuition that in any large enough
structure, however chaotic, there are regions of uniformity. Some early
theorems serve as good examples:
1. (van der Waerden) If the integers are colored (with a finite
collection of colors) then at least one color class contains arithmetic
progressions of arbitrary length.
2. (Schur) If the integers are colored (with a finite collection
of colors) then at least one color class contains a set
{x, y, z} such that x + y = z.
3. (Ramsey) For any positive integer k,
all sufficiently large graphs contain
either a complete graph on k
vertices or an independent set on k
vertices.
In this talk, I'll describe a proof of Ramsey's theorem and state one of
the cornerstones of the theory: the celebrated Hales-Jewett theorem.
Finally, I'll discuss a nonconstructive but powerful method for
producing large “Ramsey graphs”−
graphs that contain no small cliques or independent sets.
Comments: Free Refreshments
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Colloquium
Speaker: Andrei Zelevinsky (Northeastern University)
Time: Thursday, March 23, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Cluster algebras (introduced jointly with S.Fomin) have found
applications in a diverse variety of settings: total positivity,
representation theory, quiver representations, Teichmuller theory,
Poisson geometry, discrete dynamical systems, tropical geometry, and
algebraic combinatorics. The structure of a cluster algebra is
encoded by a family of Laurent polynomials expressing distinguished
generators (cluster variables) in terms of an "initial cluster"
consisting of finitely many algebraically independent cluster
variables. We will discuss an interpretation of these Laurent
polynomials (due to F.Chapoton and P.Caldero) in terms of the geometry of Grassmannians of quiver representations.
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Logic Seminar
Speaker: Philip Scowcroft (Wesleyan University)
Time: Monday, March 27, 2006 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: By Belegradek's definition, an ordered Abelian group G is poly-regular just in case it is the union of a well-ordered continuous chain S of convex subgroups, starting with {0} and ending with G, in which successive quotients are regular (and so elementarily equivalent to Archimedean ordered groups). Each poly-regular G has a shortest corresponding chain S, whose length is called the (poly-regular) rank of G. This talk will describe first-order theories, of poly-regular groups of infinite rank, resembling the theories of poly-regular groups of finite rank analyzed by Belegradek.
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Algebra Seminar
S.I.G.M.A. Seminar
Speaker: Joint Discussion (University of Connecticut)
Time: Wednesday, March 29, 2006 at 4:00 pm
Place: Dodd building Auditorium (UConn - Storrs)
Abstract: Artist Bernar Venet will discuss how art
led him to mathematics. Then Mathematician Daina
Taimina will discuss how mathematics led her to
art. A catered reception will follow in the Fine
Arts building.
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UConn Math Club
Speaker: Daina Taimina (Cornell)
Time: Wednesday, March 29, 2006 at 4:00 pm
Place: Dodd Auditorium 319 (UConn - Storrs)
Abstract: Artist Bernar Venet will discuss how art
led him to mathematics. Then mathematician
Daina Taimina will discuss how mathematics led
her to art.
A catered reception will follow in the Fine Arts building.
A related exhibit, called Math Counts, is open until April 7th
in the School of Fine Arts. See http://www.sfa.uconn.edu/cag/cag.html
for more information.
Comments: Free Refreshments
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Colloquium
Speaker: Tom Braden (UMass)
Time: Thursday, March 30, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract:
Cauchy's rigidity theorem states that a convex polytope with triangular
faces in ${mathbf R}^3$ is rigid, meaning that if its edges are bars
of a fixed length, the only motions of the resulting framework come from
rigid motions of three-dimensional space. In fact, it is even
infinitesimally rigid, meaning that the lengths of the bars need
only be fixed to first order.
In three dimensions, removing a single bar from the framework will
cause it to flex. In higher dimensions, frameworks of simplicial
polytopes are still rigid, but in general some bars can be removed
without losing rigidity. The number of removable edges is one of a
series of important combinatorial invariants of polytopes. For
polytopes with rational vertices, these numbers have another beautiful
interpretation as dimensions of certain cohomology groups of toric
varieties. This has given a fruitful connection between combinatorics
and algebraic geometry, where ideas from algebraic geometry have been
used to motivate and prove theorems in combinatorics and vice-versa.
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Analysis and Probability Seminar
Speaker: Mordecay Zippin (The Hebrew University)
Time: Friday, March 31, 2006 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
Comments: Prof. Zippin is currently visiting UConn.
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Logic Seminar
Speaker: Rebecca Weber (Dartmouth)
Time: Monday, April 3, 2006 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: The work to be discussed is part of a larger program to connect
computability-theoretic properties of Turing degrees to definability
within the lattice of degrees. It is joint with Rod Downey and Noam
Greenberg, both at Victoria University of Wellington, New Zealand.
Every nondistributive lattice contains either M_5 ("1-3-1") or N_5
("pentagon") as a sublattice. The particular question at hand is where in
the upper semi-lattice of c.e. Turing degrees these lattices do or do not
embed. For the pentagon the question was tackled by Ambos-Spies and
Fejer; the 1-3-1 is the topic of the present work.
The 1-3-1 is composed of five elements: a top, a bottom, and three
incomparable points between. A "critical triple" is a trio of Turing
degrees which acts very much like the middle of a 1-3-1, though it is
open whether the existence of a critical triple guarantees the existence
of a 1-3-1. In this work, we obtained a complete characterization of the
c.e. Turing degrees which bound critical triples.
I will sketch some background and discuss the main ideas of the proofs
involved. My goal is that the talk be accessible to graduate students.
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Geometry Seminar
Speaker: Bruce Kleiner (Yale University)
Time: Tuesday, April 4, 2006 at 4:00 pm
Place: MSB 117 (UConn - Storrs)
Abstract: The uniformization theorem says that any
Riemannian metric on the 2-sphere admits a conformal
parametrization by the standard 2-sphere. Motivation
from geometric group theory, geometric topology,
and rigidity theory led to the formulation of analogous
"uniformization" (or geometrization) problems for metric
spaces. I will discuss the background and some of the
recent developments in the area.
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Colloquium
Speaker: Bruce Kleiner (Yale)
Time: Tuesday, April 4, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The uniformization theorem says that any Riemannian metric on the 2-sphere admits a conformal parametrization by the standard 2-sphere. Motivation from geometric group theory, geometric topology, and rigidity theory led to the formulation of analogous "uniformization" (or geometrization) problems for metric spaces. I will discuss the background and some of the recent developments in the area.
Comments: Special colloquium joint with the topology seminar on TUESDAY
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UConn Math Club
Speaker: Math Dept. members (University of Connecticut)
Time: Wednesday, April 5, 2006 at 5:30 pm
Place: MSB 315 (UConn - Storrs)
Abstract: If you are considering graduate school in
mathematics after college, come to this panel discussion where
you will hear from members of the UConn math department about their
experiences planning for and applying to graduate
school. The discussion will then be opened to answer
your questions. A packet
containing a suggested reading list and some general
advice will be distributed too.
Comments: Free Refreshments
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S.I.G.M.A. Seminar
Speaker: ADAM GAMZON (University of Connecticut)
Time: Thursday, April 6, 2006 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: This will be an introductory talk defining quadratic forms both concretely and in a coordinate-free manner. The goal is to conclude with a classification of nondegenerate quadratic forms over C and R up to equivalence. Quadratic forms play an important role in geometry, analysis and algebra (as well as other areas of mathematics). The audience should have a basic knowledge of linear algebra.
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Analysis and Probability Seminar
Speaker: James Bridgeman (University of Connecticut)
Time: Friday, April 7, 2006 at 3:00 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Most of the usual stochastic interest rate models were designed and
calibrated to provide plausible behavior in expected value and variance,
which are the raw material for first approximation pricing and hedging of
financial instruments. Regulators require actuaries to stress test the
financial positions of insurance companies over long projection horizons
against extreme interest rate paths. The behavior of extreme paths in the
usual stochastic interest rate models is not nearly so plausible as the
behavior of their expected values and variances. The talk will propose a
new (to the insurance application) class of models that deliver more
plausible extreme paths while preserving the usual expected value and
variance behavior.
Comments: The room is not the usual room.
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Logic Seminar
Speaker: Andre Nies (University of Connecticut)
Time: Monday, April 10, 2006 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: We discuss applications of concepts related to randomness in
computability. One example is Kucera's injury-free solution of Post's problem. A
further one is the class of K-trivial sets, which forms an ideal of the Turing
degrees with nice properties.
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Geometry Seminar
Speaker: Shabnam Beheshti (University of Massachusetts, Amherst)
Time: Tuesday, April 11, 2006 at 4:00 pm
Place: MSB 117 (UConn - Storrs)
Abstract: A soliton metric is a metric of the form $ds^2=cos^2(u/2)dx^2pm sin^2(u/2)dt^2$, where $u=u(x,t)$ is a solid wave solution of a Sine-Gordon equation: $u_{xx}pm u_{tt}= pm Asin(u)$. We explore the relationship between soliton metrics and black holes in various two-dimensional models for classical gravity: Jackiw-Teitelboim Gravity (JT), String-Inspired Gravity (SIG), and Spherically Symmetric Gravity (SSG). In particular, we explore some concrete examples for which maps between these two spaces can be explicitly found and study a scalar field known as a dilaton, governing the black hole metric.
The talk has some physical connections, but it is primarily mathematical
and is intended to be accessible to graduate students.
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S.I.G.M.A. Seminar
Speaker: Oscar Levin (University of Connecticut)
Time: Wednesday, April 12, 2006 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Combinatorial Game Theory tries to find winning strategies for
games such as Nim, Hackenbush, Dots and Boxes, and even Go and Chess. In this talk we shall look at some of the more prevalent strategies used to accomplish these tasks. Then, if time permits, we shall look at why this admittedly fun activity can be considered mathematics.
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UConn Math Club
Speaker: Aggelos Kiayias (University of Connecticut)
Time: Wednesday, April 12, 2006 at 5:30 pm
Place: ITE 125 (UConn - Storrs)
Abstract: How is it possible for two parties that never met face-to-face to start
sending messages to each other that nobody can comprehend? The remarkable
cryptographic solution to this paradoxical problem is currently pumping
inside each personal computer and is one of the fundamental ingredients that
transformed the Internet from the mere academic tool of its early days to
the information superhighway of today. The mathematics of Internet security
is enticing and forms a sub-genre of its own kind: number theory,
probability, statistics, combinatorics and many more are all orchestrated
together for the solution of the modern version of the ancient problem of
secret writing.
In this talk I will present an overview of the mathematics
of modern cryptography and the techniques that employ them to solve
fundamental questions in secure communication as the one posed above.
Comments: Free Refreshments
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Colloquium
Speaker: Michael L. Overton (Courant Institute, NYU)
Time: Thursday, April 13, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We discuss a variety of matrix distance problems.
For a given square complex matrix $A$, these include
the nearest singular matrix, the nearest unstable matrix,
and the nearest matrix with multiple eigenvalues.
For a given pair $A$ and $B$, we also consider
(for $A$ square) the nearest uncontrollable pair
as well as (for both $A$ and $B$ square) the nearest
pair with a common eigenvalue. We restrict our attention
to the spectral and Frobenius norms, and emphasize the
crucial role of pseudospectra. Finally, we discuss some
structured nearest matrix problems. The issues include
both characterizations of solutions and algorithms for
finding them.
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Logic Seminar
Speaker: Denis Hirschfeldt (University of Chicago)
Time: Monday, April 17, 2006 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: I will discuss proof-theoretic and computability-theoretic aspects of certain theorems from combinatorics and model theory that fall outside the usual "big five" systems of reverse mathematics. In particular, I will focus on joint work with Richard Shore on the theorem that every infinite linear order contains an infinite ascending or descending sequence; and on joint work with Richard Shore and Ted Slaman on the theorem that every countable complete atomic theory has a countable atomic model.
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Algebra Seminar
Speaker: Russ Merris (Williams College)
Time: Tuesday, April 18, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Let G =3D (V,E) be a "simple" graph with vertex
set V =3D {1,2, ... ,n} and edge set E. The Laplacian
matrix L(G) =3D D(G) - A(G), where D(G) is the diagonal
matrix of vertex degrees and A(G) is the ordinary
adjacency matrix. Because graphs G and H are
isomorphic if and only if L(G) and L(H) are permutation
similar, the (permutation) similarity invariants of L(G)
are natural graph invariants, at least from an algebraic
perspective. The speaker will discuss a selection of these
invariants.
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Geometry Seminar
Speaker: Michael Sullivan (University of Massachusetts, Amherst)
Time: Tuesday, April 18, 2006 at 4:00 pm
Place: MSB 117 (UConn - Storrs)
Abstract: Legendrian contact homology is a theory based on holomorphic disks used to
study Legendrian submanifolds of contact manifolds. After introducing these
ideas, I will discuss recent applications of contacat homology as well as
attempts to generalize this theory.
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S.I.G.M.A. Seminar
Speaker: Tara Holm (University of Connecticut)
Time: Wednesday, April 19, 2006 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The symmetries of a symplectic manifold are reflected in
its moment polytope. There is a dictionary translating the geometry into combinatorics, and vice versa. I will start with the definition of a polytope, introduce enough symplectic geometry to motivate the moment polytope, and then I will discuss several of the dictionary entries.
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UConn Math Club
Speaker: Tom Meyer (University of Connecticut)
Time: Wednesday, April 19, 2006 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: In surveying any region of appreciable size
on the Earth, the curvature of the surface
needs to be taken into account. In particular,
the ordinary geometry of the plane must be
replaced by a suitable geometry for a sphere,
including spherical trigonometry.
We will illustrate this by discussing
how to compare the positions of two
points on the Earth.
Comments: Free Refreshments
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Colloquium
Speaker: Umbero Mosco (Worcester Polytechnic Institute)
Time: Thursday, April 20, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Some peculiar features of fractals are described in the perspective of classical partial differential equations and boundary value problems.
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Analysis and Probability Seminar
Speaker: Cristian Rios (Trinity College)
Time: Friday, April 21, 2006 at 3:00 pm
Place: MSB 319 (UConn - Storrs)
Abstract: We will first give some background on the weak formulation of Monge-Ampere
equations, the classic elliptic regularity theory and relevant examples
concerning the degenerate elliptic theory. Then we will present a tool we
developed to treat higher dimensional equations which is an extension of the
classical partial Legendre transform in the plane. This method is suitable
to treat degenerate equations and it is the first transform technique to be
successfully applicable to Monge-Ampere equations in dimensions higher than
two. Some positive new results will be given including interesting geometric
applications.
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Algebra Seminar
Speaker: Lance Miller (University of Connecticut)
Time: Tuesday, April 25, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: In this talk, I will present recent structure theory for the Module of
r-differentiable splines of polyhedral complex in real Euclidean
space, developed by Lauren Rose. This decomposition depends on the
cycle structure of the dual graph of the polyhedral complex. If time
permits I will also discuss how this decomposition can give us insight
into the equivariant cohomology of toric varieties as well as some
speculative extensions to other manifolds.
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Geometry Seminar
Speaker: Jean Steiner (Cournant Institute)
Time: Wednesday, April 26, 2006 at 3:00 pm
Place: MSB MSB 415 (UConn - Storrs)
Comments: note unusual time, day, and place
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Colloquium
Speaker: Farshid Hajir (UMass)
Time: Wednesday, April 26, 2006 at 3:30 pm
Place: IMS 20 (UConn - Storrs)
Comments: Awards Day Colloquium, WEDNESDAY
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UConn Math Club
Speaker: Farshid Hajir (UMass Amherst)
Time: Wednesday, April 26, 2006 at 4:00 pm
Place: IMS 20 (UConn - Storrs)
Abstract: Not so long ago, it was unusual for a research article in mathematics to
have more than one author. Today, multi-author articles are as common (if
not more so) than single-author ones. How did this transformation come
about? I'll limit myself mostly to describing some stories of mathematical
collaboration from my own experience.
Comments: Free Refreshments
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S.I.G.M.A. Seminar
Speaker: Matt Jura (University of Connecticut)
Time: Wednesday, April 26, 2006 at 5:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: This talk will give a basic introduction to category theory, with the goal of presenting the Yoneda Lemma, which can be considered an extreme generalization of Cayley's Theorem for groups. An interesting detour into adjoint situations will be taken as well. No knowledge of category theory is necessary. A small amount of algebra and topology will be assumed.
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UConn Math Club
Speaker: Steve Conrad (Roslyn HS (ret.))
Time: Wednesday, May 3, 2006 at 5:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Do you want to teach math in grades 7-12? That's what I did
for 32 years. I'll show you how I (eventually) learned to
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get all my students to do all their homework
-
end all cheating on tests
-
improve classroom effectiveness year after year
-
write college recommendations that make a difference
-
turn lead into gold (just kidding)
I taught in New York City for 14 years
and then in an affluent New York City suburb until I retired.
Comments: Free Refreshments
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University of Connecticut | 
