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Fall 2005
Colloquium
Analysis and Probability Seminar
Speaker: Alexander Stokolos (DePaul University)
Time: Friday, September 2, 2005 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
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Geometry Seminar
Speaker: Jesse Ratzkin (University of Connecticut)
Time: Tuesday, September 6, 2005 at 4:00 pm
Place: MSB 211 (note special room) (UConn - Storrs)
Abstract: I will describe continuing work with Karsten Grosse-Brauckmann, Nick Korevaar,
Rob Kusner, and John Sullivan regarding the nondegeneracy and moduli space
theory of constant mean curvature surfaces. One can think of a nondegenerate
CMC surface as infinitesimally rigid. As such, nondegeneracy implies local
regularity of the moduli space.
I will begin with the previous work of Grosse-Brauckmann, Kusner, and Sullivan,
which establishes a topological model for the moduli space, and then describe our
recent work in proving regularity.
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S.I.G.M.A. Seminar
Speaker: Reed Solomon (University of Connecticut)
Time: Wednesday, September 7, 2005 at 4:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Computability theorists have various ways of measuring when one
set is "computationally simpler" than another set. Typically, these
measures of complexity give rise to an equivalence relation on the setsets
of the natural numbers and the result of moding out by this relation is
called a degree structure. The equivalence class of a set, which is
called its degree, measures the complexity of the set. After giving some
examples of degree structures, I will discuss the kinds of questions
computability theorists tend to ask about these structures and at least
sketch one sample proof about the Turing degrees.
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Analysis and Probability Seminar
Speaker: $Unique empty (University of Connecticut)
Time: Friday, September 9, 2005 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
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UConn Math Club
Speaker: Mark Skandera (Haverford)
Time: Friday, September 9, 2005 at 5:30 pm
Place: MSB 215 (UConn - Storrs)
Abstract: A matrix is called totally nonnegative if each of its square
submatrices has a nonnegative determinant. Such matrices arise in a
variety of applications such as differential equations, chemistry,
and stochastic processes. The Vandermonde matrix
and the Hilbert matrix
1 1/2 1/3 1/4
1/2 1/3 1/4 1/5
1/3 1/4 1/5 1/6
1/4 1/5 1/6 1/7
are examples of totally nonnegative matrices.
We will discuss combinatorial interpretations of such matrices and of
related functions called totally nonnegative polynomials. Some
familiarity with linear algebra will be helpful but not necessary.
Comments: Free Refreshments
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Logic Seminar
Speaker: Joe Miller (University of Connecticut)
Time: Monday, September 12, 2005 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: We show that the Turing degrees are not sufficient to measure the complexity of continuous functions on [0,1]. Computability of continuous real functions is a standard, and well-understood notion from computable analysis. However, no satisfactory theory of degrees of continuous functions exists. We supply such a theory and show that the degrees of continuous functions form a proper extension of the Turing degrees and a proper subclass of the enumeration degrees (or partial degrees).
The key to proving these theorems is the reduction of questions about degrees of continuous functions to questions about sequences of reals. The construction of a sequence of reals which can not be computably diagonalized is used to prove that there are continuous functions without a Turing degree. Such a function is also shown to have no least Turing degree representation, settling a question asked by Lempp and Pour-El. On the other hand, by proving that any sequence of computable real numbers is computably diagonalizable, we show that there are enumeration degrees which contain no continuous functions. As a corollary, it is shown that every non-computable continuous real function computes a non-computable subset of natural numbers. Proofs draw from classical and constructive analysis, as well as from computability theory.
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Colloquium
Speaker: Herb Clemens (Ohio State University)
Time: Tuesday, September 13, 2005 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: A brief review of the theory of deformations of complex structures
on a differentiable manifold will be followed by a formulation of the
classical theory of normal functions as obstructions to the deformation of
complex subvarieties.
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S.I.G.M.A. Seminar
Speaker: Herb Clemens (Ohio State University)
Time: Wednesday, September 14, 2005 at 4:00 pm
Place: Dodd Center Konover Auditorium (UConn - Storrs)
Abstract: The SIGMA Seminar will not host a speaker this week to allow graduate students to attend the talk given by Dr. Herb Clemens . This talk and discussion will begin with the confessions of a mathematician who is a traitor to his class. He is on the 'wrong' side in the math wars, convinced that by and large his colleagues have the math right but the politics wrong, both at home and abroad. The floor will then be opened to discussion.
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UConn Math Club
Speaker: Keith Conrad (University of Connecticut)
Time: Wednesday, September 14, 2005 at 5:30 pm
Place: MSB 215 (UConn - Storrs)
Abstract: Numerical codes, such as ISBN numbers on books or the UPC code on
other packaged goods, are ubiquitous in
the marketplace. Nearly all of these codes come with a special
number, called the check digit, whose purpose is to
prevent the codes from being incorrectly processed. We
will explain the mathematics behind the design of some of
these check digit protocols and see how they are capable of
detecting (or not detecting) certain kinds of errors.
In a few years the publishing industry will convert to a new
ISBN check digit protocol, and we will see why the
error-detecting capability of the new
system is in a sense worse than the current version!
Prior experience with modular arithmetic will be helpful, but in any
case it will be explained as needed through examples.
Comments: Free Refreshments
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Analysis and Probability Seminar
Speaker: Masha Gordina (University of Connecticut)
Time: Friday, September 16, 2005 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
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Logic Seminar
Speaker: John Baldwin (University of Illinois at Chicago)
Time: Monday, September 19, 2005 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: Zilber has proved some surprising equivalences (modulo a weak form of GCH) between arithmetic properties of semi-abelian varieties A and categoricity up to aleph_omega of the exact sequence 0 -> Z -> V -> a -> 0. We use the work of tameness and categoricity transfer (Shelah, Grossberg, Vandieren, Kolisnikov, Lessman, Villaveces, Zambrano) to replace categoricity up to aleph_omega by aleph_1 categoricity.
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Algebra Seminar
Geometry Seminar
Speaker: Jesse Ratzkin (University of Connecticut)
Time: Tuesday, September 20, 2005 at 4:00 pm
Place: MSB 117 (UConn - Storrs)
Abstract: I will describe continuing work with Karsten Grosse-Brauckmann, Nick Korevaar,
Rob Kusner, and John Sullivan regarding the nondegeneracy and moduli space theory of
constant mean curvature surfaces. One can think of a nondegenerate CMC surface as
infinitesimally rigid. As such, nondegeneracy implies local regularity of the moduli space.
I will begin with the previous work of Grosse-Brauckmann, Kusner, and Sullivan, which
establishes a topological model for the moduli space, and then describe our recent
work in proving regularity.
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S.I.G.M.A. Seminar
Speaker: Lance Miller (University of Connecticut)
Time: Wednesday, September 21, 2005 at 4:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Polynomial rings are very nice in that we can write down an arbitrary polynomial ( here in one variable ) p(x) = a_0 + a_1x + a_2x^2 + ... + a_n x^n. The reason here is that our polynomial ring R[x] is actually a direct sum of linear subspaces R_k generated by x^k. We will show how this notion can be generalized to other algebraic structures by use of group gradings. This talk will discuss some of the group gradings that occur on matrix algebra, and possibly some extentions into incidence algebras, which are closely related to matrix algebras. If time permits, some attention will be given to the use of graded objects in projective algebraic geometry.
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UConn Math Club
Speaker: Helen Moore (American Institute of Mathematics)
Time: Wednesday, September 21, 2005 at 5:30 pm
Place: MSB 215 (UConn - Storrs)
Abstract: How does HIV interact with the human immune system?
Mathematics has been used to shine light on this mystery. In
particular, the predator-prey models taught in some calculus
courses have been very successful in capturing the struggle
between the immune system and diseases. I'll talk about a
few simple mathematical results for models of HIV and leukemia,
resulting treatment recommendations, and some of the remaining
urgent questions for these diseases.
Comments: Free Refreshments
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Colloquium
Speaker: Helen Moore (American Institute for Mathematics)
Time: Thursday, September 22, 2005 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: I will talk about some specific applications of mathematical
modeling to HIV and leukemia. I will discuss how differential
equation models can be applied to experimental or clinical time
series data, including the use of control theory to compute
optimal drug doses. I will also mention some statistical issues
in handling uncertainty in parameters, and the challenges and
rewards of interdisciplinary projects such as modeling diseases.
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Analysis and Probability Seminar
Speaker: Martynas Manstavicius (University of Connecticut)
Time: Friday, September 23, 2005 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
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Logic Seminar
Speaker: Eric Rosen (Wesleyan University)
Time: Monday, September 26, 2005 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: An important problem in the model theory of differentially closed fields is to classify all the strongly minimal sets. In the 1990's, Hrushovski and Sokolovic classified the non-trivial sets, i.e., those whose associated combinatorial geometry is non-trivial. Although some progress has been made towards understanding the trivial strongly minimal sets, the problem in full generality remains completely open.
In this talk, we will describe the background to the problem and recall what is already known. We will then give a classification of all trivial order one strongly minimal sets, that is, those that 'live' on algebraic curves. This partially generalizes and extends work of Hrushovski and Itai.
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Algebra Seminar
Speaker: Keith Conrad (University of Connecticut)
Time: Tuesday, September 27, 2005 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
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Geometry Seminar
Speaker: Kazuyuki Hasegawa (Tokyo Science University)
Time: Tuesday, September 27, 2005 at 4:00 pm
Place: MSB 117 (UConn - Storrs)
Abstract: We study surfaces in four dimensional manifolds
whose twistor lifts are harmonic sections, which are generalizations of
superminimal surfaces.
We give the lower bound for the energy densities of the
twistor lifts in the case where the ambient space is the four dimensional Euclidean space
and characterize the surfaces which attain the lower bound.
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S.I.G.M.A. Seminar
Speaker: Lara Diamond (NSA)
Time: Wednesday, September 28, 2005 at 4:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Lara Diamond, Director of the National Security Agency's Summer Program in
Operations Research Technology (SPORT) will talk about the SPORT program,
which gives graduate students and seniors who will attend graduate school
the following fall an opportunity to apply their academic skills to
real-world problems. Examples of unclassified projects undertaken by
previous SPORT interns will be covered, and questions about the program will
be welcome. Both Lara and Andrea Muchinsky, who will also be visiting, are
former SPORT interns.
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UConn Math Club
Speaker: Jay Pottharst (Harvard)
Time: Wednesday, September 28, 2005 at 5:30 pm
Place: MSB 215 (UConn - Storrs)
Abstract: The Fundamental Theorem of Algebra says that all nonconstant polynomials
have roots in the complex numbers. You might have heard this before, but
if you are like me then a proof of this theorem was withheld from you for
a few years. Your wait is over. In this talk we will discuss some basic
facts about calculus of functions of a complex variable, and then use them
to prove the Fundamental Theorem of Algebra.
Prerequisites for this talk are familiarity with the arithmetic of complex
numbers (addition and multiplication, absolute value and polar form), and
traditional calculus of two variables (namely Green's theorem).
Comments: Free Refreshments
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Colloquium
Speaker: David Cox (Amherst College)
Time: Thursday, September 29, 2005 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: This lecture will discuss some of the recent interactions between geometric modeling and pure matematics. It seems easy to draw curves and surfaces on a computer screen using a parametrization by polynomials or rational functions. The process of converting the parametrization into an equation for the curve or surface is called implicitization. One way to visualize a curve is by the common point of intersection of two moving lines; similarly, the common point of intersection of three moving planes can sweep out a surface. The existence of these moving lines and moving planes is related to the study of syzygies in commutative algebra -- the Hilbert syzygy theorem from 1890 will make an unexpected appearance in the curve case. The surface case is more sophisticated because of the presence of base points.
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Logic Seminar
Speaker: Jan van Mill (Vrije Universiteit and Wesleyan University)
Time: Monday, October 3, 2005 at 4:45 pm
Place: Exley Science Center Room 618 (Wesleyan University)
Abstract: We present an example of a homogeneous (separable metrizable)
analytic space on
which no analytic group acts transitively.
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Geometry Seminar
Speaker: Jesse Ratzkin (University of Connecticut)
Time: Tuesday, October 4, 2005 at 4:00 pm
Place: MSB 117 (UConn - Storrs)
Abstract: I will describe continuing work with Karsten Grosse-Brauckmann, Nick Korevaar,
Rob Kusner, and John Sullivan regarding the nondegeneracy and moduli space theory of
constant mean curvature surfaces. One can think of a nondegenerate CMC surface as
infinitesimally rigid. As such, nondegeneracy implies local regularity of the moduli space.
I will begin with the previous work of Grosse-Brauckmann, Kusner, and Sullivan, which
establishes a topological model for the moduli space, and then describe our recent work in proving regularity.
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S.I.G.M.A. Seminar
Speaker: Domina Spencer (University of Connecticut)
Time: Wednesday, October 5, 2005 at 4:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: One hundred years ago, in 1905, Einstein stated that the
postulates on which the special theory of relativity was based were
(1) The velocity of light is a constant c. (2) Electromagnetic theory
is based on the four Maxwell equations. We can compliment Einstein
for stating his postulates clearly. But today it is necessary to
conclude that neither of Einstein's postulates are valid.
Einstein's postulate on the velocity of light must be replaced
by the Universal Time Postulate on the velocity of light which has
been proven to be the only postulate that explains how all moving
clocks can be synchronized.
Instead of the Maxwell equations, all electromagnetic phenomena
hitherto investigated can be derived from the New Gaussian Equation
for the force between moving charges. This equation is based on
relative velocity as was proposed by Gauss.. Maxwell himself
states in the last chapter of his two volume treatise on Electricity
and Magnetism that the keystone of electrodynamics should be a single
equation for the force between moving charges.
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UConn Math Club
Speaker: Tara Holm (University of Connecticut)
Time: Wednesday, October 5, 2005 at 5:30 pm
Place: MSB 215 (UConn - Storrs)
Abstract: Back in the days of the ancient Greeks, Euclid studied geometry in
the plane by drawing straight lines and circles. Meanwhile, the art of
folding paper flourished in Japan as a decorative art. Origami may now be
used to understand the geometry first codified by Euclid. By folding a piece
of paper, we create a line. The additional moves allowed in origami improve
on Euclid’s constructions by straightedge-and-compass. Your geometry
teachers may have told you that it’s
impossible to trisect an angle, but
with origami moves this becomes possible!
Some familiarity with straightedge-and-compass constructions will be
helpful, but is not required.
Comments: Free Refreshments
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Colloquium
Speaker: Matthew Ando (UIUC)
Time: Thursday, October 6, 2005 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: In algebraic topology one detects topological phenomena via algebraic
invariants. In many cases of current interest, the algebraic
invariant is an algebro-geometric moduli space (or some object
constructed from it). For example, elliptic genera take values in
modular forms, that is, functions on the "space" of elliptic curves
(truthfully, sections of a line bundle over it). I shall explain one
source of this pattern, and describe some results which follow from
this point of view.
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Analysis and Probability Seminar
Speaker: Luke Rogers (Cornell)
Time: Friday, October 7, 2005 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
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Algebra Seminar
Speaker: Lance Miller (University of Connecticut)
Time: Tuesday, October 11, 2005 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Group gradings of matrix algebras have been recently studied. Two
important classes of gradings play a large role in the
classification, namely good gradings, and elementary gradings. These
notions are equivalent in the case of matrix algebras. Incidence
algebras are subalgebras of matrix algebras defined using a locally
finite partially ordered set.
In Dr. Molli Jones' study of group
gradings of incidence algebras, she showed that these two types of
gradings are not always equivalent. This talk will cover some recent
attempts of Dr. Spiegel and myself to classify which group gradings
are equivalent to good group gradings.
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Geometry Seminar
Speaker: Fred Gardiner (CUNY)
Time: Tuesday, October 11, 2005 at 4:00 pm
Place: MSB 117 (UConn - Storrs)
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S.I.G.M.A. Seminar
Speaker: Mei Gao (Pratt and Whitney)
Time: Wednesday, October 12, 2005 at 4:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Briefly introduce Weibull distribution and how to applied
it in reliability analysis .
I will also talk about my industrial experience and give some
suggestion for the people who is
looking for a carrier in industry.
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UConn Math Club
Speaker: Michael Bush (UMass Amherst)
Time: Wednesday, October 12, 2005 at 5:30 pm
Place: MSB 215 (UConn - Storrs)
Abstract: Most people have seen how to solve the quadratic
equation ax2 + bx + c = 0
by “completing the square”
(or simply using the quadratic formula). In this talk we
will discuss similar methods for solving the general
cubic and quartic equations, as well as the situation
for equations of degree greater than 4. Some of the
colorful history and stories surrounding the discovery
of these results will be mentioned.
Most of the talk should be accessible to anyone with a
knowledge of high-school algebra.
Comments: Free Refreshments
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Colloquium
Speaker: Kiyoshi Igusa (Brandeis)
Time: Thursday, October 13, 2005 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: There is a well known relationship between graphs, ribbon graphs and
the cohomology of the outer automorphism groups of the free group and the
mapping class group of marked surfaces. Although the stable cohomology of these groups haverecently been determined by Madsen, Weiss and Galatius there are still many unanswered questions.
I will explain the interpretation of tautological classes as higher torsion invariants and what are the implications of this interpretation. The axiomatic approach to higher torsion and the canonical thickening of graphs helps to simplify the theory.
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Analysis and Probability Seminar
Speaker: Evarist Gine (University of Connecticut)
Time: Friday, October 14, 2005 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
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Geometry Seminar
Speaker: Masha Gordina (University of Connecticut)
Time: Tuesday, October 18, 2005 at 4:00 pm
Place: MSB 117 (UConn - Storrs)
Abstract: First I'll explain why a probabilist might want to know the Ricci
curvature of a group or a Riemannian manifold. Then I'll talk about how
the notions of covariant derivative, curvature tensor etc. can be defined
for a class of infinite-dimensional groups of operators. These are natural
"limits" of classical matrix groups. The approach follows J.Milnor's paper
(1976) on finite-dimensional Lie groups where he studied how the
Riemannian geometry changes for different inner products on the
corresponding Lie algebra. If time permits I'll talk about the Virasoro
algebra and the Riemannian geometry of the associated infinite-dimensional
complex manifold. The first part of talk is based on the paper in the
Journal of Functional Analysis (2005), the Virasoro case is a joint
preprint with Paul Lescot.
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S.I.G.M.A. Seminar
Speaker: Masha Gordina (University of Connecticut)
Time: Wednesday, October 19, 2005 at 4:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: I'll begin with the concept of the Brownian motion, and its
mathematical model. Then I'll describe connections of the theory of
random processes with different fields (PDEs, mathematical physics,
differential geometry etc.). Finally, I'll try to illustrate how one can
get a Brownian motion to live on a curved space.
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Colloquium
Speaker: Karan Singh (University of Toronto)
Time: Thursday, October 20, 2005 at 4:00 pm
Place: ITEB 336 conference room (UConn - Storrs)
Abstract: Computer graphics is rapidly striding toward a state where the real and virtual in an animation blend indistinguishably together. Beyond the mere exercise of recreating reality, the 2005 Oscar winning computer animated short film "Ryan" aims to show the realism of the messy, chaotic and glorious entity we call "human nature". Director Chris Landreth refers to this pursuit as "psychorealism". This talk showcases a technique quintessential to the film, which allows artists to transcend the linear perspective of a pin-hole camera model. The talk will develop a conceptual framework to construct and interactively control shape and illumination under nonlinear projection and address
their implementation within a conventional animation pipeline. A number of applications of the framework ranging from artistic depiction to scientific visualization will be discussed.
Comments: Joint with CS. Notice the location. Tea at 3:30 in ITEB 336 as well.
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Analysis and Probability Seminar
Speaker: Alexander Teplyaev (University of Connecticut)
Time: Friday, October 21, 2005 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We develop a new approach to formulate and prove the
weak uncertainty inequality which was recently introduced
by Okoudjou and Strichartz. We assume either an appropriate
measure growth condition with respect to the effective
resistance metric, or, in the absence of such a metric,
we assume the Poincare inequality and inverse volume
doubling property. Our results can be applied to a wide
variety of metric measure spaces, including graphs, fractals
and manifolds. This is a joint work with Kasso Okoudjou.
If time permits, I also will talk about recent results
on random Sierpinsky gaskets.
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UConn Math Club
Speaker: Karan Singh (University of Toronto)
Time: Friday, October 21, 2005 at 5:30 pm
Place: MSB 215 (UConn - Storrs)
Abstract: The modeling of curves in 3D geometry presents a challenging problem for
users of graphics systems. An artist or animator wants to precisely control the final shape, especially when the curves contact complicated surfaces.
This talk addresses the problem with a novel 3D curve primitive called a cord.
A cord is defined by a guide curve, which represents an approximate 3D path the user wishes the cord to follow around the geometry. The guide curve, along with various attributes, analytically and continuously defines the shape of a cord. Cords can exhibit the visual appearance of a range of materials, including strings, wires, and rubber bands, while allowing animators the precise control of shape needed for keyframe animation. Cords also find applications in visualization and nonphotorealistic rendering and will be shown in the context of the animated short film “Ryan,” which won the Oscar this year for best animated short film.
Comments: (Note the day!) Free Refreshments
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Logic Seminar
Speaker: David Marker (University of Illinois at Chicago)
Time: Monday, October 24, 2005 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: We will look at Zilber's axioms for pseudoexponentiation. In
particular we will examine whether the simplest case of the
strong exponential closure axiom is true for the complex exponential.
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Algebra Seminar
Speaker: Kyu-Hwan Lee (University of Connecticut)
Time: Tuesday, October 25, 2005 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The Gröbner basis theory is a standard computational tool
in Commutative Algebra. We will see how the theory can be
generalized for representations of associative algebras, and will
consider some applications for representations of Lie algebras
and Hecke algebras.
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Geometry Seminar
S.I.G.M.A. Seminar
Speaker:
Time: Wednesday, October 26, 2005 at 4:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: TBA
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UConn Math Club
Speaker: Ben Mares (MIT)
Time: Wednesday, October 26, 2005 at 5:30 pm
Place: MSB 215 (UConn - Storrs)
Abstract: Can a function in one real variable be discontinuous at every rational
number but continuous at every irrational number? Such a function not only
exists, but we can write down an explicit formula, graph it with a computer,
and visualize the result.
The main emphasis will be on cool pictures of this and similar functions of
one variable. I will discuss examples of functions with oddly behaved
derivatives. I will also discuss extension problems and limits.
Comments: Free Refreshments
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Colloquium
Speaker: Ofer Zeitouni (University of Minnesota)
Time: Thursday, October 27, 2005 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Random walks in random environments in dimension 1 exhibit many unusual features: slowdown, aging, stable limits, and anomalous diffusivity,
holding even in the perturbative regime. The higher dimensional case is believed not to exhibit such rich behavior, but the proof of such a statement still presents many challenges, in spite of the considerable progress achieved in recent years. I will describe the background and some
recent results, including the breakdown of certain 0-1 laws in ergodic random environment on the one hand, and diffusive behavior in the perturbative regime on the other.
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Logic Seminar
Speaker: Alex Raichev (University of Wisconsin)
Time: Monday, October 31, 2005 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: I will discuss some recent progress in the study of relative randomness via
rK-reducibility, a refinement of Turing reducibility. This talk will be very
scary.
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Algebra Seminar
Speaker: Kyu-Hwan Lee (University of Connecticut)
Time: Tuesday, November 1, 2005 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
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Geometry Seminar
Speaker: Franz Pedit (University of Massachusetts, Amherst)
Time: Tuesday, November 1, 2005 at 4:00 pm
Place: MSB 215 (UConn - Storrs)
Abstract: I will explain how the space of conformal maps from a 2-torus to the 4-sphere
has the structure of a ``phase space" for a very simple integrable system consisting of complex curves and their Jacobians. The conformal maps themselves are then linear flows of this system; more generally, the Jacobians describe the Davey-Stewartson hierarchy of mathematical physics. The link between conformal maps from 2-tori and complex curves and their Jacobians is provided by the determinant locus of a holomorphic family of Dirac operators. These operators are the quaternionic holomorphic structures induced by the
conformal maps of a Riemann surface (in our case of genus 1) into the 4-sphere
(similar to the complex holomorphic line bundles, i.e., or divisor classes, arising from conformal, i.e., meromorphic, functions on a Riemann surface).
Comments: Note special room!
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S.I.G.M.A. Seminar
Speaker: Kasra Rafi (University of Connecticut)
Time: Wednesday, November 2, 2005 at 4:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We give an introduction to the field
of geometric group theory, exploring how
geometric tools and ideas such as hyperbolicity
could be useful in solving algebraic problems.
This will be an elementary talk, requiring only
basic knowledge of group theory.
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UConn Math Club
Speaker: Abhijnan Rej (BU)
Time: Wednesday, November 2, 2005 at 5:30 pm
Place: MSB 215 (UConn - Storrs)
Abstract: Consider the following statement from elementary geometry:
“Given any two points, there is a unique line containing them.”
Now consider the statement:
“Given any two lines, there is a unique point contained in
them” (the intersection point).
The words “line” and “point”
can be interchanged in the
the first statement to give the second statement and vice versa.
Exchanging the words “point” and “line”
in other statements also yields true results. This is called “point-line
duality.”
Actually, a pair of parallel lines do not contain a common point,
so we have to enlarge our view of geometry to allow parallel
lines to meet. Point-line duality will lead us to a
new geometry with coordinates that are independent of any scale
(“projective geometry”). If time permits, we will look at some
examples of point-line duality on spaces with only a finite number of
points.
This talk will be accessible to anyone with a high school math background.
Comments: Free Refreshments
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Colloquium
Speaker: Michael Roeckner (Purdue University)
Time: Friday, November 4, 2005 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We shall first review the connection between ordinary stochastic
differential equations (SODE) on R^d and parabolic partial differential
equations (such as the classical heat equation). The point will be that
the latter can be viewed as a linearization of the first. Subsequently, we
shall display this connection also for SODE's in infinite dimensions. A
purely analytic approach to solve the corresponding (generalized) heat
equations in infinitely many variables will be presented. Applications
include the case where the infinite dimensional SODE is a parabolic
stochastic partial differential equation, as e.g. the stochastic
Ginzburg-Landau, the generalized stochastic Burgers, and the stochastic
Navier-Stokes equation. In this talk we shall particularly concentrate on
applying the results to the stochastic porous media equation.
Comments: Notice the unusual day. The talk is on a FRIDAY.
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Logic Seminar
Speaker: Daniel Miller (Wesleyan University)
Time: Monday, November 7, 2005 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
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Algebra Seminar
Speaker: Eugene Spiegel (University of Connecticut)
Time: Tuesday, November 8, 2005 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We consider when a transpose can be defined on an incidence algebra, and,
in particular, on the ring of n x n upper triangular matrices.
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Geometry Seminar
Speaker: Christoph Bohle (T. U. Berlin)
Time: Tuesday, November 8, 2005 at 4:00 pm
Place: MSB 215 (UConn - Storrs)
Comments: Note special room!
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S.I.G.M.A. Seminar
Speaker: Kyu-Hwan Lee (University of Connecticut)
Time: Wednesday, November 9, 2005 at 4:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We will introduce modular forms and will consider its connection to the the study of the Monster, i.e. the largest of the sporadic simple groups.
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UConn Math Club
Speaker: Liz Yockey (University of Connecticut)
Time: Wednesday, November 9, 2005 at 5:30 pm
Place: MSB 215 (UConn - Storrs)
Abstract: If you are given two line segments, it is easy to construct
a line segment whose length is the sum of their lengths,
purely geometrically: use the line segment obtained by
placing the two line segments next to each other. Its length is the sum.
Differences of lengths can be found purely geometrically
too: place the line segments on top of each other and use the
extra amount on the longer segment. But what about products? That is, if you have a line segment with length x and a line segment with length y, can you construct geometrically out of these a line
segment with length xy? Or how about a line
segment with length x/y?
We will see (and practice!) how to make constructions like these using
the tools of classical Greek geometry: an unmarked straightedge and
a compass. As an application we will meet a purely geometric
construction of a regular pentagon.
Comments: Better Refreshments2
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Colloquium
Speaker: Walter Gloeckle (Ruhr-University of Bochum, Germany)
Time: Thursday, November 10, 2005 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The Faddeev-Yakubovsky equations are introduced and numerical
algorithms for their solutions are presented. Applications to
few-nucleon systems based on modern high precision nuclear forces
are shown and the theoretical results are compared to data.
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Analysis and Probability Seminar
Speaker: Erin Terwilleger-Mullen (University of Connecticut)
Time: Friday, November 11, 2005 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
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Logic Seminar
Speaker: Bakhadyr Khoussainov (Auckland University and Cornell University)
Time: Monday, November 14, 2005 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
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Geometry Seminar
Speaker: Graeme Wilkin (Brown University)
Time: Tuesday, November 15, 2005 at 4:00 pm
Place: MSB 117 (UConn - Storrs)
Abstract: (joint with George Daskalopoulos and Jonathan Weitsman)
I will describe a version of Morse theory on spaces with mild
singularities that we have developed in order to study the toploogy of the
moduli space of semistable rank 2 Higgs bundles. This approach is in the
spirit of the Atiyah-Bott approach for studying semistable
holomorphic bundles, and provides a natural proof of the surjectivity of
the hyperkahler Kirwan map in the non-fixed determinant case.
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S.I.G.M.A. Seminar
Speaker: Will Dicharry (University of Connecticut)
Time: Wednesday, November 16, 2005 at 4:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: In 1900, the German physicist Max Planck published a paper entitled
On the theory of the energy distribution law of the normal
spectrum in which he proposed a radical solution to an unsolved problem in
classical thermodynamics. It was in this paper that quantum theory was
born. We will discuss briefly the development of mathematical quantum
theory leading up to von Neumann's rigorous formulation of quantum
mechanics in Hilbert space. Along the way, we will see an example of a
physical situation where classical mechanics and quantum mechanics
differ and we will finish with a rigorous formulation and proof of Heisenberg's
Uncertainty Principle, one of the fundamental results of quantum
mechanics.
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UConn Math Club
Speaker: Jesse Ratzkin (University of Connecticut)
Time: Wednesday, November 16, 2005 at 5:30 pm
Place: MSB 215 (UConn - Storrs)
Abstract: You’re probably thinking “I know what a sphere
is; it’s the locus of all points a fixed distance from a center.”
The definition you're thinking of is accurate, but you might
want some other ways to distinguish spheres from other
surfaces. I will discuss some geometric properties of
surfaces which seem like good characterizations of
spheres. Some of them are, and some are not.
To understand this lecture, you will need to know the
Pythagorean theorem (to compute distances), and possibly
how to differentiate and integrate. It might also help to draw
some pictures of spheres and other surfaces. (Go on, try it now!)
Comments: Free Refreshments
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Colloquium
Speaker: Dirk Kreimer (Boston University/IHES)
Time: Thursday, November 17, 2005 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Physics succeeds in correctly predicting experiments utilizing the techniques of quantum field theory in phenomena ranging from the very small -particle physics- to the macroscopic world of phase transitions.
More and more, we understand that quantum field theory connects to number theory in unexpected and instructive manners, making use of the structure of the polylogarithm, and even of motives, in ways which inform the mathematician as well as the physicist. The talk exhibits these developments emphasizing structural similarities.
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Algebra Seminar
Speaker: Myung-Hwan Kim (Seoul National University / Wesleyan University)
Time: Tuesday, November 29, 2005 at 3:30 pm
Place: MSB 215 (UConn - Storrs)
Abstract: Representation theory of quadratic forms cherishes a long and
splendid history since Pythagoras. For example, positive integers
that are representable by sums of two, three, and four squares
were determined by great names like Fermat and Euler, Gauss, and
Lagrange, respectively. Hilbert paid a tribute to this
fascinating subject by posting two problems among his famous 23
problems - the 11th and the 17th.
In this talk, a brief history and recent developments on
universal forms are introduced. (For a given set S of quadratic forms, a
quadratic form that represents all the forms in S is called
an S-universal form.) Recent developments include
Conway-Schneeberger's fifteen theorem on N-universal forms where N is the
set of all positive integers, Bhargava's finiteness theorem
on representability of some infinite subsets of N,
and their generalizations to higher rank representability.
Some applications and related topics are also discussed.
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Geometry Seminar
Speaker: Edward Moore (University of Connecticut)
Time: Tuesday, November 29, 2005 at 4:00 pm
Place: MSB 117 (UConn - Storrs)
Abstract: Approximating spline curves is critically important to
geometric modeling and engineering simulation. The talk will introduce
a new method for guaranteeing topologically correct approximations of
spline curves, which relies on the control polygon after repeatedly
subdividing the curve. Particular focus is on the use of ambient
isotopy as the measure of topological equivalence, which is stricter
than the more traditional use of homeomorphism. Such topological
guarantees will meet the demands of future Computer-Aided Geometric Design
(CAGD) and Computer-Aided Molecular Design (CAMD) systems that require
more robust simulation.
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S.I.G.M.A. Seminar
Speaker: Sarah Glaz (University of Connecticut)
Time: Wednesday, November 30, 2005 at 4:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: A Prufer domain is an integral domain whose finitely generated ideals are invertible. This notion, defined by Heinz Prufer in 1932, became one of the central tools for the development of non-Noetherian commutative algebra. In the early seventies alone, commutative algebraists proved twenty-two conditions equivalent to Prufer's original definition for integral domains. Just as the theory of integral domains was immensely enriched by the introduction of this notion, so was the theory of general rings enriched by the extensions of this notion to rings with zero-divisors.
This talk will present a short overview of the long history of the various ways in which the Prufer domain notion may be extended to rings with zero-divisors, and the impact of the various extensions on the theory of general rings. The main focus of the talk will be on my recent work, and on my current work with Silvana Bazzoni in that direction.
I will define all concepts, stay away from technical proofs, provide examples, and offer glimpses of still open problems.
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UConn Math Club
Speaker: Bill Abikoff (University of Connecticut)
Time: Wednesday, November 30, 2005 at 5:30 pm
Place: MSB 215 (UConn - Storrs)
Abstract: It is relatively easy to determine the Platonic solids from the Euler
characteristic. I'll talk about both of them and, additionally, notions of
symmetry in two and three dimensions.
Comments: Free Refreshments
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Colloquium
Speaker: Takashi Kimura (Boston University)
Time: Thursday, December 1, 2005 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We will introduce a noncommutative ring associated
to an almost complex manifold with the action of a finite group
called its stringy cohomology whose ring of invariants yield the
so-called orbifold cohomology of the quotient orbifold due to
Chen-Ruan. We will give a simple, new definition of these invariants
and its generalizations.
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Analysis and Probability Seminar
Speaker: Ron Blei (University of Connecticut)
Time: Friday, December 2, 2005 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
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Logic Seminar
Speaker: Reed Solomon (University of Connecticut)
Time: Monday, December 5, 2005 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
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Algebra Seminar
Speaker: K.C. O'Meara (University of Connecticut)
Time: Tuesday, December 6, 2005 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
<Extra Information>
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S.I.G.M.A. Seminar
Speaker: Rachel Schwell (University of Connecticut)
Time: Wednesday, December 7, 2005 at 4:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Mathematical operads are tools that describe an algebraic structure that can
be attached to many different sets. We will define operads and algebras over
operads, and demonstrate them through accessible examples, namely
real-valued functions and trees. We will then introduce a set of polyhedra
whose faces are given by the different associations one can insert in an
n-letter multiplication, called Stasheff polyhedra or associahedra. We will
conclude with a nice theorem that links these polyhedra to based loop
spaces. Further applications of operads can be found in algebraic topology,
representation theory, algebraic geometry, combinatorics, knot theory,
quantum physics, and string theory.
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