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Fall 2006
Colloquium
S.I.G.M.A. Seminar
Speaker: Reed Solomon (University of Connecticut)
Time: Wednesday, September 6, 2006 at 4:20 pm
Place: MSB 118 (UConn - Storrs)
Abstract: For any set A of functions on the natural numbers, we can define a
game G(A) as follows. Two players take turns playing natural numbers
a_0, a_1, a_2, etc. with Player I choosing the even indexed numbers
and Player II choosing the odd indexed numbers. At the end of the
game, the players have constructed a function g on the natural
numbers. We say that Player I wins the game if g is an element of
the set A and Player II wins the games if g is not an element of A.
Perhaps surprisingly, if the set A is Borel, then one of the players
is guaranteed to have a winning strategy in this game. The Axiom of
Determinancy says something even stronger -- it states that for any
set A, one of the players has a winning strategy. In this talk, we
will go through a simple proof that for closed sets A, the game G(A)
is determined. Next, we will look at several consequences of the
Axiom of Determinancy in computability theory and in set theory. I
will not presuppose any background in computability theory or set
theory (modulo a minimal amount of hand waving) for this talk.
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UConn Math Club
Speaker: Keith Conrad (University of Connecticut)
Time: Wednesday, September 6, 2006 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: This talk will explore a discrete version of calculus which
applies to sequences: integrals are replaced by sums and
derivatives are replaced by
a discrete difference operator.
In this setting, summation formulas such as
12 + 22 + … + n2 =
n(n+1)(2n+1)/6
can be derived naturally using a discrete analogue of
the fundamental theorem of calculus, in much the same
way that integrals are computed.
We will also meet a discrete
analogue of integration by parts.
Comments: Free Refreshments
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Colloquium
Speaker: Paul-Jean Cahen (Université Paul Cézanne, Aix-Marseille III/UConn)
Time: Thursday, September 7, 2006 at 4:00 pm
Place: MSB 118 (Storrs)
Abstract: The binomial polynomial $(Xn)$ clearly takes each integer to an integer, although its coefficients
are not in $SZ.$ Integer-valued polynomials have been known for a long time and used in calculus.
They form a ring:
$$int(SZ)={finSQ[X]mid f(SZ)subseteqSZ}$$
which turns out to be one of the most natural examples of a non-Noetherian domain. Integer-valued
polynomials indeed provide an excellent source of numerous easy counterexamples.
These polynomials are best viewed as functions, mapping $SZ$ into $SZ,$ continuous in the
$p$-adic topology (for each prime $p$). They form a dense subset of the ring of continuous
functions (a $p$-adic version of the Stone-Weierstrass theorem which dates back to Dieudonn'e).
More generally, if $D$ is an integral domain with quotient field $K$, and $E$ a subset of $D$, the
ring of integer-valued polynomials on $E$ is the ring
$$inted={fin K[X]mid f(D)subseteq D}.$$
There are topological and algebraic aspects to this topic. This is a very rich theory: several
indeterminates were considered as early as in the beginning of the last century; integer-valued
rational functions, polynomials (or rational functions) which are integer-valued together with
their derivatives up to some order have also been studied. We shall briefly tour these questions in
our survey.
pdf version of
the abstract
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Analysis and Probability Seminar
Speaker: Alex Stokolos (DePaul University)
Time: Friday, September 8, 2006 at 3:00 pm
Place: MSB 403 (UConn - Storrs)
Abstract: First, I will remind basic concepts of the differentiation of
integrals theory. Then, I will discuss relationship between certain
multipliers generalizing the Hilbert transform and maximal operators
generalizing the Hardy-Littewood maximal function. The ideas here are
arguments of sort used by C.Fefferman in order to disprove disc
conjecture.
Some new results will be presented too.
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Algebra Seminar
Algebra Seminar
Geometry Seminar
Speaker: Kasra Rafi (University of Connecticut)
Time: Tuesday, September 12, 2006 at 4:30 pm
Place: MSB 117 (UConn - Storrs)
Abstract: It is known that the volume of a ball of radius R in
Teichmuller space grows exponentially with respect to R.
We show, however, that its "circumference" grow only
quadratically. This provides another point of view from
which the Teichmuller space is different from a hyperbolic
space. This is joint work with Moon Duchin.
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S.I.G.M.A. Seminar
Speaker: Gorjan Alagic (University of Connecticut)
Time: Wednesday, September 13, 2006 at 4:20 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Discrete Fourier Analysis is an area of mathematics replete with
interesting practical applications, none of which will be discussed in
this talk. The goal of the talk will instead be to develop a very basic
understanding of the mathematical properties of the Fourier Transform on
finite abelian groups. We will apply our new knowledge by proving a simple
uncertainty theorem, which states that a function and its transform cannot
both be highly concentrated. Finally, we will briefly discuss why one can
actually develop a sensible notion of Fourier Analysis in the setting of
nonabelian groups.
If time allows, we will provide some hints as to why all of this might be
related to Ben Green and Terence Tao's amazing (see: Fields medal) result
on arithmetic progressions in the primes.
No background is assumed, beyond a basic familiarity with groups.
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UConn Math Club
Speaker: Tom Roby (University of Connecticut)
Time: Wednesday, September 13, 2006 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Many interesting formulas can be given bijective
proofs: count the elements of a set in two different ways,
or show that there is a correspondence between
two different sets to get an equality. Proofs of this type can give
better insight than others into why some facts are true.
We will discuss many examples, involving binomial
coefficients, Fibonacci numbers, and a famous theorem of Fermat.
Comments: Free Refreshments
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Colloquium
Speaker: Lauren Williams (Harvard)
Time: Thursday, September 14, 2006 at 4:00 pm
Place: MSB 118 (Storrs)
Abstract: The partially asymmetric exclusion process (PASEP) is an important model
from statistical mechanics which describes a system of interacting
particles hopping left and right on a one-dimensional lattice of n
sites. It is partially asymmetric in the sense that the probability
of hopping left is q times the probability of hopping right.
Additionally, particles may enter from the left with probability
&alpha and exit from the right with probability &beta.
We will explain a close connection between the PASEP and the combinatorics of permutation tableaux. (These tableaux come indirectly from the totally nonnegative part of the Grassmannian, via work of Postnikov.) Namely, in the long time limit, the probability that the PASEP is in a particular configuration &tau is essentially the generating function for permutation tableaux of shape &lambda(&tau) enumerated according to three statistics. Applications include some monotonicity results for the PASEP, and enumerative results for permutations.
This work is joint with Sylvie Corteel.
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Analysis and Probability Seminar
Speaker: Alex Stokolos (DePaul University)
Time: Friday, September 15, 2006 at 3:00 pm
Place: MSB 403 (UConn - Storrs)
Abstract: In this lecture I will discuss Tauberian condition of
A.Cordoba and R.Fefferman introduced in the previous talk. Also, I will
demonstrate that a maximal operator associated with the homothecy
invariant density basis of convex sets is bounded in L^p for some large
value p. The key elements of the proofs in both talks are certain
geometric considerations, thus the talks should be accessible to
graduate students.
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Logic Seminar
Speaker: Yun Lu (Wesleyan University)
Time: Monday, September 18, 2006 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: Let M be a countable omega-categorical structure with a finite relational language. A reduct of M can be regarded as a closed subgroup of Sym(M) containing Aut(M). Motivated by a paper of Thomas in 1996 classifying certain reducts of graphs, we show that there are only finitely many reducts on random bipartite graphs.
To do this we apply Thomas' combinatorial approach, which uses a result of Nesetril-Rodl in the context of a strong finite submodel property, and are able to classify the reducts of the random bipartite graphs. In this talk, we will describe the classification of the reducts, and sketch some parts of the proof as time permits.
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Algebra Seminar
Speaker: Gorjan Alagic (University of Connecticut)
Time: Tuesday, September 19, 2006 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Uncertainty principles are assertions of the form 'a function and its
Fourier transform cannot be simultaneously highly concentrated.' The first
such principle for functions on finite abelian groups was proved by Donoho
and Stark in 1989, and states that the product of the supports of a
function and its transform is at least the size of the group. More
recently, Tao showed in 2003 that in cyclic groups, the sum of these
supports is at least the order of the group plus one. In this talk, we
will discuss extensions of uncertainty principles to the nonabelian
setting. This is joint work with Alexander Russell.
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Geometry Seminar
Speaker: Rob Kusner (UMass Amherst)
Time: Tuesday, September 19, 2006 at 4:30 pm
Place: MSB 117 (UConn - Storrs)
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S.I.G.M.A. Seminar
Speaker: Lance Miller (University of Connecticut)
Time: Wednesday, September 20, 2006 at 4:20 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We all know that there are an infinite number of prime numbers.
In 1837 Dirichlet showed that there were also an infinite
number of primes in any congruence class a mod m for (a,m) = 1. This
work lead him to define L-functions, and in the opinion of Harold
Davenport marks the begining of Analytic Number Theory. We will
present a treatment of zeta-functions and L functions with the aim to
prove this
result. We will only require basic group theory and complex analysis.
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UConn Math Club
Speaker: Avraham Bourla (University of Connecticut)
Time: Wednesday, September 20, 2006 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Cryptography is the science of writing messages in a way that can be read
by only the ones for whom they are intended. In our discussion, which will be given at an introductory level, we will give a brief history of the subject and
introduce the notion of private key and public key systems of encryption.
We will discover why prime factorization and prime numbers play such an important role in modern day cryptography (that is, since the 1970s) and create our own public key cipher. As a consequence we'll see a connection to
computer algorithms and the unsolved P vs. NP completeness problem.
Comments: Free Refreshments
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Colloquium
Speaker: Richard Schwartz (Brown University)
Time: Thursday, September 21, 2006 at 4:00 pm
Place: MSB 118 (Storrs)
Abstract: Recently Pat Hooper and I proved that a triangle has
a periodic billiard path provided it is sufficiently close to
being an isosceles triangle. This innocent sounding result
hides the extreme combinatorial complexity of triangular billiards,
as I will demonstrate in the talk. I'll try to explain how ideas
of self-similarity and Fourier series play a role
in the proof. If time permits, I
will demonstrate McBilliards, a graphical research tool created
by Hooper and myself, which allows the user to explore and
organize periodic billiard paths in triangles. The ultimate
goal of this program is to answer the age-old question "Does
every triangle have a periodic billiard path?"
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Analysis and Probability Seminar
Speaker: Richard Bass (University of Connecticut)
Time: Friday, September 22, 2006 at 3:00 pm
Place: MSB 403 (UConn - Storrs)
Abstract: I'll talk about the degenerate elliptic operator:
$$sum_{i=1}^2 [x_1 x_2 a(x) D_{ii} f(x)+ b_i(x) D_i f(x)]$$
in the positive quadrant, where the $a(x)$ are
continuous and positive and the $b_i$ are continuous and non-negative.
This equation comes from a mutually catalytic model in
population genetics. The main tool to proving uniqueness
is Cotlar's lemma, a theorem in harmonic analysis. This is joint
work with Ed Perkins of UBC.
Comments: This talk has been categorized by the speaker as general.
See the guidelines above.
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Mathematics Education
Speaker: Fabiana Cardetti (University of Connecticut)
Time: Monday, September 25, 2006 at 5:00 pm
Place: MSB 403 (UConn - Storrs)
Abstract: Since the Fall Semester of 2005 the mathematics department has been offering Math 202W a writing course that is taken concurrently with Math 210 the standard multivariable calculus course. The purpose in Math 202W is to use diary writing to chronicle the students teaching and learning experience in their respective sections of Math 210. In this talk, I will be sharing our experience teaching this course, the surprising lessons learned, and the interesting themes that emerged from the students? reports.
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S.I.G.M.A. Seminar
Speaker: Oscar Levin (University of Connecticut)
Time: Wednesday, September 27, 2006 at 4:20 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The Four Color Theorem states that every map can be colored with at
most four colors in such a way that no bordering countries share the
same color. The theorem was first proved in 1976, however in 1879
Alfred Kempe gave a "proof" which stood unchallenged for 11 years. In
this talk we will build up the necessary graph theory to convince
ourselves that Kempe's proof is correct, and then see why it is not.
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UConn Math Club
Speaker: Joe Miller (University of Connecticut)
Time: Wednesday, September 27, 2006 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Hex is a simple two-player game invented independently by Piet Hein
and John Nash (of “A Beautiful Mind” fame).
A nice argument shows that
the game cannot end in a draw, so one of the players must have a
winning strategy. Moreover, we know which one. Using a
strategy-stealing argument, we will prove that if the first player
plays flawlessly, then he will always win. Can such a game be any fun?
Yes, because there's a catch. The proof that the first player can
always win gives absolutely no hint as to how the first player should
play. It is what we call a non-constructive proof. So, the first
player knows that he can win, but he doesn't know how to
win. Instead of being provably pointless, Hex is perfectly playable.
There is even a book written about Hex strategy.
Comments: Free Refreshments
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Colloquium
Speaker: Eyal Markman (UMass)
Time: Thursday, September 28, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Calabi-Yau manifolds are complex (kahler) manifolds with a nowhere
vanishing holomorphic volume form. They play an important role in
String theory. The collection of holomorphic vector bundles on
Calabi-Yau manifolds admit symmetries, known as Fourier-Mukai
transformations.
Two dimensional Calabi-Yau manifolds are holomorphic symplectic surfaces.
Examples include resolution of simple surface singularities (ALE
surfaces), and two compact types: complex tori, and K3 surfaces.
The theory of vector bundles on these surfaces
is particularly well behaved, with many beautiful structures.
Vector bundles over ALE surfaces are parametrized by Nakajima's
Quiver varieties, and lead to representations of Kac-Moody algebras.
Fourier-Mukai transformations play the role of Weyl group elements.
We will survey the above, and indicate partial analogues over
K3 surfaces and complex tori.
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Analysis and Probability Seminar
Speaker: Leonid Slavin (University of Connecticut)
Time: Friday, September 29, 2006 at 3:00 pm
Place: MSB 403 (UConn - Storrs)
Abstract: Computing the operator norms of maximal functions on Lp(Rn) is a
classical harmonic analysis problem. This has been done in one dimension
in the general case and for all n in the martingale case.
The Bellman function method has in recent years been shown to hold much
promise in finding best known/sharp constants in various settings. This
problem allows for a transparent Bellman function setup. Finding the
corresponding Bellman function would, among other things, deliver the
exact value of the norm. The dyadic Bellman functions have been computed
by Melas using combinatorial techniques.
We attempt to compute these dyadic functions using the classical Bellman
PDE and make a transition to the general case (ideally, in the
multi-dimensional setting). This is a report on joint work in progress
with Alex Stokolos. The talk will lay out the basics of the method and
should be accessible to the general analytical audience.
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Algebra Seminar
Speaker: Paul-Jean Cahen (University of Connecticut)
Time: Tuesday, October 3, 2006 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Various generalizatrions have been given of factorial sequences. Almost
all of them can be interpreted with integer-valued polynomials.
Nice proofs can then be given of various properties. New questions arise
in this context. Several of them concern simultaneous orderings.
(This is a joint survey paper with Jean-Luc Chabert).
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Geometry Seminar
Speaker: Jane Gilman (Rutgers University and Yale University)
Time: Tuesday, October 3, 2006 at 4:30 pm
Place: MSB 311 (UConn - Storrs)
Abstract: There are certain families of words and word sequences (words in the generators of a two--generator group) that arise frequently in the Teichmuller theory of hyperbolic three--manifolds and Kleinian and Fuscian groups and in the disceteness problem for two generator matric groups. We survey some of the families of such words and sequences: the semigroup of so called good words of Gehring-- Martin, the so called killer words of Gabi--Meyerhoff--Thurston, the Farey words of Keen--Series and Minsky, and the Fibonacci sequences of Gilman--Jiang. We establish connections between these families.
Comments: Note the special room.
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S.I.G.M.A. Seminar
Speaker: Dennis Eichhorn (University of Connecticut)
Time: Wednesday, October 4, 2006 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: In this talk, we take a whirlwind tour of the theory of
partitions. Beautiful results from this area's rich history will
presented, and the connections between partition theory and many other
fields will be discussed. The talk will be aimed at the
partition-theoretically uninitiated, and should be accessible to
everyone.
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UConn Math Club
Speaker: Kiran Kedlaya (MIT)
Time: Wednesday, October 4, 2006 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: It's pretty easy to divide a cake among two people so that each person thinks his piece is at least as good as the other: have one person divide the cake into two equal-looking pieces and have the other person pick one.
But how do you divide a cake among three people so that each person thinks his piece is at least as good as either of the other two? I'll describe an answer, due to Francis Su, which surprisingly is quite closely related to a basic fact from topology called the Brouwer fixed point theorem.
USG funded
Comments: Free Refreshments
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Colloquium
Speaker: Michael Thaddeus (Columbia University)
Time: Thursday, October 5, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Mirror symmetry is a duality between pairs of algebraic varieties
inspired by string theory. In general mirror partners are very
difficult to construct. But we will show that for quotients of complex
tori by a finite group acting by translations and rotations, mirror
partners can be obtained by a simple construction
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Analysis and Probability Seminar
Speaker: Richard Nickl (University of Connecticut)
Time: Friday, October 6, 2006 at 3:00 pm
Place: MSB 319 (UConn - Storrs)
Abstract: We consider sequences of probability measures P_n that are
random in the sense that they are functions of a given i.i.d. sample
of n random variables with common law P. Examples are: the empirical
measure; smoothed versions of the empirical measure; truncated
Fourier series expansions of the empirical measure; as well as
nonparametric maximum likelihood estimators. We discuss a variety of
limit theorems for the (centered) random measure processes (P_n-P) at
the rate n^1/2 of the central limit theorem.
Comments: The speaker has categorized this talk as general.
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PDE and Image Analysis Seminar
Speaker: Changfeng Gui (University of Connecticut)
Time: Monday, October 9, 2006 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
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Logic Seminar
Speaker: Jim Schmerl (University of Connecticut)
Time: Monday, October 9, 2006 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: Ramsey's Theorem has inspired the subject of Ramsey Theory.
Euclidean Ramsey Theory is that aspect of Ramsey Theory involving
Euclidean spaces R^n and having some geometric content. A basic result
is the Gallai-Witt Theorem: If X,Y are finite subsets of R^n, then for any
red/blue coloring of R^n, there is a monochromatically red set similar to X
or a monochromotically blue set similar to Y. Can this theorem be
extended to
infinite sets? An early example due to Erdos, Graham et al shows that not
both X,Y can be infinite. A later example by Baumgartner shows that X cannot
be infinite if Y is a 3-element collinear set. I will show that X cannot
be infinite
if Y consists of the n+1 vertices of an n-simplex. The proof has a
model-theoretic flavor.
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Algebra Seminar
Speaker: Paul-Jean Cahen (University of Connecticut)
Time: Tuesday, October 10, 2006 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
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Geometry Seminar
Speaker: Martin Bridgeman (Boston College)
Time: Tuesday, October 10, 2006 at 4:30 pm
Place: MSB 117 (UConn - Storrs)
Abstract: We analyse how the Hausdorff dimension of the limit set changes near the fuchsian locus in quasifuchsian space of a surface. We describe a new metric on Teichmuller space obtained by taking the second derivative of the Hausdorff dimension and show that this new metric is bounded below by the classical Weil-Petersson metric. We use this to relate the change in Hausdorff dimension under bending along a measured lamination to the length in the Weil-Petersson metric of the associated earthquake vector of the lamination.
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Mathematics Education
Speaker: Paul-Jean Cahen (Université Paul Cézanne, Aix-Marseille III/UConn)
Time: Wednesday, October 11, 2006 at 3:00 pm
Place: Gentry 142 (UConn - Storrs)
Abstract: The educational outreach program: "A Scientist in the Classroom" is run by CCSTI-
Agora des Sciences (Centre de Culture Scientifique Technique et Industrielle), an association devoted to the dissemination of scientific culture in the Provence-Alpes-
Cote d'Azur (PACA) region. The program brings university faculty and research fellows into the local high-school classrooms, for lectures and discussions on scientific topics.
In the first part of the talk I will give a general description of this program.
In the second part of the talk I will elaborate on my personal experience as a participating faculty from the University of Marseille, and include the highlights of one of my lectures: The Story of Pi. 3.14.... , following the trail of known digits after the decimal point through history, one embarks on a voyage around the world, from antiquity to modern times, and through all areas of mathematical knowledge.
Comments: Light refreshments will be provided.
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S.I.G.M.A. Seminar
Speaker: Keith Conrad (University of Connecticut)
Time: Wednesday, October 11, 2006 at 5:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We will introduce the Riemann hypothesis and illustrate
its importance by explaining some of its consequences to
problems that, on the surface, appear unrelated to it.
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Analysis and Probability Seminar
Speaker: Ryan Mullen (University of Connecticut)
Time: Friday, October 13, 2006 at 3:00 pm
Place: MSB 403 (UConn - Storrs)
Abstract: Let $A^p$ be the Banach space of all continuous functions on the
torus whose Fourier coefficients are in $ell^p$. For some $p$ it
can be shown that $A^p$ is not an algebra. In this talk we will
journey through my thought train on our way to realizing this fact.
At the end we will show analogous results for $A^{p,infty}$ (The
space of all continuous functions on the torus whose Fourier
coefficients are in weak $ell^p$). Concluding with a curious
difference between the two types of spaces for $p=1$.
Comments: The speaker has categorized this talk as general.
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UConn Math Club
Speaker: Nick Flowers (Morgan Stanley)
Time: Friday, October 13, 2006 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: The Black-Scholes formula is a fundamental result in mathematical
finance, which explains how to set the price of options (under
suitable assumptions). We will introduce options, derive
the Black-Scholes formula, and explain the financial insight
behind the formula. It will be assumed the audience
knows what a partial derivative is, but techniques for
solving partial differential equations will not be required.
If time permits, after the talk I will explain a little bit
about what life is like as a “quant” and answer
any questions students have about careers in finance.
USG funded
Comments: Free Refreshments
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PDE and Image Analysis Seminar
Speaker: Chunming Li (Vanderbilt University Institute of Imaging Science)
Time: Monday, October 16, 2006 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Blood vessel segmentation has important applications in image-guided
neurosurgery, pre-operation planning and clinical analysis. In
typical blood vessel images, the pixel intensity in the vessel and
the background is not statistically homogeneous, such as due to the
beam-hardening effect in X-ray CT or variable contrast distribution
in MRI. Many existing segmentation methods suffer from errors due to
image inhomogeneities. In this talk, I will first review some
existing active contour models for image segmentation with their
advantages and disadvantages. Then, I will introduce a novel
region-based active contour/surface mode and its application for
vessel segmentation. Our method is based on a mild assumption that
an image is locally binary. In our method, the active
contours/surfaces move in the image domain to minimize a local
binary fitting energy. The proposed active contour/surface model can
be formulated as a variational level set method. Due to the local
binary fitting energy in the proposed active contour model, our
method is able to segment images with non-homogeneous regions and
multiple distinct means of pixel intensity. In particular, our
method has been applied for 2D and 3D vessel segmentation with
satisfactory results. In addition, I will also demonstrate a
potential application of our method for DTI (diffusion tensor image)
segmentation with some preliminary results. Basic concepts in DTI
will be briefly reviewed.
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Algebra Seminar
Speaker: Keith Conrad (University of Connecticut)
Time: Tuesday, October 17, 2006 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
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S.I.G.M.A. Seminar
Speaker: Upendra Prasad (University of Connecticut)
Time: Wednesday, October 18, 2006 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: I will discuss flock behaviours in birds, fish schools etc. with a
decentralized coordination rule based on a Nearest Neighbourhood Model.
This model has got a lot of applications in explaining the pattern in
flock movements and in computer animation. No specific knowledge is
required, only some basic idea of matrices and graph theory.
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UConn Math Club
Speaker: Paul-Jean Cahen (Univ. Marseille)
Time: Wednesday, October 18, 2006 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: It is often claimed that the Babylonians were the first to solve quadratic
equations. But is it so?
We will talk about problems encountered in their tablets, how they
solved them, and give a little insight into what an equation
is and what algebra
means (originally). Then we will talk about cubics and explain
Cardano's formula for their roots, which
shows how cubics (not quadratics!) are at the origin of complex numbers.
USG funded
Comments: Free Refreshments
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Colloquium
Speaker: Gregg Zuckerman (Yale)
Time: Thursday, October 19, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
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Analysis and Probability Seminar
Speaker: Matt Cecil (University of Connecticut)
Time: Friday, October 20, 2006 at 3:00 pm
Place: MSB 403 (UConn - Storrs)
Abstract: The Taylor map is unitary map from the Hilbert space of holomorphic
functions which are square integrable with respect to a gaussian measure
to the symmetric tensor algebra over C. It is one aspect of a larger
correspondence which is used in the physical analysis of the quantum
harmonic oscillator. I'll review the classical case and indicate how this
map can be extended to functions defined on the infinite dimensional space
of paths on C.
Comments: The speaker has labeled this talk as general
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PDE and Image Analysis Seminar
Speaker: Changfeng Gui (University of Connecticut)
Time: Monday, October 23, 2006 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: In this talk I will present a new hamiltonian identity for PDEs and systems of PDEs.
I will also show some interesting applications of the identity to problems
in phase transition, such as the proof of Young's law in triple junction configuration for a vector-valued Allen Cahn model and the derivation of
a necessary condition for the existence of saddle solutions for Allen-Cahn
equation with asymmetric double well potential.
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Logic Seminar
Speaker: David Marker (University of Illinois at Chicago)
Time: Monday, October 23, 2006 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: If E is a Borel equivalence relation with countable classes there is an infinitary sentence with isomorphism relation bireducible to E. Hjorth and Kechris asked if this is true for first order theories. I'll show that it is not for theories with uncountably many types.
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Algebra Seminar
Speaker: Keith Conrad (University of Connecticut)
Time: Tuesday, October 24, 2006 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
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Special Talks
Speaker: Richard Nickl (University of Connecticut)
Time: Tuesday, October 24, 2006 at 4:00 pm
Place: MSB 315 (Storrs)
Abstract: This will be a continuation of the previous two seminars.
A paper by Jozsef Beck in ZW 70 (1985) 289-306, “Lower bounds
on the approximation of the multivariate empirical process,” has among
other things a theorem saying that for balls in dimension d the empirical
process for the uniform probability on the unit cube differs from its Gaussian
limit by at least of order $n^{-1/(2d)}$, which gives quite a slow rate in high
dimensions.
Beck’s proof seems difficult. The talk will get into the proofs in the
paper and an effort to understand them. Lemmas 3 and 5 were dealt with
in the first talk; the second focused on Lemma 4. This seminar will deal
with Lemma 1.
Comments: Boston Stochastics Seminar. Tea is offered at 3:45 pm in the Math Lounge on the first floor of MSB.
|
Geometry Seminar
Speaker: Dylan Thurston (Columbia University)
Time: Tuesday, October 24, 2006 at 4:30 pm
Place: MSB 117 (UConn - Storrs)
Abstract: We give a completely combinatorial definition and proof of invariance of Heegaard-Floer homology for links in the 3-sphere. The definition is based on a grid-link presentation of the link, also known as an arc presentation. The Euler characteristic gives an apparently new method of computing the Alexander polynomial, dubbed the Minesweeper Method. Parts of this talk are work of Manolescu, Ozsvath, and Sarkar (math.GT/0607691), and parts are joint work with Manolescu, Ozsvath, and Szabo.
|
Colloquium
Speaker: Leonid Gurvits (Los Alamos Natl. Lab)
Time: Wednesday, October 25, 2006 at 2:00 pm
Place: ITEB 336 (UConn - Storrs)
Abstract: The van der Waerden conjecture states that the permanent of n by n
doubly stochastic matrix A satisfies the
inequality Per(A) >= n! / n^n (VDW bound) and was finally proven
(independently)
by D.I. Falikman and G.P. Egorychev in 1981.
Its worthy successor, the SCHRIJVER-VALIANT conjecture on the lower
bound on the number of perfect
matchings in k-regular bipartite graphs was posed in 1980 and
resolved by A.Schrijver in 1998.
The Schrijver's proof is one the most remarkable (and "highly
complicated") results in the graph theory.
We introduce and prove a vast generalization of the VAN der WAERDEN
conjecture as well SCHRIJVER-VALIANT
conjecture.
Our generalization not only affects the world of permanents, but also
has important implications concerning
PDEs, stability and control theory, complexity theory. Besides,
our proof is much shorter and conceptually simpler than the original
proofs; it proves VAN der WAERDEN/SCHRIJVER-VALIANT conjectures
in "one shot".
The main tool in our generalizations and proofs is a concept of
hyperbolic polynomials.
Hyperbolic polynomials were originally introduced and studied in the
PDE theory.
They are also closely related to the multivariate stable polynomials.
VAN der WAERDEN/SCHRIJVER-VALIANT CONJECTURES correspond to the
hyperbolic polynomials being
products of linear forms.
Our proof is relatively simple and "noncomputational"; it actually
improves Schrijver's lower bound,
provides a generalization for non-regular graphs,
and uses very basic (more or less centered around
Gauss-Lukas theorem) properties of hyperbolic polynomials.
The theory is fairly straightly generalized to handle the number of
partial matchings (joint work with S. Friedland).
One of the applications results in the best estimate of the
3-dimensional monomer-dimer entropy.
Time permit, I will describe my recent result on analogues of VAN
der WAERDEN/SCHRIJVER-VALIANT CONJECTURES for
the mixed volume of compact convex sets . This generalization goes
beyond hyperbolic polynomials and results
in a randomized poly-time algorithm to approximate the mixed volume
of n convex compact subsets in R^n within
a multiplicative factor e^n.
The talk is based on the speaker's paper available at
http://xxx.lanl.gov/abs/math.CO/0510452.
See also a shorter version in Proc. of STOC-2006 .
Comments: Joint with CS. New time!!, Wednesday colloquium, not at the usual time and not at the usual place
|
S.I.G.M.A. Seminar
Speaker: Sarah Frey (University of Connecticut)
Time: Wednesday, October 25, 2006 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: In 1911, A.E.H. Love published a linear elastic model for the deformation
of a homogeneous, compressible sphere due to tidal forces. Recent
numerical evaluations of the solution to his governing equations reveal
the existence of bodies for which infinitesimal tide raisers can raise
tides of
arbitrary height. We will investigate the nature of these surprising
singularities by looking in detail at the related, simpler problem of a
sphere collapsing under its own self-gravity.
|
UConn Math Club
Speaker: Mike Rosen (Brown)
Time: Wednesday, October 25, 2006 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Number theory begins by investigating properties of the
integers. Analogous properties can also be asked about
polynomials. For instance, we can consider Fermat's last theorem in its
classical form (are there positive integer
solutions
to xn +
yn = zn when
n > 2?)
and for polynomials (can we solve
f(t)n +
g(t)n = h(t)n
in polynomials?) We will also discuss the
abc conjecture for the integers and for polynomials,
give a proof of the conjecture in
the polynomial case, and use that to give a proof of Fermat's last theorem
for polynomials. We will then explore other uses for the
abc conjecture.
Finally, we will consider a generalization of the
abc conjecture and, if
time permits, give the outline of a proof in the polynomial case.
USG funded
Comments: Free Refreshments
|
Analysis and Probability Seminar
Speaker: (University of Connecticut)
Time: Friday, October 27, 2006 at 3:00 pm
Place: MSB 403 (UConn - Storrs)
|
PDE and Image Analysis Seminar
Speaker: Michael Plum (University of Karlsruhe)
Time: Monday, October 30, 2006 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: ABSTRACT
The lecture is concerned with numerical enclosure methods for
nonlinear elliptic boundary value problems. Here, analytical
and numerical methods are combined to prove rigorously the existence
of a solution in some ”close” neighborhood of an
approximate solution computed by numerical means. Thus, besides the
existence proof, verified bounds for the error (i.e.
the difference between exact and approximate solution) are provided.
For the first step, consisting of the computation of an approximate
solution ù in some appropriate Sobolev space, no
error control is needed, so a wide range of numerical methods
(including multigrid schemes) is at hand here. Using ù, the
given problem is rewritten as a fixed-point equation for the error,
and the goal is to apply a fixed-point theorem providing
the desired error bound.
The conditions required by the chosen fixed-point theorem are now
verified by a combination of analytical arguments
(e.g. explicit Sobolev embeddings) and verified numerical computations
of certain auxiliary terms.
The method is illustrated by several examples (on bounded as well as
on unbounded domains), where in particular it
gives existence proofs in cases where no purely analytical proof is
known.
|
Logic Seminar
Speaker: CT Chong (National University of Singapore)
Time: Monday, October 30, 2006 at 3:30 pm
Place: Exley Science Center 121 (Wesleyan University)
Abstract: The talk is based on joint work with Ted Slaman and Yue Yang. We sketch a proof of the following theorem: The combinatorial principle COH (cohesiveness) is Pi^1_1 conservative over models of RCA_0+BSigma_2.
Comments: Note the unusual time and room!
|
Mathematics Education
Speaker: Deborah Hughes Hallett (University of Arizona/Harvard University)
Time: Monday, October 30, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Over the past two decades, a spotlight has been on calculus, precalculus,
and college algebra courses. In this talk, we will look at why this
happened, what the challenges were, and how changes in curriculum,
pedagogy, and technology have changed the course. What do we expect in the
future? What does research tell us about how to encourage students to
think deeply about what they are learning? How do we ensure our calculus
courses are good preparation for the future?
Comments: tea at 3:30 pm
|
Algebra Seminar
Speaker: Dennis Eichhorn (University of Connecticut)
Time: Tuesday, October 31, 2006 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: A natural question to ask is, "How many ways can an integer n
be expressed as a sum of positive integers?" This question is the
cornerstone of the area of mathematics known as Partition Theory, and it
is surprisingly difficult to answer. For example, if we let p(n) be the
number of these expressions of n, even the parity of p(n) remains
something of a mystery, despite the fact that it has been studied for
over a century. In particular, although empirical evidence (the first
several million values) seems to indicate that Po(N) = [the number of odd
values of p(n) up to N] is asymptotic to N/2, no one has even been able
to show that Po(N) is larger than the square root of N for N sufficiently
large. Until recently, the best known lower bound for Po(N) was proven
using properties of l-adic Galois representations and the theory of
modular forms. In this talk, we give a better lower bound using
elementary generating function techniques coupled with results from
classical analytic number theory. This talk will be aimed at the
partition theoretically uninitiated, and a great deal of background will
be provided.
|
Geometry Seminar
Speaker: Elizabeth Denne (Harvard University)
Time: Tuesday, October 31, 2006 at 4:30 pm
Place: MSB 117 (UConn - Storrs)
Abstract: The ropelength problem asks to minimize the length of a knotted curve subject to maintaining an embedded tube of fixed radius around the curve; this is a mathematical model of tying the knot tight in rope of fixed thickness. This talk will discuss some of the known results to this problem. Then, using the existence of a special quadrisecant line, we show the ropelength of any nontrivial knot to be at least 15.66. Numerical experiments have found a trefoil with ropelength less than 16.372.
|
S.I.G.M.A. Seminar
Speaker: Kristen Sellke (University of Connecticut)
Time: Wednesday, November 1, 2006 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: A focus of knot theory has always been to determine characteristics of knots which are invariant under ambient isotopy. Some early knot invariants are tricolorability and the Alexander polynomial. We will look at these knot invariants as well as the more recent Jones polynomial and its extension to 3-manifolds via skein modules.
|
UConn Math Club
Speaker: Jesse Kass (Harvard)
Time: Wednesday, November 1, 2006 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: By today's standards, the classic video game Asteroids is almost
primitive. In the game, the player flys a wedge-shaped spaceship and
destroys asteroids. Outer space is represented by a 2-dimensional map
which is superficially similar to the map of Earth. While the game play of
Asteroids is rather simple, the underlying mathematics is not!
In my talk, I will use the example of the game Asteroids to explore the
nature of abstract shapes in 2 dimensions and beyond. I'll discuss some
interesting aspects of “Asteroids space”
and compare these properties to the
properties of more familiar shapes.
USG funded
Comments: Free Refreshments
|
Colloquium
Speaker: Daniel Hershkowitz (Technion,)
Time: Thursday, November 2, 2006 at 4:00 pm
Place: MSB 118 (Storrs)
Abstract: A complex square matrix A is said to be stable if the spectrum of A
lies in the open left or right half-plane. This, as well as other
related types of matrix stability, play an important role in various
applications. As such, matrix stability has been intensively
investigated in the past two centuries. A plausible way for finding
necessary and/or sufficient conditions for matrix stability is to
examine classes of matrices that are known to be stable, and to
identify common properties of these classes. Indeed, some well known
classes of stable matrices share properties associated with
nonnegativity, such as positivity of the principal minors
(P-matrices) and weak sign symmetry. It was conjectured by Carlson
that the combination P-matrix + weak sign symmetry implies stability.
This conjecture was recently disproved by Holtz. However, if we
replace the weak sign symmetry by the stronger sign symmetry
property, then it was shown already by Carlson that P-matrix + sign
symmetry implies stability. The talk will review various results that
relate positivity of the principal minors, weak sign symmetry, sign
symmetry and stability.
|
Analysis and Probability Seminar
Speaker: Michael Marcus (CUNY)
Time: Friday, November 3, 2006 at 3:00 pm
Place: MSB 403 (UConn - Storrs)
Abstract: This talk has been cancelled due to illness in the family.
Abstract
|
Logic Seminar
Speaker: Norman Danner (Wesleyan University)
Time: Monday, November 6, 2006 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: The weak pigeonhole principle (WPHP) states that there is no injective
function from a set of size $n^2$ to a set of size~$n$, or dually,
that there is no surjective function from the smaller set to the
larger one. If the weak pigeonhole principle for polynomial-time
computable functions is provable at the first level of the bounded
arithmetic hierarchy $S_2^1$ (probably the most important level
from the standpoint of computational complexity), then the RSA
cryptosystem is insecure, so even if it is provable, it is (hopefully!)
difficult to find the proof. Of course, *some* version ought to
be provable, and an interesting question is where the "threshold
of difficulty" is. In this talk I will start with a review of the
necessary notions from bounded arithmetic and the main results about
provability of WPHP. Then I will present a specific function algebra
for which a variant of the weak pigeonhole principle can be proved
in $S_2^1$. The proof is interesting in that it gives specific
tie-in between complexity and WPHP via a notion of complexity on
binary strings. This is joint work with Chris Pollett of San Jose
State University.
|
Special Talks
Speaker: Richard Nickl (University of Connecticut)
Time: Tuesday, November 7, 2006 at 4:00 pm
Place: MSB 315 (UConn - Storrs)
Abstract: This will be a continuation of the previous four seminars.
A paper by József Beck in ZW 70 (1985) 289-306, "Lower bounds
on the approximation of the multivariate empirical process," has among
other things a theorem saying that for balls in dimension d the empirical
process for the uniform probability on the unit cube differs from its Gaussian
limit by at least of order n-1/(2d) , which gives quite a slow rate in high
dimensions.
Beck's proof seems difficult. The talk will get into the proofs in the
paper and an effort to understand them. Lemmas 3 and 5 were dealt with
in the first talk; the second focused on Lemma 4. This seminar will continue
with Lemma 1.
Comments: Boston Stochastics Seminar. For rides from Boston, contact Richard Dudley.
|
S.I.G.M.A. Seminar
Speaker: Panel (University of Connecticut)
Time: Wednesday, November 8, 2006 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The best sources of information and advice for applying for jobs
in academia are those who have successfully done so. This week's seminar
will consist of a Q & A with a panel of professors who have recently gone
through the application process and have many valuable tips to share with
those seeking to do the same. The panel also includes faculty members who
have recently been on hiring committees and can give their viewpoint from
the other side. The panel members are Kristen Sellke, Ning Khamsemanan, Sarah Frey, Reed Solomon, Matt Cecil, and Fabiana Cardetti,. This promises to be an
extremely informative and useful session for all graduate students,
particularly for those looking to apply for jobs within the next few years.
You won't want to miss this valuable opportunity!
|
UConn Math Club
Speaker: Robert Makuch (Yale)
Time: Wednesday, November 8, 2006 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: In addition to discussing the main topic of the talk, which
should be clear from the title and will not be too technical, I would
also like to describe what my professional life is like
and how math and statistics can
play a useful role in society.
Note: The speaker received a BA in math from UConn in 1972.
Comments: Free Refreshments
Additional Comments: USG funded
|
Colloquium
Speaker: Joel Zinn (Texas A&M)
Time: Thursday, November 9, 2006 at 4:00 pm
Place: MSB 118 (Storrs)
Abstract: The main use of the Central Limit Theorem in Statistics is to estimate the mean (when the variance is known). One reason it is easy to use is that the necessary and sufficient condition is in terms of a simple function of the distribution, namely, the variance. When used in the infinite dimensional setting the necessary and sufficient conditions are not always deterministic. We will suggest some modifications to the classical empirical, which will allow the related limit theorem to be applied in a wider variety of situations.
|
Analysis and Probability Seminar
Speaker: Erin Terwilleger (University of Connecticut)
Time: Friday, November 10, 2006 at 3:00 pm
Place: MSB 403 (UConn - Storrs)
Abstract: Our main result characterizes the boundedness of certain Hankel
operators defined on the product Hardy space of square integrable
functions
analytic in each of n>2 variables separately. We define a Hankel
operator H_b to be pointwise multiplication by the conjugate of a
function b and then projecting onto the subspace of L^2 anti-analytic
in each variable.
We show that the operator norm of the Hankel operator H_b is
equivalent to the function b being in the the product BMO space,
dual to product H^1, as identified by S.-Y. Chang and R. Fefferman.
This fact has well known equivalences in terms of commutators and the
weak factorization of H^1 in higher parameters.
The proof we present is inductive and is influenced by the proof of
Ferguson and Lacey in the two parameter case. One is able to obtain
a lower bound in terms of a new $BMO$ space with one less parameter.
Then one is able to bootstrap up to the full $BMO$ using a particular
form of a lemma of Journ'e. In addition, the boundedness of certain
paraproduct operators plays a key role.
|
Logic Seminar
Speaker: Manuel Lerman (University of Connecticut)
Time: Monday, November 13, 2006 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: One of the central areas of research in degree theory over the
past 40+ years has been the attempt to characterize, as much as possible,
the complexity of the central degree-theoretic structures. One direction
has been to try to characterize the natural fragments of the elementary
theories that are decidable. Most of the questions have been answered,
but a few remain. We discuss our result that the existential theory
mentioned in the title is decidable, and give a brief survey of the
remaining open questions.
The framework for priority arguments, introduced by Lempp and the speaker,
is heavily used in the proof; we will not focus on the technical details
about the framework, but rather on identifying the properties of the
framework needed, and how the framework is used in the proof.
|
UConn Math Club
Speaker: Monique Ethier (University of Connecticut)
Time: Monday, November 13, 2006 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: A fixed point of a function f (x)
is a solution of the equation f (x) = x.
For example, the function cos x has one fixed point,
approximately .73908,
which can be found graphically by intersecting the graphs of
y = x and y = cos x;
at the intersection point (x, cos x) we have
cos x = x.
The fixed point of cosine can also be found numerically by hitting the
cosine button (in radians, please) on your calculator
repeatedly starting from any initial value you wish:
x0, cos x0,
cos(cos x0),
cos(cos(cos x0)),... will
always tend to the fixed point .73908... (try it!).
We will indicate why the concept of a fixed point is
important in mathematics, and in particular see how
a fractal like the Sierpinski gasket
is a “fixed point”
which can be approximated by iteration
starting from any initial set in the plane.
Comments: Free Refreshments
|
Algebra Seminar
Speaker: Mizan Khan (Eastern Connecticut State University)
Time: Tuesday, November 14, 2006 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We will discuss a heuristic estimate for the number of vertices of the convex closure of the graph of the modular hyperbola xy=1(mod n). The heuristic is based on an aymptotic formula of Renyi and Sulanke. This is joint work with Igor Shparlinski and Christian Yankov.
|
Geometry Seminar
Speaker: George Daskalopoulos (Brown University)
Time: Tuesday, November 14, 2006 at 4:30 pm
Place: MSB 117 (UConn - Storrs)
|
Mathematics Education
Speaker: Sarah Glaz (University of Connecticut)
Time: Wednesday, November 15, 2006 at 3:00 pm
Place: Gentry 142 (UConn - Storrs)
Abstract: This talks will describe an innovative course, developed by the speaker, at the University of Connecticut. The course’s purpose is to provide an engaging and effective preparation for science courses for students whose high school algebra needs reinforcement. The course combines a college-oriented review of Intermediate Algebra with weekly group projects in mathematical modeling, and uses online resources to enhance teaching and to facilitate the coordination of the course across University of Connecticut’s six campuses.
|
S.I.G.M.A. Seminar
Speaker: Matt Jura (University of Connecticut)
Time: Wednesday, November 15, 2006 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Fuzzy concepts arise naturally. Think about the way in which you would
describe how informative a certain Sigma talk is. Would you say ``Very
Informative," or ``Moderately Not Informative," or perhaps something else?
This is an example of a fuzzy concept. In this talk we will discuss the
basics of Fuzzy Set Theory in full mathematical rigor. We will begin with
the definition of a fuzzy set with numerous examples, then go over the
basic fuzzy set operations. We will then define the notion of a crisp set
and talk about the Resolution Theorems, a Representation Theorem,
Extension Principles, and Factor Spaces (time permitting).
|
Analysis and Probability Seminar
Speaker: Evarist Gine (University of Connecticut)
Time: Friday, November 17, 2006 at 3:00 pm
Place: MSB 403 (UConn - Storrs)
Abstract: Postpone till December 1, 2006
|
PDE and Image Analysis Seminar
Speaker: Joe Mckenna (University of Connecticut)
Time: Monday, November 27, 2006 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: A well-known theorem of Gidas-Ni-Nirenberg says that positive
solutions of semilinear elliptic equations have the same symmetries as
the domain. A natural question is if there is a similar result for the
various numerical approximate equations. We give some counterexamples
and some theorems.
|
Logic Seminar
Speaker: Stuart Zoble (Wesleyan University)
Time: Monday, November 27, 2006 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: Bounded Forcing Axioms are obtained from forcing axioms
by restricting the size of the dense sets, and can be characterized as
generic absoluteness principles. Bounded Martin's Maximum (BMM) is
equivalent to the assertion that H(omega_2) is Sigma_1 elementary in
H(omega_2)^{V[G]} whenever G is generic for a stationary set preserving
forcing notion. The consistency strength of BMM is unknown at present -
it lies somewhere between a strong cardinal and omega + 1 Woodin
cardinals. We present a strengthening of BMM which implies Projective Determinacy.
|
UConn Math Club
Speaker: James Chernesky (University of Connecticut)
Time: Monday, November 27, 2006 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: In high school we learned how to tell if polynomials of degree 2
factor by using the quadratic formula. However, this
method can't be used for higher
degree polynomials. We will look
at a number of criteria that will help us decide if a polynomial
of larger degree factors or not (with rational coefficients).
Some basic knowledge of modular arithmetic will be required.
Comments: Free Refreshments
|
Algebra Seminar
Speaker: Sug-Woo Shin (Harvard University)
Time: Tuesday, November 28, 2006 at 3:00 pm
Place: MSB 207 (UConn - Storrs)
Abstract: A big theme of the Langlands program is to construct a correspondence between l-adic representations of global Galois groups into GL(n) and automorphic representations of GL(n). Such a correspondence is determined, if it exists, by matching the images of Frobenius elements and the Satake parameters at all unramified primes. We first consider the case n=1 in which this matching is made via global class field theory and expressible in terms of local factors of L-functions. However, the local L-factors are 1 at ramified primes and do not provide meaningful information. The behavior at ramified primes is captured by local class field theory and its compatibility with global theory. When n=2, the Eichler-Shimura theory constructs Galois representations, which have expected properties at unramified primes, from modular forms. Again, the local-global compatibility at ramified primes (which do not divide l) completes our understanding. For n>2, most instances of Langlands correspondence have been established by studying Shimura varieties and their reduction at unramified (and ramified) primes. After reviewing the theory for n=1 and n=2, we will briefly explain the general picture for n>2 and some of the recent results.
Comments: Note the time and room change.
|
Colloquium
Speaker: John Boone Greer (Courant Institute of Mathematical Sciences, NYU)
Time: Tuesday, November 28, 2006 at 4:00 pm
Place: MSB 407 (UConn - Storrs)
Abstract: I will discuss a recent proof of a weak upper bound on the coarsening
rate of a discrete-in-space version of an ill-posed, nonlinear
diffusion equation. The continuum version of the equation violates
parabolicity and lacks a complete well-posedness theory. In
particular, numerical simulations indicate very sensitive dependence
on initial data. Nevertheless, models based on its discrete-in-space
version, which I will discuss, are widely used in a number of
applications, including population dynamics (chemotactic movement of
bacteria), granular flow (formation of shear bands), and computer
vision (image denoising and segmentation). The bounds have
implications for all three applications. This is joint work with Selim
Esedoglu (U. of Michigan Mathematics).
|
Geometry Seminar
Speaker: Kristen Sellke (University of Connecticut)
Time: Tuesday, November 28, 2006 at 4:30 pm
Place: MSB 117 (UConn - Storrs)
Abstract: The Kauffman bracket skein module is a 3-manifold invariant. We will give an overview of its computation for the complement of certain torus knots. Then, we will use the skein module to show that the noncommutative A-ideal (a generalization of the A-polynomial) is non-trivial.
|
Colloquium
Speaker: Dmitry Panchenko (MIT)
Time: Thursday, November 30, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: In order to study certain questions concerning the distribution of the overlap in the Sherrington-Kirkpatrick type models, such as the chaos and ultrametricity problems, it seems natural to study the free energy of multiple systems with constrained overlaps. One can write analogues of Guerra's replica symmetry breaking bound for such systems but it is not at all obvious how to choose informative functional order parameters in these bounds. We were able to make some progress for spherical pure $p$-spin SK models where many computations can be made explicitly. For pure 2-spin model we prove ultrametricity (absence of frustration) and chaos in an external field. For the pure $p$-spin model for even $p>4$ without an external field we describe three possible values
of the overlap of two systems at different temperatures. We also prove a somewhat unexpected result which shows that in the 2-spin model the support of the joint overlap distribution is not always witnessed at the level of the free energy and, for example, ultrametricity holds only in a weak sense.
(joint work with Michel Talagrand)
|
Analysis and Probability Seminar
Speaker: Evarist Gine (University of Connecticut)
Time: Friday, December 1, 2006 at 3:00 pm
Place: MSB 403 (UConn - Storrs)
Abstract: EMPIRICAL GRAPH LAPLACIAN
APPROXIMATION OF LAPLACE-BELTRAMI OPERATORS: LARGE SAMPLE RESULTS by
Evarist Giné and Vladimir Koltchinskii
Abstract: In data mining, and in other situations one is confronted
with intrinsically low dimensional data lying in a very high
dimensional space.
Then the question arises as to whether on can infer properties of the
underlying underlying low dimensional space from the data, both for
its own interest and also in order to analyze the data. It is fair to
assume the data lie in a Riemannian manifold, and the Laplace-
Beltrami operator is a key object there for many reasons. In this
talk I will present work joint with Vladimir Koltchinskii on how (and
how well) to approximate the Laplace-Beltrami operator from a
sequence of independent random variables drawn according to the
uniform distribution (the normalized volume element) from the manifold.
More details
|
PDE and Image Analysis Seminar
Speaker: Joe Mckenna (University of Connecticut)
Time: Monday, December 4, 2006 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: egin{abstract} A-priori bounds for positive, very weak solutions of
semilinear elliptic boundary value problems $-Delta u = f(x,u)$ on
a
bounded domain $OmegasubsetR^n$ with $u=0$ on $partialOmega$
are
studied, where the nonlinearity $0leq f(x,s)$ grows at most like
$s^p$. If
$Omega$ is a Lipschitz domain we exhibit two exponents $p_ast$ and
$p^ast$, which depend on the boundary behaviour of the
Green-function and
on the smallest interior opening angle of $partialOmega$. We prove
that
for $1p^ast$ we construct a nonlinearity
$f(x,s)=a(x)s^p$
together with a positive very weak solution which does not belong to
$L^infty$. Finally we exhibit a class of domains for which
$p_ast=p^ast$. For such domains we have found a true critical
exponent for
very weak solutions. In the case of smooth domains
$p_ast=p^ast=frac{n+1}{n-1}$ is an exponent which is well known
from
classical work of Brezis-Turner and from recent work of
Quittner-Souplet.
end{abstract}
|
Logic Seminar
Speaker: Reed Solomon (University of Connecticut)
Time: Monday, December 4, 2006 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: The subject of this talk relates a number of important themes in the history of computability theory including the study of minimal degrees, the study of computably enumerable degrees and the study of various notions of when one set is computationally simpler than (that is, reducible to) another set. In particular, we will consider the question of when a given reduction gives rise to a degree structure in which there are c.e. sets of minimal degree. The new results I will talk about are joint work with Rod Downey.
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Colloquium
Speaker: Becca Thomases (Courant Institute of
Courant Institute of Mathematical Sciences, NYU)
Time: Tuesday, December 5, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Viscoelastic flow modelled by the Oldroyd-B equations will be
discussed from an analytical and numerical perspective. First I will
present a local energy decay theorem which applies to a large class
of hyperbolic systems including the Oldyoryd-B model. This decay
theorem is used to prove that global smooth solutions exist for small
initial data. While small solutions are global, the problem for large
data is much more complicated. I will present numerical work on the
Oldroyd-B equations which shows that the system develops
singularities in the stress field. These signularities develop
exponentially in time at hypebolic points in the flow and their
algebraic structure depends critically on the Weissenberg number. A
local approximation to the solution at the hyperbolic point is
constructed and their is excellent agreement between the local
solution and the simulations.
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Geometry Seminar
Speaker: Ed Taylor (Weslyan University)
Time: Tuesday, December 5, 2006 at 4:30 pm
Place: MSB 117 (UConn - Storrs)
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S.I.G.M.A. Seminar
Speaker: Paul-Jean Cahen (University of Connecticut)
Time: Wednesday, December 6, 2006 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Interpolar functions were apparently introduced by Ampere (Annales de M. Ger-
gonne, 1826) and then studied by Cauchy. We will give an account of a paper by the
last in the Comptes Rendus de l’Academie des Sciences (1840). Interpolar functions
offer an interesting generalization of Taylor ’s classical approximation formula. For
a function f (x), one sets
f (a, b) = (f (a) - f (b))/( a - b),
f (a, b, c) = ( f (a, b) - f (a, c) ) / ( b - c ) , . . .
and then obtain formulae such that
f (x) = f (a) + (x - a)f (a, b) + (x - a)(x - b)f (a, b, c) + . . .
+(x - a)(x - b) . . . (x - h)f (a, b, c, . . . , h, k).
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Colloquium
Speaker: Xiaodong Yan ( Michigan State University)
Time: Thursday, December 7, 2006 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Abstract: Late time coarsening has been observed in epitaxial growth
models.Results from experiments and numerics on isotropic epitaxial
growth models suggest that the characteristic length scale $L(t)$ grows as
$t^{frac{1}{3}}$ at late times. We
prove a weak one-sided version of
this statement. Our analysis follows a strategy introduced by Kohn and
Otto in their study of phase transition, combining (i) a dissipation relation,
(ii) an isoperimetric
inequality, and (iii) an ODE lemma. The interpolation inequality is new
and rather subtle; our proof is by contradiction, relies on recent
compactness results for the Aviles-Giga energy. We also mention results
for nonisotropic epitaxial growth models and some open problems on
coarsening rates. This talk is based on joint work with R. V. Kohn from
Courant.
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University of Connecticut | 
