2007-2008
March 28, 2008
J.B. Nation (University of Hawaii)
MATHEMATICS ON OTHER PLANETS
How
do Aliens do Mathematics? This talk gives a gentle
introduction to universal algebra through a tour of
mathematics throughout the solar system. All the major
planets and some Kuiperbelt objects are included for the
same low fare. We leave it to the audience to
distinguish real facts from the facts the speaker makes
up!
Nov. 30, 2007
Briana Foster-Greenwood (UNT)
Deformation Theory
Nov. 8, 2007
Dr. Matt Papanikolas, Texas A&M
AGANT seminar
at UNT"Frobenius Difference
Equations and Applications"We will focus
on Frobenius difference equations over function fields
of characteristic p, whose solutions are related to
periods of Drinfeld modules. More specifically we show
that the transcendence degree of the period matrix of a
Drinfeld module is equal to the dimension of its
associated difference Galois group. We will
discuss applications to various transcendence problems
over function fields.
The website is
http://math.unt.edu/research.shtml#events
.
Note that the speaker will also give a talk in UNT's
Millican Colloquium Series on Fri Nov 9 at 4 pm in GAB
206.
For a map of campus, parking etc, see
http://www.unt.edu/pais/map/campusmap.htm#
.
(GAB (math dept) is in NE quadrant of campus & Curry
Hall is nearby) If you will be coming from outside UNT
and think you might be a little late, please RSVP to Dr
W Cherry ( wcherry@unt.edu
) or to the UNT math dept ( 940 565 3592).
October 26, 2007
Dr.
Vyjayanthi Chari, Professor
Department of Mathematics
University of California -at Riverside
University of Texas at Arlington http://www.uta.edu/math/pages/main/seminar.htm#colloquim
"Quivers
and Current Algebras Associated to Simple Lie Algebras"
May 4, 2007
Sibylle Schroll (Oxford)
"Algebras and tilings of the plane"
ABSTRACT: We will consider tilings of the
plane by rhombi and show how one can associate algebras
to these tilings. The representation theory of these
algebras is closely linked to the representation theory
of symmetric
groups. (The talk will be accessible to graduate
students.) |
April 19, 2007
Ralf Schmidt (Univ.
of Oklahoma)
"Modular forms for the
paramodular group"
| Given a classical elliptic
modular form f, infinitely many more modular forms can
be constructed from f using a rather trivial procedure.
All these other modular forms are called "old". A
modular form that is not old is called a "newform". It
is the newforms that lead to a nice theory.
Attempts have been made to generalize the theory of
old- and newforms to higher degree modular forms, so far
with limited success. The talk will explain the
implications of a joint work with Brooks Roberts on this
subject. It involves the theory of Jacobi forms. |
March 15, 2007
Dr. Thomas Cassidy,
Bucknell UniversityMarch 8, 2007
"Poincare-Birkhoff-Witt
Deformations of Graded Algebras"
Graded algebras can be deformed in
non-homogeneous ways to create Poincare-Birkhoff-Witt (PBW)
deformations. Over a field K, a deformation, U, of a
graded K-algebra, A, is said to be of PBW type if the
graded algebra associated to U is isomorphic to A. It
has been shown for Koszul and N-Koszul algebras that the
deformation is PBW if and only if the relations of U
satisfy a Jacobi-type condition. I will discuss recent
work with Brad Shelton (U. of Oregon) extending these
results to an arbitrary graded K-algebra, using the
notion of central extensions of algebras and a
homological constant attached to A, which we call the
complexity of A.
Pramod Achar from LSU
The geometry of special
pieces
"Special
pieces'' are certain subvarieties of the unipotent variety
of a reductive algebraic group, closely related to 2-sided
Kazhdan-Lusztig cells in the Weyl group. The geometry
of the unipotent variety plays a vital role in the
representation theory of algebraic groups, and in this talk,
I'll discuss a small corner of this vast topic: a set of
conjectures by Lusztig on what special pieces should look
like. This is joint work with D. Sage.
Thursday, March 1,
2007
Tatyana Chmutova
(Student of Pavel Etingof, now postdoc at Michigan)
Twisted symplectic
reflection algebrasJan. 23rd, 2007
Symplectic reflection algebras associated to
a finite subgroup $G$ of $Sp(U)$ were introduced by
P.~Etingof and V.~Ginzburg in 2000. These algebras and their
representations turned out to be related to numerous other
areas of mathematics, and hence they were studied
extensively during the last several years.We will
consider two generalizations of symplectic reflection
algebras. The first one is a notion of symplectic reflection
algebra associated to a finite group $G$ mapping, not
necessarily injectively, to $Sp(U)$. The second one is a
twisted symplectic reflection algebra associated to a finite
group $G$ with its symplectic representation $U$ and a two-cocycle
$\psi$.
We will see that these two generalizations are
connected: the case of noninjective $U$ can be reduced
to the injective one, but in this reduction the cocycle
$\psi$ might become nontrivial even if at the beginning
it was trivial.
Olav Richter
Rankin-Cohen brackets
In this talk, we will
define various automorphic forms (modular forms, Jacobi
forms, and Siegel modular forms) and highlight several
examples and applications. In particular, we will discuss
Rankin-Cohen brackets, which are bilinear differential
operators that assign to two automorphic forms a new
automorphic form. Rankin-Cohen brackets occur naturally in
different areas of mathematics, such as invariant theory,
quantum theory, and conformal field theory, and they yield
interesting applications, especially in number theory. It is
known that a unique Rankin-Cohen bracket exists for Siegel
modular forms of degree n, but a closed formula has only
been determined for n=1 and 2 and in a very few special
cases when n>2. I will report on joint work with Imamoglu,
where we construct an explicit formula for a Rankin-Cohen
bracket for Siegel modular forms of degree n on a certain
subgroup of the symplectic group. Moreover, we lift that
bracket via a Poincare series to a Siegel cusp form on the
full symplectic group.
2005-2006
November 3, 2006
Neeraj Bajracharya (continuation)
Minimum rotation angle
q required for indefiniteness of {AB+BA}, where both A and B
are positive definite matrices.
Background: In 1960,
Prof. Olga Tausky posed a research problem: Given Hermitian
matrices A and B, what can be said about the eigenvalues of
the Jordan product {AB+BA}? Prof. Strang answered this
question in his 1962 paper and gave a formula when {AB+BA}
will be indefinite.
October 20, 2006
Neeraj Bajracharya
Minimum rotation angle
q required for indefiniteness of {AB+BA}, where both A and B
are positive definite matrices.
October 13, 2006
Dr. Conley
"More Office Hours on Supersymmetry and Physics"
October 6, 2006
Dr. Conley
"More Office Hours on Supersymmetry and Physics".
September 29, 2006
We will ask Dr. Conley questions on the
connections between representation theory and physics.
Graduate students welcome.
Office Hours on Physics and Representation Theory
September 8, 2006
Anne Shepler (UNT)
Hochschild Cohomology and Hecke algebras
We will present a generic "Graded Hecke Algebra" which
encompasses a wide net of algebras defined by Lusztig,
Drinfeld, Etingof-Ginzberg, Cherednik, and others. We will
discuss how Hochschild cohomology influences these algebras,
and then develop new techniques (using invariant theory and
the theory of hyperplane arrangements) for computing
Hochschild cohomology. We will show how an explicit
computation of Hochschild cohomology then determines these
algebras and also predicts new fruitful algebras (some of
which have previously appeared in the literature in
different forms).
April 28, 2006
Ze-Li Dou (TCU)
L-functions and lifting
I shall introduce L-functions in the most
classical setting first, and explain briefly their
importance in number theory. I'll then generalize the notion
and explain the meaning of a lifting; some conjectures
considered central in contemporary number theory will be
mentioned in the process. Time permitting, I might mention
some original work on theta lifting and on an association
between special values of certain zeta functions and periods
of automorphic forms.
April 7, 2006
Charlie Conley (UNT)
Hochschild Cohomology
March 3, 2006
Nat Thiem (Stanford)
2004 -
2005
Nov. 18, 2005
Dec. 9, 2006, continuation
Paisa Seeluangsawat, UNT
Dickson Invariants
Let V be a vector space over a finite field. Dickson
Invariants are the ring of polynomials in
V which are invariant under GL(V). We follow Wilkerson's and
Kane's presentation of constructing a finite generating set
of these invariants.
October 7, 2005
Dr. Michael Monticino, UNT
Teller Staffing in
Retail Banks
Approximately seventy-four percent of retail bank
employees are tellers. Salaries for these tellers are a
bank's chief source of labor costs and hence significantly
impact the bottom-line. On the other side of the ledger,
tellers are a bank's primary contact point with customers.
Tellers define the experience most customers have with their
bank. The teller is an essential component both in retaining
and increasing the "wallet share" from customers. Staffing
more tellers than needed to handle customer traffic
unnecessarily increases labor costs, while customer service
suffers if insufficient numbers of tellers are scheduled.
Understaffing also affects employee morale. Overworked,
harried tellers do not stay with a bank long. Attrition for
tellers ranges between 30-50% annually, with the average
tenure for a teller between six to twelve months. Thus,
getting the right number of tellers in a branch at the right
times is essential to controlling costs, retaining customers
and employees, and growing a bank's revenue.
This talk will discuss the development of a Teller
Staffing product for retail banks in collaboration with ARGO
Data Resources, Inc. ARGO specializes in data delivery and
integration technology for the financial services industry.
ARGO currently has a fifty percent market share of the top
ranking 30 U.S. banks where over five million financial
transactions every hour are processed with ARGO systems. The
Teller Staffing product combines mathematical methods with
state of the art information technology, allowing banks to
capture minute-by-minute transaction and service time data
to make branch level staffing recommendations based on
individual branch transaction volume patterns and teller
service time statistics. The talk will provide an overview
of forecasting methods, queuing theory applied to staffing,
as well as the practical challenges of applying mathematics
in a real-world business setting.
September 30, 2005
Prof. Giorgio Fusco, UNT
Periodic Solutions of the N-Body Probem
September 23, 2005
Pieter Allaart, UNT
Benford's law: history and recent developments.
March 4, 2005
Dr. Robert Kallman, UNT
"An Algebraic Topology for Matrix Groups"
We all know Cayley's Theorem (theorem -1 in finite group
theory) that every finite group of order n is isomorphic to
a subgroup of S_{n}, the symmetric group on n elements. It
is also clear that any countable group is isomorphic to a
subgroup of S_{\infty}, the group of permutations (i.e.,
bijections) of the natural numbers. In November 1935
Schreier and Ulam asked (and apparently answered) if the
additive group of the real numbers is isomorphic to a
subgroup of S_{\infty}. They certainly had more in mind and
in 1960 Ulam asked explicitly if the group of all rotations
in three-dimensional space is isomorphic to a subgroup of
S_{\infty}. "Or, perhaps quite generally: is every Lie group
isomorphic (as an abstract group) to a subgroup of the group
S_{\infty}?" In this lecture we will answer this question
and more for matrix groups and show how it leads to a rather
peculiar, purely algebraically defined, but nontrivial and
nondiscrete Hausdorff topological group structure on matrix
groups whose cardinality is less than or equal to that of
the continuum. There are many open questions in this subject
area.
Feb. 11, 2005
Dr. Matt Douglass, UNT
"Induced Representations and Hecke Algebras"
Abstract: We will discuss induced
representations, Frobenius reciprocity, and Hecke algebras.
Linear algebra is a prerequisite for this talk!
Oct. 22 and Nov 5, 2004
Dr. Doug Brozovic, UNT
"An Introduction to Orthogonal Groups over Finite
Fields"
The notions of symmetric bilinear and quadratic forms are
familiar and exceptionally useful in many areas of
mathematics. Most people's experience with these forms,
their corresponding geometries, and their associated
isometry groups, is restricted to the context in which the
underlying field is the real numbers or the complex numbers.
The goal of this series of two talks will be a brief
overview of orthogonal geometries corresponding to finite
dimensional vector spaces over finite fields and a
consideration of the associated finite isometry groups.
We will begin with a review of the relevant information
regarding the group of invertible linear transformations of
a finite vector space, including a discussion of the full
automorphism group of the projective special linear groups.
From there, we will describe the distinct isometry classes
of orthogonal spaces. We will conclude with a discussion of
the corresponding orthogonal groups, their normal subgroups
and their automorphism groups.
These talks will be directed to graduate students who
have successfully completed Math 5520--those currently
enrolled may also benefit, especially if they have taken
Math 4450 or its equivalent.
Oct. 8, 2004
Title: "Automorphisms of Polish Fields"
Dr. Robert Kallman, UNT
Abstract: A theorem giving what appears
to be a new, general principle about complete separable
metric fields will be stated and the proof at least
sketched. This theorem seems to be the underlying reason
behind a variety of known purely algebraic facts about local
fields. It also has as easy corollaries what might be new
facts about local and other fields.
Oct. 1, 2004
"Parking Functions for Cats"
Dr. Joseph Kung, UNT
Sept. 10, 2004
"Invariants in the cohomology of the complement of a
Coxeter Arrangement."
Matt Douglass, UNT
Abstract: We'll analyze a correspondence between
special involutions in a Coxeter group and the
representation afforded by the cohomology of the complement,
or more generally, the Orlik-Solomon algebra, of the
associated hyperplane arrangement.
April 30, 2004
"Boundary manifolds of arrangements"
Dan Cohen, Louisiana State University
Let A be an arrangement of projective hyperplanes, and
let M be the boundary of a regular neighborhood of A.
We investigate the structure of the cohomology ring of
M.
April 16, 2004
"Weyl group invariants and homology of generalized
Steinberg varieties"
Matt Douglass, UNT
It's a "classical" theorem that the cohomology groups of the
comples Grassmannian Gr(p,q) can be computed as the S_p x
S_q invariants in the cohomology of the flag manifold of a
p+q dimensional, comples vector space (S_p is the symmetric
group on p letters). In this talk, we'll show that the
analog of this result holds for generalized Steinberg
varieties. (A generalized Steinberg variety is the fibered
product of a pair of varieties, each of which is a
generalization of a flag manifold.
February 6, 2004
"Monomial groups: Representations and the Robinson-Schensted
Correspondence"
Matt Douglas, University of North Texas.
In this talk, we'll discuss irreducible representations of
monomial groups G (r,1,n) and describe the extension of the
Robinson-Schensted algorithm for these groups.
2003 -2004
December 5, 2003
"Shephard Groups"
Anne Shepler, University of North Texas
A Shephard group is the symmetry group of a regular
polytope in real or complex space (for example, the symmetry
group of the dodecahedron). Many Shephard groups are Weyl
and Coxeter groups, but others are complex reflection groups
generated by reflections of order > 2. We discuss the length
function for Shephard groups and work of Brieskorn and Saito
on braid groups. Broue, Malle, and Rouquier investigate the
braid group of general complex reflection groups: the braid
group is the fundamental group of the orbit space obtained
after removing the reflecting hyperplanes. We also discuss
the Shephard complex, an analogue of the Coxeter complex.
October 31, 2003
Title: "What is representation theory?
Representation theory and geometry"
Matt Douglass, University of North Texas
Abstract: Continuing in the "What is
representation theory?" theme, we'll start with a quick
overview of some different aspects of representation theory
in an effort to show how representation theory interacts
with algebra, analysis, and topology. Then as a specific
example we'll revisit the representations of the Lie algebra
of 2 by 2 matrices that Charlie constructed using generators
and relations and show how they arise naturally when you
study the geometry divisors) or topology (line bundles) of
the projective plane. [Even though it may not sound like it,
this talk will also continue two other established themes:
it will be accessible to/intended for graduate students and
it will not be based on any previous talks.]
October 17, 2003
Title: "Straightening Out Specht Modules. Title:
Straightening Out Specht Modules"
Joseph Kung, University of North Texas
(Continuation of last week, graduate students most
welcome!)
Abstract: We discuss relations between
Determinantal Varieties and Specht Modules.
October 10, 2003
Title: "What is representation theory? A different
viewpoint: The Symmetric Group for Cats"
Joseph Kung, University of North Texas
(For graduate students; not based on any previous talks.)
Abstract: (This is another talk in the
series "What is representation theory?".
This talk is NOT based on any previous talks and is intended
for graduate students.) We will describe the irreducible
representations of the symmetric group over the complex
numbers. These are called "Specht modules". There is a major
research problem associated with Specht modules: find a
natural proof (without using Schur's character theory) that
they are in fact irreducible
representations.
October 3, 2003
Title: "What is representation theory? An
introduction to the Lie algebras of 2 by 2 and 3 by 3
matrices, PART II"
Charles Conley, University of North Texas
Abstract: This week we will examine the
representations of sl(3), the Lie algebra of traceless 3 by
3 matrices. We will define the weights of such
representations and see why they are symmetric under the
Weyl group of sl(3), the symmetries of the equilateral
triangle. Then we will describe the classification of the
irreducible representations of sl(3) by their highest
weights and compute the weights of some examples in order to
see their triangular symmetry concretely. Time permitting,
we will touch on a few applications of the theory such as
the Kostant multiplicity formula, Gell'Mann's use of the
10-dimensional representation to predict the Omega particle
in 1964, and noncommutative harmonic analysis.
September 26, 2003
Title: "What is representation theory? An
introduction to the Lie algebras of 2 by 2 and 3 by 3
matrices"
Charles Conley, University of North Texas
Abstract: (The speaker will not assume
any prior knowledge of Lie groups, Lie algebras, or their
representations: he will try to ensure that anyone who can
multiply matrices and has heard of homomorphisms will be
able to understand most of the talk.)
This is the first of a series of talks intended to
introduce graduate students to representations of groups. A
representation of a group is a homomorphism from the group
into a group of matrices. Surprisingly, it is in many ways
easier to study representations of infinite groups than
finite ones, at least infinite groups whose underlying sets
are manifolds. This is because such groups, called Lie
groups, have Lie algebras. I will begin by defining the Lie
algebra structure of the set of n by n matrices and the
notion of representations of Lie algebras. Next I will make
a few remarks on the link between Lie groups and Lie
algebras and some of the uses of Lie groups, for example in
explaining the famous Zeeman splitting of spectral lines in
physics. Then we will get to work describing the
representations of the 2 by 2 and 3 by 3 matrices by means
of the idea of weights.
2002 - 2003
November 22, 2002
Title: "A q-analogue of the Coxeter complex II"
Sibylle Schroll
November 15, 2002
Title: "A q-analogue of the Coxeter complex I"
Sibylle Schroll
November 1, 2002
Title: "The Graded Hecke Algebra and Complex
Reflection Groups"
Anne Shepler, University of North Texas
October 25, 2002
Title: "Graded Hecke Algebras and Hyperplane
Arrangements"
Anne Shepler, University of North Texas
October 18, 2002
Title: "Introduction to Hecke Algebras: Finite and
p-adic Groups"
Matt Douglass, University of North Texas
April 12, 2002
Title: "SL(2, R) Symmetries of Differential
Operators and Representation Theory"
Mark Sepanski, Baylor University
Abstract: This talk studies a two
parameter family of partial differential operators including
the heat and Schrodinger operators. Though not obvious, a
simple calculation using Lie's prolongation method shows the
symmetry group of these operators is generically isomorphic
to SL(2, R). However, the action only exponentiates to a
local action of the Lie group. In this talk, we how there is
a special subspace of smooth functions on which this local
action extends to a representation of the entire Lie group.
This information is used to construct the entire principal
series of SL(2, R). Moreover, natural explanations are given
for why these operators admit an SL(2, R) symmetry.
May 2, 2003
Title: "Partition Problems"
Neal Brand, University of North Texas
(accessible to undergraduate and graduate students!)
April 18, 2003
Title: "A Group Theorist's Introduction to Finite
Translation Planes"
Doug Brozovic, University of North Texas
April 11, 2003
Title: "A Group Theorist's Introduction to Finite
Translation Planes"
Doug Brozovic, University of North Texas
April 4, 2003
Title: "Transcendence of Numbers generated by
Morphisms"
Luca Zamboni, University of North Texas
Abstract: How random are the digits of an
algebraic number in a given base? A common conjectured
answer to this vague question is that these digits are
'really, totally, awesomely-random'. An alternative
formulation of this idea is that the digits occurring in the
k-ary expansion of an algebraic number cannot be obtained
via a simple algorithm. For example, the Champernowne
number, obtained by concatenating the decimal expansions of
the consecutive integers, i.e.,
0.12345678910111213141516.... was shown to be transcendental
by Mahler in 1937. We will prove that a positive real number
whose base 2 expansion is a fixed point of a morphism on the
symbols {0,1} which is either constant length or primitive,
must be a transcendental number.
February 28, 2003
Title: "Extremal Projectors"
Charles Conley, University of North Texas
(Okay for graduate students)
Abstract: The extremal projector of a
reductive Lie algebra is an operator in a certain extension
of its universal enveloping algebra which projects any
finite dimensional representation to its highest weight
vectors. I will discuss different types of explicit formulae
for extremal projectors (and, if time permits, their
relative analogs). I will try to make the talk accessible to
people unfamiliar with Lie theory by focusing on the
concrete matrix Lie algebras sl(2) and sl(3) and defining
their representations as they arise.
February 21, 2003
Title: "On the Coxeter complex and Alvis Curtis
duality"
Sibylle Schroll, University Paris 13
Abstract: M. Cabanes and J. Rickard
showed that the Alvis-Curtis character duality of a finite
group of Lie type is induced in non defining characteristic
l by a derived equivalence given by tensoring with a bounded
complex X, and they further conjecture that this derived
equivalence should actually be a homotopy equivalence. In
this talk we are going to show, that for the special case of
principal blocks of general linear groups with abelian
Sylow-l-subgroups this is true, by an explicit verification
relating the complex X to the Coxeter complex of the
corresponding Weyl group.
February 14, 2003
Title: "A Group Theorist's Introduction to Finite
Translation Planes"
Doug Brozovic, University of North Texas
Abstract: In this first of three
lectures, I will lay the definitional foundation for
discussing finite projective planes and, in particular,
translation planes. This first lecture (Feb 14th) will be
elementary (and very accessible to graduate students).
February 7, 2003
Title: "Fourier Transforms, Alvis-Curtis duality,
and characters of finite, Lie groups"
Matt Douglass, University of North Texas
Abstract: The determination of the
character values of a finite group of Lie type can be
reduced to computing the Fourier transforms of functions on
the corresponding Lie algebra. In this talk we'll show that
Foureir transform commutes with Alvis-Curtis duality for
functions on a finite, reductive Lie algebra.
2000 - 2001
March 30, 2001
Title: "Structure of Lie Groups VI"
Robert Donley, University of North Texas
March 9, 2001
Title: "Structure of Lie Groups V"
Robert Donley, University of North Texas
March 2, 2001
Title: "Structure of Lie Groups IV"
Robert Donley, University of North Texas
February 23, 2001
Title: "Structure of Lie Groups III"
Robert Donley, University of North Texas;
February 9, 2001
Title: "Structure of Lie groups, part II"
Robert Donley, University of North Texas
November 3, 2000
Title: "Borel-Moore Homology of Generalized
Steinberg varities"
J. Matthew Douglass, University of North Texas
October 27, 2000
Title: "Equivariant K-theory of generalized
Steinberg varieties"
J. Matthew Douglass, University of North Texas,
October 20, 2000
Title: "Equivariant K-theory of generalized
Steinberg varieties"
J. Matthew Douglass, University of North Texas
October 13, 2000
Title: "Introduction to equivariant K-theory"
J. Matthew Douglass, University of North Texas
October 6, 2000
Title: "Borel-Moore homology of generalized
Steinberg varieties"
J. Matthew Douglass, University of North Texas
September 29, 2000
Title: "The geometry of generalized Steinberg
varieties"
J. Matthew Douglass, University of North Texas
September 15, 2000
Title: "Tempered Representations and the Discrete
Series"
Robert Donley, University of North Texas
September 8
Title: "Harish-Chandra modules and real prarabolic
induction"
Robert Donley, University of North Texas
