Return to Gene Abrams' home page
The Colorado Springs Algebra Seminar
"Rings and Wings"
The Colorado Springs Algebra Seminar typically meets six or seven times per semester, roughly every other Wednesday, from 4:30 until 5:30(ish). Often the meeting place is the campus of the University of Colorado at Colorado Springs, but other venues have been used as well.
We encourage talks from all areas of algebra.
Talks are typically attended by math faculty from throughout the Pikes Peak region, including the University of Colorado at Colorado Springs, The Colorado College, and Colorado State University  Pueblo. Talks are also often attended by graduate students and advanced undergraduate students.
Talks are usually given by those who typically attend, as well as any outoftown visiting algebraists who may happen along ...
It is now traditional that, on completion of the presentation, those who are interested head to a local eatery / watering hole (often Clyde's on the UCCS campus) for dinner or liquid refreshment or snacks (e.g., Buffalo Wings?).
Contact the seminar organizer, Gene Abrams abrams@math.uccs.edu if you are interested in participating.
On this page we will also typically include other talks which will happen in the Pikes Peak region which may be of interest to algebraists.
Spring 2019 Schedule
The talks will happen (generally) 4:30  5:30pm on Wednesdays
Note: the Algebra Seminar alternates various Wednesday afternoons with the Applied Analysis Seminar, see
https://www.uccs.edu/math/events/aaaseminar
DATE 
SPEAKER 
TITLE 
ABSTRACT 







February 13  Zak Mesyan UCCS 
Transformation Semigroups and Their Topologies 
Endomorphism rings, permutation groups, and transformation semigroups play fundamental roles in the theories of rings, groups, and 
February 20  [could be you!] 


February 27  Shishir Agrawal Colorado College 
How local systems arise 
We'll begin by meandering through a bit of algebraic topology and complex analysis, discussing what local systems are and how differential equations give rise to local systems via the RiemannHilbert correspondence. This will motivate a transition to algebra and a discussion of positive characteristic analogs of this correspondence. Due initially to Katz and then expanded upon by Emerton and Kisin, these analogs show that étale local systems on smooth algebraic varieties in positive characteristic arise via difference equations (which are encoded by objects known as Fcrystals). We'll conclude with a discussion of how Bhatt and Scholze's proétale topology should streamline the proof of this positive characteristic version of the RiemannHilbert correspondence. 
March 6  [could be you!] 

THURSDAY March 7 UCCS Math Dept Colloquium 
Jason Boynton North Dakota State U 
Factorization in rings of polynomials of the form D+M (and generalizations)  https://www.uccs.edu/math/sites/math/files/inlinefiles/Colloquium_Boynton.pdf 
March 13 CANCELLED due to blizzard, to be rescheduled 
Derek Wise

Fractals and Monads  Fractals in geometry are deeply related to monads in algebra. In particular, fractals and other selfsimilar structures are often generated by "iterating" functions, but the relevant type of iteration is best understood in terms of certain monads. Moreover, a fractal can often be understood algebraically as an algebra for the corresponding monad. This talk will be a gentle introduction to monads, and some of my recent explorations in using them to understand fractals. I will take a practical approach, working mostly with examples, and also showing how monads can be used concretely in methods of actually drawing pictures of fractals. This will also also include a glimpse of the role of monads in computer science, though no particular knowledge of computer science will be assumed. 
March 20 CANCELLED, hopefully to be rescheduled for AY 2019/2020 
Keith Kearnes CU Boulder 
Commutator theory for grouplike algebras  I will speak about a common generalization of the group commutator and ideal multiplication for rings. I will also discuss its generalization to higher arity commutator operations. 
THURSDAY March 21 UCCS Math Dept Colloquium 
Daniel Herden Baylor University 
Local automorphisms and incidence algebras  https://www.uccs.edu/math/sites/math/files/inlinefiles/Colloquium_Herden.pdf 
[[March 27]]  [[ Spring Break ]]  
April 3  Luke Harmon UCCS 
Lowerfinite partially ordered sets  We will introduce the ordertheoretic notion of a lowerfinite partially ordered set and focus, in particular, on the partially ordered set formed by the submodules (ordered by containment) of a module over a commutative, unital ring. Our goal is to classify all of the lowerfinite modules over a commutative, unital ring. The results we have obtained to this end will be presented in a highly accessible manner. 
April 10  
April 17  
THURSDAY April 18 UCCS Math Dept Colloquium 
John Lorch Ball State University 

April 24  
May 1  Gene Abrams UCCS 

May 8  [could be you!] 


Fall 2018 Schedule
The talks will happen (generally) 4:30  5:30pm on Wednesdays
(Note: starting Spring 2018, the Algebra Seminar alternates various Wednesday afternoons with the Applied Analysis Seminar, see
https://www.uccs.edu/math/events/aaaseminar )
DATE 
SPEAKER 
TITLE 
ABSTRACT 







October 10  Greg Oman, UCCS 
Divisible multiplicative groups of fields 
Some time ago, Laszlo Fuchs asked the following question: which abelian groups can be realized as the multiplicative group of (nonzero elements of) a field? This question and several variants have been studied by Fuchs, Contessa, Mott, Guralnick, and Wiegand, among others. In this talk, we outline a solution of the problem within the subclass of divisible abelian groups, that is, we characterize which divisible abelian groups can be realized as the multiplicative group of a field. Some simple applications as well as more recent progress on the question will be presented as well, timepermitting. 
Ocober 24  Damiano Fulghesu, Minnesota St. University, Moorhead 
Tiling of finitely generated groups  Let G be a finitely generated group. We say that a subset K of G is a (right) tile if there exists a subset C of G such that the family of sets cK, as c varies in C, is a partition of the group G. 
November 7  David Milovich, Welkin Sciences (Colo Spgs)

Higherorder amalgamation of algebraic structures 
Call two algebraic structures A, B For example, any two overlapping Boolean rings I will survey what I know about nary amalgamation for various familiar algebraic structures and then introduce a nontrivial sufficient condition for nary amalgamation stated in terms of category theory. 
November 28  Beth Malmskog, Colorado College 
Locally Recoverable Codes with Many Recovery Sets from Fiber Products of Curves  Error correcting codes are systems for incorporating redundancy into stored or transmitted data, so that errors can be identified and even corrected. A good error correcting code is efficient and can correct many errors relative to its efficiency. These codes are ubiquitous in the digital age, and many excellent codes arise from algebraic constructions. The increasing importance of cloud computing and storage has created a need for codes that protect against server failure in large computing facilities. One way of approaching this problem is to ask for local recovery. An error correcting code is said to be locally recoverable if any symbol in a code word can be recovered by accessing a subset of the other symbols. This subset is known as the helper or recovery set for the given symbol. It may be desirable to have many disjoint recovery sets for each symbol, in case of multiple server failures or to provide many options for recovery. Barg, Tamo, and Vladut recently constructed LRCs with one and two disjoint recovery sets from algebraic curves. This talk presents a generalization of this construction to three or more recovery sets, using fiber products curves over finite fields. This is joint work with Kathryn Haymaker and Gretchen Matthews. 
THURSDAY November 29 12:30  1:30 Osborne Science Bldg Room A327 (part of the UCCS math department colloquium series) 
Kulumani M. Rangaswamy 
The multiplicative ideal theory of Leavitt path algebras: Are Leavitt path algebras really commutative algebras in noncommutative clothing?

https://www.uccs.edu/math/sites/math/files/inlinefiles/Colloquium_Ranga.pdf 



Spring 2018 Schedule
The talks will happen (generally) 4:30  5:30pm on Wednesdays
Note: starting Spring 2018, the Algebra Seminar will alternate various Wednesday afternoons with the newlyformed Applied Analysis Seminar
DATE 
SPEAKER 
TITLE 
ABSTRACT 
February 7 
Greg Oman, UCCS 
Commutative (unital) Artinian rings are Noetherian: a brief history and an elegant proof

The study of socalled "chain conditions" for ideals of a ring began to take root in work of Emmy Noether and Emil Artin dating back to the early 20th century. Recall that a commutative ring R is Noetherian if R does not have an infinite, strictly ascending chain of ideals; R is Artinian if R has no infinite, strictly decreasing chain of ideals (there are noncommutative analogs, of course). A curious fact is that if R is a commutative ring with identity (yes, 1 is required for the following result), then R being Artinian is sufficient to guarantee that R is Noetherian, but the converse does not hold. In this talk, I will outline the standard proof of this result and conclude with a (more recent) short and elegant proof due to Karamzadeh. 
Feb 14  
Feb 21  Zak Mesyan, UCCS 
InfiniteDimensional Triangularization 
One of the most commonly used tools in linear algebra, both theoretically and computationally, is the fact that every matrix with entries from an algebraically closed field is similar to an 
Feb 28  [[ analysis seminar ]]  
Mar 7  Luke Harmon, UCCS 
Rings Between Z and Q 
In this expository talk, we will use fundamental techniques in commutative ring theory related to prime ideals, multiplicative sets, and localization to categorize all of the subrings of the rationals that contain the integers as a subring. 
Mar 14  Ethan Berkove, Lafayette College 
Short Paths and Long Titles: Travels through the Sierpinski carpet, Menger sponge, and beyond. (Joint work with Derek Smith) 
The Sierpinski carpet and Menger sponge are fractals which can be thought of as two and three dimensional versions of the Cantor set. Like the Cantor set, each is formed by starting with a shape (a square for the carpet, a cube for the sponge) and then recursively removing certain subsets of it. Unlike the Cantor set, what remains is connected in the following sense: given any two points s and f in the carpet or sponge, there is a path from s to f that stays in the carpet or sponge. In this talk, we’ll discuss what we know about the shortest path from s to f in the carpet, sponge, and even higher dimensional versions of these fractals. The proofs required a surprising (at least to us) breadth of techniques, from combinatorics, geometry, and even linear programming. 
Mar 21  John McHugh, UCCS and U. Vermont 
An Introduction to Character Theory

This presentation will begin with a discussion of the complex representation theory of finite groups including the theorems of Maschke and Wedderburn. After studying the basic properties of representations, we will move on to discuss the character theory of finite groups. This is a powerful subfield of representation theory which allows one to dissect the structure of a finite group via examinations of associated numerical invariants. For example, if one knows the "character table" of a given finite group G (which turns out to be a square matrix of finite dimension) then one can tell right away what the normal subgroups of G are and even whether or not G is abelian, nilpotent, solvable, or simple. This presentation will be aimed at those who have never seen the theory before or have not seen it in a long time. To understand everything in the presentation, one should have a decent grasp on finite group theory, ring theory (including algebras over fields), and modules. 
[Mar 28]  [[[ Spring Break ]]]  
Apr 4  Kulumani M. Rangaswamy, UCCS 
The history and the evolution of the concept of primitive rings  This expository talk will trace the origin and the development of the concept of primitive rings and outline their properties, with a leisurely review of the earlier works of Lie, Wedderburn, Artin, Jacobson, Kaplansky and others. This talk will mostly be at a level that our graduate students will be able to follow. 
Apr 11  [[ analysis seminar ]]  
Apr 18  Gene Abrams, UCCS 
Leavitt path algebras are Bezout  We show that for any graph $E$ and any field $K$, any finitely generated left ideal of the Leavitt path algebra $L_K(E)$ is principal (i.e., generated by a single element). In other words, $L_K(E)$ is Bezout. We'll give some background on the subject, and present some of the moreintriguing aspects of the proof. 
Apr 25  Matt Welz, Fort Lewis College 
The Finite Simple Groups and an Introduction to Fusion Systems  The Classification of Finite Simple Groups is one of the greatest achievements of 20th century mathematics. An immense undertaking, filling over 10,000 journal pages across hundreds of articles, the Classification provides a "periodic table" of the finite simple groups. The sometimes mysterious ramifications of this massive project extend not only to mathematics beyond group theory, but to theoretical physics and chemistry. In this talk, I shall discuss various aspects of the finite simple groups, including the"Monster", the largest of the "sporadic" simple groups, and how the Classification motivates my research on fusion systems. 
May 2  [[ analysis seminar ]] 
Fall 2017 Schedule
All talks in ENGR 239 (Second Floor Seminar Room, Engineering and Applied Sciences Building) on the UCCS campus, unless otherwise indicated.
All "Rings and Wings" talks begin at 3:15pm, unless otherwise indicated.
Contact Gene Abrams (preferably a few days in advance of the talk) if you need a UCCS parking permit.
DATE 
SPEAKER 
TITLE 
ABSTRACT 
Wednesday Sept 13 
Greg Oman, UCCS 
A gentle introduction to model theory (and what it can do for you algebraically)

In this talk, I'll present a rigorous (but somewhat gentle) introduction to the syntax and semantics of firstorder logic. Timepermitting, I will discuss the classical theorems, including the Compactness Theorem, the LowenheimSkolem Theorems, Ultraproducts, and Los' Theorem (read "Washes Theorem"). I'll provide applications to ring theory, Given recent applications of model theory to C*algebras, my goal is to argue that the basic tools of model theory can be useful to the algebraist in a variety of contexts. 
Wednesday Sept 27 
K. M. Rangaswamy, UCCS 
Cotorsioness of modules and a problem of George Bergman


Wednesday Oct 25  Dan Bossaller, Ohio U.  Leavitt Path Algebras having Bases Consisting Solely of Strongly Regular Elements

Leavitt path algebras were introduced independently by Abrams and ArandaPino in 2005 and Ara, Moreno, and Pardo in 2007 as purely algebraic analogues of the graph $C^*$ algebras introduced by Kumjian, Pask, Raeburn, and Renault in 1997 and 1998. Various recent papers deal with the family of so called ``invertible algebras," those algebras over arbitrary (not necessarily commutative) unital rings which have bases that consist solely of invertible elements. Many familiar algebras satisfy this property, including all finite dimension algebras over fields other than $\mathbb{F}_2$ and all $n \times n$ matrix algebras over unital rings. L\'opezPermouth and Pilewski gave a complete characterization of precisely which Leavitt path algebras of finite graphs are invertible. In this talk I will introduce the concept of a locally invertible algebra, that is, an algebra $A$ having basis $\mathcal{B}$ such that for every $b \in \mathcal{B}$, there exists some idempotent $e$ for which $b$ is invertible in the corner algebra $eAe$. We will show that this definition is equivalent to the algebra having a basis consisting solely of strongly regular elements, and then we will give various examples and nonexamples of locally invertible algebras. Afterwards we will examine local invertibility in the context of Leavitt path algebras, in particular giving a complete characterization of strongly regular monomials and, as a corollary, showing that all von Neumann regular and all directly finite Leavitt path algebras are locally invertible. If time permits, we will show that the algebraic analogues of many algebras from operator theory are locally invertible. 
THURSDAY, October 26 12:301:30 UCCS Mathematics Department Colloquium Series 
Dan Bossaller, Ohio U.  Associativity and Infinite Matrices

In a typical first course in linear algebra, finding a solution to a set of $m$ linear equations in $n$ unknowns guides much of the course. The representation of this system as the equation $Ax = b$ where $A$ is an $m \times n$ matrix (with $m$ and $n$ finite), $x \in K^n$, and $b \in K^m$ for some field $K$ is a central feature throughout. In order to find a solution, one would find a solution to this matrix equation $Ax = b$ by multiplying both sides by some matrix of row operations $U$ to write the matrix $A$ into some easily solvable form such as upper upper triangular form, row echelon form, etc. From there one solves the transformed equation, $(UA)x = Ub$, to get a solution to the original equation. One assures that this is indeed a solution by multiplying on the left by the inverse matrix $V$ for $U$. In the case of an infinite number of equations in infinitely many unknowns, the relevant matrices are infinite so one must take care that $V$, $U$, and $A$ are all multipliable matrices and that their product is associative. In this talk we will explore conditions under which the product of three matrices is associative. This talk will be accessible to a wide mathematical audience, requiring no more than an understanding of basic linear algebra. 
Wednesday Nov 1  Gerard Koffi, U. Nebraska Kearney  Classification of distributive/thin representations via incidence algebras

This talk will overview our recent work on application of incidence algebras of a finite poset P to classify various type of representations. In particular, we provide a unified approach to classify distributive, thin and finitely many orbits representations. The main tool is to introduce deformations of the incidence algebras which turns out to be the locally heriditary semisdistributive algebras and are classified in terms of the cohomology of the simplicial realization of the poset P. 
Wednesday Nov 15  Jonathan Poritz CSU Pueblo 
Algebraic Turing Machines, with Applications to Quantum Computation  Alan Turing created the concept of what we now call "Turing machines" in his work on the Entscheidungsproblem ["decision problem"], one of David Hilbert's great problems motivating 20th century mathematics. A key insight in Turing's work was the centrality of "universal Turing machines" [UTMs], which could simulate any other Turing machine. By now Turing machines are as fundamental to theoretical computer science as bugs are to entomology and in applications, we tend to think of realworld, physical computational devices as engineered (and sadly finite) realizations of UTMs. There are, however, other equivalent models of computation which tend to be used in specific situations, including [Turing's thesis advisor] Alonzo Church's "lambdacalculus" and the "circuit model." In this talk, I will present yet another model of computation by means of a construction which relies heavily on algebraic structures. The advantage of this construction is that it admits mathematically natural generalizations, one of which is equivalent to the model of of "probabilistic Turing machines" which are used in crypto and complexity theory. Another generalization (not even particularly complex mathematically) yields the recent and revolutionary (and terrifying, if you do crypto) idea of quantum computation. An advantage of this approach (to mathematicians, at least) is that allows precise mathematical statements and conjectures about ideas like what is universality and why quantum computers seem to be exponentially faster than classical ones. 
Wednesday Nov 29  John Beachy Northern Illinois U. 
Universal localization of piecewise Noetherian rings 
A commutative ring R is called piecewise Noetherian if it has a Noetherian spectrum and for each prime ideal P the set of Pprimary ideals satisfies the ACC. In the noncommutative case there is a comparable definition, equivalent to the statement that R has ACC on prime ideals and for each ideal I the factor ring R has finite reduced rank. After introducing piecewise Noetherian rings, the talk will explore the conjecture that this class of rings is the right one in which to study universal localization at semiprime Goldie ideals. 
Spring 2017 Schedule
All talks in ENGR 187 (First Floor Seminar Room, Engineering and Applied Sciences Building) on the UCCS campus, unless otherwise indicated.
All "Rings and Wings" talks begin at 3:45pm, unless otherwise indicated.
Contact Gene Abrams (preferably a few days in advance of the talk) if you need a UCCS parking permit.
DATE 
SPEAKER 
TITLE 
ABSTRACT 
*** Special Day *** Friday April 14 
Kevin O'Meara U. Christchurch (New Zealand) 
The Gerstenhaber Problem and a computer search for a counterexample  Fifty six years on, it remains an open question whether Gerstenhaber’s (most surprising) theorem (Annals Math 1961) for two commuting n×n matrices A,B 2 Mn(F) over a field F also holds for three commuting matrices A,B,C in Mn(F):
Our programs are written in MATLAB and use exact integer arithmetic. The 500 × 500 matrix size is not a true indication of the very large matrices M we 
Wednesday April 26 
Roozbeh Hazrat University of Western Sydney (Australia) 
Weighted Leavitt path algebras  Weighted Leavitt path algebras are a generalisation of Leavitt path algebras (with graphs of weight 1) and cover the algebras $L_K(n,n+k)$ constructed by Leavitt. In this talk we explain the concept and prove some theorems on the structure of these algebras. This is a joint work with Raimund Preusser (Bielefeld/Brasila). 
Fall 2016 Schedule
All talks in ENGR 239 (Second Floor Seminar Room, Engineering and Applied Sciences Building) on the UCCS campus, unless otherwise indicated.
(note: this is a different room than the one we've used in the past two semesters.)
All "Rings and Wings" talks begin at 3:45pm, unless otherwise indicated.
Contact Gene Abrams (preferably a few days in advance of the talk) if you need a UCCS parking permit.
DATE 
SPEAKER 
TITLE 
ABSTRACT 
August 24 
Jason Bell University of Waterloo 
Iterative algebras  There has been a lot of recent work on graded nil algebras by Smoktunowicz, Greenfeld, and others. These are Ngraded algebras in which every homogeneous element is nilpotent and their study was motivated in part by trying to gain insight into unsolved Kurosh/Koethetype problems about rings by studying the graded counterparts of these problems. We give a combinatorial construction of a family of graded nil rings, which we call iterative algebras, and we use these to answer some questions of Greenfeld, Leroy, Smoktunowicz, and Ziembowski. We give a survey of some of the ring theoretic properties of these algebras and give some open questions about them. This is part of joint works with Blake Madill and Be'eri Greenfeld. 
August 31  NO seminar  x  
September 7 CANCELLED rescheduled to Dec 7 
Andrew Kelley SUNY  Binghamton 
Subgroup growth: a brief survey  The phrase "growth of groups" may bring to mind Gromov's celebrated theorem on polynomial *word* growth. However, there is another area of growth of groups that has received much attention, namely subgroup growth: How many subgroups of a given index does a finitely generated group have? As the index increases, this number may grow rapidly. How fast (asymptotically) is this so called "subgroup growth"? And how does it relate to the algebraic, structural properties of the group? In this survey, I will mention a few important results and techniques. As it turns out, some questions in subgroup growth relate to rings and modules, and I plan to briefly mention this as well. 
September 14  
September 21  Greg Oman UCCS 
How did you come up with that?  Over the years, I have had the good fortune to work with a variety of undergraduate and graduate students. Most of these students have asked me the following important question: "How did you come up with the problem you gave me?" Giving a complete and fully satisfactory answer to this question is no easy task. In this talk, I will attempt to give *an* answer to this query. In particular, I will illustrate the problemcreating and problemsolving process of doing research mathematics via a microcosm: specifically, with a recreational problem I have created. My plan is to informally discuss the sorts of questions I have asked to come up with the problem, giving a "behindthescenes" peak into the process of inventing new mathematics. The mathematics involves only the notion of "group" and "homomorphism"; having taken an introductory course in modern algebra is more than sufficient to guarantee that you will comprehend the mathematics presented in my talk. 
September 28  
**** THURSDAY OCTOBER 6 12:15  1:30pm (UCCS Math Department Colloquium) *** 
Ben Steinberg City College of New York and CUNY Graduate Center

Representation theory and random walks 
We discuss how a number of very natural Markov chains, including card shuffling and the Tsetlin library, can be modeled as random walks on finite monoids and how the representation theory of these monoids can be used to compute the eigenvalues of the transition matrices of these walks. No prior knowledge about Markov chains or monoids will be assumed. 
October 12  James Mitchell St. Andrews University (Scotland) 
Chains of subsemigroups  The length of a semigroup S is defined to be the largest size of a chain of subsemigroups of S. An exact formula for the length of the symmetric group on n points was found by Cameron, Solomon and Turull; the length is roughly 3n/2. In general, it follows by Lagrange's Theorem that the length of a group is at most the logarithm of the group order. Semigroups refuse to be as wellbehaved. The only valid upper bound for the length of an arbitrary semigroup is its size. For example, any zerosemigroup has length equal to its size. Even for less degenerate and more natural examples of semigroups, the contrast to groups is noticable. We will see that the length of the full transformation semigroup on n points, the semigroup analogue to the symmetric group, is asymptotically at least a constant multiple of its size. 
October 19  
October 26  Indah Emilia Wijayanti Universitas Gadjah Mada (Indonesia); Fulbright Scholar, currently visiting Ohio University 
On Nice Modules 
A ring with an identity is called a clean ring if every element of the ring decomposes as a sum of an idempotent and a unit of the ring. We introduce and investigate the new concept of a nice module, that is a module whose every submodule has a clean endomorphism ring. We present some sufficient conditions under which a module is nice, give examples of modules that are nice and those are not nice, show how to construct nice modules and raise an interesting question in the meantime. 
November 2  
November 9  
November 16  
November 23  NO seminar  Thanksgiving  x  
November 30  
THURSDAY December 1 UCCS Math Dept Colloquium 12:30  1:30pm refreshments at 12:15 Osborne A204

Andrew Kelley SUNY Binghamton 
Maximal subgroup growth of some groups  Let m_n(G) denote the number of maximal subgroups of a finitely generated group G of index n. How do the algebraic/structural properties of G control the growth rate of m_n(G)? Others have researched the broad picture and described what it means for m_n(G) to be bounded above by a polynomial in n. However, there are only a few groups whose degree of growth is known. If we restrict to particularly nice classes of groups however, then asymptotic formulas (or bounds) can be given. We will focus on metabelian groups, especially those that are abelian by cyclic. Beyond this, current progress on virtually abelian groups and BaumslagSolitar groups may also be mentioned. 
December 7  Andrew Kelley (rescheduled from Sept 7) 
Subgroup growth: a brief survey  The phrase "growth of groups" may bring to mind Gromov's celebrated theorem on polynomial *word* growth. However, there is another area of growth of groups that has received much attention, namely subgroup growth: How many subgroups of a given index does a finitely generated group have? As the index increases, this number may grow rapidly. How fast (asymptotically) is this so called "subgroup growth"? And how does it relate to the algebraic, structural properties of the group? In this survey, I will mention a few important results and techniques. As it turns out, some questions in subgroup growth relate to rings and modules, and I plan to briefly mention this as well. 
Spring 2016 Schedule
All talks in ENGR 201 (Engineering Dean's Conference Room) on the UCCS campus, unless otherwise indicated.
(note: this is a different room than the one we've used in the past, but the same room as we used in Spring 2015...)
All "Rings and Wings" talks begin at 3:45pm, unless otherwise indicated.
Contact Gene Abrams (preferably a few days in advance of the talk) if you need a UCCS parking permit.
DATE 
SPEAKER 
TITLE 
ABSTRACT 
February 3 
[available] 

February 10  Kulumani Rangaswamy UCCS 
On prime ideals in Leavitt path algebras  In this talk I’ll present some information about prime factorization of ideals in a Leavitt path algebra L. This may include some (preliminary) results showing how the behavior of graded ideals influence that of the nongraded ideals in L. 
February 17  [available]  
February 24 TALK TO BE HELD AT COLORADO COLLEGE, TUTT SCIENCE BUILDING ROOM 229 
Michael Penn Colorado College 
Vertex Operator Algebras: Motivation, Definition, and Examples Part I 
Vertex operator algebras(VOA) are a relatively new class of algebraic objects which have found uses across many branches of mathematics and physics: representation theory, modular forms and qseries, the study of finite simple groups, string theory, and topological quantum field theory. In this talk we will explore three equivalent formulations of a vertex algebra and provide a few examples — the Heisenberg(VOA) and lattice VOAs. The Heisenberg VOA can be considered a “quantum” version of the classical polynomial algebra, while lattice VOAs will form the basis of a second talk where we will cover several recent results. 
March 2 TALK TO BE HELD AT COLORADO COLLEGE, TUTT SCIENCE BUILDING ROOM 229 
Michael Penn Colorado College 
Vertex Operator Algebras: Motivation, Definition, and Examples Part II 
(see above) 
March 9  [available]  
March 16  [talk rescheduled to April 6] 


March 23 
NONE  Spring Break


March 30  Daniel Goncalves UFSC  SC  Brasil 
Simplicity of partial skew group rings with applications to Leavitt path algebras  In this talk I will make an introduction to algebraic partial actions and their associated partial skew group rings, describing a simplicity criteria for certain partial skew group rings. As a motivating example I will show how to realize Leavitt path algebras as partial skew group rings and derive the simplicity criteria for Leavitt path algebras from partial skew ring theory. 
April 6  Greg Oman UCCS 
Polynomial and power series rings with finite quotients 
An old textbook problem posed by Kaplansky is to show that the group Z of integers is the unique infinite abelian group G with the property that G/H is finite for every nonzero subgroup H of G. In the literature, rings R with the property that R/I is finite for every nonzero twosided ideal I are called rings with finite quotients (alternatively, residually finite rings). In this talk, we classify the rings R (assumed only to be associative, not necessarily with 1) for which the polynomial ring R[X] (respectively, power series ring R[[X]]) has finite quotients. An analogous problem for onesided ideals will also be discussed. This is joint work with Adam Salminen of The University of Evansville. 
THURSDAY APRIL 7 12:30  1:30 UCCS COLLOQUIUM 
Ikko Saito UCCS 

April 13  [available] 

April 20  Be'eri Greenfeld Bar Ilan Univ.  Israel 
Growth, Geometry and Representations of some Noncommutative Graded Algebras 
The investigation of growth of finitely generated groups has been a fruitful, well studied area for mathematicians, since Gromov's remarkable theorem (that a finitely generated group with polynomially bounded growth is virtually nilpotent), through Grigorchuk's inspiring example of a group with intermediate (i.e. superpolynomial but subexponential) growth, and until recent results of Tao and others. The parallel study for finitely generated (associative, not necessarily commutative) algebras turns out to be very much different. For example, we show how many superpolynomial functions are realized as the growth types of prime algebras, improving a recent result of Bartholdi and Smoktunowicz. For algebras of polynomially bounded growth, the degree of the polynomial (the GKdimension) turns out to be an important invariant of the algebra. It naturally appears in the study of holonomicity in the theory of Dmodules, and also enabled Artin and Van den Bergh to investigate NC (noncommutative) projective schemes  which are essentially graded domains with polynomial growth. While NC projective curves were classified, the conjectured classification of NC projective surfaces is still open. We study the behavior of the classical (namely, Krull) dimension for surfaces, and show it is always bounded (even for nonnoetherian surfaces).
From a representationtheoretic point of view, we finally show that prime, graded algebras with restricted growth either satisfy a polynomial identity or act faithfully on a simple module; this provides an affirmative answer to a graded version of a longstanding question raised by Braun and Small. This is partially based on joint work with Leroy, Smoktunowicz and Ziembowski and on separate sole research by the speaker. 
FRIDAY April 22 
Sergio LopezPermouth Ohio University 
Modules over Infinite Dimensional Algebras  Let A be an infinite dimensional K algebra, where K is a field and let B be a basis for A. In this talk we explore a property of the basis B that guarantees that K^B (the direct product of copies indexed by B of the field K) can be made into an Amodule in a natural way. We call bases satisfying that property "amenable" and we show that not all amenable bases yield isomorphic Amodules. Then we consider a relation (which we name congeniality) that guarantees that two different bases yield isomorphic Amodule structures on K^B. We will look at several examples in the familiar setting of the algebra K[x] of polynomials with coefficients in K. Finally, if time allows we will mention some results regarding these notions in the context of Leavitt Path Algebras (joint work with Lulwah AEssa and Najat Muthana). 
April 27  Cristobal Gil Universidad de Malaga  Spain 
The commutative core of a Leavitt path algebra.  Leavitt path algebras are the algebraic version of CuntzKrieger graph $C^*$algebras. The relation between these two classes of graph algebras has been mutually beneficial. The algebraic and analytic theories share important similarities, but also present some remarkable differences. This is the case for the topic discussed in this talk: the analytic result was given by Nagy and Reznikoff for the $C^*$algebras $C^*(E)$, and we give here the algebraic analogue for the Leavitt path algebras $L_R(E)$. We will introduce the commutative core $M_R(E)$: a maximal commutative subalgebra inside $L_R(E)$, which in particular contains the diagonal subalgebra. Furthermore, we will characterize injectivity of representations which gives a generalization of the CuntzKrieger uniqueness theorem: the result says that a representation of $L_R(E)$ is injective if and only if it is injective on $M_R(E)$. On the other hand, we will generalize and simplify the result about commutative Leavitt path algebras over fields. This work was done jointly with Alireza NasrIsfahani. 
May 4  [available]  
Fall 2015 Schedule
All talks in ENGR 201 (Engineering Dean's Conference Room) on the UCCS campus, unless otherwise indicated.
(note: this is a different room than the one we've used in the past, but the same room as we used in Spring 2015...)
All "Rings and Wings" talks begin at 3:45pm, unless otherwise indicated.
Contact Gene Abrams (preferably a few days in advance of the talk) if you need a UCCS parking permit.
DATE 
SPEAKER 
TITLE 
ABSTRACT 



Wednesday, September 9 
Bob Carlson UCCS 
Quantum Cayley Graphs for Free Groups (Talk 1 of 2) Talk #1 will aim for a broad audience, and will be “introductory”. The second followup talk will drill down deeper. We will schedule the second talk at the end of the first talk.

The spectral theory of selfadjoint operators provides an abstract framework for solving some of the main differential equations of mathematical physics: the heat equation, wave equation, and Schr{\"o}dinger equation. When the operators are invariant under a group action, a much more detailed analysis is often possible. This work on invariant differential operators on the metric Cayley graphs of free groups throws differential equations, graphs, group actions, functional analysis, algebraic topology, linear algebra, and a pinch of algebraic geometry into the blender. What emerges is a surprisingly satisfying concoction.
CLICK HERE FOR THE BEAMER SLIDES OF THE TALKS

Wednesday, September 30 
Bob Carlson UCCS 
Quantum Cayley Graphs for Free Groups (Talk 2 of 2) 
see above 
Wednesday, October 14 
Darren Funk Neubauer Colorado State University Pueblo 
Bidiagonal Pairs and Bidiagonal Triples  Roughly speaking, a bidiagonal pair is a pair of diagonalizable linear maps on a finitedimensional vector space, each of which acts in a bidiagonal fashion on the eigenspaces of the other. Bidiagonal pairs have been classified. The proof of this classification reveals that every bidiagonal pair can be extended to a triple of linear maps, in which each map acts bidiagonally on the eigenspaces of the other two. This leads to the notion of a bidiagonal triple. This talk will describe two different ways to define a bidiagonal triple, and then discuss the relationship between bidiagonal pairs and these two types of triples. There are a number of connections between bidiagonal pairs/triples and the representation theory of various well known algebras. The talk will describe these connections in detail. 
Wednesday, October 28 
Joe Timmer University of Colorado Boulder 
Hopf Algebras and Group Factorizations  With a group factorization $L=FG$ of a finite group and a field $k$ one may construct the bismash product Hopf algebra $H = k^G \# k F$. The connections between the representations of $L$ and $H$ have many similar qualities, especially when one looks at the FrobeniusSchur indicator.
In this talk, we will review (almost) all the background necessary for understanding the constructions of these Hopf algebras in question, the concept of indicators for Hopf algebras and also consider the case of factorizing the symmetric group $S_n$. 
Wednesday, November 11 
Gonzalo Aranda Pino Universidad de Málaga 
Decomposable Leavitt path algebras for arbitrary graphs 
Path algebras are algebras associated to graphs whose bases as vector spaces consist of the sets of all paths in a graph. On the other hand, classical Leavitt algebras are universal examples of algebras without the Invariant Basis Number condition (that is, of algebras having bases with different cardinal). Leavitt path algebras are natural generalizations of the aforementioned path and classical Leavitt algebras. In this talk we will characterize the Leavitt path algebras that are indecomposable (as a direct sum of twosided ideals) in terms of the underlying graph. When the algebra decomposes, it actually does so as a direct sum of Leavitt path algebras for some suitable graphs, and under certain finiteness conditions a unique indecomposable decomposition exists. This is a report on the joint paper: G. Aranda Pino, A. NasrIsfahani, "Decomposable Leavitt path algebras for arbitrary graphs", Forum Mathematicum, (to appear)" 
Wednesday, December 2 
John Beachy Northern Illinois University 
Universal Localization at Semiprime Ideals  P.M.Cohn defined the universal localization at a semiprime ideal S of a Noetherian ring to be the ring universal with respect to inverting all matrices regular modulo S. The universal localization coincides with the Ore localization, when that exists, and Goldie's localization is a homomorphic image of the universal localization. I will review the construction and some basic properties, and then focus on some of the difficulties and open questions. While wellbehaved modulo powers of its Jacobson radical, the "bottom" part of the universal localization is hard to calculate. It also fails to preserve chain conditions even for very wellbehaved rings. But I still believe that it may provide the language necessary to extend some commutative localization techniques to the noncommutative case. 
Spring 2015 Schedule
All talks in ENGR 201 (Engineering Dean's Conference Room) on the UCCS campus, unless otherwise indicated.
(note: this is a different room than the one we've used in the past ...)
All "Rings and Wings" talks begin at 3:45pm, unless otherwise indicated.
Contact Gene Abrams (preferably a few days in advance of the talk) if you need a UCCS parking permit.
DATE 
SPEAKER 
TITLE 
ABSTRACT 
Wednesday, February 25

Zak Mesyan UCCS 
InfiniteDimensional Diagonalization 
Let V be an arbitrary vector space over a field K, and let End(V) be the ring of all Klinear transformations of V. We characterize the diagonalizable linear transformations in End(V), as well as the (simultaneously) diagonalizable subalgebras of End(V), generalizing results from classical finitedimensional linear algebra. These characterizations are formulated in terms of a natural topology on End(V), which reduces to the discrete topology when V is finitedimensional. This work was done jointly with Mio Iovanov and Manny Reyes. 
Wednesday, March 4 
Gonzalo Aranda Pino Universidad de Málaga

KumjianPask algebras of higher rank graphs. 
In this talk I will present the basic definitions and first results of the theory of the KumjianPask algebras. These algebras are both the higherrank generalizations of the Leavitt path algebras (a higherrank graph essentially being a multilayered or multidimensional graph) and the algebraic analogs of the graph C*algebras of higherrank graphs. After the main definitions and examples, we prove graded and CuntzKrieger uniqueness theorems for these algebras, establish the simplicity result and analyze their ideal structure. This is a report of the paper:G. Aranda Pino, J. Clark, A. an Huef and I. Raeburn, "KumjianPask algebras of higher rank graphs", Trans. Amer. Math. Soc. 365 (7), 36133641 (2013). 
Wednesday, April 1

Kulumani Rangaswamy UCCS 
Leavitt path algebras asgraded algebras(Preliminary report)


Wednesday, April 15**
**This talk will happen 4:30  5:45 
Ehsaan Hossain University of Waterloo 
Quillen and Suslin's Famous Theorem  In differential geometry and topology, it's well known that all continuous vector bundles on a contractible topological space, such as $\mathbf{R}^n$, are continously trivial. This can be extended to even show that all holomorphic vector bundles on $\mathbf{C}^n$ are \textit{holomorphically} trivial. Since the affine $n$space $\mathbf{A}^n$ is also contractible in the Zariski topology, it was conjectured by Serre in the 50's that $mathbf{A}^n$ admits no nontrivial \textit{algebraic} vector bundles. This became known as Serre's Problem. On the algebraic side of things, this question can be interpreted as asking whether all finite projective modules are free over a polynomial ring $k[x_1,\ldots,x_n]$. As a result of the work of D. Quillen in the '70s, and independently by A. Suslin, it was shown that all finite projective modules over $k[x_1,\ldots,x_n]$ are free, and consequently Quillen earned the Fields Medal in '78. L. Vaserstein gave an elementary proof of Quillen's result using the theory of unimodular rows. In this talk I hope to share the rich history of Serre's Problem and give an overview of Vaserstein's simplification. 
Wednesday, April 22**
**This talk will happen 4:30  5:45 This talk will happen in ENGR 247

Cristóbal Gil Universidad de Málaga 
Leavitt path algebras of Cayley graphs $C_n^3$. 
Let $n$ be a positive integer and for each $0\leq j\leq n1$ we let $C_n^j$ denote Cayley graph for the cyclic group $\mathbb{Z}_n$ with respect to the subset $\{1,j\}$. For each pair $(n,j)$, the size of the Grothendieck group of the Leavitt path algebra $L_K(C_n^j)$ is related to a collection of integer sequences described by Haselgrove. When $j = 0,1,2$ it is possible to analyze the Grothendieck group of the Leavitt path algebras $L_K(C_n^j)$ in order to explicitly realize them as the Leavitt path algebras of graphs having at most three vertices, thanks to a KirchbergPhillips type result. The case $j=2$ has some surprising connection to the classical Fibonacci sequence and also in case $j=3$, it is related to a sequence of Fibonaccitype, called Narayana's cow sequence. 
Thursday, April 30 UCCS Math Department Colloquium 12:15  1:30pm OSB A327 
Cristóbal Gil Universidad de Málaga 
Leavitt path algebras of Cayley graphs.  Leavitt path algebras are natural generalizations of path algebras (or algebras associated to graphs). On the other hand, they include the algebras without the Invariant Basis Number (IBN) property originally introduced by Leavitt, and many other interesting properties. Also Leavitt path algebras are the algebraic counterparts of C*algebras. Let $n$ be a positive integer and for each $0\leq j \leq n1$ we let $C_n^j$ denote Cayley graph for the cyclic group $\mathbb{Z}_n$ with respect to the subset $\{1,j\}$. When $j = 0,1,2$ it is possible to analyze the Grothendieck group of the Leavitt path algebras $L_K(C_n^j)$ in order to explicitly realize them as the Leavitt path algebras of graphs having at most three vertices. The case $j=2$ has some surprising connection to the classical Fibonacci sequence. In case $j=3$, it is related to a ``Fibonaccilike" sequence, called Narayana's cow sequence. I will discuss some known properties of the structure of the group in the $j=3$ case, and give some conjecture. 
Wednesday, May 6 3:45  5:XX ENGR 201 
Francesca Mantese Università degli Studi di Verona

Extensions of Chen simple modules over Leavitt path algebras

Let $E$ be a directed graph, K any field, and let $L_K(E)$ denote the Leavitt path algebra of $E$ with coefficients in $K$. 
Thursday, May 7 UCCS Math Department Colloquium 12:15  1:30pm OSB A327 
Alberto Tonolo Università degli Studi di Padova 
Equivalences between categories of modules.  Two equal problems have equal solutions: therefore it is not necessary to solve both of them. There are relationships weaker than equality which are useful in the same sense. For instance, two equivalent linear systems are not equal, but they have the same solutions. Another example that one meets very soon in abstract algebra is the concept of isomorphism: two isomorphic objects share the same algebraic properties. In this talk we will concentrate on Rings. Isomorphic rings are not equal, but they can be thought as essentially the same, only with different labels on the individual elements. In this talk I will present other notions of ``similarity'' between rings; in particular we will discuss Morita equivalent and Tilting equivalent rings. They are relationships defined between rings that preserves some ringtheoretic properties. Giving priority more to comprehensibility than to precision, I hope to be able to give you through examples the taste of an important contemporary field of research. 







Fall 2014 Schedule
All talks in ENGR 239 (Engineering Conference Rooms) on the UCCS campus, unless otherwise indicated.
All talks begin at 4:00pm, unless otherwise indicated.
Contact Gene Abrams (preferably a few days in advance of the talk) if you need a UCCS parking permit.
DATE 
SPEAKER 
TITLE 
ABSTRACT 
Wednesday, Sept 10

K.M. Rangaswamy UCCS 
Leavitt path algebras satisfying a polynomial identity. 
Leavitt path algebras L of arbitrary graphs E satisfying polynomial identities are characterized both graphically and algebraically. Connections to the GelfandKirillov dimension of L are explored. 
Thursday, October 9 UCCS Math Dept. Colloquium OSB A324 (Daniels K12 Room) 12:30  1:30 
Jonathan Brown Kansas St. University

The center of rings associated to directed graphs 
In 2005 Abrams and Aranda Pino began a program studying rings constructed from directed graphs. These rings, called Leavitt Path algebras, generalized the rings without invariant basis number introduced by Leavitt in the 1950's. Leavitt path algebras are the algebraic analogues of the graph C*algebras and have provided a bridge for communication between ring theorists and operator algebraists. Many of the properties of Leavitt path algebras can be inferred from properties of the graph, and for this reason provide a convenient way to construct examples of algebras with a particular set of attributes. In this talk we will explore how central elements of the algebra can be read from the graph. 
Thursday, October 23 UCCS Math Dept. Annual Distinguished Lecture UCCS Library, 2nd Floor Apse 12:30  1:30 (refereshments @12:15)

Jason Bell University of Waterloo 
Game theoryand the mathematics of altruism

Game theory is a branch of mathematics that deals with strategy and decision making and is applied in economics, computer science, biology, and many other disciplines as well. We will discuss some of the basic points of game theory and discuss the socalled iterated prisoner dilemma, a game that is of central importance in the study of cooperation between individuals. We will then describe various strategies to this game and explain why altruism is something that can evolve naturally. 
Friday October 31 2:00  3:00p ENGR 239 
Jeff Boersema Seattle University (visiting U. New Mexico) 
Real structures in graph C*algebras  Real C*algebras are the counterpart to C*algebras in which we replace the field of complex scalars by the reals. Any real C*algebra A can be embedded uniquely in a complex C*algebra isomorphic to A + iA (called the complexification); but two different real C*algebras can have the same complexification up to isomorphism. The general problem is to find, for a given complex C*algebra, all real corresponding C*algebras. We will introduce a graphbased construction for identifying real structures in graph algebras. 
Wednesday November 5 4:00 5:XX 
Greg Oman UCCS 
Strongly Jonsson binary relational structures 
Let X be a set, and let R be a binary relation on X. Say that a subset Y of X is an Rlower set provided whenever y is in Y and xRy, then also x is in Y. Say that the structure (X,R) is strongly Jonsson provided distinct Rlower subsets of X have distinct cardinalities. In this note, we consider the problem of classifying the strongly Jonsson binary relational structures. In particular, we relate the problem to the wellknown (and unsolved) "distinct subset sum problem" in combinatorics. 
Wednesday November 19 4:00  5:XX 
Zak Mesyan UCCS 
to be announced  
Wednesday December 3 4:00  5:XX 
Derek Wise U. Erlangen (Germany) 
An Elementary Introduction to Weak Hopf Algebras  Weak Hopf algebras combine two important generalizations of the notion of a group: Hopf algebras and groupoids. In a Hopf algebra, we replace the set of group elements with a vector space and systematically require all of the structure, such as multiplication and inversion, to be linear. This generalizes the "classical" notion of symmetry to "quantum" symmetry. In a groupoid, on the other hand, we replace the group multiplication by a partiallydefined operation: only specified pairs of elements can be multiplied. This generalizes the notion of symmetry to include not only transformations of a single object but also symmetries between different objects. The theory of weak Hopf algebras combines key aspects of these two generalizations, describing "multiobject quantum symmetries." 
POSTPONED UNTIL SPRING 2015

Gonzalo Aranda Pino U. Malaga (Spain) 
KumjianPask algebras of higher rank graphs.  In this talk I will present the basic definitions and first results of the theory of the KumjianPask algebras. These algebras are both the higherrank generalizations of the Leavitt path algebras (a higherrank graph essentially being a multilayered or multidimensional graph) and the algebraic analogs of the graph C*algebras of higherrank graphs. After the main definitions and examples, we prove graded and CuntzKrieger uniqueness theorems for these algebras, establish the simplicity result and analyze their ideal structure. This is a report of the paper: G. Aranda Pino, J. Clark, A. an Huef and I. Raeburn, "KumjianPask algebras of higher rank graphs", Trans. Amer. Math. Soc. 365 (7), 36133641 (2013). 
Spring 2014 Schedule
All talks in OSB A342 (Small Conference Room) on the UCCS campus, unless otherwise indicated.
All talks begin at 4:00pm, unless otherwise indicated.
Contact Gene Abrams (preferably a few days in advance of the talk) if you need a UCCS parking permit.
DATE 
SPEAKER 
TITLE 
ABSTRACT 
Wednesday, March 12 OSB A342 (Small Conference Room)

Greg Oman UCCS 
Small and large ideals of an associative ring 
Abstract. Let R be an associative ring with identity, and let I be an (left, right, twosided) ideal of R. Say that I is small if I<R and large if R/I<R. In this talk, I will present results on small and large ideals. In particular, I will discuss their interdependence and how they influence the structure of R. Conversely, I will give examples to show how the ideal structure of R determines the existence of small and large ideals. 
Thursday, April 3 UCCS Math Dept. Colloquium OSB A324 (Daniels K12 Room) 12:30  1:30 
Kulumani Rangaswamy UCCS

The Leavitt path algebras of directed graphs  The Leavitt path algebra L of a directed graph E over a field K is endowed with nicely amalgamating different structures: L is an associative algebra over the field K, it is a graded ring, L possesses a compatible involution and all these structures are intertwined by the enveloping properties of the graph E. L is highly noncommutative, but the presence of the involution makes the usual leftright differences for noncommutative algebras disappear in L. This talk will describe some of the intrinsic properties and recent results on Leavitt path algebras and illustrate how Leavitt path algebras have become powerful tools in constructing examples of various types of algebras. 
Friday, April 25 CC Fearless Friday Series 12:00  1:00 Tutt Lecture Hall, Tutt Science Bldg. Colorado College Undergraduateoriented presentation

Gene Abrams UCCS 
Fibonacci’s Rabbits Visit the Mad Veterinarian 
Since its origin (more than eight centuries ago) as a puzzle about the number of rabbits in a (fantasmagorically expanding) colony, the Fibonacci Sequence 1,1,2,3,5,8,13,... has arguably become the most wellknown of numerical lists, due in part to its simple recursion formula, as well as to the numerous connections it enjoys with many branches of mathematics and science. Since their origins (less than two decades ago) as puzzles about the number of animals in a (fantasmagorically strange) veterinarian’s office, the (not so wellknown) Mad Vet Scenarios have provided a source of thoughtprovoking entertainment to internet gamers and math enthusiasts alike. In this talk we’ll show how Fibonacci’s puzzle about rabbits is naturally connected to the puzzles found in the Mad Vet’s office. Along the way, we’ll show how an investigation into Mad Vet Scenarios has led to the discovery of some heretofore unrecorded properties of the Fibonacci Sequence. This talk is rated G, meaning that it is intended for the most General of audiences. No prior familiarity with Fibonacci’s breeding rabbits, or with the Mad Veterinarian’s transmogrification machines, or with any other type of fantasmagorical animal population dynamics, will be assumed. 
Wednesday, April 30 OSB A342 (Small Conference Room) 
Mark Tomforde University of Houston 
Classification of Leavitt path algebras using algebraic Ktheory  Leavitt path algebras are algebraic counterparts of graph C*algebras that include the algebras without the Invariant Number Basis (IBN) property originally introduced by Leavitt, several ultramatricial algebras, and many other interesting examples. In the theory of C*algebras, operator algebra Ktheory has proven to be a very useful and powerful tool for classification. In this talk we will examine the algebraic Ktheory of the Leavitt path algebras and the extent to which it can be used to classify Leavitt path algebras up to Morita equivalence. While algebraic Ktheory is notoriously difficult to compute in general, we will present cases in which the algebraic Ktheory of Leavitt path algebras may be explicitly computed using some simple formulas. We will also describe various classes of Leavitt path algebras that can be classified up to Morita equivalence by algebraic Ktheory and discuss what Ktheoretic data is needed for each class. Surprisingly, the underlying field of the algebra plays an important role in this classification. 
Thursday, May 1 OSB A 324 (Daniels K12 Room) 
Mark Tomforde University of Houston 
Using results from dynamical systems to classify algebras and C*algebras 
In the subject of symbolic dynamics, the shift spaces of finite type arise as edge shifts of finite directed graphs. The classification of these shift spaces was used in the 1980’s to classify certain C*algebras constructed from directed graphs, known as CuntzKrieger C*algebras, and moreover, the dynamical systems methods were key ingredients in the proofs. More recently, similar techniques have been used to classify certain algebras constructed from directed graphs, which are known as Leavitt path algebras. In this talk I will give an overview of the dynamical systems results, describe how they have led to methods for classifying C*algebras and algebras, and discuss the current status of these classification programs and existing open problems. 
Fall 2013 Schedule
All talks in ENGR 239 on the UCCS campus, unless otherwise indicated.
All talks begin at 4:00pm, unless otherwise indicated.
Contact Gene Abrams (preferably a few days in advance of the talk) if you need a UCCS parking permit.
DATE 
SPEAKER 
TITLE 
ABSTRACT 
Thursday, August 29 *** UCCS Colloquium Series

Zak Mesyan UCCS 
Evaluating polynomials on matrices 
A
classical theorem of Shoda from 1936 says that over any field K (of
characteristic 0), every matrix with trace 0 can be expressed as a
commutator ABBA, or stated another way, that evaluating the polynomial
f(x,y)=xyyx on matrices over K gives precisely all the matrices having
trace 0. I will describe various attempts over the years to generalize
this result.

September 25  Kulumani Rangaswamy UCCS

Endomorphism rings of Leavitt path algebras  Leavitt path algebras L(E) of a graph E are in general nonunital rings unless the number of vertices in E is finite. Regarding a Leavitt path algebra L(E) as a right L(E)module, I will talk about the various ringtheoretic properties of the endomorphism ring A of L(E) and relate them to corresponding graphtheoretical properties of E. Interestingly, these properties of the graph E are much stronger that those on E in order for L(E) to have the same property as A. 
October 16 
Greg Oman UCCS 
Strongly Jonsson and strongly HS modules 
Borrowing from universal algebraic terminology, an infinite module M over a ring R is called a Jonsson module provided every proper submodule of M has smaller cardinality than M. Call M strongly Jonsson (and drop the requirement that M be infinite) provided distinct submodules of M have distinct cardinalities (the cyclic and quasicyclic groups have this property). Dually, M is said to be homomorphically smaller (HS for short) if M/N has smaller cardinality than M for every nonzero submodule N of M. Say that M is strongly HS provided M/N and M/K have distinct cardinalities for distinct subgroups N and K of M (the abelian group Z of integers has this property; again, we drop the requirement that M be infinite). In this talk, we discuss the above notions. In particular, we present classification theorems for modules over an arbitrary commutative ring R. 
October 30 
Gonzalo Aranda Pino Universidad de Malaga (Spain) 
Leavitt path algebras of generalized Cayley graphs  Path algebras are algebras associated to graphs whose bases as vector spaces consist of the sets of all paths in a graph. On the other hand, classical Leavitt algebras are universal examples of algebras without the Invariant Basis Number condition (that is, of algebras having bases with different cardinal). Leavitt path algebras are then natural generalizations of the aforementioned path and classical Leavitt algebras, as well as algebraic versions of graph C*algebras. Let $n$ be a positive integer. For each $0\leq j \leq n1$ we let $C_n^j$ denote Cayley graph for the cyclic group $Z_n$ with respect to the subset $\{1, j\}$. For any such pair $(n,j)$ we compute the size of the Grothendieck group of the Leavitt path algebra $L_K(C_n^j)$; the analysis is related to a collection of integer sequences described by Haselgrove in the 1940's. When $j=0,1,$ or $2$, we are able to extract enough additional information about the structure of these Grothendieck groups so that we may apply a KirchbergPhillipstype result to explicitly realize the algebras $L_K(C_n^j)$ as the Leavitt path algebras of graphs having at most three vertices. The analysis in the $j=2$ case leads us to some perhaps surprising and apparently nontrivial connections to the classical Fibonacci sequence. 
Spring 2013 Schedule
All talks in ENGR 239 on the UCCS campus, unless otherwise indicated.
All talks begin at 4:00pm, unless otherwise indicated.
Contact Gene Abrams (preferably a few days in advance of the talk) if you need a UCCS parking permit.
DATE 
SPEAKER 
TITLE 
ABSTRACT 
January 30

Stefan Erickson The Colorado College TALK TO BE HELD IN TUTT SCIENCE BUILDING ON THE COLORADO COLLEGE CAMPUS, ROOM 221 
Endomorphism Rings of Elliptic Curves 

February 13 
(cancelled) 

February 27 
P.N. Anh Mathematics Institute, Hungarian Academy of Sciences, Budapest TALK TO BE HELD IN TUTT SCIENCE BUILDING ON THE COLORADO COLLEGE CAMPUS, ROOM 229 
A generalization of Clifford's Theorem 

March 13 
Mike Siddoway The Colorado College TALK TO BE HELD IN TUTT SCIENCE BUILDING ON THE COLORADO COLLEGE CAMPUS, ROOM 229 
Ideals, Gauss' Lemma, Valuations, Eisenstein's Criterion 

** Thursday, March 21 12:30  1:30 UCCS Math Dept. Colloquium 
Murad Ozaydin University of Oklahoma 
"The linear Diophantine Frobenius problem: an elementary introduction to numerical methods" 

April 3 
Benjamin Schoonmaker MS Applied Math student, UCCS 
An examination of the K_0 groups of the Leavitt path algebras of some Cayley graphs 

April 17 
Zak Mesyan UCCS 
Generalizations of Shoda's Theorem 
Abstract: A celebrated theorem of Shoda from 1936 states that over any field (of characteristic 0), every matrix with trace 0 can be expressed as a commutator ABBA. I will describe various attempts to generalize this result over the years. 
** Friday April 19 2:00  3:00 UCCS, room tba 
Efren Ruiz University of Hawai'i Hilo 
Classification of graph algebras: The Invariant and Status Quo 

** Tuesday, April 31 12:30  1:30 UCCS Math Dept. Colloquium 
Mercedes Siles Molina Universidad de Malaga (Spain) 
Graph algebras: from analysis to algebra and back 

May 1 
Pere Ara Universitat Autonoma de Barcelona 
Lamplighter groups and separated graphs 

Previous semesters:
Fall 2012 Schedule
DATE 
SPEAKER 
TITLE 
ABSTRACT 
November 28 
Darren FunkNeubauer Colorado State University  Pueblo 
An Introduction to Bidiagonal Pairs 
I will introduce a linear algebraic object called a bidiagonal pair and present a theorem which classifies these objects. Roughly speaking, a bidiagonal pair is an ordered pair of diagonalizable linear transformations on a finite dimensional vector space, each of which acts in a bidiagonal fashion on the eigenspaces of the other. Understanding the definition of a bidiagonal pair and the statement of the classification theorem only requires a basic knowledge of undergraduate linear algebra. However, the proof of the classification theorem makes use of the representation theory of Lie algebras and quantum groups. I will discuss the origin of bidiagonal pairs in Lie theory, but no Lie theory will be assumed in following the talk. 
November 14 
Matthew Eric Bassett Queen's College, London

A Tour of Hopf Algebras and Their Applications, plus some remarks about class field theory

From their beginnings in algebraic topology, Hopf algebras  later quantum groups  have found uses ranged from number theory to noncommutative geometry. In this talk, we'll discuss their uses in studying Galois modules, to constructing noncommutative geometries, and, time permitting, say a few words about the structure of the quantum groupflavoured Hopf algebras via their categories of [co]modules. I'll also mention some results from a recent paper by Cornelissen, expanding on BostConnes type system results. 
October 24 
Kulumani M. Rangaswamy UCCS 
Centers of path algebras, Cohn algebras, and Leavitt path algebras

This talk will attempt to describe the centers of path algebras, the Cohn algebras and the Leavitt path algebras of an arbitrary graph E over a field K. 
October 10 
Muge Kanuni Er Boğaziçi Univesity Dept of Mathematics Visiting Fulbright Scholar to UCCS 
"An approach to calculating the global dimension of some Artinian algebras" 
In this talk, we will focus on two aspects: *** joint work with A. Kaygun 
September 26 
Kulumani M. Rangaswamy UCCS 
A descriptinon of results in the article "Irreducible representations of Leavitt path algebras" by XiaoWu Chen 

September 12 
Greg Oman UCCS 
Rings whose multiplicative endomorphisms are power functions. 
Let F be a finite field of order p^n. It is wellknown that there are exactly n field automorphisms of F. In particular, they are all power functions. In this note, we "throw away" addition and enlarge the class of rings to the class of commutative rings with identity. We then consider the following question: For which rings R is it the case that every multiplicative endomorphism of R (a map which preserves multiplication, sends 0 to 0, and sends 1 to 1) is equal to a power function? 
Spring 2012 Schedule
DATE 
SPEAKER 
TITLE 
ABSTRACT 
February 1 
Zak Mesyan UCCS 
Simple Lie algebras arising from Leavitt path algebras 

February 15 
Sergio Lopez Permouth Ohio University

Characterizing rings in terms of the extent of the injectivity and projectivity of their modules. 
Given a ring R, we define its right iprofile (resp. right pprofile) to be the collection of injectivity domains (resp. projectivity domains) of right Rmodules. We study the lattice theoretic properties of these profiles. We show that the iprofile is equivalent to an interval of the lattice of linear filters of right ideals of R. This allows us to apply torsion theoretic techniques to study the iprofile of a ring. We show through and example that the pprofile of a ring is not necessarily a set, and we characterize the pprofile of a right perfect ring. We then apply our results to the study of a special class of QFrings. The study of rings in terms of their (i or p)profile generalizes the study of rings with no right (i or p)middle class, initiated in recent papers by Er, LopezPermouth and Sokmez, and by Holston, LopezPermouth and OrhanErtas. 
March 7 
Darren FunkNeubauer CSU  Pueblo 
Introduction to the theory of tridiagonal and bidiagonal pairs: Part 1

Tridiagonal pairs and bidiagonal pairs are linear algebraic objects which originally arose in the context of algebraic graph theory, but now appear in many other areas of mathematics. Roughly speaking, a tridiagonal (resp. bidiagonal) pair is a pair of diagonalizable linear transformations on a finite dimensional vector space which act tridiagonally (resp. bidiagonally) on each others eigenspaces. In these two seminar talks I will do the following: give the formal defintions of tridiagonal and bidiagonal pair, give some concrete examples of them, discuss the history of how they arose, discuss how these objects arise in the representation theory of Lie algebras (my research area), and discuss attempts to classify these objects. These talks will not assume any specialized knowledge of graph theory, Lie theory, or representation theory. The only prerequiste for the talk is a solid understanding of linear algebra. 
March 21 
Darren FunkNeubauer CSU  Pueblo 
Introduction to the theory of tridiagonal and bidiagonal pairs: Part 2 

April 4 
Greg Oman UCCS 
Modules which are isomorphic to their factor modules. 
Call a module M homomorphically congruent (HC) provided M is infinite and M\cong M/N for every submodule N of M for which M=M/N. We will give some background showing how we arrived at this definition (i.e. how it is a natural outgrowth of notions wellstudied in the literature) and present the principal results on HC modules. 
Friday, April 20 
Cornelius Pillen University of South Alabama 
Cohomology of Finite Groups of Lie Type 
A longstanding open problem of major interest for algebraists and topologists has been to determine the cohomology rings of finite groups of Lie type in the socalled defining characteristic. Little is known in general about these rings. It is not even known in which positive degree the first nontrivial cohomology classes occurs, a question that was first posed and partially answered by Quillen in the 1970s. Being far from wellunderstood, the cohomologies of the corresponding Lie algebras and Frobenius kernels, nevertheless, are better understood theories that can be used as a tool for investigations into the cohomology rings of finite groups. Recently developed methods and techniques in linking these theories will be presented. These techniques will allow us to use Kostant's partition functions to provide answers to Quillen's question. 
May 2 *** at Colorado College 
Mike Siddoway Colorado College 
Divisibility Theory of Rings with Zero Divisors 
The "divisibility theory" of a commutative ring is the semigroup of finitely generated ideals partially ordered by inverse inclusion. For instance, for a Bezout ring this amounts to the semigroup of principal ideals. The divisibility theory for valuation domains is well known through the groundbreaking work of Krull in the early 20th century, though his approach did not directly consider the semigroup of finitely generated ideals. Rings with zero divisors present interesting complications. Aside from the longsettled case of valuation rings, the divisibility theory of rings with zero divisors has not added a new class of rings since the 1960s. One of our results states that a semigroup is a semihereditary Bezout semigroup if and only if it is isomorphic to the semigroup of principal ideals in a semihereditary Bezout ring partially ordered by reverse inclusion. This is joint work with Pham Ngoc Anh of the Hungarian Academy of Sciences and recalls the studies of Krull on valuation domains and Kaplansky, Jaffard, and Ohm on Bezout domains. Our results are the first major developments along these lines for rings with zero divisors. 