Institute for Mathematics and its Applications University of Minnesota 400 Lind Hall 207 Church Street SE Minneapolis, MN 55455 
20062007 Program
See http://www.ima.umn.edu/20062007 for a full description of the 20062007 program on Applications of Algebraic Geometry.
The BlackwellTapia Conference, the premier national event for underrepresented mathematical sciences researchers took place on Friday and Saturday, Nov. 3 and 4 at the IMA. Over 150 scientists and mathematicians participated in this event. A high point of the meeting was the awarding of 2006 BlackwellTapia prize to Massey for his outstanding achievements in queuing theory, stochastic networks, modeling of communications systems, and for increasing diversity in mathematical sciences. To kick off the conference, Tapia gave an inspiring talk to more than 100 area high school students with his Math is Cool presentation. This conference received a lot of publicity and coverage by the local and national media. You can find more information (including a photo gallery) about this event at BlackwellTapia conference web page.
Opportunities at the IMA: If you are interested or know of anyone who is interested in applying for one of the IMA General Membership, New Directions Professorship or Postdoctoral Fellowship positions in connection with the 20072008 thematic program: Mathematics of Molecular and Cellular Biology, the deadline for applying for these positions is January 5, 2007. You can find the applications for these positions at our Applications site.
New Directions Short Course: The IMA is currently accepting applications for the 2007 New Directions Short Course  Compressive Sampling and Frontiers in Signal Processing June 4  15, 2007, taught by Emmanuel Candes, Ron DeVore and Rich Barniuk. This exploding area of research has connections to many areas of mathematics and presents many research opportunities. No prior background in signal processing is expected. Participants will receive full travel and lodging support during the workshop. Participation is by application only. Application deadline: April 1, 2007.
IMA is seeking a new director: The IMA is looking for a new director to begin in summer 2008.
11:15a12:15p  IMA postdoc seminar: TBA  Benjamin J. Howard (University of Minnesota Twin Cities)  Lind Hall 409  PS 
11:15a12:15p  Algebraic geometry and applications seminar: Gröbner walks and Scarf homotopies  Niels Lauritzen (Aarhus University)  Lind Hall 409  AGS 
11:15a12:15p  Real algebraic geometry tutorial: Quadratic forms and root counting  Kenneth R. Driessel (Iowa State University)  Lind Hall 409  RAG 
8:15a8:45a  Registration and coffee  EE/CS 3176  SW12.89.06  
8:45a9:00a  Welcome to the IMA  Douglas N. Arnold (University of Minnesota Twin Cities)  EE/CS 3180  SW12.89.06 
9:00a10:00a  Structured math on the web  T. V. Raman (Google Inc.)  EE/CS 3180  SW12.89.06 
10:00a10:15a  Discussion and coffee break  EE/CS 3180  SW12.89.06  
10:15a10:45a  Relevance ranking and hit packaging in math search  Abdou Youssef (George Washington University)  EE/CS 3180  SW12.89.06 
10:45a11:15a  The MathFind search engine  Robert Miner (Design Science, Inc.)  EE/CS 3180  SW12.89.06 
11:15a11:30a  break  EE/CS 3176  SW12.89.06  
11:30a12:00p  Textbased input formats for mathematical formulas  Peter Jipsen (Chapman University)  EE/CS 3180  SW12.89.06 
12:00p12:30p  The current state and future of jsMath  Davide P. Cervone (Union CollegeUnion University)  EE/CS 3180  SW12.89.06 
12:30p2:00p  Discussion and lunch break  EE/CS 3180  SW12.89.06  
2:00p2:30p  Blogging with MathML  Jacques Distler (University of Texas)  EE/CS 3180  SW12.89.06 
2:30p3:00p  Collaborative curriculum development in engineering and The sciences: The connexions 7 year experience with MathML  Ross Reedstrom (Rice University)  EE/CS 3180  SW12.89.06 
3:00p3:30p  High performance mathematics and its management  Jonathan Borwein (Dalhousie University)  EE/CS 3180  SW12.89.06 
3:30p4:00p  Group photo and coffee break  EE/CS 3180  SW12.89.06  
4:00p4:30p  The ellipsis in mathematical documents  Alan P. Sexton (University of Birmingham) Volker Sorge (University of Birmingham)  EE/CS 3180  SW12.89.06 
4:30p5:30p  Panel on digital libraries of today  Thierry Bouche (Université de Grenoble I (Joseph Fourier)) Petr Sojka (Masaryk University) Wojtek Sylwestrzak (University of Warsaw) Philippe Tondeur (University of Illinois at UrbanaChampaign) Bernd Wegner (TU Berlin)  EE/CS 3180  SW12.89.06 
5:30p5:45p  Discussion  EE/CS 3180  SW12.89.06 
8:45a9:00a  Coffee  EE/CS 3176  SW12.89.06  
9:00a10:00a  The slow evolution of mathematical communication  Andrew M. Odlyzko (University of Minnesota Twin Cities)  EE/CS 3180  SW12.89.06 
10:00a10:15a  Discussion and coffee break  EE/CS 3180  SW12.89.06  
10:15a10:45a  Using metadata for the interlinking of digitized mathematics  Thomas Fischer (State and University Library Goettingen)  EE/CS 3180  SW12.89.06 
10:45a11:15a  DLMF, LaTeXML and some lessons learned  Bruce R. Miller (National Institute of Standards and Technology)  EE/CS 3180  SW12.89.06 
11:15a11:30a  break  EE/CS 3176  SW12.89.06  
11:30a12:00p  Interfaces for mathematical communication  Elena Smirnova (University of Western Ontario) Stephen M. Watt (University of Western Ontario)  EE/CS 3180  SW12.89.06 
12:00p12:30p  A "Semantic Web" for science and technology communicating the content of mathematics "In the Large"  Michael Kohlhase (International University Bremen)  EE/CS 3180  SW12.89.06 
12:30p2:00p  lunch  SW12.89.06  
2:00p2:30p  How can we speak math?  Richard Fateman (University of California)  EE/CS 3180  SW12.89.06 
2:30p3:00p  Overview of accessible math  Neil Soiffer (Design Science, Inc.)  EE/CS 3180  SW12.89.06 
3:00p3:30p  Discussion and coffee break  EE/CS 3180  SW12.89.06  
3:30p4:00p  Edocument mathematical multilingual processing  Azzeddine Lazrek (Cadi Ayyad University)  EE/CS 3180  SW12.89.06 
4:00p4:30p  Advanced language technologies for mathematical markup  Olga Caprotti (University of Helsinki)  EE/CS 3180  SW12.89.06 
4:30p4:45p  Closing discussion  EE/CS 3180  SW12.89.06 
11:15a12:15p  IMA postdoc seminar: TBA  Carl Toews (University of Minnesota Twin Cities)  Lind Hall 409  PS 
11:15a12:15p  Algebraic geometry and applications seminar: Some algorithmic aspects of local cohomology  Gennady Lyubeznik (University of Minnesota Twin Cities)  Lind Hall 409  AGS 
All Day  Christmas Day. The IMA is closed. 
All Day  The IMA is closed. 
Jonathan Borwein (Dalhousie University)  High performance mathematics and its management 
Abstract: Seventyfive years ago Kurt Gödel overturned the mathematical apple cart: he proved entirely deductively that mathematics is not entirely deductive,while holding quite different ideas about legitimate forms of mathematical reasoning: If mathematics describes an objective world just like physics, there is no reason why inductive methods should not be applied in mathematics just the same as in physics. (Kurt Gödel, 1951) This talk provides an introduction to Experimental Mathematics, its theory and its practice. I will focus on the differences between Discovering Truths and Proving Theorems and on the implications for knowledge management and communication. I shall explore various of the computational tools available for deciding what to believe in mathematics, andusing accessible examplesillustrate the rich experimental toolbox mathematicians now have access to. These tools range from webinterfaces and databases to preprint repositories and digital library collections, and prominently include NIST's forthcoming Digital Library of Mathematical Functions. In an attempt to explain how mathematicians may use High Performance Computing (HPC) and what they have to offer other computational scientists, I will touch upon various Computational Mathematics Challenge Problems.  
Olga Caprotti (University of Helsinki)  Advanced language technologies for mathematical markup 
Abstract: Mathematical markup languages like OpenMath and MathML offer the possibility to represent mathematical content in a level of abstraction that is not dependent on localized information. This representation typically focuses on the semantics of the mathematical object and postpones localization aspects of mathematics, such as those influenced by notation and by culture, to the rendering process of the markup. While typesetting of mathematical markup has been the object of a numerous efforts, from MathMLpresentation to SVG converters, the rendering of mathematics in a "verbalized" jargon has not yet received similar attention. In this talk, I will present the results of the WebALT EU eContent project concerning the application of language technologies to the automatic generation of text from mathematical markup. Mathematical jargon is an important aspect of the education of students. Not only does a teacher train pupils in problem solving skills, but she also makes sure that they acquire a proper way of expressing mathematical concepts. To our knowledge, digital eLearning resources have used a representation in which text is intermixed with mathematical expressions even in situations where the actual abstract representation, for instance of the statement of a theorem, can be reduced to a single mathematical object. One reason for this representation choice is that the rendering process would otherwise produce a symbolic, typeset mathematical formula that might prove too difficult to understand for the students or simply just too hard to read. However, by representing this kind of mathematical text in a languageindependent format such as the one provided by markup languages, it is possible to apply language technologies that generate the same text in a variety of languages including English, Spanish, Finnish, Swedish, French and Italian. The project results include editors for mathematical multilingual markup, a web service for generating multiple languages versions and a digital repository of multilingual interactive mathematical exercises and drill questions.  
Davide P. Cervone (Union CollegeUnion University)  The current state and future of jsMath 
Abstract: JsMath is a means of displaying mathematics in web pages that works across multiple browsers (MSIE, Firefox, Opera, Safari, etc.) and multiple platforms (Windows, unix, Mac OS X). It uses JavaScript, cascading style sheets (CSS), and unicode fonts to render TeX code embedded in an HTML document into typeset mathematics within the browser. Over the past two years, jsMath has found a home within a number of online contentgeneration systems (e.g., bulletin boards, blogs, coursemanagement systems) because it allows participants to enter mathematics in a straightforward and possibly familiar format while still producing quality output in all the major browsers, both on screen and in print, without the need of complicated installations on the server or extra downloads by the user. This talk will describe some of jsMath's most important features and how these can be controlled by the page author, and will point out some of the issues that need to be addressed when adding jsMath into a content management system. Finally, we will discuss some of the future plans for jsMath, including incorporation of MathML input and output into jsMath.  
Jacques Distler (University of Texas)  Blogging with MathML 
Abstract: Four years ago, I set out to see whether one could used weblogs as an effective vehicle for communicating ideas in Physics. Not knowing any better, I decided to use the muchheralded, but seldomused web technologies of XHTML+MathML (with the occasional bit of SVG, for good measure). Between my own blog, Musings, and The String Coffee Table, which I host on my server, there are nearly a thousand posts, and many thousands of comments, making them one of the largest collections of MathML on the web. On the one hand, this was a social experiment, in adopting the web (and weblogs, in particular) as a conduit for scientific communications. On the other hand, it was a technological experiment, in making the technology "easy enough for mere physicists to use." I would like to address both aspects in this talk.  
Richard Fateman (University of California)  How can we speak math? 
Abstract: Surprisingly, we can speak mathematics to a computer probably more rapidly and accurately than handwriting. Even better is to speak and use pointing or handwriting. A combination may allow us to identify and cancel errors in one mode or another. In some cases speaking may be more convenient than typing, even for rapid typists: many mathematical symbols missing on the keyboard can be easily spoken. Even without venturing into Greek, handwriting or even typing "fifty million" is probably slower and more errorprone than speaking it. Pursuing the goal of effectively speaking small pieces of mathematics, we wondered how hard it would be to speak arbitrarily long sections of mathematics, including nested complex expressions. We first describe programs for the inverse problem: computer generation of mathematical speech. In so doing we find that we need to suggest a few speaking conventions to overcome the unfortunately ambiguous and inconsistent common usages of mathematics. Then we consider tools and guidelines to make it more plausible for humans to speak full mathematical formulas so they can be recognized by a computer using a speech recognizer program. We describe our prototype programs which do somewhat less than we propose, but are effective in that speech can either be used alone, or used to fill in boxes (superscripts, etc.) or larger pieces, or for choosing alternatives from plausible symbol recognition from handwriting. We believe the principle barriers to engineering a more complete program can be overcome, though a driving application may be essential for refining prototypes into useful programs. This paper is not intended to be the last word on the subject, but to expose problems and approaches relevant to the task.  
Thomas Fischer (State and University Library Goettingen)  Using metadata for the interlinking of digitized mathematics 
Abstract: This is work related to communication with Thierry Bouche (Cellule MathDoc
and Institut Fourier, Grenoble) and David Ruddy (Cornell University
Library)
For the access to mathematical research literature, mathematicians usually
employ review journals such as Mathematical Reviews and Zentralblatt der
Mathematik. These provide a rich network of interlinked (via references and
citations) mathematical sources. To make this even more useful, the review
journals could be used as hubs for the linkage not only to printed and born
digital material, but also to digitized versions of this literature.
An examination of the currently available metadata indicates not only that
the present formats do not identify the mathematical literature with sufficient
precision, but also that the metadata formats in use are inadequate, unless overloaded
with complex syntactical schemes. A richer and more rigid scheme for the
expression of the metadata is needed, and different approaches are investigated:


Peter Jipsen (Chapman University)  Textbased input formats for mathematical formulas 
Abstract: This talk discusses and compares several approaches that can be used to produce mathematical content on the web. Emphasis is placed on the input that the user has to create, in particular on easeofuse, readability, familiarity, generality, availability and other criteria. While LaTeX to PDF is generally considered the de facto standard in research publications, we will also examine input languages for several computer algebra systems, online assessment/courseware systems and word processors, as well as ASCIIMath. Since the ASCIIMath language is a relative newcomer (but mostly a refinement of the well known tradition of approximating formulas by ascii characters), the talk includes a brief description and motivation for some of the design decisions. The core of this mathematical input language consists of only 8 lines of BNF, yet it can express most of undergraduate mathematics in a predictable way that generally matches what users expect. In addition the language constructs map in a direct way to a subset of Presentation MathML. E.g. 4/3pir^{3} translates to <mfrac><mn>4</mn><mn>3</mn></mfrac><mi>π</mi> <msup><mi>r</mi><mn>3</mn></msup> and displays in standard typeset form. A JavaScript implementation ASCIIMathML.js parses this syntax and applies the translation in the client's browser. This program has been downloaded by thousands of users in over 90 countries and is currently used in numerous blogs, wikis and course management systems, partly because it enables crossbrowser MathML to display in legacy HTML (rather than XHTML) pages. Since the language overlaps with LaTeX and TI83 syntax, it is familiar to mathematicians and school children, and is also used as input for online calculators. ASCIIMath has been implemented by others in PHP and C#, as well as modified to LaTeXMathML.js. Experiments with an online WYSIWYG HTML editor, called ASciencePad, indicate that ASCIIMath is a convenient alternative to toolbardriven formula editors. In summary, it appears that an input format like ASCIIMath is a desirable addition to the various ways of creating mathematical content online. Further information can be found at www.chapman.edu/~jipsen/asciimath.html.  
Michael Kohlhase (International University Bremen)  A "Semantic Web" for science and technology communicating the content of mathematics "In the Large" 
Abstract: The distributivity of information and services over the Internet has changed all aspects of life. The process of developing and deploying science and technology is no exception to this. Its individual aspects are already supported by a variety of software systems, but the systems are, by and large, not able to interoperate since they use differing data formats, make differing model assumptions, and are bound to an implicitly given context that is only documented in publications about the systems. We anticipate a new quality to emerge if humans and systems can interoperate to cover the whole workflow of research, education, and application. To further this vision we need to develop, implement, and provide semanticbased and contextaware techniques for acquiring, organizing, processing, sharing, and using knowledge in Science and Technology. In this talk I will present an alternative vision of a 'Semantic Web' for Science and Technology. Like Tim BernersLee's vision we aim to make the Web (here scientific knowledge) machineunderstandable instead of merely machinereadable. However, instead of a topdown metadatadriven approach, which tries to approximate the content of documents by linking them to web ontologies (expressed in terminologic logics), we explore a bottomup approach and focus on making explicit the intrinsic structure of the underlying scientific knowledge. A connection of documents to web ontologies is still possible, but a secondary effect. I will make these ideas concrete with the XMLbased content/context format for mathematic discourses (OMDoc: Open Mathematical Documents) that supports novel web services by blending formal and natural elements. The core purpose of the OMDoc format is to enable communication of mathematics "in the large." Most current representation formats for mathematics concentrate on representing mathematical formulae and give the representations meaning by providing a fixed context (in the specification). As these contexts only cover specific mathematical areas, we can only cover mathematics "mathematics in the small" with this approach. OMDoc extends MathML and OpenMath by a rich markup language for (meaningproviding) contexts, which even provides constructs to interrelate contexts. Thus it can emulate other representation languages by marking up their inscribed contexts, and can act as an interoperability format between languages and even software systems. Taken to the extreme, it can even act as an interoperability format between scientific disciplines; I will discuss this using the the ongoing extension efforts towards STMML2 (Science, Technology & Medical Markup Language).  
Niels Lauritzen (Aarhus University)  Algebraic geometry and applications seminar: Gröbner walks and Scarf homotopies 
Abstract: We give a light introduction to Gröbner basis conversion and outline emerging insights on the connection to a classical algorithm by Scarf in optimization.  
Azzeddine Lazrek (Cadi Ayyad University)  Edocument mathematical multilingual processing 
Abstract: In Arabic handbooks, there are, at least, two models for writing mathematical expression
according to the local area and the study level:


Gennady Lyubeznik (University of Minnesota Twin Cities)  Algebraic geometry and applications seminar: Some algorithmic aspects of local cohomology 
Abstract: One application of local cohomology is that it provides a lower bound on the number of defining equations of algebraic varieties. To be useful for this application, local cohomology must be efficiently computable. We will discuss some computability issues and resulting lower bounds for the number of defining equations of some interesting varieties.  
Bruce R. Miller (National Institute of Standards and Technology)  DLMF, LaTeXML and some lessons learned 
Abstract: The Digital Library of Mathematical Functions is nearing public release. While our situation is unique — a moderate sized, controlled, collection of documents intended as a reference work — perhaps our experiences can help others in related endeavours. After providing an update of DLMF and LaTeXML (the tool used in its creation), I would like to talk about some of the lessons learned, and promote discussion about things the community can do to make these kinds of projects both easier and better in the future. Digital Libraries within the context of Mathematical Knowledge Management might fall into two categories: more formal, behindthescenes, computeroriented libraries (or databases) and looser, more traditional readeroriented libraries. Without in the least diminishing the former, I will concentrate on the issues of the latter. Such libraries consist not only of mathematical content, but mixed with text, tables, figures etc. We must be able to project such libraries into attractive, readable, accessible web sites. The usefulness of the data will be greatly enhanced if we can fully expose the implied interconnections between symbols and concepts found in such documents. While it is often a requirement that a highquality printed format be available, such sites can be much more than "Books on the web." As the content is not automatically generated by (say) a theorem prover, convenient document authoring is a major concern. Useful interrelations, enhancements and metadata are seldom automatically inferable. Thus, both the desire and means to provide this information is needed: significant buyin by authors and editors; as well as additional markup. With handauthored documents, there is also the issue of getting sufficiently unambiguous representation of the mathematics while preserving the authors intended presentation. We have adopted LaTeX as the document source language, and thus need to go beyond the typical TeX markup with more semantic macros and declarations. While we are beginning to see success in mathematical search, such search must contend with this mixed representation and with the typical sloppiness of user queries. Looking towards the future, we would all like to leverage each others ideas and tools. Perhaps some standardization of rich document formats is possible; should it be based on proprietary or ad hoc formats; OMDoc or DocBook? For those in the "niche within a niche" of LaTeX based Digital Libraries, development and wider adoption of more semantic math markup would be helpful, whatever tools are being used to process it.  
Robert Miner (Design Science, Inc.)  The MathFind search engine 
Abstract: The talk will describe the architecture and implementation of the MathFind search engine, a mathaware search engine under development by Design Science. Users can use mathematical expressions as query terms along with the usual text query terms. Math search terms are entered via a graphical equation editor applet. Ranked results are returned, with the rank for math expressions based on structural similarity. The MathFind engine is implemented as an extension to the popular Apache Lucene search engine. Content is converted to a common XHTML + MathML format for indexing. MathML terms are normalized and stored as sequences of textencoded tokens in the Lucene index. Query terms are similarly tokenized, and the search is performed by custom code by doing lowlevel atomic Lucene queries. Final rankings are computed as from atomic term queries with weightings based on analysis of the MathML structure. We are hoping to eventually index a large corpus of electronic documents. To begin, we are attempting to convert and index the ArXiv, using Hermes and LaTeXML, two promising LateX to XTHML+MathML translators. We are also working to arrange to index several other collections where unpublished XML+MathML source code is available by special arrangement. We are also running a customized version of the Apache Nutch web crawler to index online documents containing math in a variety of formats.  
Andrew M. Odlyzko (University of Minnesota Twin Cities)  The slow evolution of mathematical communication 
Abstract: Digital technologies are advancing rapidly. But their acceptance by scholars varies considerably. Some, such as computerized typesetting and email, have become universal among mathematicians, while others, such as Open Access, are advancing very slowly. While this is frustrating to technology enthusiasts, it should not be too surprising, as it follows a common historical pattern. While each technology is different, people do not change, and they have often been slow to embrace even revolutionary innovations. There are common patterns in the diffusion of earlier technologies, and some possible lessons will be drawn from them for math communication.  
T. V. Raman (Google Inc.)  Structured math on the web 
Abstract: It is now 10 years since we started work on MathML. At the time, the Web was still in its early stages, and we began the work in a spirit of extreme optimism. After all, the Web emerged from the need to exchange scientific information, and we were all excited by the possibilities presented by being able to exchange more than just plain text — we looked forward to a time where online hypertexts would include structured mathematics that could be interactively manipulated and presented via a multiplicity of output modalities. With 20/20 hindsight, it is clear that we had taken an overly narrow view of the Web; having invented it in the context of scientific information exchange, we had assumed that all evolutions on the Web would be driven by the needs of scientific education. The marketplace however taught us otherwise, and today, sceptics would say that structured mathematics on the Web is a failure and never likely to happen within mainstream browsers. But in the midst of depression there is hopeMathML never became a mainstream browser feature and might well be called a failure by sceptics; however, the Web platform has now reached a level of maturity where adoption of new technologies by mainstream browsers is no longer a prerequisite for success. With the emerging ability to deliver highly interactive Web applications that produce and consume structured XML, I believe we're now entering a new era of the Web where innovative user experience that leverages rich content such as MathML can be delivered to the enduser without waiting for browser vendors to ship their next longawaited upgrade. Looking forward, what new innovations can we deliver in the field of online Mathematics, and how will these in turn contribute to future innovations on the Web?  
Ross Reedstrom (Rice University)  Collaborative curriculum development in engineering and The sciences: The connexions 7 year experience with MathML 
Abstract: Connexions uses a collaborative, communitydriven approach to content creation, organization, and dissemination. We provide a set of open source tools and an open repository for the publication and exchange of educational materials, by anyone, from anywhere , to anyone, anywhere. More than three thousand modules in 13 languages are used by over a million people worldwide for both formal and selfguided learning in fields ranging from computer science to music and from mathematics to biodiversity. These XMLbased modules allow instructors to compose customized courses, providing students with new opportunities to explore the connections between different ideas and domains, as well as to extend the repository with additional materials of their own. A significant core of our content is in engineering and other mathematically intensive disciplines. We use content MathML source materials, transforming to presentation MathML for web presentation, and PDF for print. Since are not ourselves the authors of most of the content, we do not have direct control over tools and methods our authors use to create markup. While requiring cMathML provides well known, significant advantages for users of the repository (flexible format output via transformations, alternative notational conventions, consistent notation using mixed sources, etc.), it has a significant cost for our authors. Lack of tools is still the limiting factor for adding more math in more modules. The current version of the MathML standard is somewhat limited in the fields of math covered by semantic markup. Specific notational conventions can also be difficult to accommodate. Regardless, over half of our content contains math. We are currently working to improve our tools for input as well providing validity checking (as a subset of theorem proving) of math. Providing means to explore this body of materials via structural math search, in combination with other metadata and fulltext searches, has just now become useful. We will discuss currently successful methods of assisting authors in creating MathML markup, what hasn't worked, how the math interacts with other aspects of distributed collaboration (through both space and time), and some characterization of the body of math available from the Connexions Repository.  
Alan P. Sexton (University of Birmingham), Volker Sorge (University of Birmingham)  The ellipsis in mathematical documents 
Abstract: An ellipsis is a series of dots which indicates the omission of some part of a text which the reader should be able to reconstruct from its context. The most complex and sophisticated use of ellipses occur in matrix expressions, where whole classes of matrices of variable dimension are described with their use. But ellipses also occur in discussions of sequences, series, polynomials, sets, systems of equations and generally wherever there is a collection of mathematical objects described by a pattern rather than an explicit enumeration or a closed form. However, while ellipses are very common in mathematical and scientific documents, relatively little work on their recognition, semantic analysis, formal representation, and electronic communication has been carried out. In our work, we have shown how a matrix expression containing ellipses can be analysed to extract a semantic representation that can be used for a number of purposes including validating and improving optical character recognition of matrix expressions, symbolic calculation of expressions with such matrices and rerepresentation as lambda expressions for use by theorem provers. This work has opened a number of new research avenues for machine support for mathematicians, scientists and engineers: since we can represent underspecified matrices with ellipses, we can develop systems to solve matrix problems for arbitrary dimensions directly, rather than only for individual subcases of specific dimension; we can consider the question of generalising specific solutions without ellipses to general patterns of solutions with ellipses. In this talk we shall summarise our research results in this area to date and outline its possible generalisation to deal with ellipsis constructs in other areas. We shall also suggest a structured way of representing ellipses in a uniform format suitable for electronic communication.  
Elena Smirnova (University of Western Ontario), Stephen M. Watt (University of Western Ontario)  Interfaces for mathematical communication 
Abstract: In this talk we discuss one of the essential aspects of mathematical communication: providing interfaces to mathematical environments. This involves mathematical data and knowledge representation, communication protocols and organization of digital libraries. Each of these three subjects represents a complex problem studied extensively for the past decades. We present an overview of the stateoftheart that has been developed over the course of several research networks connecting two large communities: mathematical knowledge management and mathematical communication. In this talk we report on the main outcomes of these projects that have been achieved both in collaboration and independently by our group at the Ontario Research Centre for Computer Algebra. First, we briefly address the issues accompanying the problem of mathematical knowledge representation, such as customizing notation for mathematical content and translation between most popular mathematical data formats. We describe how these problems can be approached to ensure conservation of highlevel semantic content. Secondly, we describe an approach to providing interoperability between different mathematical environments. We concentrate on systemindependent standards, designed to describe mathematical content and problem domains. These comprise languages and ontologies developed by the MONET (Mathematics On the NET) Consortium to enable unambiguous communication between distributed mathematical components. Finally, we discuss the problem of creation and organization of databases to store mathematical context. We present our approach to collecting and storing the information about mathematical content, retrieved from webbased mathematical archives. We demonstrate the use of these databases by the example of assisting in online mathematical handwriting analysis. Specifically, we show how we use the information derived from the analysis of a digital libraries to prioritize character choices in a mathematical handwriting application.  
Neil Soiffer (Design Science, Inc.)  Overview of accessible math 
Abstract: Computers and the internet have been a boon to those with visual disabilities. Screen readers and other assistive technology provide access to information that would have previously been inaccessible to these individuals. While access to mathematical information is harder to access than textual information, significant work has been done to make math accessible.
There are several US and international laws that impose legal mandates on accessible material. These mandates provide an economic incentive for researchers and businesses to provide accessible solutions. These mandates are based on standards such as DAISY, and use MathML to encode math.
Mathematical expressions have been a focus for math accessibility solutions, and much of this work uses MathML:


Abdou Youssef (George Washington University)  Relevance ranking and hit packaging in math search 
Abstract: As in most search applications, math search involves relevance ranking and hit packaging. That is, hits must be ordered using quantitative relevance scores, and every hit must be accompanied by a small amount of qualitative relevance information that conveys what the hit is about and why it matched. Determining and quantifying relevance is a very hard problem in text search, and is at least as hard in math search. The relevance score must factor in not only query terms, but also a priori information about the hit target such as: (1) whether the target is/has definitions, notations, graphs, theorems, proofs, and so on; (2) expertpredetermined weights of certain entities (e.g., concepts, functions names, operators, etc.) in the target document; (3) number of databasewide or Webwide links pointing to the hit target; and (4) frequency of useraccess to that target. Hit packaging is primarily a process of document summarization that is biased by both the userquery and the same kinds of a priori information used in relevance scoring. One way to summarize a document is to partition it into small fragments and select several of the most relevant fragments; fragments from the document metadata, if any, may also be included in the summary. This talk will identify the issues involved in relevance ranking and hit packaging in math search, and discuss approaches for addressing them. 
JungHa An  University of Minnesota Twin Cities  9/1/2005  8/31/2007 
Douglas N. Arnold  University of Minnesota Twin Cities  7/15/2001  8/31/2007 
Donald G. Aronson  University of Minnesota Twin Cities  9/1/2002  8/31/2007 
Tom Banchoff  Brown University  12/7/2006  12/9/2006 
Daniel J. Bates  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Yermal Sujeet Bhat  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Jonathan Borwein  Dalhousie University  12/7/2006  12/9/2006 
Thierry Bouche  Université de Grenoble I (Joseph Fourier)  12/7/2006  12/10/2006 
Drew Burton  American Mathematical Society  12/7/2006  12/9/2006 
Olga Caprotti  University of Helsinki  12/7/2006  12/10/2006 
Davide P. Cervone  Union CollegeUnion University  12/7/2006  12/10/2006 
Bruce Char  Drexel University  12/7/2006  12/9/2006 
Ionut CiocanFontanine  University of Minnesota Twin Cities  9/1/2006  6/30/2007 
Tim Cole  University of Illinois at UrbanaChampaign  12/7/2006  12/10/2006 
Joseph Angus Corneli  NONE  12/8/2006  12/9/2006 
James Davenport  University of Bath  12/7/2006  12/10/2006 
Keith Dennis  Cornell University  12/7/2006  12/10/2006 
Jacques Distler  University of Texas  12/7/2006  12/9/2006 
Michael Doob  University of Manitoba  12/7/2006  12/9/2006 
Kenneth R. Driessel  Iowa State University  9/1/2006  5/31/2007 
Makan Fardad  University of Minnesota Twin Cities  8/26/2006  8/13/2007 
Richard Fateman  University of California  12/7/2006  12/9/2006 
Thomas Fischer  State and University Library Goettingen  12/7/2006  12/10/2006 
Kristine Fowler  University of Minnesota Twin Cities  12/8/2006  12/9/2006 
Edward Fox  Virginia Polytechnic Institute and State University  12/7/2006  12/9/2006 
Michael E. Gage  University of Rochester  12/7/2006  12/10/2006 
Xuhong Gao  Clemson University  9/3/2006  12/20/2006 
John Gardner  Oregon State University  12/7/2006  12/10/2006 
Jason E. Gower  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Gerry Grenier  IEEE  12/7/2006  12/9/2006 
Barbara K. Hamilton  IDACCR  12/7/2006  12/10/2006 
Gloria Haro Ortega  University of Minnesota Twin Cities  9/1/2005  8/31/2007 
David Harvey  Harvard University  12/7/2006  12/9/2006 
Milena Hering  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Russ Herman  University of North Carolina  12/7/2006  12/10/2006 
Benjamin J. Howard  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Evelyne Hubert  Institut National de Recherche en Informatique Automatique (INRIA)  9/1/2006  6/30/2007 
Carol Hutchins  New York University  12/7/2006  12/9/2006 
Patrick Ion  Mathematical Reviews  12/7/2006  12/10/2006 
Farhad Jafari  University of Wyoming  9/1/2006  6/30/2007 
Anders Nedergaard Jensen  Aarhus University  9/6/2006  6/30/2007 
Peter Jipsen  Chapman University  12/7/2006  12/10/2006 
Erich Kaltofen  North Carolina State University  12/7/2006  12/9/2006 
Gene Klotz  Swarthmore College  12/7/2006  12/10/2006 
Michael Kohlhase  International University Bremen  12/7/2006  12/9/2006 
SongHwa Kwon  University of Minnesota Twin Cities  8/30/2005  8/31/2007 
Gavin LaRose  University of Michigan  12/7/2006  12/9/2006 
Yves Laurent  Université de Grenoble I (Joseph Fourier)  12/7/2006  12/10/2006 
Niels Lauritzen  Aarhus University  8/28/2006  6/30/2007 
Azzeddine Lazrek  Cadi Ayyad University  12/5/2006  12/11/2006 
Anton Leykin  University of Minnesota Twin Cities  8/16/2006  8/15/2007 
Hstau Liao  University of Minnesota Twin Cities  9/2/2005  8/31/2007 
Paul Libbrecht  Universität des Saarlandes  12/7/2006  12/9/2006 
Birgit Loch  University of Southern Queensland  12/6/2006  12/10/2006 
Laura Lurati  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Gennady Lyubeznik  University of Minnesota Twin Cities  9/1/2006  6/30/2007 
Mason Macklem  Dalhousie University  12/7/2006  12/9/2006 
Hannah Markwig  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Thomas Markwig  Universität Kaiserslautern  9/1/2006  6/30/2007 
Manolis Mavrikis  University of Edinburgh  12/7/2006  12/10/2006 
Bruce R. Miller  National Institute of Standards and Technology  12/7/2006  12/10/2006 
Robert Miner  Design Science, Inc.  12/7/2006  12/9/2006 
Richard Moeckel  University of Minnesota Twin Cities  9/1/2006  6/30/2007 
Lawrence Moore  Duke University  12/7/2006  12/9/2006 
Rajesh Munavalli  Design Science, Inc.  12/7/2006  12/9/2006 
Uwe Nagel  University of Kentucky  9/1/2006  6/1/2007 
Jiawang Nie  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Andrew M. Odlyzko  University of Minnesota Twin Cities  12/8/2006  12/9/2006 
Chris Peterson  Colorado State University  9/5/2006  12/14/2006 
Sorin Popescu  SUNY  9/1/2006  12/31/2006 
Loïc Pottier  Institut National de Recherche en Informatique Automatique (INRIA)  12/6/2006  12/10/2006 
T. V. Raman  Google Inc.  12/7/2006  12/10/2006 
Ross Reedstrom  Rice University  12/7/2006  12/9/2006 
Gregory J. Reid  University of Western Ontario  9/6/2006  12/1/2006 
Victor Reiner  University of Minnesota Twin Cities  9/1/2006  6/30/2007 
Joel Roberts  University of Minnesota Twin Cities  9/1/2006  6/30/2007 
Robby Robson  Eduworks Corporation  12/7/2006  12/10/2006 
Bjarke Hammersholt Roune  Aarhus University  9/12/2006  6/30/2007 
David W. Ruddy  Cornell University  12/7/2006  12/9/2006 
David Rusin  Northern Illinois University  9/1/2006  12/31/2006 
Arnd Scheel  University of Minnesota Twin Cities  7/15/2004  8/31/2007 
Dave Schleppenbach  gh, LLC  12/7/2006  12/9/2006 
Mika Seppala  University of Helsinki  12/7/2006  12/9/2006 
Alan P. Sexton  University of Birmingham  12/7/2006  12/10/2006 
Chehrzad Shakiban  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Roger Sidje  University of Queensland  12/7/2006  12/10/2006 
Kyle Siegrist  University of Alabama  12/7/2006  12/9/2006 
Elena Smirnova  University of Western Ontario  12/7/2006  12/10/2006 
David A. Smith  Duke University  12/7/2006  12/9/2006 
Neil Soiffer  Design Science, Inc.  12/7/2006  12/9/2006 
Petr Sojka  Masaryk University  12/7/2006  12/9/2006 
Andrew Sommese  University of Notre Dame  9/1/2006  12/31/2006 
Volker Sorge  University of Birmingham  12/7/2006  12/10/2006 
Steven Sperber  University of Minnesota Twin Cities  9/1/2006  6/30/2007 
Thomas Speyer  John Wiley & Sons  12/7/2006  12/9/2006 
Ioan Alexandru Sucan  Rice University  12/7/2006  12/9/2006 
Masakazu Suzuki  Kyushu University  12/7/2006  12/9/2006 
Wojtek Sylwestrzak  University of Warsaw  12/7/2006  12/10/2006 
Eduardo Tabacman  Design Science, Inc.  12/7/2006  12/9/2006 
Carl Toews  University of Minnesota Twin Cities  9/1/2005  8/31/2007 
Philippe Tondeur  University of Illinois at UrbanaChampaign  12/7/2006  12/9/2006 
Paul Topping  Design Science, Inc.  12/7/2006  12/9/2006 
Mehul Trivedi  Rutgers University  12/7/2006  12/9/2006 
Martha Tucker  University of Washington  12/7/2006  12/9/2006 
John Voight  University of Minnesota Twin Cities  8/15/2006  8/31/2007 
Stephen M. Watt  University of Western Ontario  12/7/2006  12/9/2006 
Bernd Wegner  TU Berlin  12/7/2006  12/11/2006 
Eric Weisstein  Wolfram Research, Inc.  12/7/2006  12/9/2006 
Esther R. Widiasih  University of Minnesota Twin Cities  12/8/2006  12/9/2006 
Wenyuan Wu  University of Western Ontario  9/6/2006  12/1/2006 
Abdou Youssef  George Washington University  12/7/2006  12/9/2006 
Hongchao Zhang  University of Minnesota Twin Cities  9/1/2006  8/31/2007 
Yan Zhuang  University of Illinois  9/1/2006  12/1/2006 