61. COLT2003 Call For Open Problems COLT2003 Call for open problems. COLT2003 will include a session devoted tothe presentation of open problems. Characteristics of a good open problem. http://learningtheory.org/colt2003/OpenProblems/solicitation.html

COLT2003 Call for open problems COLT2003 will include a session devoted to the presentation of open problems. A two page description of the accepted problems will also appear in the COLT proceedings. The idea is to facilitate collaborations and to encourage new people to get into the field. The writeup of an open problem should include: A clear and self contained description of a single open problem. Motivation for the study of this problem. The current state of understanding for this problem, including known partial solutions and citations of published work. The deadline for submission of open problems is May 10, 2003. This description should be written in the COLT proceedings format ( LLNCS format Please submit the problem electronically to (my-last-name) at merl dot com On the subject line please include: open problem for colt2003 The submissions themselves should be in postscript (letter size page) and should be included as attachments to the email. Characteristics of a good open problem There is no requirement to satisfy all of these characterizations, but the more the better.

62. Dynamical Systems Home Page Conference listings, survey articles, open problems, people, jobs, and seminars. http://www.math.sunysb.edu/dynamics/

Dynamical Systems Homepage Institute for Mathematical Sciences SUNY at Stony Brook A list of recent past conferences , and some upcoming conferences in the field. There is a special Joint Symplectic Topology/Dynamics Seminar held at Courant Institute or at Stony Brook every 3 weeks. Seminar schedules in the tri-state area. Take a look at the pictures from the conference "Around Dynamics" held in honor of Jack Milnor. A searchable list of people working in the field, and some other similar lists Browse our Thesis Server or submit your own work. The Dynamical Systems electronic preprint list at Stony Brook, has merged into the Dynamical Systems section of the XXX mathematics e-print server Here are several other electronic preprint servers We also have collected links to some survey articles in Dynamical Systems, available on-line. Programs :Links to a great variety of programs to draw pictures of dynamical objects. There is a bibliography list , constantly updating. Open problems in Dynamical Systems. Links to similar pages Leave a comment about these pages.

63. FoIKS - Intro International Symposium on Foundations of Information and Knowledge Systems. Burg (Spreewald), Germany; 1417 February 2000. List of open problems. http://www.informatik.tu-cottbus.de/~foiks/

International Symposium on Foundations of Information and Knowledge Systems (FoIKS 2000) next FoIKS will be held in february/march 2002

64. Open Problems In Continuum Theory open problems in Continuum Theory. FastCounter by bCentral. 8, 1983, 361394.open problems in topology, Edited by Jan van Mill and George M. Reed. http://web.umr.edu/~continua/

Open Problems in Continuum Theory FastCounter by bCentral Last Modified Monday, 24-May-2004 13:41:49 CDT Edited by Janusz R. Prajs Technical editor J. Charatonik In the first half of the twentieth century, when foundations of general topology had been established, many famous topologists were particularly interested in properties of compact connected metric spaces, called continua . What later emerged as continuum theory Janusz R. Prajs Department of Mathematics and Statistics California State University, Sacramento 6000 J Street Sacramento, CA 95819-6051 prajs@csus.edu or J. Charatonik Department of Mathematics and Statistics University of Missouri-Rolla Rolla MO wjcharat@umr.edu News on the List May 24, 2004 Problems 20, 21 and remarks by Jo Heath has been added. March 31, 2004 Problem 9 was solved in the negative. March 29, 2004 Problem 25 was added. April 2, 2003 As you can see we have moved to a different account. Please change the address in your favorites list. March 13, 2003 Problem 11 was added. January 20, 2003 Problems 7, 15, and 16, all on homogeneous continua, were added.

65. LookSmart - Directory - Open Problems In Graph Theory Mathematics Graph Theory open problems. open problems in GraphTheory Offers unsolved problems in the field of graph theory. http://search.looksmart.com/p/browse/us1/us317914/us328800/us10163846/us10163989

@import url(/css/us/style.css); @import url(/css/us/searchResult1.css); Home IN the directory this category YOU ARE HERE Home Sciences Mathematics Graph Theory Open Problems in Graph Theory - Offers unsolved problems in the field of graph theory. Directory Listings About American Institute of Mathematics - Perfect Graphs Learn what unsolved problems exist in the field of perfect graphs, and what mathematicians believe may hold true about these problems. Andre Kazdy - Some Open Problems Problems involving cyclic neofields and tree embeddings provides challenges for graph theorists. Bojan Mohar - Problems Slovenian mathematician offers a selection of unsolved problems in graph theory. Includes archives. Dan Archdeacon - Problems in Topological Graph Theory Professor at the University of Vermont presents unsolved graph theory problems on topics including coloring, symmetries, and book embedding. Douglas B. West - Past Open Problems Columns Check out these examples of problems which mathematicians have not been able to solve. Problems involve graph theory. Jerry Spinrad - Some Open Problems Lists several unsolved graph theory problems, breaking them down into categories including bi-partite, circular-arc graphs, and comparability graphs.

66. The Furstenburg Conjecture And Rigidity If two commuting endomorphisms of a torus are incommensurable (no power of one is a power of the other), then their joint action should be rigid. Some of the conjectures and open problems compiled by the AIM. http://aimath.org/WWN/furstenburg/

The Furstenburg Conjecture and Rigidity This web page highlights some of the conjectures and open problems concerning The Furstenburg Conjecture and Rigidity. Click on the subject to see a short article on that topic. If you would like to print a hard copy of the entire web page, you can download a dvi postscript or pdf version. The Furstenburg Conjecture and Rigidity Statement of the Conjecture History and past results Analogous problems ... Approaches to a counterexample

67. LookSmart - Directory - Open Problems In Combinatorics Combinatorics open problems. open problems in Combinatorics Offersunsolved problems which involve the math of combinatorics. http://search.looksmart.com/p/browse/us1/us317914/us328800/us10164855/us10164869

@import url(/css/us/style.css); @import url(/css/us/searchResult1.css); Home IN the directory this category YOU ARE HERE Home Sciences Mathematics Combinatorics Open Problems in Combinatorics - Offers unsolved problems which involve the math of combinatorics. Directory Listings About Mohammed Katoozian - Mathematic Olympiad Problems Collected from different organizations and competitions worldwide, this page offers a selection of combinatorics problems as well as other math problems. Rob Hochberg - Open Problems for Undergraduates Combinatorial problems provide a challenge level appropriate for undergraduate research and examination. Zsolt Tuza - Unsolved Combinatorial Problems Lists many of the known unsolved problems in the field of combinatorics. We're always looking for ways to improve your search experience. Tell us how we're doing. Join the Zeal community and help build the "Open Problems in Combinatorics" Directory Category IN the directory this category About Us Advertise with Us Advertiser Log-in Terms of Service

68. Open Problems Previous Algorithm Summary open problems. Is there a faster algorithmfor sorting signed permutations using reversals ? Given 3 http://www.math.tau.ac.il/~rshamir/algmb/00/scribe00/html/lec10/node20.html

Next: Bibliography Up: An Algorithm for Sorting Previous: Algorithm Summary Open Problems Is there a faster algorithm for sorting signed permutations using reversals ? Given 3 signed permutations , find an efficient algorithm that minimizes (finding an exact solution is NP-hard [ Find the reversal distance between two signed digit sequences with equal number of occurrences of each digit. Find how many sequences of reversals realize d Find among the minimum sequences one that has some additional properties. Peer Itsik

69. Problems HotLog Here is a list of selected open problems in the areas of myinterests. They are grouped thematically. Click on a problem http://www.phil.uu.nl/~lev/problems.html

Here is a list of selected open problems in the areas of my interests. They are grouped thematically. Click on a problem to get a comment and possibly some related questions. If you would like to make a comment or contribute a question, please mail to lev@phil.uu.nl . Presumably easier problems suitable, e.g., for a graduate project are marked by (*). Problems in Provability Logic Intuitionistic arithmetic The provability logic of Heyting arithmetic HA: decidability, axiomatization. [Markov] The propositional logic of Kleene realizability. [Plisko] Dialectica interpretation. [De Jongh, Visser] Characterization of subalgebras of the Lindenbaum Heyting algebra of HA. The predicate logics of some extensions of HA: HA+MP, HA+ECT The admissible propositional inference rules for HA+MP and HA+ECT Are the Lindenbaum Heyting algebras of HA and HA+RFN(HA) isomorphic? Is the elementary theory of the Lindenbaum Heyting algebra of HA decidable? Which fragments of it are? (*) [De Jongh, Visser] Is the downwards extension property of intuitionistic propositional theories equivalent to the property of being projective for infinitely axiomatizable theories? Bounded arithmetic The provability logic of bounded arithmetics S and S : decidability, axiomatization.

70. Perfect Graphs Conjectures and open problems, maintained at the AIM. http://www.aimath.org/WWN/perfectgraph/

Perfect Graphs This web page highlights some of the conjectures and open problems concerning Perfect Graphs. If you would like to print a hard copy of the whole outline, you can download a dvi postscript or pdf version. Recognition of Perfect Graphs Polynomial Recognition Algorithm Found Interaction Between Skew-Partitions and 2-joins The Perfect-Graph Robust Algorithm Problem ... A Possible New Problem Skew-Partitions Extending a Skew -Partition Graphs Without Skew-Partitions Graphs Without Star Cutsets Finding Skew-Partitions in Berge Graphs ... beta-perfect graphs Partitionable Graphs Perfect, Partitionable, and Kernel-Solvable Graphs Partitionable graphs and odd holes A Property of Partitionable Graphs The Imperfection Ratio Integer Programming Partitionable Graphs as Cutting Planes for Packing Problems? Feasibility/Membership Problem For the Theta Body Balanced Graphs P4-structure and Its Relatives The individual participant contributions may have problems because converting complicated TeX into a web page is not an exact science. The dvi, ps, or pdf versions are your best bet.

71. Open Problems In Computer Virus Research Skip to main content open problems in Computer Virus Research. Conclusion.We have examined a few open problems in computer virus research. http://www.research.ibm.com/antivirus/SciPapers/White/Problems/Problems.html

Open Problems in Computer Virus Research Steve R. White IBM Thomas J. Watson Research Center Yorktown Heights, NY USA Presented at Virus Bulletin Conference, Munich, Germany, October 1998 Abstract Introduction Some people believe that there is no longer any interesting research to do in the field of protection from computer viruses - that all of the important technology has already been developed - that it is now a simple matter of programming to keep up with the problem. Others believe that "virus research" simply means "analyzing viruses." To dispel these misimpressions, we discuss several important research problems in the area, reviewing what is known on each problem and what remains open. The purpose of this paper is not to give solutions to these problems. Rather it is to outline the problems, to suggest approaches, and to encourage those interested in research in this field to pursue them. The problems we have selected have two characteristics. The first is that, if the problem were solved, it would significantly improve our ability to deal with the virus problem as it is likely to evolve in the near future. The second is that the problem constitutes an actual research problem, so that a definitive solution would be publishable in peer-reviewed computer science journals, and could form the basis for an M.S. thesis or, in some cases, a Ph.D. thesis. We discuss five problems: As more viruses are written for new platforms, new heuristic detection techniques must be developed and deployed. But we often have no way of knowing, in advance, the extent to which these techniques will have problems with false positives and false negatives. That is, we don't know how well they will work or how many problems they will cause. We show that analytic techniques can be developed which estimate these characteristics and suggest how these might be developed for several classes of heuristics.

72. Algorithmic Information Theory open problems and links to software. http://www.cs.auckland.ac.nz/CDMTCS/docs/ait.html

A LGORITHMIC I NFORMATION T HEORY Algorithmic information theory ( AIT ) is the result of putting Shannon's information theory and Turing's computability theory into a cocktail shaker and shaking vigorously. The basic idea is to measure the complexity of an object by the size in bits of the smallest program for computing it. ( G. J. Chaitin A NNIVERSARIES G. J. Chaitin. On the length of programs for computing finite binary sequences, J. Assoc. Comput. Mach. A. M. Turing. On computable numbers, with an application to the Entscheidungsproblem, Proc. Lond. Math. Soc. (ser. 2) 42 (1936), 230-265; a correction 43 (1936), 544-546. O PEN P ROBLEMS Here is a compressed PostScript document containing a list of open problems in AIT. S OFTWARE FOR AIT Have a browse on Greg Chaitin's home page for some AIT-related software. Back to main page Information

73. Www.math.upenn.edu/~chung/ep.dvi Book Announcement BR J. Hilgert, JD Lawson, KH Neeb, EB Vinberg Positivity in Lie Theory open problems. This book consists of 15 articles, eachof which is an introduction to a set of open research problems in Lie theory. http://www.math.upenn.edu/~chung/ep.dvi

74. Future Directions In Algorithmic Number Theory Some of the conjectures and open problems motivated by the PRIMES is in P papers, compiled at the AIM. http://aimath.org/WWN/primesinp/

Future directions in algorithmic number theory This web page highlights some of the conjectures and open problems concerning Future directions in algorithmic number theory. If you would like to print a hard copy of the whole outline, you can download a dvi postscript or pdf version. Lecture Notes Agrawal: Primality Testing Agrawal: Finding Quadratic Nonresidues Bernstein: Proving Primality After Agrawal-Kayal-Saxena ... Remarks on Agrawal's Conjecture

75. Mathsoft: Mathsoft Unsolved Problems: Unsolved Problems On Other Sites MegaMath open problems (Los Alamos and University of Idaho); M. Beeler,RW Gosper and R. Schroeppel s Hakmem collection, MIT AI Memo 239; http://www.mathsoft.com/mathresources/problems/article/0,,1999,00.html

search site map about us  + news  + ... Unsolved Problems Unsolved Problems Links On a Generalized Fermat-Wiles Equation Zero Divisor Structure in Real Algebras Sleeping Habits of Armadillos Mathsoft Constants ... Math Resources Unsolved Problems on Other Sites Jeff Lagarias' 3x+1 problem and related problems The Generalized 3x+1 Mapping (University of Queensland) and 1999 Conference on the Collatz Problem Proceedings Alex Lopez-Ortiz's sci.math FAQ on Famous Problems in Mathematics (University of New Brunswick) Chris Caldwell's Riemann Hypothesis (University of Tennessee at Martin); also Daniel Bump's Riemann Hypothesis (Stanford University) and Barry Cipra's A Prime Case of Chaos MathPro Press Unsolved Math Problem of the Week column and General References Twin Primes Conjecture and Goldbach's Conjecture, discussed in Prime Numbers: Some Unsolved Problems , part of MacTutor History of Mathematics (University of St Andrews); also Chris Caldwell's Prime Conjectures and Open Questions (University of Tennessee at Martin) Jan Otto Munch Pedersen's Known Amicable Pairs (Vejle Business College, Denmark) and Chris Caldwell's

76. Computability Theory Directory of researchers working in computability theory, and list of open problems. http://www.nd.edu/~cholak/computability/computability.html

Computability Theory Bibliographic Database for Computability Theory Open Questions in Recursion Theory: LaTeX or pdf Other Useful Sites: Association for Symbolic Logic People who work (or have worked) in Computability Theory: Klaus Ambos-Spies George Barmpalias Valeriy Bulitko Sam Buss ... Sy Friedman Edward R. Griffor Valentina Harizanov Leo Harrington Denis R. Hirschfeldt Jeff Hirst ... Steffen Lempp Manuel Lerman Iraj Kalantari Jan Kraijeck Matrin Kummer David Marker Anil Nerode Yiannis Moschovakis Andre Nies ... Stan Wainer Dongping Yang Mike Yates People whose work had great impact on the field: Charles Babbage Alonzo Church Robin Gandy Reuben Goodstein ... Computability Theory E-mailing List Research Announcements Recursive Function Theory Newsletter Meetings (see the Association for Symbolic Logic for ASL meetings) Graduate School in Computability Theory The University of Connecticut Math Department Univeristy of Notre Dame Job Announcements As with most web pages, this page is a continuously evolving resource. It will only develop into a useful resource for computability theorists if they help by adding information related to computability theory to the web and this page. Therefore computability theorists are encouraged to add information and links to this page. There are two ways of achieving this. The preferred method is to add the information to the web yourself and email me at Peter.Cholak.1@nd.edu

77. Survey Of Venn Diagrams -- Open Problems Venn Diagram References combinatorial facts, beautiful figures, n=3and beyond, some open problems. Venn Diagram Survey open problems. http://www.combinatorics.org/Surveys/ds5/VennOpenEJC.html

T HE E LECTRONIC ... OMBINATORICS (ed. March 2001), DS #5. Venn Diagram Survey Open Problems Open problems related to Venn diagrams. Find a symmetric Venn diagram for n = 13, or prove that no such diagram exists. How many symmetric Venn diagrams are there for n = 5? There is only one symmetric simple 5-Venn diagram. How many symmetric Venn diagrams are there for n = 7? How many of these are simple? Is it true that every simple Venn diagram of n curves can be extended to a simple Venn diagram of n +1 curves by the addition of a suitable curve? [That this is true is a conjecture of Winkler [ Wi ]. This was proven to be true for not necessarily simple Venn diagrams by Chilakamarri, Hamburger, and Pippert [ Equivalently: Is every planar dual graph of a simple Venn diagram Hamiltonian? ]. His other problem of finding a 6-Venn diagram in which each curve is a triangle has been answered affirmatively. See the six amazing triangles Find a Brunnian link whose minimal projection is a symmetric Venn diagram of order 7 or prove that no such link exists. Find a symmetric k -fold ( k n = 2 there are diagrams For , find a "symmetric" diagram on the sphere where the group of symmetries is different than those used in the section on symmetric Venn diagrams. In that section the group of symmetries consisted of rotations about a single axis, or rotations and a flip about that axis. In other words, the problem is: Are there other groups of isometries that act transitively on the curves of some Venn diagram on the sphere?

78. Teaching open problems. Relation between oriented circuit double cover andcircular flow number. Status of open problems in my survey paper. http://www.math.nsysu.edu.tw/~zhu/open-problem.htm

Open problems Relation between oriented circuit double cover and circular flow number k-flow graph double cover conjecture Chi-critical graph conjecture Chi_c of subgraphs ... Chi_c of product graphs Chi_c of Mycielski graphs Chi_f of product graphs Subgraph induced by a circular coloring Chi_c of graphs embedded on surfaces Chi_c of line graphs ... Status of open problems in my survey paper

79. CONCLUSION AND OPEN PROBLEMS CONCLUSION AND open problems. Important open problems include Treatmentof rules of the form and relinquishing definability conditions. http://www.isc.cnrs.fr/wp/schlechta/node30.html

Next: Bibliography Up: REPRESENTATION RESULTS FOR LIMIT Previous: Proof: CONCLUSION AND OPEN PROBLEMS We have solved the representation problem for an important class of limit preferential structures. The main ideas were to redefine the problem - in a reasonable and intuitvely acceptable way - and focus on the operation (or which is essentially a more elaborate variant of the classical OR rule, and then to apply our techniques for constructing representing structures - especially indexing by trees - to the problem. We have used compactness in an essential way, so our results were limited to rules of the form Important open problems include: Treatment of rules of the form and relinquishing definability conditions. Both problems seem to be related, and based on the compactness problem. Emanuelle Reynaud - Equipe HPM

80. The Formal Approach To Meaning Short survey of semantics of natural language by Barbara Abbott, at University of Michigan. Focusses upon Montague semantics, and tries to give a feel for the main open problems in the field. http://www.msu.edu/user/abbottb/formal.htm

The formal approach to meaning: Formal semantics and its recent developments [This paper is in Journal of Foreign Languages (Shanghai), 119:1 (January 1999), 2-20.] Barbara Abbott Michigan State University June 1998 abbottb@pilot.msu.edu Like Spanish moss on a live oak tree, the scientific study of meaning in language has expanded in the last 100 years, and continues to expand steadily. In this essay I want to chart some central themes in that expansion, including their histories and their important figures. Our attention will be directed toward what is called 'formal semantics', which is the adaptation to natural language of analytical techniques from logic.[ The first, background, section of the paper will survey the changing attitudes of linguists toward semantics into the last third of the century. The second and third sections will examine current formal approaches to meaning. In the final section I will summarize some of the common assumptions of the approaches examined in the middle sections of the paper, sketch a few alternatives, and make some daring predictions. 'Meaning' is a broad term that can encompass any aspect of the potential for cognitive or emotive impact of speech on interlocutors. However in linguistic semantics these days the cognitive aspects are the center of focus. On the other hand the traditional distinction between semantics, as the study of the relation between linguistic expressions and what they are used to talk about (people and things, events and situations, etc.) and pragmatics, as the study of anything involving the use of language, has become less certain and is in fact lost in several different current approaches.

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