41. Open Problems In Group Theory open problems in combinatorial and geometric group theory We have collectedhere over 150 open problems in combinatorial group theory http://zebra.sci.ccny.cuny.edu/web/nygtc/problems/oproblems.html

Open Problems in combinatorial and geometric group theory We have collected here over 150 open problems in combinatorial group theory, and we invite the mathematical community to submit more problems as well as comments, suggestions, and/or criticism. Please send us e-mail at sphynx@rio.sci.ccny.cuny.edu This collection of problems has been selected by G.Baumslag, A.Miasnikov and V.Shpilrain with the help of several members and friends of the New York Group Theory Cooperative. In particular, we are grateful to G.Bergman G.Conner W.Dicks R.Gilman ... I.Kapovich , V. Remeslennikov, V.Roman'kov E.Ventura and D.Wise for useful comments and discussions. Our policy Hall of Fame We have arranged the problems under the following headings: Outstanding Problems Free groups One-relator groups Finitely presented groups ... Algorithmic problems Periodic groups (under construction) Groups of matrices Hyperbolic and automatic groups Nilpotent groups Metabelian groups ... Group actions

42. Uni Dortmund, Informatik 2: BDD-Book Solutions By Ingo Wegener (SIAM, 2000). Errata, solutions to exercises, updates on open problems. http://ls2-www.cs.uni-dortmund.de/monographs/bdd/

Branching Programs and Binary Decision Diagrams by Ingo Wegener The book is now available from the Society of Industrial and Applied Mathematics. The official SIAM homepage includes an abstract and an order form. Resources PostScript PDF Last update Solutions of Exercises 2000-August-24 Solutions of Open Problems 2002-Oct-30 Errors and Misprints 2002-Jun-12 If you find typos etc. or if you have remarks, contact us via (for technical problems) or (for questions to the author). Other monographs by authors at Lehrstuhl Informatik 2. Startseite Lehre Team Service Lehrstuhl Informatik 2, im Oktober 2002. Kontakt

43. World Of Groups Part of the World Wide Algebra project. open problems in combinatorial group theory, a list of personal web pages, conferences and seminars, and useful links. http://www.grouptheory.info/

44. RISC Open Problems 12 open problems in Industrial Robotics. Although The list below ofthe 12 open problems is presented in no particular order. The http://www.cs.berkeley.edu/projects/risc/open_probs.html

12 Open Problems in Industrial Robotics Although there are countless open problems in robotics, we hope that by defining what we consider to be the 12 most important open problems in RISC robotics , effort can be concentrated in those areas. In the past year, a number of new problems have emerged. Our objective is to identify new theoretical problems with near-term relevance for industrial robotics. We welcome feedback and/or comments to this list. In addition we would like to add pointers to people currently working on particular problems so that open communication is maintained and duplicate work does not occur. Also, pointers to relevant papers should be added. We welcome submissions of work in progress in this location for feedback. For any comments or changes please contact Eric Paulos The current list came out of a workshop held at Adept by Ken Goldberg in December 1994 and as he points out, "The goal is to specify problems as crisply as possible; the list below is just a first cut." In addition, full credit for this exceptional list should go to Ken Goldberg The list below of the 12 open problems is presented in no particular order. The challenge for each problem is is to define optimality and then find an efficient algorithm or prove that no such algorithm exists.

45. Education Programs At DIMACS Assistance in educating K12 and undergraduate students about discreet mathematics. Lists programs and open problems in the field. http://dimacs.rutgers.edu:80/Education/

Education Programs at DIMACS: Programs for K-12 Programs for faculty: DIMACS Connect Institute (DCI) DREI- DIMACS Research and Education Institute K-8 Teachers - Leadership Institutes: Exploring Discrete Mathematics in the Classroom Workshops In Your District: Exploring Discrete Mathematics New Jersey Mathematics Coalition - improving K-12 mathematics education. Programs for students: Young Scholars Program in Discrete Mathematics Undergraduate Education Programs for faculty: Reconnect Conference Reconnecting Teaching Faculty to the Mathematical Sciences Enterprise Series of Two Two-Day Workshops for Two-Year College Teachers Reconnecting Two Year College Faculty to the Mathematical Sciences Enterprise Programs for students: Open Problems for Undergraduates in discrete mathematics and theoretical computer sciences. The problems are contributed by DIMACS members and others. Research Experiences for Undergraduates Past Activities DIMACS Home Page Alphabetical Index of DIMACS Web Pages Contacting the Center Document last modified on April 11, 2000.

46. Some Problems In Matroid Theory Compiled by Thomas Zaslavsky.Category Science Math Combinatorics open problems......Some Problems in Matroid Theory. Compiled by Thomas Zaslavsky. Sources.Oxley's book has an entire chapter of open problems. (Some http://www.math.binghamton.edu/zaslav/Matroids/matroidprobs.html

Some Problems in Matroid Theory Compiled by Thomas Zaslavsky Sources Oxley's book has an entire chapter of open problems. (Some may have been solved by now.) Joseph P.S. Kung has written two articles called ``surveys'' that are replete with new results and open problems: ``Extremal matroid theory'', in: Neil Robertson and Paul Seymour, eds., Graph Structure Theory , pp. 21-61. Contemporary Mathematics, Vol. 147. American Mathematical Society, Providence, R.I., 1993. ``Critical problems'', in: Joseph E. Bonin, James G. Oxley, and Brigitte Servatius, eds., Matroid Theory , pp. 1-127. Contemporary Mathematics, Vol. 197. American Mathematical Society, Providence, R.I., 1996. Some Problems I've Found Interesting Bonin's Projective Bound Suppose a simple matroid G of rank r that does not split has no more than q r-1 points in each cocircuit. Conjecture r - 1)/(q - 1), which is the number of points in an r-1-dimensional projective geometry of order q if such exists. Furthermore, the upper bound is attained only by projective geometries. "Splitting" means that G is the union of two disjoint proper flats. This problem was proposed by Joe Bonin.

47. Patrice Ossona De Mendez - Bibliography Compiled by Patrice Ossona de Mendez. http://www.ehess.fr/centres/cams/person/pom/open.html

48. ALifeVIII Open Problems In Artificial Life up Up Alife VIII ALifeVIII open problems in Artificial Life. published in Bedauet al., open problems in artificial life, Artificial Life 6 (2000) 363376 http://parallel.hpc.unsw.edu.au/complex/alife8/open-prob.html

49. Other Sites With This Page open problems in Dynamical Systems Ergodic Theory. Welcome! 9, Polygonal BilliardsSome open problems Submitted by Pascal Hubert Serge Troubetzkoy. http://iml.univ-mrs.fr/~kolyada/opds/

Other sites with this page O pen P roblems in D ynamical S ystems E rgodic T heory Welcome! Katsiveli - 2000 Open Problems Session (Chairman - Benjamin Weiss ). New problems are being added to it. If you would like to submit some open problems to this page, please send them to me Anyone who has never had any (open) problem has never tried anything new. Anyone who has published a paper has solved a problem and maybe has some other open problems. Why not to present them at this www page? Sergiy Kolyada Geometric Models of Pisot Substitutions and Non-Commutative Arithmetic Submitted by Pierre Arnoux Corrections - 29.11.2001 Ergodic Ramsey Theory - an Update Submitted by Vitaly Bergelson ( See also: http://www.math.ohio-state.edu/~vitaly/ Dense Periodic Points in Cellular Automata Submitted by Francois Blanchard Non-Discrete Locally Compact Second Countable Groups Submitted by Sergey Gefter Martingale Convergence and Ergodic Theorems Submitted by Alexander Kachurovskii The problem is closed Entropy, Periodic Points and Transitivity of Maps Submitted by Sergiy Kolyada Lubomir Snoha Corrections - 26.10.2002

50. Open Problems Virtual Library. Software. open problems. Open Positions. Societies. Conf./Workshops. MTBIOACTIVITIES. GALLERY. open problems. Entries total 3, Entries 1 3. Topic, http://www.mtbio.de/info.php3?aktID=Problems

51. Process Algebra: Open Problems And Future Directions Process Algebra open problems and Future Directions July 2125, 2003University of Bologna Residential Center Bertinoro (Forlì), Italy. http://www.cs.auc.dk/~luca/BICI/pa2003.html

Process Algebra: Open Problems and Future Directions July 21-25, 2003 University of Bologna Residential Center Bertinoro ), Italy What the Meeting is About Seminar Schedule Format for the Workshop Location ... Local Weather Forecast What the Meeting is About Process algebra (also known under the names `process calculi' or `process theory') is a successful method for reasoning about concurrent systems that originates from original insights of key figures like Bergstra, Hoare, Klop and Milner. The foundations of process algebra have been studied thoroughly over the last twenty years, and are still leading to large numbers of interesting results and fruitful ideas. In recent years, powerful tool sets for the analysis of concurrent systems, such as Caesar/Aldebaran, muCRL, Concurrency Factory, FDR, FC2Tools and Concurrency Workbench Edinburgh, have been developed on the basis of process algebra. A wide range of advanced protocols and distributed algorithms have been verified using process algebraic methods, and/or analyzed using the aforementioned tool sets. The aim of this workshop will be to highlight the most important open problems in the field of process algebra, and to stimulate international cooperation on their solutions. Special emphasis will also be given to future directions in the study of process algebra, and to new application areas.

52. Generic Programming Projects And Open Problems Generic Programming Projects and open problems. David R. Musser 1Rensselaer Polytechnic Institute Troy, New York 12180 musser@cs http://www.cs.rpi.edu/~musser/gp/pop/

Generic Programming Projects and Open Problems David R. Musser Rensselaer Polytechnic Institute Troy, New York 12180 musser@cs.rpi.edu Alexander A. Stepanov Silicon Graphics Inc. 2011 N. Shoreline Boulevard Mountain View, CA 94043-1389 stepanov@sgi.com Last updated: August 25, 1998 There is a At the Dagstuhl Seminar on Generic Programming The current state of this list should not, of course, be considered "complete" in any way. It is being made available on the WWW for the Dagstuhl participants and others to make additions or revisions. It will likely continually grow, but hopefully it can be pruned as projects are completed or open problems are solved! (These can be highlighted or maintained separately as a record of progress.) Suggestions are also sought for improving the level and type of information provided with projects and problems. For example, should there be a rating system to help readers understand the level of difficulty and/or importance attached to a project or problem by its proposer? Originally Alex Stepanov rated the projects on his list according to both difficulty and importance, each on a scale of 1 to 5. Those ratings are currently not included here, but if there is enough interest they could be added, perhaps after translation to an agreed-up scale. Revision History Postscript Version for Printing 1 Theory Concept Development ... Footnotes

53. Heroix EQ Event Monitor Help. open problems for the Enterprise 2/14/2003 93222PM Default View - sorted by Event Date/Time (Descending) http://webeventmonitor.heroix.com/Default.asp?view=OpenProblems&sort=default

54. NSenet - Navier-Stokes Equations On Net open problems. http://wwwlma.univ-bpclermont.fr/NSenet/openproblems/

Open problems Presentation Introduction Press review Information Correspondents ... Mailing list and FAQ People Links Bibliography Books Accepted Papers Preprints Actualities Conferences Announcements Journals Documentation Lecture Notes Open Problems Comments on books Simulation Packages PhD PhD thesis summaries PhD/Postdoctoral Positions Open Positions All persons are kindly invited to send an e-mail to NSemaster@math.univ-bpclermont.fr in order to send open problems on Navier Stokes equations and related topics. Open problem proposed by G.P. Galdi (Pittsburgh University, USA, April 2000) postscript version This open problem concerns existence of Leray's (symmetric) solutions for the twodimensional steady, exterior domain for arbitrary Reynolds number. Open problem proposed by the Clay Mathematical Institute Clay Mathematical Institute offers $1,000,000 prize for a solution to any one of seven mathematical problems. One of them concerns 3D Navier-Stokes existence and smoothness, see Navier-Stokes for the description by Charles Fefferman. nsemaster@math.univ-bpclermont.fr

55. Kézdy -- Some Open Problems K©zdy's open problems. http://athena.louisville.edu/~aekezd01/open/open.html

Sums Modulo n, Cyclic Neofields, and Tree Embeddings These problems arise from some of my work with Hunter Snevily (University of Idaho at Moscow, ID). Z n is alternating if f(i,j) = - f(j,i) (mod n), for all i,j. Permutations are viewed as sequences, so the permutation in S n is viewed as the sequence (n). For i,j, define the distance in from i to j, denoted d(i,j), as the quantity (j) - (i). Clearly d(i,j) = -d(j,i) (i.e. d is an alternating function). Conjecture A: f: [k] x [k] Z n , there exists a permutation in S k , such that d(i,j) f(i,j) (mod n), for all distinct i,j in [k] We have proven Conjecture A when n is prime. For a = (a ,a ,...,a k ) in Z n k , let (n, a ) denote the number of permutations in S k such that (n, a a in Z n k n ``, by H. Snevily, Amer. Math. Monthly, No. 6, June-July (1999), 584-585). Conjecture B : N(n,k) is monotone in n and k. Specifically, N(n,k) and N(n,k) Conjecture C : For n sufficiently large with respect to k, N(n,2k) = (k!) and N(n,2k+1) = (k+1)(k!) Note that, if true, Conjecture C would be sharp because a =(0,...0,n-1...n-1) achieves the bound (where the number of 0's is floor(k/2) and the number of n-1's is ceiling(k/2)).

56. Open Problems In Mathematical Systems And Control Theory Electronic book on open problems in Mathematical Systems and ControlTheory. Editors Vincent Blondel , University of Louvain, Belgium http://www.inma.ucl.ac.be/~blondel/op/

57. Open Problems In Mathematical Systems And Control Theory open problems in Mathematical Systems and Control Theory. 5. open problemsin sequential parametric estimation ErWei Bai, Roberto Tempo, Yinyu Ye. http://www.inma.ucl.ac.be/~blondel/books/openprobs/list.html

58. The Open Problems Project A project to record open problems of interest to researchers in computational geometry and related fields. http://www.cs.smith.edu/~orourke/TOPP/

Next: Numerical List of All The Open Problems Project edited by Erik D. Demaine Joseph S. B. Mitchell Joseph O'Rourke Introduction This is the beginning of a project to record open problems of interest to researchers in computational geometry and related fields. It commenced with the publication of thirty problems in Computational Geometry Column 42 [ ] (see Problems 1-30 ), but has grown much beyond that. We encourage correspondence to improve the entries; please send email to TOPP@cs.smith.edu . If you would like to submit a new problem, please fill out this template Each problem is assigned a unique number for citation purposes. Problem numbers also indicate the order in which the problems were entered. Each problem is classified as belonging to one or more categories. The problems are also available as a single Postscript or PDF file. To begin navigating through the open problems, you may select from a category of interest below, or view a list of all problems sorted numerically Categorized List of All Problems Below, each category lists the problems that are classified under that category. Note that each problem may be classified under several categories.

59. The Valuation Theory Home Page - Open Problems The Valuation Theory Home Page. open problems. Open Problem 1 GeneralizeAbhyankar's Going Up and Coming Down for local uniformization http://math.usask.ca/fvk/Probl.html

The Valuation Theory Home Page Open Problems Open Problem 1: Generalize Abhyankar's "Going Up" and "Coming Down" for local uniformization to arbitrary finite transcendence degree. Possible applications: To local uniformization and resolution of singularities, in particular, in positive characteristic. Posted by F.-V. Kuhlmann on February 4, 1999 A valued field (K,v) is called spherically complete if every nest of balls has a non-empty intersection. This holds if and only if every Pseudo-Cauchy sequence in K has a pseudo limit in K. By the work of Kaplansky, this in turn holds if and only if the field is maximally valued, i.e., has no proper immediate extensions. Take a polynomial f with coefficients in K. The following is known: 1) If f is a polynomial in one variable, then the image f(K) is spherically complete, just as a set with the ultrametric induced by the valuation v. If f is an additive polynomial in several variables, then under a certain additional condition, f(K) is again spherically complete. Open Problem 2: Prove or disprove that f(K) is spherically complete for all additive polynomials in several variables.

60. 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.

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