21. Open Problems In Mathematical Physics This page leads to a collection of significant open problems gathered from colleagues during the academic year 1998/99. They are offered in the belief that http://www.math.princeton.edu/~aizenman/OpenProblems.iamp/

Open Problems in Mathematical Physics Quick Access: Soft phases in 2D O(N) models Quantum Hall Conductance dimensions ... IAMP This page leads to a collection of significant open problems gathered from colleagues during the academic year 1998/99. They are offered in the belief that good challenges stimulate our work, tempered by the dictum that preformulated questions should not discourage one from seeking new perspectives. All are invited to send pertinent comments, references to solutions, and contributions for this page to M. Aizenman (Editor): aizenman@princeton.edu List by Contributors By order of submission General Framework Quantum Field Theory Statistical Physics Quantum Many Body Systems Geometry and Physics Schroedinger Operators Disordered Systems Non-equilibrium Relativity and Gravitation Dynamical Systems Fluid Dynamics (Layout webmaster: aizenman@fas.harvard.edu

22. Open Problems In Mathematics And Physics - Home Links to open problems in mathematics, physics and other subjects. http://openproblems.net/

Open Problems In Mathematics And Physics Home Home OPEN QUESTIONS GENERAL Lists of unsolved problems Science magazine 125 big questions Areas long to learn: quantum groups motivic cohomology , local and micro local analysis of large finite groups Exotic areas: infinite Banach spaces , large and inaccessible cardinals Some recent links between mathematics and physics Number theory and physics Conjectured links between the Riemann zeta function and chaotic quantum-mechanical systems Deep and relatively recent ideas in mathematics and physics Standard model and mathematics: Gauge field or connection Dirac operators or fundamental classes in K-theory ( Atiyah-Singer index theorem String theory and mathematics: Mirror symmetry Conformal field theory Mathematics behind supersymmetry Mathematics of M-Theory Chern-Simons theory Higher gauge theory ... Geometric Langlands Program Unified theory: Langlands Program Witten on Langlands Theory of "motives" Lists of unsolved problems ... PRICE P versus NP The Hodge Conjecture The Poincaré Conjecture (solved) The Riemann Hypothesis Yang-Mills Existence and Mass Gap Navier-Stokes Existence and Smoothness The Birch and Swinnerton-Dyer Conjecture Mathworld list Mathematical challenges of the 21st century including moduli spaces and borderland physics Goldbach conjecture Normality of pi digits in an integer base Unsolved problems and difficult to understand areas PRICES Fields Medal and Rolf Nevanlinna Prize Abel Prize PHYSICS Important unsolved problems in physics Quantum gravity Explaining high-Tc superconductors

23. OPEN PROBLEMS IN DATA STREAMS AND RELATED TOPICS IITK WORKSHOP ON Please send any comments/corrections regarding this document to andrewm@ucsd.edu. http://www.cs.umass.edu/~mcgregor/papers/07-openproblems.pdf

24. Open Problems - Filters On Posets Filters on Posets and Generalizations, a math book In this section I will formulate some conjectures about lattices of filter objects on a set. http://filters.wikidot.com/open-problems

25. 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.

26. Open Problems List A collection of papers outlining unsolved problems maintained at Stony Brook. http://www.math.sunysb.edu/dynamics/open.html

Open Problems in Dynamical Systems Open problems in holomorphic dynamics Two lists of problems are currently available on-line: Conformal Dynamics Problem List Ed. by B. Bielefeld, IMS at Stony Brook Preprint 1990/1 and more recent Problems in Holomorphic Dynamics Ed. by B. Bielefeld and M. Lyubich, IMS at Stony Brook Preprint 92/7 In addition some open questions may be found in these surveys Open problems in dynamics in several complex variables is a part of Several complex variables problems list available from Several complex variables preprint server in Indiana. Please send your problems to Gregery Buzzard at gbuzzard@iu-math.math.indiana.edu Problems in Low-Dimensional Topology a 380 pages PostScript file edited by Rob Kirby contain some problems on Topological Dynamics. Topology of hyperbolic attractors. A problem submitted by Christian Bonatti. A collection maintained by Sergiy Kolyada and Michal Misiurewicz Is entropy effectively computable? A problem by John Milnor We are soliciting open problems in various areas of Dynamical Systems for posting on this page. You can post a problem by filling out this form or by sending an e-mail to webmaster@math.sunysb.edu

27. CMU-IBM Cyber-Infrastructure For MINLP Open Problems. If you have an optimization problem for which You have a problem satement but nota model fomulation; You have a model but you are not sure if it is properly formulated http://www.minlp.org/openproblems/index.php

Username Password Home Goals Participants Instructions ... Resources HOME > OPEN PROBLEMS Open Problems If you have an optimization problem for which: You have a problem satement but nota model fomulation You have a model but you are not sure if it is properly formulated You have a model but do not know how to solve it Please submit it through a pdf file. For this you need to first register and login . After that click on the link below, provide a title for your problem and upload your pdf file. We hope we will have someone respond to your open problem. CMU-IBM Cyber-Infrastructure for MINLP This cyber-infrastructure project has been funded by the National Science Foundation under Grant OCI-0750826

28. Prime Conjectures And Open Question Prime Conjectures and Open Questions (Another of the Prime Pages resources). Our book Prime Curios! The Dictionary of Prime Number Trivia is now http://primes.utm.edu/notes/conjectures/

Prime Conjectures and Open Questions (Another of the Prime Pages ' resources) Our book " Prime Curios! The Dictionary of Prime Number Trivia " is now available on CreateSpace Amazon Home Search Site ... Submit primes Below are just a few of the many conjectures concerning primes. Goldbach's Conjecture: Every even n Goldbach wrote a letter to Euler in 1742 suggesting that . Euler replied that this is equivalent to this is now known as Goldbach's conjecture. Schnizel showed that Goldbach's conjecture is equivalent to distinct primes It has been proven that every even integer is the sum of at most six primes [ ] (Goldbach's conjecture suggests two) and in 1966 Chen proved every sufficiently large even integer is the sum of a prime plus a number with no more than two prime factors (a P ). In 1993 Sinisalo verified Goldbach's conjecture for all integers less than 4 ]. More recently Jean-Marc Deshouillers, Yannick Saouter and Herman te Riele have verified this up to 10

29. Open Problems And Projects Stephen Wolfram File Format PDF/Adobe Acrobat Quick View http://www.wolframscience.com/openproblems/NKSOpenProblems.pdf

30. Open Problems Thoughts on teaching science and whatever else comes to mind. Title from, among other places, the Clay Shirky tweet The only good measure of student progress I know is the http://openproblems.blogspot.com/

Open Problems Thoughts on teaching science and whatever else comes to mind. Title from, among other places, the Clay Shirky tweet: "[T]he only good measure of student progress I know is the number of open problems they can successfully characterize." Saturday, May 22, 2010 Assessment Some grading thoughts: 1. Grades and scores can be used to communicate understanding. Or they can be used to communicate achievement. Or adherence to policies and procedures. Problems arise in interpreting scores and grades when a single score or grade is used to communicate many of these at the same time. 2. It is probably not an accident that we've settled on a 4-point scale referred to five letters. It's hard to figure out what's in somebody else's mind. It is certainly folly to try to extract this information to the 0.1% accuracy many grading program offer. 20% feels like a more realistic degree of fuzziness - so five letter grades each taking up about 20% of the grading scale just strikes me as a natural evolution. Maybe 6 maybe 4 maybe even (at a stretch) 10, but certainly not 100. 3. Points-bucket grading systems discourage several important aspects of learning in the real world: the need for revision and subsequent growth that absolutely forgives early (later corrected) misconceptions; the fact that IF not WHEN the student learns is what matters; the quickly learned lesson that a "points hole" that seems inescapable is a powerful deterrent towards effort.

31. 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 Small Transversals in Partitionable Graphs ... The Imperfection Ratio Integer Programming Partitionable Graphs as Cutting Planes for Packing Problems? Feasibility/Membership Problem For the Theta Body Balanced Graphs Balanced circulants ... P4-structure and Its Relatives The individual 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.

32. ALifeVIII: Open Problems In Artificial Life ALifeVIII Open Problems in Artificial Life alife ALife Restricted area Organizer's Corner Collar Admin As published in Bedau et al., Open problems in artificial life, http://www.alife.org/alife8/open-prob.html

Up: Alife VIII ALifeVIII: Open Problems in Artificial Life ALife VIII Proceedings ALife VIII Workshops Proceedings Call for Papers Topics ... Artificial Life Links affiliated conference Restricted area Organizer's Corner Collar Admin As published in Bedau et al. , Open problems in artificial life, Artificial Life How does life arise from the nonliving? Generate a molecular proto-organism in vitro Achieve the transition to life in an artificial chemistry in silico Determine whether fundamentally novel living organisms can exist Simulate a unicellular organism over its entire lifecycle Explain how rules and symbols are generated from physical dynamics in living systems What are the potentials and limits of living systems? Determine what is inevitable in the open-ended evolution of life Determine minimal conditions for evolutionary transitions from specific to generic response systems Create a formal framework for synthesizing dynamical hierarchies at all scales Determine the predictability of evolutionary consequences of manipulating organisms and ecosystems Develop a theory of information processing, information flow and information generation for evolving systems

33. Open Problems Welcome to King Saud University. The largest Higher Education Center in Saudi Arabia. KSU goes back in history to more than fifty years; it encompasses more than twenty eight http://faculty.ksu.edu.sa/smecheri/Pages/OpenProblems.aspx

34. REDIRECT, Department Of Mathematics, Texas A&M University Problems taken from workshop lectures given at Texas A M University. http://www.math.tamu.edu/research/workshops/linanalysis/problems.html

Courses Undergraduate Graduate Positions Available ... Contact Us PAGE HAS MOVED The page you have requested has moved to http://www.math.tamu.edu/conferences/linanalysis/problems.html Please update your bookmarks when the page refreshes (10 seconds). College of Science Accessibility Webmaster

35. Open Problems In Algebraic Topology Problems in algebraic topology, listed by Mark Hovey, mathematician at Wesleyan University. http://math.wesleyan.edu/~mhovey/problems/

Mark Hovey's Algebraic Topology Problem List This list of problems is designed as a resource for algebraic topologists. The problems are not guaranteed to be good in any wayI just sat down and wrote them all in a couple of days. Some of them are no doubt out of reach, and some are probably even worseuninteresting. I ask that anybody who gets anywhere on any of these problems, has some new problems to add, or has corrections to any of them, please keep me informed (mhovey@wesleyan.edu). If I mention a name in a problem, it might be good to consult that person before working too hard on the problem. However, even if the problems we work on are internal to algebraic topology, we must strive to express ourselves better. If we expect our papers to be accepted in mathematical journals with a wide audience, such as the Annals, JAMS, or the Inventiones, then we must make sure our introductions are readable by generic good mathematicians. I always think of the French, myselfI want Serre to be able to understand what my paper is about. Another idea is to think of your advisor's advisor, who was probably trained 40 or 50 years ago. Make sure your advisor's advisor can understand your introduction. Another point of view comes from Mike Hopkins, who told me that we must tell a story in the introduction. Don't jump right into the middle of it with "Let E be an E-infinity ring spectrum". That does not help our field. Here are the problems: Major problems in the field Morava K- and E-theory Elliptic cohomology Applications ... Miscellaneous Unstable modules and algebras over the Steenrod algebra (coming soon)

36. Open Problems Open Problems. The field of Grammatical Inference enjoys the uncanny distinction of being faced with a variety of open problems that remain to be solved. http://www.cs.iastate.edu/~honavar/gi/open.html

Open Problems The field of Grammatical Inference enjoys the uncanny distinction of being faced with a variety of open problems that remain to be solved. This page is provided to make researchers and practitioners aware of the different open problems and to motivate them to tackle these problems. It is impossible for us to catalog all the open problems in Grammatical Inference but this page is designed to allow people to contribute to the growing list. Polynomial Identification with Probability One Colin de la Higuera , November 6th, 1998 Several different algorithms have been proposed to learn Stochastic Deterministic Finite State Automata Absence of empirical data David G. Stork , February 1st, 1999 What problems in computational linguistics are primarily or entirely limited by lack of empirical data? That is, suppose we had a perfect oracle that could generate an extremely large number of samples (labelled sentences, spelling variants, etc., as appropriate) that could be used with existing inference or learning techniques. What problems would then be solved? I am especially interested in citable articles that give evidence for such a claim. I am compiling such a list of areas in a range of disciplines (optical character recognition, path planning, etc.) for a review article on the status of pattern recognition and machine intelligence.

37. Open Mathematical Questions At Jdawiseman.com A few unsolved mathematical questions put together by Julian D. A. Wiseman. http://www.jdawiseman.com/papers/easymath/open_questions.html

Main index Other Papers index About author Open Mathematical Questions at jdawiseman.com Julian D. A. Wiseman, January 2009 Contents: s n n Matching stars ... Medals: comparing golds and silvers and bronzes Publication history: only here. Usual and terms apply. Scattered around jdawiseman.com, lodged within other essays, are various unsolved mathematical questions. These might be within the reach of a competent undergraduate student of mathematics. A solution to the first of the three would certainly be worthy of a paper in a mathematical journal, and solutions to either of the others might be worthy of mention. This list might grow over time. Those giving serious attention to more than none of these problems are invited to tell this to the author , so that others may be forewarned that an answer is growing. Unless requested otherwise, problems will be marked with the names of those working on them. s n n This problem taken from The expected value of s n n A game is played by repeatedly tossing a fair coin, stopping any time after the first toss. On stopping the score is the proportion of tosses that are heads. Given optimal strategy, what is the expected score? Assume that there have already been h and t tails, at which state the expected value of the game is defined to be EV(

38. A Survey Of Venn Diagrams: Open Problems Venn Diagram Survey open problems Open problems related to Venn diagrams. Combinatorial Problems. Is it true that every simple Venn diagram of n curves can be extended to http://www.combinatorics.org/Surveys/ds5/VennOpenEJC.html

T HE E LECTRONIC ... OMBINATORICS (ed. June 2005), DS #5. Venn Diagram Survey Open Problems Open problems related to Venn diagrams. Combinatorial Problems 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 ]. It 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? Find a simple symmetric 11-Venn diagram. More generally, find a general construction for simple symmetric Venn diagrams. Find a minimum-vertex symmetric 11-Venn diagram. Such a Venn diagram would have 209 vertices. Find a polar symmetric 11-Venn diagram. 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? It is known that there are at least 33 simple symmetric Venn diagrams. Find a Brunnian link whose minimal projection is a symmetric Venn diagram of order 7 or prove that no such link exists.

39. Problems In Signed, Gain, And Biased Graphs Compiled by Thomas Zaslavsky. http://www.math.binghamton.edu/zaslav/Bsg/sgbgprobs.html

Problems in Signed, Gain, and Biased Graphs Compiled by Thomas Zaslavsky This is a fairly miscellaneous and incomplete selection of problems that I happen to have taken an interest in not necessarily an active interest. Some are open and some are solved or partially solved as for example a problem may have been shown to be NP-complete but special cases could still be solved exactly or algorithmically. This list is intended to supplement the many problems in the Bibliography . There is just a small amount of duplication. For the present, the problems here all concern signed graphs. However, many of them have obvious generalizations. References are as cited in the Bibliography . All the terms employed should be defined in the Glossary . If you find any missing, or if you have suggestions for this page, please notify me! NOTE: A PostScript version is available. It is slightly more up-to-date and it is the only one that will be maintained and expanded. I. Direct Measures of Imbalance (June 8-10 1998) Imbalance of a signed graph can be measured in numerous ways. Here are problems concerning some measures that have appeared in the literature. The greatest interest has been in the edge version of frustration. (The problems in part II can be regarded as measuring imbalance in a different way.)

40. Problems In Graph Theory Maintained by Peter Cameron. http://www.maths.qmw.ac.uk/~pjc/oldprob.html

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