[{"status":"public","abstract":[{"text":"This work deals with an algebro–geometric theory of solutions of the classical Yang–Baxter equation based on torsion free coherent sheaves of Lie algebras on Weierstraß cubic curves.","lang":"eng"}],"publication":"Communications in Mathematical Physics","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"602"}],"user_id":"49063","_id":"44333","page":"123–169","intvolume":"       364","citation":{"apa":"Burban, I., &#38; Galinat, L. (2018). Torsion free sheaves on Weierstraß cubic curves and the classical Yang-Baxter equation. <i>Communications in Mathematical Physics</i>, <i>364</i>(1), 123–169. <a href=\"https://doi.org/10.1007/s00220-018-3172-2\">https://doi.org/10.1007/s00220-018-3172-2</a>","mla":"Burban, Igor, and L. Galinat. “Torsion Free Sheaves on Weierstraß Cubic Curves and the Classical Yang-Baxter Equation.” <i>Communications in Mathematical Physics</i>, vol. 364, no. 1, 2018, pp. 123–169, doi:<a href=\"https://doi.org/10.1007/s00220-018-3172-2\">10.1007/s00220-018-3172-2</a>.","short":"I. Burban, L. Galinat, Communications in Mathematical Physics 364 (2018) 123–169.","bibtex":"@article{Burban_Galinat_2018, title={Torsion free sheaves on Weierstraß cubic curves and the classical Yang-Baxter equation}, volume={364}, DOI={<a href=\"https://doi.org/10.1007/s00220-018-3172-2\">10.1007/s00220-018-3172-2</a>}, number={1}, journal={Communications in Mathematical Physics}, author={Burban, Igor and Galinat, L.}, year={2018}, pages={123–169} }","ieee":"I. Burban and L. Galinat, “Torsion free sheaves on Weierstraß cubic curves and the classical Yang-Baxter equation,” <i>Communications in Mathematical Physics</i>, vol. 364, no. 1, pp. 123–169, 2018, doi: <a href=\"https://doi.org/10.1007/s00220-018-3172-2\">10.1007/s00220-018-3172-2</a>.","chicago":"Burban, Igor, and L. Galinat. “Torsion Free Sheaves on Weierstraß Cubic Curves and the Classical Yang-Baxter Equation.” <i>Communications in Mathematical Physics</i> 364, no. 1 (2018): 123–169. <a href=\"https://doi.org/10.1007/s00220-018-3172-2\">https://doi.org/10.1007/s00220-018-3172-2</a>.","ama":"Burban I, Galinat L. Torsion free sheaves on Weierstraß cubic curves and the classical Yang-Baxter equation. <i>Communications in Mathematical Physics</i>. 2018;364(1):123–169. doi:<a href=\"https://doi.org/10.1007/s00220-018-3172-2\">10.1007/s00220-018-3172-2</a>"},"year":"2018","issue":"1","publication_status":"published","doi":"10.1007/s00220-018-3172-2","title":"Torsion free sheaves on Weierstraß cubic curves and the classical Yang-Baxter equation","volume":364,"date_created":"2023-05-02T18:50:35Z","author":[{"first_name":"Igor","full_name":"Burban, Igor","id":"72064","last_name":"Burban"},{"first_name":"L.","last_name":"Galinat","full_name":"Galinat, L."}],"date_updated":"2023-05-07T01:34:43Z"},{"citation":{"ama":"Burban I, Drozd Yu. Non-commutative nodal curves and derived tame algebras. Published online 2018.","ieee":"I. Burban and Yu. Drozd, “Non-commutative nodal curves and derived tame algebras.” 2018.","chicago":"Burban, Igor, and Yu. 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Entwicklung des Begriffsverständnisses zu Vierecksfiguren in der Grundschule – Erste Ergebnisse aus dem Projekt BegriV. In: Fachgruppe Didaktik der Mathematik der Universität Paderborn, ed. <i>Beiträge zum Mathematikunterricht</i>. WTM-Verlag; 2018:377–380.","ieee":"J. Bruns, E. Unterhauser, and H. Gasteiger, “Entwicklung des Begriffsverständnisses zu Vierecksfiguren in der Grundschule – Erste Ergebnisse aus dem Projekt BegriV,” in <i>Beiträge zum Mathematikunterricht</i>, 2018, pp. 377–380.","chicago":"Bruns, Julia, E. Unterhauser, and H. Gasteiger. “Entwicklung des Begriffsverständnisses zu Vierecksfiguren in der Grundschule – Erste Ergebnisse aus dem Projekt BegriV.” In <i>Beiträge zum Mathematikunterricht</i>, edited by Fachgruppe Didaktik der Mathematik der Universität Paderborn, 377–380. Münster: WTM-Verlag, 2018.","bibtex":"@inproceedings{Bruns_Unterhauser_Gasteiger_2018, place={Münster}, title={Entwicklung des Begriffsverständnisses zu Vierecksfiguren in der Grundschule – Erste Ergebnisse aus dem Projekt BegriV}, booktitle={Beiträge zum Mathematikunterricht}, publisher={WTM-Verlag}, author={Bruns, Julia and Unterhauser, E. and Gasteiger, H.}, editor={Fachgruppe Didaktik der Mathematik der Universität Paderborn}, year={2018}, pages={377–380} }","short":"J. Bruns, E. Unterhauser, H. Gasteiger, in: Fachgruppe Didaktik der Mathematik der Universität Paderborn (Ed.), Beiträge zum Mathematikunterricht, WTM-Verlag, Münster, 2018, pp. 377–380.","mla":"Bruns, Julia, et al. “Entwicklung des Begriffsverständnisses zu Vierecksfiguren in der Grundschule – Erste Ergebnisse aus dem Projekt BegriV.” <i>Beiträge zum Mathematikunterricht</i>, edited by Fachgruppe Didaktik der Mathematik der Universität Paderborn, WTM-Verlag, 2018, pp. 377–380.","apa":"Bruns, J., Unterhauser, E., &#38; Gasteiger, H. (2018). Entwicklung des Begriffsverständnisses zu Vierecksfiguren in der Grundschule – Erste Ergebnisse aus dem Projekt BegriV. In Fachgruppe Didaktik der Mathematik der Universität Paderborn (Ed.), <i>Beiträge zum Mathematikunterricht</i> (pp. 377–380). WTM-Verlag."},"place":"Münster","year":"2018","publication_status":"published"},{"title":"Gemeinsame Arbeitsphasen produktiv nutzen – verschiedene Methoden kooperativen Lernens im Mathematikunterricht der Grundschule","date_updated":"2023-06-20T18:50:53Z","author":[{"orcid":"https://orcid.org/0000-0002-6604-5864","last_name":"Bruns","full_name":"Bruns, Julia","id":"72183","first_name":"Julia"},{"first_name":"H.","full_name":"Gasteiger, H.","last_name":"Gasteiger"}],"date_created":"2023-06-20T18:50:42Z","volume":205,"year":"2018","citation":{"apa":"Bruns, J., &#38; Gasteiger, H. (2018). Gemeinsame Arbeitsphasen produktiv nutzen – verschiedene Methoden kooperativen Lernens im Mathematikunterricht der Grundschule. <i>mathematik lehren</i>, <i>205</i>, 10–13.","mla":"Bruns, Julia, and H. Gasteiger. “Gemeinsame Arbeitsphasen produktiv nutzen – verschiedene Methoden kooperativen Lernens im Mathematikunterricht der Grundschule.” <i>mathematik lehren</i>, vol. 205, 2018, pp. 10–13.","short":"J. Bruns, H. Gasteiger, mathematik lehren 205 (2018) 10–13.","bibtex":"@article{Bruns_Gasteiger_2018, title={Gemeinsame Arbeitsphasen produktiv nutzen – verschiedene Methoden kooperativen Lernens im Mathematikunterricht der Grundschule}, volume={205}, journal={mathematik lehren}, author={Bruns, Julia and Gasteiger, H.}, year={2018}, pages={10–13} }","ama":"Bruns J, Gasteiger H. Gemeinsame Arbeitsphasen produktiv nutzen – verschiedene Methoden kooperativen Lernens im Mathematikunterricht der Grundschule. <i>mathematik lehren</i>. 2018;205:10–13.","ieee":"J. Bruns and H. Gasteiger, “Gemeinsame Arbeitsphasen produktiv nutzen – verschiedene Methoden kooperativen Lernens im Mathematikunterricht der Grundschule,” <i>mathematik lehren</i>, vol. 205, pp. 10–13, 2018.","chicago":"Bruns, Julia, and H. Gasteiger. “Gemeinsame Arbeitsphasen produktiv nutzen – verschiedene Methoden kooperativen Lernens im Mathematikunterricht der Grundschule.” <i>mathematik lehren</i> 205 (2018): 10–13."},"intvolume":"       205","page":"10–13","publication_status":"published","language":[{"iso":"ger"}],"_id":"45690","user_id":"49063","department":[{"_id":"97"},{"_id":"611"}],"status":"public","type":"journal_article","publication":"mathematik lehren"},{"_id":"36485","user_id":"49063","department":[{"_id":"611"},{"_id":"97"}],"language":[{"iso":"eng"}],"type":"book_chapter","publication":"Contemporary Research and Perspectives on Early Childhood Mathematics Education","abstract":[{"lang":"eng","text":"This chapter presents an overview of the contributions in TSG 1: Early Childhood Mathematics Education at ICME-13 which focused on issues from the perspective of early childhood educators. A basic assumption of this chapter is that the opportunities for young children to develop mathematical understandings and skills are influenced by several conditions at a macro, meso and micro level. First, curricula provide a framework for early mathematics teaching and learning with varying expectations (by teachers) about what can occur in the pre-school environment—informal learning (such as through play), content to learn and activities to experience. Second, early childhood educators’ mathematical knowledge, pedagogical knowledge, understandings, beliefs, and perceptions influence how they enact these expectations. These competencies can be developed and supported by professional learning. Third, educational programs, resources and activities used in the pre-school environment impact on the mathematical opportunities children engage in at the micro level."}],"editor":[{"full_name":"Elia, Iliada","last_name":"Elia","first_name":"Iliada"},{"first_name":"Joanne","last_name":"Mulligan","full_name":"Mulligan, Joanne"},{"full_name":"Anderson, Ann","last_name":"Anderson","first_name":"Ann"},{"last_name":"Baccaglini-Frank","full_name":"Baccaglini-Frank, Anna","first_name":"Anna"},{"first_name":"Christiane","last_name":"Benz","full_name":"Benz, Christiane"}],"status":"public","date_updated":"2023-06-20T19:16:42Z","publisher":"Springer International Publishing","author":[{"last_name":"Cooke","full_name":"Cooke, Audrey","first_name":"Audrey"},{"last_name":"Bruns","orcid":"https://orcid.org/0000-0002-6604-5864","id":"72183","full_name":"Bruns, Julia","first_name":"Julia"}],"date_created":"2023-01-12T15:36:28Z","title":"Early Childhood Educators’ Issues and Perspectives in Mathematics Education","doi":"10.1007/978-3-319-73432-3_14","publication_status":"published","publication_identifier":{"isbn":["978-3-319-73432-3"]},"year":"2018","place":"Cham, Switzerland","citation":{"short":"A. Cooke, J. Bruns, in: I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, C. Benz (Eds.), Contemporary Research and Perspectives on Early Childhood Mathematics Education, Springer International Publishing, Cham, Switzerland, 2018, pp. 267–289.","mla":"Cooke, Audrey, and Julia Bruns. “Early Childhood Educators’ Issues and Perspectives in Mathematics Education.” <i>Contemporary Research and Perspectives on Early Childhood Mathematics Education</i>, edited by Iliada Elia et al., Springer International Publishing, 2018, pp. 267–289, doi:<a href=\"https://doi.org/10.1007/978-3-319-73432-3_14\">10.1007/978-3-319-73432-3_14</a>.","bibtex":"@inbook{Cooke_Bruns_2018, place={Cham, Switzerland}, title={Early Childhood Educators’ Issues and Perspectives in Mathematics Education}, DOI={<a href=\"https://doi.org/10.1007/978-3-319-73432-3_14\">10.1007/978-3-319-73432-3_14</a>}, booktitle={Contemporary Research and Perspectives on Early Childhood Mathematics Education}, publisher={Springer International Publishing}, author={Cooke, Audrey and Bruns, Julia}, editor={Elia, Iliada and Mulligan, Joanne and Anderson, Ann and Baccaglini-Frank, Anna and Benz, Christiane}, year={2018}, pages={267–289} }","apa":"Cooke, A., &#38; Bruns, J. (2018). Early Childhood Educators’ Issues and Perspectives in Mathematics Education. In I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, &#38; C. Benz (Eds.), <i>Contemporary Research and Perspectives on Early Childhood Mathematics Education</i> (pp. 267–289). Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-319-73432-3_14\">https://doi.org/10.1007/978-3-319-73432-3_14</a>","chicago":"Cooke, Audrey, and Julia Bruns. “Early Childhood Educators’ Issues and Perspectives in Mathematics Education.” In <i>Contemporary Research and Perspectives on Early Childhood Mathematics Education</i>, edited by Iliada Elia, Joanne Mulligan, Ann Anderson, Anna Baccaglini-Frank, and Christiane Benz, 267–289. Cham, Switzerland: Springer International Publishing, 2018. <a href=\"https://doi.org/10.1007/978-3-319-73432-3_14\">https://doi.org/10.1007/978-3-319-73432-3_14</a>.","ieee":"A. Cooke and J. Bruns, “Early Childhood Educators’ Issues and Perspectives in Mathematics Education,” in <i>Contemporary Research and Perspectives on Early Childhood Mathematics Education</i>, I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, and C. Benz, Eds. Cham, Switzerland: Springer International Publishing, 2018, pp. 267–289.","ama":"Cooke A, Bruns J. Early Childhood Educators’ Issues and Perspectives in Mathematics Education. In: Elia I, Mulligan J, Anderson A, Baccaglini-Frank A, Benz C, eds. <i>Contemporary Research and Perspectives on Early Childhood Mathematics Education</i>. Springer International Publishing; 2018:267–289. doi:<a href=\"https://doi.org/10.1007/978-3-319-73432-3_14\">10.1007/978-3-319-73432-3_14</a>"},"page":"267–289"},{"user_id":"49063","department":[{"_id":"611"},{"_id":"97"}],"_id":"36480","language":[{"iso":"ger"}],"type":"book_chapter","publication":"Mathematikfortbildungen professionalisieren: Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik","status":"public","abstract":[{"text":"Im vorangegangenen Kapitel wurde die Vorgeschichte beschrieben, wie es durch Initiative der Deutsche Telekom Stiftung zur Gründung des DZLM gekommen ist. In diesem zweiten Kapitel werden die Tätigkeitsfelder und Konzepte des DZLM in seiner ersten Förderphase vom 01.10.2011 bis 30.09.2016 beschrieben.","lang":"eng"}],"editor":[{"first_name":"Rolf","last_name":"Biehler","full_name":"Biehler, Rolf"},{"full_name":"Lange, Thomas","last_name":"Lange","first_name":"Thomas"},{"first_name":"Timo","last_name":"Leuders","full_name":"Leuders, Timo"},{"first_name":"Bettina","full_name":"Rösken-Winter, Bettina","last_name":"Rösken-Winter"},{"last_name":"Scherer","full_name":"Scherer, Petra","first_name":"Petra"},{"first_name":"Christoph","last_name":"Selter","full_name":"Selter, Christoph"}],"author":[{"full_name":"Barzel, Bärbel","last_name":"Barzel","first_name":"Bärbel"},{"first_name":"Rolf","full_name":"Biehler, Rolf","last_name":"Biehler"},{"last_name":"Blömeke","full_name":"Blömeke, Sigrid","first_name":"Sigrid"},{"last_name":"Brandtner","full_name":"Brandtner, Regine","first_name":"Regine"},{"first_name":"Julia","full_name":"Bruns, Julia","id":"72183","last_name":"Bruns","orcid":"https://orcid.org/0000-0002-6604-5864"},{"full_name":"Dohrmann, Christian","last_name":"Dohrmann","first_name":"Christian"},{"first_name":"Ulrich","last_name":"Kortenkamp","full_name":"Kortenkamp, Ulrich"},{"last_name":"Lange","full_name":"Lange, Thomas","first_name":"Thomas"},{"first_name":"Timo","full_name":"Leuders, Timo","last_name":"Leuders"},{"last_name":"Rösken-Winter","full_name":"Rösken-Winter, Bettina","first_name":"Bettina"},{"full_name":"Scherer, Petra","last_name":"Scherer","first_name":"Petra"},{"first_name":"Christoph","last_name":"Selter","full_name":"Selter, Christoph"}],"date_created":"2023-01-12T15:27:17Z","date_updated":"2023-06-20T19:17:25Z","publisher":"Springer Fachmedien Wiesbaden","doi":"10.1007/978-3-658-19028-6_2","title":"Das Deutsche Zentrum für Lehrerbildung Mathematik – DZLM","publication_status":"published","publication_identifier":{"isbn":["978-3-658-19028-6"]},"citation":{"bibtex":"@inbook{Barzel_Biehler_Blömeke_Brandtner_Bruns_Dohrmann_Kortenkamp_Lange_Leuders_Rösken-Winter_et al._2018, place={Wiesbaden}, title={Das Deutsche Zentrum für Lehrerbildung Mathematik – DZLM}, DOI={<a href=\"https://doi.org/10.1007/978-3-658-19028-6_2\">10.1007/978-3-658-19028-6_2</a>}, booktitle={Mathematikfortbildungen professionalisieren: Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik}, publisher={Springer Fachmedien Wiesbaden}, author={Barzel, Bärbel and Biehler, Rolf and Blömeke, Sigrid and Brandtner, Regine and Bruns, Julia and Dohrmann, Christian and Kortenkamp, Ulrich and Lange, Thomas and Leuders, Timo and Rösken-Winter, Bettina and et al.}, editor={Biehler, Rolf and Lange, Thomas and Leuders, Timo and Rösken-Winter, Bettina and Scherer, Petra and Selter, Christoph}, year={2018}, pages={7–39} }","short":"B. Barzel, R. Biehler, S. Blömeke, R. Brandtner, J. Bruns, C. Dohrmann, U. Kortenkamp, T. Lange, T. Leuders, B. Rösken-Winter, P. Scherer, C. Selter, in: R. Biehler, T. Lange, T. Leuders, B. Rösken-Winter, P. Scherer, C. Selter (Eds.), Mathematikfortbildungen professionalisieren: Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik, Springer Fachmedien Wiesbaden, Wiesbaden, 2018, pp. 7–39.","mla":"Barzel, Bärbel, et al. “Das Deutsche Zentrum für Lehrerbildung Mathematik – DZLM.” <i>Mathematikfortbildungen professionalisieren: Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik</i>, edited by Rolf Biehler et al., Springer Fachmedien Wiesbaden, 2018, pp. 7–39, doi:<a href=\"https://doi.org/10.1007/978-3-658-19028-6_2\">10.1007/978-3-658-19028-6_2</a>.","apa":"Barzel, B., Biehler, R., Blömeke, S., Brandtner, R., Bruns, J., Dohrmann, C., Kortenkamp, U., Lange, T., Leuders, T., Rösken-Winter, B., Scherer, P., &#38; Selter, C. (2018). Das Deutsche Zentrum für Lehrerbildung Mathematik – DZLM. In R. Biehler, T. Lange, T. Leuders, B. Rösken-Winter, P. Scherer, &#38; C. Selter (Eds.), <i>Mathematikfortbildungen professionalisieren: Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik</i> (pp. 7–39). Springer Fachmedien Wiesbaden. <a href=\"https://doi.org/10.1007/978-3-658-19028-6_2\">https://doi.org/10.1007/978-3-658-19028-6_2</a>","chicago":"Barzel, Bärbel, Rolf Biehler, Sigrid Blömeke, Regine Brandtner, Julia Bruns, Christian Dohrmann, Ulrich Kortenkamp, et al. “Das Deutsche Zentrum für Lehrerbildung Mathematik – DZLM.” In <i>Mathematikfortbildungen professionalisieren: Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik</i>, edited by Rolf Biehler, Thomas Lange, Timo Leuders, Bettina Rösken-Winter, Petra Scherer, and Christoph Selter, 7–39. Wiesbaden: Springer Fachmedien Wiesbaden, 2018. <a href=\"https://doi.org/10.1007/978-3-658-19028-6_2\">https://doi.org/10.1007/978-3-658-19028-6_2</a>.","ieee":"B. Barzel <i>et al.</i>, “Das Deutsche Zentrum für Lehrerbildung Mathematik – DZLM,” in <i>Mathematikfortbildungen professionalisieren: Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik</i>, R. Biehler, T. Lange, T. Leuders, B. Rösken-Winter, P. Scherer, and C. Selter, Eds. Wiesbaden: Springer Fachmedien Wiesbaden, 2018, pp. 7–39.","ama":"Barzel B, Biehler R, Blömeke S, et al. Das Deutsche Zentrum für Lehrerbildung Mathematik – DZLM. In: Biehler R, Lange T, Leuders T, Rösken-Winter B, Scherer P, Selter C, eds. <i>Mathematikfortbildungen professionalisieren: Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik</i>. Springer Fachmedien Wiesbaden; 2018:7–39. doi:<a href=\"https://doi.org/10.1007/978-3-658-19028-6_2\">10.1007/978-3-658-19028-6_2</a>"},"page":"7–39","place":"Wiesbaden","year":"2018"},{"language":[{"iso":"ger"}],"_id":"36478","department":[{"_id":"611"},{"_id":"97"}],"user_id":"49063","editor":[{"first_name":"Rolf","last_name":"Biehler","full_name":"Biehler, Rolf"},{"full_name":"Lange, Thomas","last_name":"Lange","first_name":"Thomas"},{"first_name":"Timo","full_name":"Leuders, Timo","last_name":"Leuders"},{"first_name":"Bettina","last_name":"Rösken-Winter","full_name":"Rösken-Winter, Bettina"}],"status":"public","publication":"Mathematikfortbildungen professionalisieren. Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik","type":"book_chapter","title":"EmMa - Fortbildung für elementarpädagogische Fachpersonen zur frühen mathematischen Bildung","doi":"10.1007/978-3-658-19028-6_21","date_updated":"2023-06-20T19:15:55Z","publisher":"Springer","author":[{"first_name":"Julia","last_name":"Bruns","orcid":"https://orcid.org/0000-0002-6604-5864","full_name":"Bruns, Julia","id":"72183"},{"first_name":"Lars","full_name":"Eichen, Lars","last_name":"Eichen"}],"date_created":"2023-01-12T15:20:07Z","year":"2018","place":"Berlin","page":"417-434","citation":{"apa":"Bruns, J., &#38; Eichen, L. (2018). EmMa - Fortbildung für elementarpädagogische Fachpersonen zur frühen mathematischen Bildung. In R. Biehler, T. Lange, T. Leuders, &#38; B. Rösken-Winter (Eds.), <i>Mathematikfortbildungen professionalisieren. Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik</i> (pp. 417–434). Springer. <a href=\"https://doi.org/10.1007/978-3-658-19028-6_21\">https://doi.org/10.1007/978-3-658-19028-6_21</a>","bibtex":"@inbook{Bruns_Eichen_2018, place={Berlin}, title={EmMa - Fortbildung für elementarpädagogische Fachpersonen zur frühen mathematischen Bildung}, DOI={<a href=\"https://doi.org/10.1007/978-3-658-19028-6_21\">10.1007/978-3-658-19028-6_21</a>}, booktitle={Mathematikfortbildungen professionalisieren. Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik}, publisher={Springer}, author={Bruns, Julia and Eichen, Lars}, editor={Biehler, Rolf and Lange, Thomas and Leuders, Timo and Rösken-Winter, Bettina}, year={2018}, pages={417–434} }","short":"J. Bruns, L. Eichen, in: R. Biehler, T. Lange, T. Leuders, B. Rösken-Winter (Eds.), Mathematikfortbildungen professionalisieren. Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik, Springer, Berlin, 2018, pp. 417–434.","mla":"Bruns, Julia, and Lars Eichen. “EmMa - Fortbildung für elementarpädagogische Fachpersonen zur frühen mathematischen Bildung.” <i>Mathematikfortbildungen professionalisieren. Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik</i>, edited by Rolf Biehler et al., Springer, 2018, pp. 417–34, doi:<a href=\"https://doi.org/10.1007/978-3-658-19028-6_21\">10.1007/978-3-658-19028-6_21</a>.","chicago":"Bruns, Julia, and Lars Eichen. “EmMa - Fortbildung für elementarpädagogische Fachpersonen zur frühen mathematischen Bildung.” In <i>Mathematikfortbildungen professionalisieren. Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik</i>, edited by Rolf Biehler, Thomas Lange, Timo Leuders, and Bettina Rösken-Winter, 417–34. Berlin: Springer, 2018. <a href=\"https://doi.org/10.1007/978-3-658-19028-6_21\">https://doi.org/10.1007/978-3-658-19028-6_21</a>.","ieee":"J. Bruns and L. Eichen, “EmMa - Fortbildung für elementarpädagogische Fachpersonen zur frühen mathematischen Bildung,” in <i>Mathematikfortbildungen professionalisieren. Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik</i>, R. Biehler, T. Lange, T. Leuders, and B. Rösken-Winter, Eds. Berlin: Springer, 2018, pp. 417–434.","ama":"Bruns J, Eichen L. EmMa - Fortbildung für elementarpädagogische Fachpersonen zur frühen mathematischen Bildung. In: Biehler R, Lange T, Leuders T, Rösken-Winter B, eds. <i>Mathematikfortbildungen professionalisieren. Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik</i>. Springer; 2018:417-434. doi:<a href=\"https://doi.org/10.1007/978-3-658-19028-6_21\">10.1007/978-3-658-19028-6_21</a>"},"quality_controlled":"1","publication_status":"published"},{"title":"Methoden empirischer Bildungsforschung im Kontext Frühkindliche Bildung und Entwicklung","main_file_link":[{"open_access":"1","url":"https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2018052917199"}],"oa":"1","date_updated":"2023-06-20T19:17:03Z","date_created":"2023-01-12T15:12:23Z","year":"2018","corporate_editor":["Universität Osnabrück, Center for Early Childhood Development and Education Research (CEDER)"],"citation":{"apa":"Gasteiger, H., Bruns, J., &#38; Universität Osnabrück, Center for Early Childhood Development and Education Research (CEDER) (Eds.). (2018). <i>Methoden empirischer Bildungsforschung im Kontext Frühkindliche Bildung und Entwicklung</i>.","mla":"Gasteiger, Hedwig, et al., editors. <i>Methoden empirischer Bildungsforschung im Kontext Frühkindliche Bildung und Entwicklung</i>. 2018.","bibtex":"@book{Gasteiger_Bruns_Universität Osnabrück, Center for Early Childhood Development and Education Research (CEDER)_2018, title={Methoden empirischer Bildungsforschung im Kontext Frühkindliche Bildung und Entwicklung}, year={2018} }","short":"H. Gasteiger, J. Bruns, Universität Osnabrück, Center for Early Childhood Development and Education Research (CEDER), eds., Methoden empirischer Bildungsforschung im Kontext Frühkindliche Bildung und Entwicklung, 2018.","ieee":"H. Gasteiger, J. Bruns, and Universität Osnabrück, Center for Early Childhood Development and Education Research (CEDER), Eds., <i>Methoden empirischer Bildungsforschung im Kontext Frühkindliche Bildung und Entwicklung</i>. 2018.","chicago":"Gasteiger, Hedwig, Julia Bruns, and Universität Osnabrück, Center for Early Childhood Development and Education Research (CEDER), eds. <i>Methoden empirischer Bildungsforschung im Kontext Frühkindliche Bildung und Entwicklung</i>, 2018.","ama":"Gasteiger H, Bruns J, Universität Osnabrück, Center for Early Childhood Development and Education Research (CEDER), eds. <i>Methoden empirischer Bildungsforschung im Kontext Frühkindliche Bildung und Entwicklung</i>.; 2018."},"publication_status":"published","language":[{"iso":"ger"}],"_id":"36475","department":[{"_id":"611"},{"_id":"97"}],"user_id":"49063","editor":[{"first_name":"Hedwig","last_name":"Gasteiger","full_name":"Gasteiger, Hedwig"},{"first_name":"Julia","last_name":"Bruns","orcid":"https://orcid.org/0000-0002-6604-5864","id":"72183","full_name":"Bruns, Julia"}],"status":"public","type":"book_editor"},{"date_created":"2020-10-06T16:32:45Z","title":"Local intersections of Lagrangian manifolds correspond to catastrophe  theory","year":"2018","external_id":{"arxiv":["1811.10165"]},"ddc":["510"],"language":[{"iso":"eng"}],"publication":"arXiv:1811.10165","abstract":[{"text":"Two smooth map germs are right-equivalent if and only if they generate two\r\nLagrangian submanifolds in a cotangent bundle which have the same contact with\r\nthe zero-section. In this paper we provide a reverse direction to this\r\nclassical result of Golubitsky and Guillemin. Two Lagrangian submanifolds of a\r\nsymplectic manifold have the same contact with a third Lagrangian submanifold\r\nif and only if the intersection problems correspond to stably right equivalent\r\nmap germs. We, therefore, obtain a correspondence between local Lagrangian\r\nintersection problems and catastrophe theory while the classical version only\r\ncaptures tangential intersections. The correspondence is defined independently\r\nof any Lagrangian fibration of the ambient symplectic manifold, in contrast to\r\nother classical results. Moreover, we provide an extension of the\r\ncorrespondence to families of local Lagrangian intersection problems. This\r\ngives rise to a framework which allows a natural transportation of the notions\r\nof catastrophe theory such as stability, unfolding and (uni-)versality to the\r\ngeometric setting such that we obtain a classification of families of local\r\nLagrangian intersection problems. An application is the classification of\r\nLagrangian boundary value problems for symplectic maps.","lang":"eng"}],"file":[{"date_updated":"2021-12-21T16:01:03Z","date_created":"2021-12-21T16:01:03Z","creator":"coffen","file_size":662483,"description":"Two smooth map germs are right-equivalent if and only if they\ngenerate two Lagrangian submanifolds in a cotangent bundle which have the\nsame contact with the zero-section. In this paper we provide a reverse direction\nto this classical result of Golubitsky and Guillemin. Two Lagrangian submanifolds of a symplectic manifold have the same contact with a third Lagrangian\nsubmanifold if and only if the intersection problems correspond to stably right\nequivalent map germs. We, therefore, obtain a correspondence between local\nLagrangian intersection problems and catastrophe theory while the classical\nversion only captures tangential intersections. The correspondence is defined\nindependently of any Lagrangian fibration of the ambient symplectic manifold, in contrast to other classical results. Moreover, we provide an extension\nof the correspondence to families of local Lagrangian intersection problems.\nThis gives rise to a framework which allows a natural transportation of the\nnotions of catastrophe theory such as stability, unfolding and (uni-)versality\nto the geometric setting such that we obtain a classification of families of lo-\ncal Lagrangian intersection problems. An application is the classification of\nLagrangian boundary value problems for symplectic maps.","title":"Local intersections of Lagrangian manifolds correspond to catastrophe theory","file_id":"29078","access_level":"open_access","file_name":"LocalLagrangianContact.pdf","content_type":"application/pdf","relation":"main_file"}],"date_updated":"2023-08-10T08:48:55Z","oa":"1","author":[{"first_name":"Christian","full_name":"Offen, Christian","id":"85279","orcid":"https://orcid.org/0000-0002-5940-8057","last_name":"Offen"}],"publication_status":"submitted","has_accepted_license":"1","citation":{"bibtex":"@article{Offen, title={Local intersections of Lagrangian manifolds correspond to catastrophe  theory}, journal={arXiv:1811.10165}, author={Offen, Christian} }","short":"C. Offen, ArXiv:1811.10165 (n.d.).","mla":"Offen, Christian. “Local Intersections of Lagrangian Manifolds Correspond to Catastrophe  Theory.” <i>ArXiv:1811.10165</i>.","apa":"Offen, C. (n.d.). Local intersections of Lagrangian manifolds correspond to catastrophe  theory. In <i>arXiv:1811.10165</i>.","ama":"Offen C. Local intersections of Lagrangian manifolds correspond to catastrophe  theory. <i>arXiv:181110165</i>.","ieee":"C. Offen, “Local intersections of Lagrangian manifolds correspond to catastrophe  theory,” <i>arXiv:1811.10165</i>. .","chicago":"Offen, Christian. “Local Intersections of Lagrangian Manifolds Correspond to Catastrophe  Theory.” <i>ArXiv:1811.10165</i>, n.d."},"_id":"19940","user_id":"85279","department":[{"_id":"636"}],"file_date_updated":"2021-12-21T16:01:03Z","type":"preprint","status":"public"},{"publication":"New Zealand Journal of Mathematics","file":[{"file_id":"19946","access_level":"open_access","file_name":"Hamiltonian_Boundary_Value_Problems,_Conformal_Symplectic_Symmetries,_and_Conjugate_Loci.pdf","title":"Hamiltonian Boundary Value Problems, Conformal Symplectic Symmetries, and Conjugate Loci","file_size":3126111,"creator":"coffen","date_created":"2020-10-06T16:49:29Z","date_updated":"2020-10-07T14:04:01Z","relation":"main_file","content_type":"application/pdf"}],"abstract":[{"lang":"eng","text":"In this paper we continue our study of bifurcations of solutions of boundary-value problems for symplectic maps arising as Hamiltonian diffeomorphisms. These have been shown to be connected to catastrophe theory via generating functions and ordinary and reversal phase space symmetries have been considered. Here we present a convenient, coordinate free framework to analyse separated Lagrangian boundary value problems which include classical Dirichlet, Neumann and Robin boundary value problems. The framework is then used to prove the existence of obstructions arising from conformal symplectic symmetries on the bifurcation behaviour of solutions to Hamiltonian boundary value problems. Under non-degeneracy conditions, a group action by conformal symplectic symmetries has the effect that the flow map cannot degenerate in a direction which is tangential to the action. This imposes restrictions on which singularities can occur in boundary value problems. Our results generalise classical results about conjugate loci on Riemannian manifolds to a large class of Hamiltonian boundary value problems with, for example, scaling symmetries. "}],"external_id":{"arxiv":["1804.07479"]},"language":[{"iso":"eng"}],"ddc":["510"],"keyword":["Hamiltonian boundary value problems","singularities","conformal symplectic geometry","catastrophe theory","conjugate loci"],"quality_controlled":"1","year":"2018","date_created":"2020-10-06T16:39:08Z","title":"Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci","type":"journal_article","status":"public","user_id":"85279","department":[{"_id":"636"}],"_id":"19943","file_date_updated":"2020-10-07T14:04:01Z","extern":"1","article_type":"original","publication_status":"published","has_accepted_license":"1","citation":{"chicago":"McLachlan, Robert I, and Christian Offen. “Hamiltonian Boundary Value Problems, Conformal Symplectic Symmetries, and Conjugate Loci.” <i>New Zealand Journal of Mathematics</i> 48 (2018): 83–99. <a href=\"https://doi.org/10.53733/34 \">https://doi.org/10.53733/34 </a>.","ieee":"R. I. McLachlan and C. Offen, “Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci,” <i>New Zealand Journal of Mathematics</i>, vol. 48, pp. 83–99, 2018, doi: <a href=\"https://doi.org/10.53733/34 \">10.53733/34 </a>.","ama":"McLachlan RI, Offen C. Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci. <i>New Zealand Journal of Mathematics</i>. 2018;48:83-99. doi:<a href=\"https://doi.org/10.53733/34 \">10.53733/34 </a>","bibtex":"@article{McLachlan_Offen_2018, title={Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci}, volume={48}, DOI={<a href=\"https://doi.org/10.53733/34 \">10.53733/34 </a>}, journal={New Zealand Journal of Mathematics}, author={McLachlan, Robert I and Offen, Christian}, year={2018}, pages={83–99} }","mla":"McLachlan, Robert I., and Christian Offen. “Hamiltonian Boundary Value Problems, Conformal Symplectic Symmetries, and Conjugate Loci.” <i>New Zealand Journal of Mathematics</i>, vol. 48, 2018, pp. 83–99, doi:<a href=\"https://doi.org/10.53733/34 \">10.53733/34 </a>.","short":"R.I. McLachlan, C. Offen, New Zealand Journal of Mathematics 48 (2018) 83–99.","apa":"McLachlan, R. I., &#38; Offen, C. (2018). Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci. <i>New Zealand Journal of Mathematics</i>, <i>48</i>, 83–99. <a href=\"https://doi.org/10.53733/34 \">https://doi.org/10.53733/34 </a>"},"page":"83-99","intvolume":"        48","author":[{"first_name":"Robert I","full_name":"McLachlan, Robert I","last_name":"McLachlan"},{"orcid":"https://orcid.org/0000-0002-5940-8057","last_name":"Offen","id":"85279","full_name":"Offen, Christian","first_name":"Christian"}],"volume":48,"oa":"1","date_updated":"2023-09-21T07:29:24Z","main_file_link":[{"open_access":"1","url":"https://nzjmath.org/index.php/NZJMATH/article/view/34"}],"doi":"10.53733/34 "},{"citation":{"ama":"Fleischmann Y, Kempen L, Mai T, Biehler R. Die online Lernmaterialien von studiVEMINT: Einsatzszenarien im Blended Learning Format in mathematischen Vorkursen. In: Klinger M, Schüler-Meyer A, Wessel L, eds. <i>Hanse-Kolloquium Zur Hochschuldidaktik Der Mathematik</i>. WTM-Verlag; 2018:101–116.","chicago":"Fleischmann, Yael, Leander Kempen, Tobias Mai, and Rolf Biehler. “Die Online Lernmaterialien von StudiVEMINT: Einsatzszenarien Im Blended Learning Format in Mathematischen Vorkursen.” In <i>Hanse-Kolloquium Zur Hochschuldidaktik Der Mathematik</i>, edited by M. Klinger, A. Schüler-Meyer, and L. Wessel, 101–116. Münster: WTM-Verlag, 2018.","ieee":"Y. Fleischmann, L. Kempen, T. Mai, and R. Biehler, “Die online Lernmaterialien von studiVEMINT: Einsatzszenarien im Blended Learning Format in mathematischen Vorkursen,” in <i>Hanse-Kolloquium zur Hochschuldidaktik der Mathematik</i>, 2018, pp. 101–116.","bibtex":"@inproceedings{Fleischmann_Kempen_Mai_Biehler_2018, place={Münster}, title={Die online Lernmaterialien von studiVEMINT: Einsatzszenarien im Blended Learning Format in mathematischen Vorkursen}, booktitle={Hanse-Kolloquium zur Hochschuldidaktik der Mathematik}, publisher={WTM-Verlag}, author={Fleischmann, Yael and Kempen, Leander and Mai, Tobias and Biehler, Rolf}, editor={Klinger, M. and Schüler-Meyer, A. and Wessel, L.}, year={2018}, pages={101–116} }","short":"Y. Fleischmann, L. Kempen, T. Mai, R. Biehler, in: M. Klinger, A. Schüler-Meyer, L. Wessel (Eds.), Hanse-Kolloquium Zur Hochschuldidaktik Der Mathematik, WTM-Verlag, Münster, 2018, pp. 101–116.","mla":"Fleischmann, Yael, et al. “Die Online Lernmaterialien von StudiVEMINT: Einsatzszenarien Im Blended Learning Format in Mathematischen Vorkursen.” <i>Hanse-Kolloquium Zur Hochschuldidaktik Der Mathematik</i>, edited by M. Klinger et al., WTM-Verlag, 2018, pp. 101–116.","apa":"Fleischmann, Y., Kempen, L., Mai, T., &#38; Biehler, R. (2018). Die online Lernmaterialien von studiVEMINT: Einsatzszenarien im Blended Learning Format in mathematischen Vorkursen. In M. Klinger, A. Schüler-Meyer, &#38; L. Wessel (Eds.), <i>Hanse-Kolloquium zur Hochschuldidaktik der Mathematik</i> (pp. 101–116). 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Civic Engagement in Higher Education: A university course in civic statistics for mathematics preservice teachers -  Civic Engagement in Higher Education: A university course in civic statistics for mathematics preservice teachers. <i>Zeitschrift für Hochschulentwicklung</i>. 2018;13(2):169-182. doi:<a href=\"https://doi.org/10.3217/ZFHE-13-02/11\">10.3217/ZFHE-13-02/11</a>","chicago":"Biehler, Rolf, Daniel Frischemeier, and Susanne Podworny. “ Civic Engagement in Higher Education: A University Course in Civic Statistics for Mathematics Preservice Teachers -  Civic Engagement in Higher Education: A University Course in Civic Statistics for Mathematics Preservice Teachers.” <i>Zeitschrift Für Hochschulentwicklung</i> 13, no. 2 (2018): 169–82. <a href=\"https://doi.org/10.3217/ZFHE-13-02/11\">https://doi.org/10.3217/ZFHE-13-02/11</a>.","ieee":"R. Biehler, D. Frischemeier, and S. Podworny, “ Civic Engagement in Higher Education: A university course in civic statistics for mathematics preservice teachers -  Civic Engagement in Higher Education: A university course in civic statistics for mathematics preservice teachers,” <i>Zeitschrift für Hochschulentwicklung</i>, vol. 13, no. 2, pp. 169–182, 2018, doi: <a href=\"https://doi.org/10.3217/ZFHE-13-02/11\">10.3217/ZFHE-13-02/11</a>.","short":"R. Biehler, D. Frischemeier, S. Podworny, Zeitschrift Für Hochschulentwicklung 13 (2018) 169–182.","mla":"Biehler, Rolf, et al. “ Civic Engagement in Higher Education: A University Course in Civic Statistics for Mathematics Preservice Teachers -  Civic Engagement in Higher Education: A University Course in Civic Statistics for Mathematics Preservice Teachers.” <i>Zeitschrift Für Hochschulentwicklung</i>, vol. 13, no. 2, 2018, pp. 169–82, doi:<a href=\"https://doi.org/10.3217/ZFHE-13-02/11\">10.3217/ZFHE-13-02/11</a>.","bibtex":"@article{Biehler_Frischemeier_Podworny_2018, title={ Civic Engagement in Higher Education: A university course in civic statistics for mathematics preservice teachers -  Civic Engagement in Higher Education: A university course in civic statistics for mathematics preservice teachers}, volume={13}, DOI={<a href=\"https://doi.org/10.3217/ZFHE-13-02/11\">10.3217/ZFHE-13-02/11</a>}, number={2}, journal={Zeitschrift für Hochschulentwicklung}, author={Biehler, Rolf and Frischemeier, Daniel and Podworny, Susanne}, year={2018}, pages={169–182} }","apa":"Biehler, R., Frischemeier, D., &#38; Podworny, S. (2018).  Civic Engagement in Higher Education: A university course in civic statistics for mathematics preservice teachers -  Civic Engagement in Higher Education: A university course in civic statistics for mathematics preservice teachers. <i>Zeitschrift Für Hochschulentwicklung</i>, <i>13</i>(2), 169–182. <a href=\"https://doi.org/10.3217/ZFHE-13-02/11\">https://doi.org/10.3217/ZFHE-13-02/11</a>"},"intvolume":"        13","page":"169-182","year":"2018"}]