[{"oa_version":"None","date_published":"2024-01-01T00:00:00Z","year":"2024","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Spin/Pin-structures and real enumerative geometry","day":"01","article_processing_charge":"No","publication_status":"published","date_created":"2025-11-10T08:40:10Z","author":[{"first_name":"Xujia","full_name":"Chen, Xujia","last_name":"Chen","id":"968ad14a-fd86-11ee-a420-ea29715511a3"},{"last_name":"Zinger","first_name":"Aleksey","full_name":"Zinger, Aleksey"}],"type":"book","doi":"10.1142/13476","citation":{"chicago":"Chen, Xujia, and Aleksey Zinger. <i>Spin/Pin-Structures and Real Enumerative Geometry</i>. World Scientific Publishing, 2024. <a href=\"https://doi.org/10.1142/13476\">https://doi.org/10.1142/13476</a>.","short":"X. Chen, A. Zinger, Spin/Pin-Structures and Real Enumerative Geometry, World Scientific Publishing, 2024.","mla":"Chen, Xujia, and Aleksey Zinger. <i>Spin/Pin-Structures and Real Enumerative Geometry</i>. World Scientific Publishing, 2024, doi:<a href=\"https://doi.org/10.1142/13476\">10.1142/13476</a>.","ieee":"X. Chen and A. Zinger, <i>Spin/Pin-structures and real enumerative geometry</i>. World Scientific Publishing, 2024.","apa":"Chen, X., &#38; Zinger, A. (2024). <i>Spin/Pin-structures and real enumerative geometry</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/13476\">https://doi.org/10.1142/13476</a>","ama":"Chen X, Zinger A. <i>Spin/Pin-Structures and Real Enumerative Geometry</i>. World Scientific Publishing; 2024. doi:<a href=\"https://doi.org/10.1142/13476\">10.1142/13476</a>","ista":"Chen X, Zinger A. 2024. Spin/Pin-structures and real enumerative geometry, World Scientific Publishing,p."},"quality_controlled":"1","date_updated":"2025-11-10T15:28:49Z","extern":"1","publication_identifier":{"eisbn":["9789811278556"],"isbn":["9789811278532"]},"_id":"20615","month":"01","OA_type":"closed access","status":"public","scopus_import":"1","abstract":[{"text":"Spin/Pin-structures on vector bundles have long featured prominently in differential geometry, in particular providing part of the foundation for the original proof of the renowned Atiyah–Singer Index Theory. More recently, they have underpinned the symplectic topology foundations of the so-called real sector of the mirror symmetry of string theory.\r\n\r\nThis semi-expository three-part monograph provides an accessible introduction to Spin- and Pin-structures in general, demonstrates their role in the orientability considerations in symplectic topology, and presents their applications in enumerative geometry.\r\n\r\nPart I contains a systematic treatment of Spin/Pin-structures from different topological perspectives and may be suitable for an advanced undergraduate reading seminar. This leads to Part II, which systematically studies orientability problems for the determinants of real Cauchy–Riemann operators on vector bundles. Part III introduces enumerative geometry of curves in complex projective varieties and in symplectic manifolds, demonstrating some applications of the first two parts in the process. Two appendices review the Čech cohomology perspective on fiber bundles and Lie group covering spaces.","lang":"eng"}],"language":[{"iso":"eng"}],"publisher":"World Scientific Publishing"},{"_id":"20624","month":"05","extern":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2305.08811","open_access":"1"}],"citation":{"ama":"Chen X, Zinger A. Blowdowns of the Deligne-Mumford spaces of real rational curves. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/ARXIV.2305.08811\">10.48550/ARXIV.2305.08811</a>","apa":"Chen, X., &#38; Zinger, A. (n.d.). Blowdowns of the Deligne-Mumford spaces of real rational curves. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2305.08811\">https://doi.org/10.48550/ARXIV.2305.08811</a>","ista":"Chen X, Zinger A. Blowdowns of the Deligne-Mumford spaces of real rational curves. arXiv, 2305.08811.","short":"X. Chen, A. Zinger, ArXiv (n.d.).","chicago":"Chen, Xujia, and Aleksey Zinger. “Blowdowns of the Deligne-Mumford Spaces of Real Rational Curves.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/ARXIV.2305.08811\">https://doi.org/10.48550/ARXIV.2305.08811</a>.","ieee":"X. Chen and A. Zinger, “Blowdowns of the Deligne-Mumford spaces of real rational curves,” <i>arXiv</i>. .","mla":"Chen, Xujia, and Aleksey Zinger. “Blowdowns of the Deligne-Mumford Spaces of Real Rational Curves.” <i>ArXiv</i>, 2305.08811, doi:<a href=\"https://doi.org/10.48550/ARXIV.2305.08811\">10.48550/ARXIV.2305.08811</a>."},"date_updated":"2025-11-10T15:06:21Z","OA_place":"repository","language":[{"iso":"eng"}],"oa":1,"publication":"arXiv","abstract":[{"text":"We describe a sequence of smooth quotients of the Deligne-Mumford moduli space ${\\mathbb R}\\overline{\\mathcal M}_{0,\\ell+1}$ of real rational curves with $\\ell\\!+\\!1$ conjugate pairs of marked points that terminates at ${\\mathbb R}\\overline{\\mathcal M}_{0,\\ell}\\!\\times\\!{\\mathbb C}{\\mathbb P}^1$. This produces an analogue of Keel's blowup construction of the Deligne-Mumford moduli spaces $\\overline{\\mathcal M}_{\\ell+1}$ of rational curves with $\\ell\\!+\\!1$ marked points, but with an explicit description of the intermediate spaces and the blowups of three different types. The same framework readily adapts to the real moduli spaces with real points. In a sequel, we use this inductive construction of ${\\mathbb R}\\overline{\\mathcal M}_{0,\\ell+1}$ to completely determine the rational (co)homology ring of ${\\mathbb R}\\overline{\\mathcal M}_{0,\\ell}$.","lang":"eng"}],"arxiv":1,"status":"public","OA_type":"green","title":"Blowdowns of the Deligne-Mumford spaces of real rational curves","article_processing_charge":"No","day":"15","oa_version":"Preprint","date_published":"2023-05-15T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2023","external_id":{"arxiv":["2305.08811"]},"doi":"10.48550/ARXIV.2305.08811","article_number":"2305.08811","type":"preprint","author":[{"id":"968ad14a-fd86-11ee-a420-ea29715511a3","first_name":"Xujia","full_name":"Chen, Xujia","last_name":"Chen"},{"first_name":"Aleksey","full_name":"Zinger, Aleksey","last_name":"Zinger"}],"publication_status":"submitted","date_created":"2025-11-10T08:45:42Z"},{"day":"15","article_processing_charge":"No","title":"The cohomology ring of the Deligne-Mumford moduli space of real rational curves with conjugate marked points","year":"2023","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2023-05-15T00:00:00Z","oa_version":"Preprint","doi":"10.48550/ARXIV.2305.08798","article_number":"2305.08798","external_id":{"arxiv":["2305.08798"]},"publication_status":"submitted","date_created":"2025-11-10T08:46:11Z","type":"preprint","author":[{"id":"968ad14a-fd86-11ee-a420-ea29715511a3","last_name":"Chen","first_name":"Xujia","full_name":"Chen, Xujia"},{"last_name":"Georgieva","full_name":"Georgieva, Penka","first_name":"Penka"},{"last_name":"Zinger","full_name":"Zinger, Aleksey","first_name":"Aleksey"}],"month":"05","_id":"20625","date_updated":"2025-11-10T15:05:04Z","citation":{"ieee":"X. Chen, P. Georgieva, and A. Zinger, “The cohomology ring of the Deligne-Mumford moduli space of real rational curves with conjugate marked points,” <i>arXiv</i>. .","mla":"Chen, Xujia, et al. “The Cohomology Ring of the Deligne-Mumford Moduli Space of Real Rational Curves with Conjugate Marked Points.” <i>ArXiv</i>, 2305.08798, doi:<a href=\"https://doi.org/10.48550/ARXIV.2305.08798\">10.48550/ARXIV.2305.08798</a>.","short":"X. Chen, P. Georgieva, A. Zinger, ArXiv (n.d.).","chicago":"Chen, Xujia, Penka Georgieva, and Aleksey Zinger. “The Cohomology Ring of the Deligne-Mumford Moduli Space of Real Rational Curves with Conjugate Marked Points.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/ARXIV.2305.08798\">https://doi.org/10.48550/ARXIV.2305.08798</a>.","ista":"Chen X, Georgieva P, Zinger A. The cohomology ring of the Deligne-Mumford moduli space of real rational curves with conjugate marked points. arXiv, 2305.08798.","ama":"Chen X, Georgieva P, Zinger A. The cohomology ring of the Deligne-Mumford moduli space of real rational curves with conjugate marked points. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/ARXIV.2305.08798\">10.48550/ARXIV.2305.08798</a>","apa":"Chen, X., Georgieva, P., &#38; Zinger, A. (n.d.). The cohomology ring of the Deligne-Mumford moduli space of real rational curves with conjugate marked points. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2305.08798\">https://doi.org/10.48550/ARXIV.2305.08798</a>"},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2305.08798"}],"extern":"1","publication":"arXiv","abstract":[{"text":"It is a long-established and heavily-used fact that the integral cohomology ring of the Deligne-Mumford moduli space of (complex) rational curves is the polynomial ring on the boundary divisors modulo the ideal generated by the obvious geometric relations between them. We show that the rational cohomology ring of the Deligne-Mumford moduli space of real rational curves with conjugate marked points only is the polynomial ring on certain (``complex\") boundary divisors and real boundary hypersurfaces modulo the ideal generated by the obvious geometric relations between them and the geometric relation in positive dimension and codimension identified in a previous paper.","lang":"eng"}],"language":[{"iso":"eng"}],"OA_place":"repository","oa":1,"OA_type":"green","status":"public","arxiv":1},{"extern":"1","date_updated":"2025-11-10T15:00:28Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2302.03021","open_access":"1"}],"citation":{"ama":"Chen X. Kontsevich’s characteristic classes as topological invariants of configuration space bundles. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/ARXIV.2302.03021\">10.48550/ARXIV.2302.03021</a>","apa":"Chen, X. (n.d.). Kontsevich’s characteristic classes as topological invariants of configuration space bundles. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2302.03021\">https://doi.org/10.48550/ARXIV.2302.03021</a>","ista":"Chen X. Kontsevich’s characteristic classes as topological invariants of configuration space bundles. arXiv, 2302.03021.","short":"X. Chen, ArXiv (n.d.).","chicago":"Chen, Xujia. “Kontsevich’s Characteristic Classes as Topological Invariants of Configuration Space Bundles.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/ARXIV.2302.03021\">https://doi.org/10.48550/ARXIV.2302.03021</a>.","ieee":"X. Chen, “Kontsevich’s characteristic classes as topological invariants of configuration space bundles,” <i>arXiv</i>. .","mla":"Chen, Xujia. “Kontsevich’s Characteristic Classes as Topological Invariants of Configuration Space Bundles.” <i>ArXiv</i>, 2302.03021, doi:<a href=\"https://doi.org/10.48550/ARXIV.2302.03021\">10.48550/ARXIV.2302.03021</a>."},"month":"02","_id":"20626","status":"public","OA_type":"green","arxiv":1,"oa":1,"OA_place":"repository","language":[{"iso":"eng"}],"publication":"arXiv","abstract":[{"lang":"eng","text":"Kontsevich's characteristic classes are invariants of framed smooth fiber bundles with homology sphere fibers. It was shown by Watanabe that they can be used to distinguish smooth $S^4$-bundles that are all trivial as topological fiber bundles. In this article we show that this ability of Kontsevich's classes is a manifestation of the following principle: the ``real blow-up'' construction on a smooth manifold essentially depends on its smooth structure and thus, given a smooth manifold (or smooth fiber bundle) $M$, the topological invariants of spaces constructed from $M$ by real blow-ups could potentially differentiate smooth structures on $M$. The main theorem says that Kontsevich's characteristic classes of a smooth framed bundle $π$ are determined by the topology of the 2-point configuration space bundle of $π$ and framing data."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2023","oa_version":"Preprint","date_published":"2023-02-06T00:00:00Z","article_processing_charge":"No","day":"06","title":"Kontsevich's characteristic classes as topological invariants of configuration space bundles","type":"preprint","author":[{"last_name":"Chen","first_name":"Xujia","full_name":"Chen, Xujia","id":"968ad14a-fd86-11ee-a420-ea29715511a3"}],"date_created":"2025-11-10T08:46:37Z","publication_status":"submitted","external_id":{"arxiv":["2302.03021"]},"article_number":"2302.03021","doi":"10.48550/ARXIV.2302.03021"},{"type":"journal_article","date_created":"2025-11-10T08:40:40Z","publication_status":"published","doi":"10.1007/s00039-022-00596-6","article_type":"original","day":"15","OA_type":"green","oa":1,"language":[{"iso":"eng"}],"abstract":[{"text":"We establish two WDVV-style relations for the disk invariants of real symplectic fourfolds by implementing Georgieva’s suggestion to lift homology relations from the Deligne–Mumford moduli spaces of stable real curves. This is accomplished by lifting judiciously chosen cobordisms realizing these relations. The resulting lifted relations lead to the recursions for Welschinger invariants announced by Solomon in 2007 and have the same structure as his WDVV-style relations, but differ by signs from the latter. Our topological approach provides a general framework for lifting relations via morphisms between not necessarily orientable spaces.","lang":"eng"}],"extern":"1","citation":{"ama":"Chen X. Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger invariants. <i>Geometric and Functional Analysis</i>. 2022;32(3):490-567. doi:<a href=\"https://doi.org/10.1007/s00039-022-00596-6\">10.1007/s00039-022-00596-6</a>","apa":"Chen, X. (2022). Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger invariants. <i>Geometric and Functional Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00039-022-00596-6\">https://doi.org/10.1007/s00039-022-00596-6</a>","ista":"Chen X. 2022. Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger invariants. Geometric and Functional Analysis. 32(3), 490–567.","short":"X. Chen, Geometric and Functional Analysis 32 (2022) 490–567.","chicago":"Chen, Xujia. “Steenrod Pseudocycles, Lifted Cobordisms, and Solomon’s Relations for Welschinger Invariants.” <i>Geometric and Functional Analysis</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00039-022-00596-6\">https://doi.org/10.1007/s00039-022-00596-6</a>.","ieee":"X. Chen, “Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger invariants,” <i>Geometric and Functional Analysis</i>, vol. 32, no. 3. Springer Nature, pp. 490–567, 2022.","mla":"Chen, Xujia. “Steenrod Pseudocycles, Lifted Cobordisms, and Solomon’s Relations for Welschinger Invariants.” <i>Geometric and Functional Analysis</i>, vol. 32, no. 3, Springer Nature, 2022, pp. 490–567, doi:<a href=\"https://doi.org/10.1007/s00039-022-00596-6\">10.1007/s00039-022-00596-6</a>."},"date_updated":"2025-11-10T15:18:07Z","quality_controlled":"1","_id":"20616","issue":"3","author":[{"id":"968ad14a-fd86-11ee-a420-ea29715511a3","last_name":"Chen","full_name":"Chen, Xujia","first_name":"Xujia"}],"external_id":{"arxiv":["1809.08919"]},"date_published":"2022-04-15T00:00:00Z","volume":32,"oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"490-567","year":"2022","title":"Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger invariants","article_processing_charge":"No","arxiv":1,"status":"public","OA_place":"repository","publication":"Geometric and Functional Analysis","publisher":"Springer Nature","publication_identifier":{"issn":["1016-443X"],"eissn":["1420-8970"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1809.08919"}],"intvolume":"        32","month":"04"},{"author":[{"full_name":"Chen, Xujia","first_name":"Xujia","last_name":"Chen","id":"968ad14a-fd86-11ee-a420-ea29715511a3"}],"external_id":{"arxiv":["1912.05437"]},"date_published":"2022-05-01T00:00:00Z","oa_version":"Preprint","volume":2022,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2022","page":"7021-7055","title":"Solomon-Tukachinsky’s versus Welschinger’s open Gromov-Witten invariants of symplectic six-folds","article_processing_charge":"No","arxiv":1,"status":"public","OA_place":"repository","publication":"International Mathematics Research Notices","publisher":"Oxford University Press","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1912.05437","open_access":"1"}],"intvolume":"      2022","month":"05","type":"journal_article","publication_status":"published","date_created":"2025-11-10T08:40:57Z","doi":"10.1093/imrn/rnaa318","article_type":"original","day":"01","scopus_import":"1","OA_type":"green","language":[{"iso":"eng"}],"oa":1,"abstract":[{"lang":"eng","text":"Our previous paper describes a geometric translation of the construction of open Gromov–Witten invariants by Solomon and Tukachinsky from a perspective of $A_{\\infty }$-algebras of differential forms. We now use this geometric perspective to show that these invariants reduce to Welschinger’s open Gromov–Witten invariants in dimension 6, inline with their and Tian’s expectations. As an immediate corollary, we obtain a translation of Solomon–Tukachinsky’s open WDVV equations into relations for Welschinger’s invariants."}],"extern":"1","citation":{"ama":"Chen X. Solomon-Tukachinsky’s versus Welschinger’s open Gromov-Witten invariants of symplectic six-folds. <i>International Mathematics Research Notices</i>. 2022;2022(9):7021-7055. doi:<a href=\"https://doi.org/10.1093/imrn/rnaa318\">10.1093/imrn/rnaa318</a>","apa":"Chen, X. (2022). Solomon-Tukachinsky’s versus Welschinger’s open Gromov-Witten invariants of symplectic six-folds. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnaa318\">https://doi.org/10.1093/imrn/rnaa318</a>","ista":"Chen X. 2022. Solomon-Tukachinsky’s versus Welschinger’s open Gromov-Witten invariants of symplectic six-folds. International Mathematics Research Notices. 2022(9), 7021–7055.","short":"X. Chen, International Mathematics Research Notices 2022 (2022) 7021–7055.","chicago":"Chen, Xujia. “Solomon-Tukachinsky’s versus Welschinger’s Open Gromov-Witten Invariants of Symplectic Six-Folds.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2022. <a href=\"https://doi.org/10.1093/imrn/rnaa318\">https://doi.org/10.1093/imrn/rnaa318</a>.","ieee":"X. Chen, “Solomon-Tukachinsky’s versus Welschinger’s open Gromov-Witten invariants of symplectic six-folds,” <i>International Mathematics Research Notices</i>, vol. 2022, no. 9. Oxford University Press, pp. 7021–7055, 2022.","mla":"Chen, Xujia. “Solomon-Tukachinsky’s versus Welschinger’s Open Gromov-Witten Invariants of Symplectic Six-Folds.” <i>International Mathematics Research Notices</i>, vol. 2022, no. 9, Oxford University Press, 2022, pp. 7021–55, doi:<a href=\"https://doi.org/10.1093/imrn/rnaa318\">10.1093/imrn/rnaa318</a>."},"quality_controlled":"1","date_updated":"2025-11-10T14:57:33Z","_id":"20617","issue":"9"},{"publisher":"Springer Nature","OA_place":"repository","publication":"Peking Mathematical Journal ","status":"public","arxiv":1,"month":"09","intvolume":"         5","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1912.04119"}],"external_id":{"arxiv":["1912.04119"]},"author":[{"full_name":"Chen, Xujia","first_name":"Xujia","last_name":"Chen","id":"968ad14a-fd86-11ee-a420-ea29715511a3"}],"article_processing_charge":"No","title":"A geometric depiction of Solomon-Tukachinsky's construction of open GW-invariants","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2022","page":"279-348","oa_version":"Submitted Version","volume":5,"date_published":"2022-09-01T00:00:00Z","language":[{"iso":"eng"}],"oa":1,"abstract":[{"text":"The 2016 papers of J. Solomon and S. Tukachinsky use bounding chains in Fukaya's $A_{\\infty}$-algebras to define numerical disk counts relative to a Lagrangian under certain regularity assumptions on the moduli spaces of disks. We present a (self-contained) direct geometric analogue of their construction under weaker topological assumptions, extend it over arbitrary rings in the process, and sketch an extension without any assumptions over rings containing the rationals. This implements the intuitive suggestion represented by their drawing and P. Georgieva's perspective. We also note a curious relation for the standard Gromov-Witten invariants readily deducible from their work. In a sequel, we use the geometric perspective of this paper to relate Solomon-Tukachinsky's invariants to Welschinger's open invariants of symplectic sixfolds, confirming their belief and G. Tian's related expectation concerning K. Fukaya's earlier construction.","lang":"eng"}],"scopus_import":"1","OA_type":"green","_id":"20620","extern":"1","date_updated":"2025-11-10T13:51:17Z","citation":{"mla":"Chen, Xujia. “A Geometric Depiction of Solomon-Tukachinsky’s Construction of Open GW-Invariants.” <i>Peking Mathematical Journal </i>, vol. 5, Springer Nature, 2022, pp. 279–348, doi:<a href=\"https://doi.org/10.1007/s42543-021-00044-8\">10.1007/s42543-021-00044-8</a>.","ieee":"X. Chen, “A geometric depiction of Solomon-Tukachinsky’s construction of open GW-invariants,” <i>Peking Mathematical Journal </i>, vol. 5. Springer Nature, pp. 279–348, 2022.","chicago":"Chen, Xujia. “A Geometric Depiction of Solomon-Tukachinsky’s Construction of Open GW-Invariants.” <i>Peking Mathematical Journal </i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s42543-021-00044-8\">https://doi.org/10.1007/s42543-021-00044-8</a>.","short":"X. Chen, Peking Mathematical Journal  5 (2022) 279–348.","ista":"Chen X. 2022. A geometric depiction of Solomon-Tukachinsky’s construction of open GW-invariants. Peking Mathematical Journal . 5, 279–348.","apa":"Chen, X. (2022). A geometric depiction of Solomon-Tukachinsky’s construction of open GW-invariants. <i>Peking Mathematical Journal </i>. Springer Nature. <a href=\"https://doi.org/10.1007/s42543-021-00044-8\">https://doi.org/10.1007/s42543-021-00044-8</a>","ama":"Chen X. A geometric depiction of Solomon-Tukachinsky’s construction of open GW-invariants. <i>Peking Mathematical Journal </i>. 2022;5:279-348. doi:<a href=\"https://doi.org/10.1007/s42543-021-00044-8\">10.1007/s42543-021-00044-8</a>"},"quality_controlled":"1","doi":"10.1007/s42543-021-00044-8","type":"journal_article","publication_status":"published","date_created":"2025-11-10T08:43:20Z","day":"01","article_type":"original"},{"year":"2022","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2022-11-09T00:00:00Z","oa_version":"None","day":"09","article_processing_charge":"No","title":"Research on two-wheeled balance car based on improved LQR controller","date_created":"2025-11-10T08:52:47Z","conference":{"name":"IAEAC: Advanced Information Technology, Electronic and Automation Control Conference","start_date":"2022-10-03","end_date":"2022-10-05","location":"Beijing, China"},"acknowledgement":"This work was supported by the Nanchong City School-Science and Technology Strategic Cooperation Project: Research on autonomous navigation technology of mobile robot based on visual SLAM in indoor environment(SXQHJH025); Key technologies for safety inspection of intelligent vehicles in oil and gas chemical production workshops research and design (19SXHZ0022).","publication_status":"published","type":"conference","author":[{"last_name":"Yuan","full_name":"Yuan, Jiemin","first_name":"Jiemin"},{"full_name":"Chen, Haiyun","first_name":"Haiyun","last_name":"Chen"},{"last_name":"Yong","full_name":"Yong, Tao","first_name":"Tao"},{"last_name":"Lai","first_name":"Xi","full_name":"Lai, Xi"},{"last_name":"Chen","first_name":"Xujia","full_name":"Chen, Xujia","id":"968ad14a-fd86-11ee-a420-ea29715511a3"}],"doi":"10.1109/iaeac54830.2022.9930026","citation":{"mla":"Yuan, Jiemin, et al. “Research on Two-Wheeled Balance Car Based on Improved LQR Controller.” <i>6th Advanced Information Technology, Electronic and Automation Control Conference</i>, IEEE, 2022, doi:<a href=\"https://doi.org/10.1109/iaeac54830.2022.9930026\">10.1109/iaeac54830.2022.9930026</a>.","ieee":"J. Yuan, H. Chen, T. Yong, X. Lai, and X. Chen, “Research on two-wheeled balance car based on improved LQR controller,” in <i>6th Advanced Information Technology, Electronic and Automation Control Conference</i>, Beijing, China, 2022.","chicago":"Yuan, Jiemin, Haiyun Chen, Tao Yong, Xi Lai, and Xujia Chen. “Research on Two-Wheeled Balance Car Based on Improved LQR Controller.” In <i>6th Advanced Information Technology, Electronic and Automation Control Conference</i>. IEEE, 2022. <a href=\"https://doi.org/10.1109/iaeac54830.2022.9930026\">https://doi.org/10.1109/iaeac54830.2022.9930026</a>.","short":"J. Yuan, H. Chen, T. Yong, X. Lai, X. Chen, in:, 6th Advanced Information Technology, Electronic and Automation Control Conference, IEEE, 2022.","ista":"Yuan J, Chen H, Yong T, Lai X, Chen X. 2022. Research on two-wheeled balance car based on improved LQR controller. 6th Advanced Information Technology, Electronic and Automation Control Conference. IAEAC: Advanced Information Technology, Electronic and Automation Control Conference.","apa":"Yuan, J., Chen, H., Yong, T., Lai, X., &#38; Chen, X. (2022). Research on two-wheeled balance car based on improved LQR controller. In <i>6th Advanced Information Technology, Electronic and Automation Control Conference</i>. Beijing, China: IEEE. <a href=\"https://doi.org/10.1109/iaeac54830.2022.9930026\">https://doi.org/10.1109/iaeac54830.2022.9930026</a>","ama":"Yuan J, Chen H, Yong T, Lai X, Chen X. Research on two-wheeled balance car based on improved LQR controller. In: <i>6th Advanced Information Technology, Electronic and Automation Control Conference</i>. IEEE; 2022. doi:<a href=\"https://doi.org/10.1109/iaeac54830.2022.9930026\">10.1109/iaeac54830.2022.9930026</a>"},"date_updated":"2025-11-10T14:53:37Z","quality_controlled":"1","publication_identifier":{"eisbn":["9781665458641"]},"extern":"1","month":"11","_id":"20627","status":"public","scopus_import":"1","publisher":"IEEE","publication":"6th Advanced Information Technology, Electronic and Automation Control Conference","abstract":[{"text":"The modern control model of the two-wheeled balancing vehicle is established by rational simplification and linearization and selection of appropriate state space variables. The state space expressions in modern control theory are used to make up for some deficiencies in the classical inverted pendulum model. By constructing the mathematical model of the LQR controller in MATLAB, using Simulink for model design and theoretical simulation analysis according to the actual application scenario, the results show that the improved LQR controller can be used in the autonomous balance control and anti-external interference of the two-wheeled self-balancing vehicle model. Has excellent performance.","lang":"eng"}],"language":[{"iso":"eng"}]},{"doi":"10.1007/s00208-020-02130-1","date_created":"2025-11-10T08:41:40Z","publication_status":"published","type":"journal_article","day":"25","article_type":"original","abstract":[{"lang":"eng","text":"The first author’s previous work established Solomon’s WDVV-type relations for Welschinger’s invariant curve counts in real symplectic fourfolds by lifting geometric relations over possibly unorientable morphisms. We apply her framework to obtain WDVV-style relations for the disk invariants of real symplectic sixfolds with some symmetry, in particular confirming Alcolado’s prediction for P^3 and extending it to other spaces. These relations reduce the computation of Welschinger’s invariants of many real symplectic sixfolds to invariants in small degrees and provide lower bounds for counts of real rational curves with positive-dimensional insertions in some cases. In the case of P^3, our lower bounds fit perfectly with Kollár’s vanishing results."}],"language":[{"iso":"eng"}],"oa":1,"OA_type":"green","scopus_import":"1","_id":"20619","issue":"3-4","quality_controlled":"1","citation":{"short":"X. Chen, A. Zinger, Mathematische Annalen 379 (2021) 1231–1313.","chicago":"Chen, Xujia, and Aleksey Zinger. “WDVV-Type Relations for Disk Gromov–Witten Invariants in Dimension 6.” <i>Mathematische Annalen</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00208-020-02130-1\">https://doi.org/10.1007/s00208-020-02130-1</a>.","ieee":"X. Chen and A. Zinger, “WDVV-type relations for disk Gromov–Witten invariants in dimension 6,” <i>Mathematische Annalen</i>, vol. 379, no. 3–4. Springer Nature, pp. 1231–1313, 2021.","mla":"Chen, Xujia, and Aleksey Zinger. “WDVV-Type Relations for Disk Gromov–Witten Invariants in Dimension 6.” <i>Mathematische Annalen</i>, vol. 379, no. 3–4, Springer Nature, 2021, pp. 1231–313, doi:<a href=\"https://doi.org/10.1007/s00208-020-02130-1\">10.1007/s00208-020-02130-1</a>.","ama":"Chen X, Zinger A. WDVV-type relations for disk Gromov–Witten invariants in dimension 6. <i>Mathematische Annalen</i>. 2021;379(3-4):1231-1313. doi:<a href=\"https://doi.org/10.1007/s00208-020-02130-1\">10.1007/s00208-020-02130-1</a>","apa":"Chen, X., &#38; Zinger, A. (2021). WDVV-type relations for disk Gromov–Witten invariants in dimension 6. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-020-02130-1\">https://doi.org/10.1007/s00208-020-02130-1</a>","ista":"Chen X, Zinger A. 2021. WDVV-type relations for disk Gromov–Witten invariants in dimension 6. Mathematische Annalen. 379(3–4), 1231–1313."},"date_updated":"2025-11-10T15:11:29Z","extern":"1","external_id":{"arxiv":["1904.04254"]},"author":[{"id":"968ad14a-fd86-11ee-a420-ea29715511a3","last_name":"Chen","full_name":"Chen, Xujia","first_name":"Xujia"},{"first_name":"Aleksey","full_name":"Zinger, Aleksey","last_name":"Zinger"}],"article_processing_charge":"No","title":"WDVV-type relations for disk Gromov–Witten invariants in dimension 6","page":"1231-1313","year":"2021","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","volume":379,"date_published":"2021-01-25T00:00:00Z","publisher":"Springer Nature","publication":"Mathematische Annalen","OA_place":"repository","status":"public","arxiv":1,"month":"01","intvolume":"       379","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1904.04254","open_access":"1"}],"publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]}},{"day":"01","date_created":"2025-11-10T08:45:12Z","publication_status":"submitted","type":"journal_article","doi":"10.1215/21562261-2021-0005","citation":{"chicago":"Chen, Xujia, and Aleksey Zinger. “WDVV-Type Relations for Welschinger’s Invariants: Applications.” <i>Kyoto Journal of Mathematics</i>. Duke University Press, n.d. <a href=\"https://doi.org/10.1215/21562261-2021-0005\">https://doi.org/10.1215/21562261-2021-0005</a>.","short":"X. Chen, A. Zinger, Kyoto Journal of Mathematics 61 (n.d.) 339–376.","mla":"Chen, Xujia, and Aleksey Zinger. “WDVV-Type Relations for Welschinger’s Invariants: Applications.” <i>Kyoto Journal of Mathematics</i>, vol. 61, no. 2, Duke University Press, pp. 339–76, doi:<a href=\"https://doi.org/10.1215/21562261-2021-0005\">10.1215/21562261-2021-0005</a>.","ieee":"X. Chen and A. Zinger, “WDVV-type relations for Welschinger’s invariants: Applications,” <i>Kyoto Journal of Mathematics</i>, vol. 61, no. 2. Duke University Press, pp. 339–376.","apa":"Chen, X., &#38; Zinger, A. (n.d.). WDVV-type relations for Welschinger’s invariants: Applications. <i>Kyoto Journal of Mathematics</i>. Duke University Press. <a href=\"https://doi.org/10.1215/21562261-2021-0005\">https://doi.org/10.1215/21562261-2021-0005</a>","ama":"Chen X, Zinger A. WDVV-type relations for Welschinger’s invariants: Applications. <i>Kyoto Journal of Mathematics</i>. 61(2):339-376. doi:<a href=\"https://doi.org/10.1215/21562261-2021-0005\">10.1215/21562261-2021-0005</a>","ista":"Chen X, Zinger A. WDVV-type relations for Welschinger’s invariants: Applications. Kyoto Journal of Mathematics. 61(2), 339–376."},"quality_controlled":"1","date_updated":"2025-11-10T15:13:58Z","extern":"1","issue":"2","_id":"20622","OA_type":"green","abstract":[{"text":"We first recall Solomon’s relations for Welschinger invariants counting real curves in real symplectic fourfolds and the Witten–Dijkgraaf–Verlinde–Verlinde (WDVV)-style relations for Welschinger invariants counting real curves in real symplectic sixfolds with some symmetry. We then explicitly demonstrate that, in some important cases (projective spaces with standard conjugations, real blowups of the projective plane, and two- and threefold products of the one-dimensional projective space with two involutions each), these relations provide complete recursions determining all Welschinger invariants from basic input. We include extensive tables of Welschinger invariants in low degrees obtained from these recursions with Mathematica. These invariants provide lower bounds for counts of real rational curves, including with curve insertions in smooth algebraic threefolds.","lang":"eng"}],"oa":1,"language":[{"iso":"eng"}],"date_published":"2021-06-01T00:00:00Z","oa_version":"Preprint","volume":61,"page":"339-376","year":"2021","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"WDVV-type relations for Welschinger's invariants: Applications","article_processing_charge":"No","author":[{"id":"968ad14a-fd86-11ee-a420-ea29715511a3","first_name":"Xujia","full_name":"Chen, Xujia","last_name":"Chen"},{"full_name":"Zinger, Aleksey","first_name":"Aleksey","last_name":"Zinger"}],"external_id":{"arxiv":["1809.08938"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1809.08938","open_access":"1"}],"publication_identifier":{"eissn":["2154-3321"]},"intvolume":"        61","month":"06","arxiv":1,"status":"public","publication":"Kyoto Journal of Mathematics","OA_place":"repository","publisher":"Duke University Press"}]