---
OA_type: closed access
_id: '20615'
abstract:
- lang: eng
  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."
article_processing_charge: No
author:
- first_name: Xujia
  full_name: Chen, Xujia
  id: 968ad14a-fd86-11ee-a420-ea29715511a3
  last_name: Chen
- first_name: Aleksey
  full_name: Zinger, Aleksey
  last_name: Zinger
citation:
  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>
  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>
  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>.
  ieee: X. Chen and A. Zinger, <i>Spin/Pin-structures and real enumerative geometry</i>.
    World Scientific Publishing, 2024.
  ista: Chen X, Zinger A. 2024. Spin/Pin-structures and real enumerative geometry,
    World Scientific Publishing,p.
  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>.
  short: X. Chen, A. Zinger, Spin/Pin-Structures and Real Enumerative Geometry, World
    Scientific Publishing, 2024.
date_created: 2025-11-10T08:40:10Z
date_published: 2024-01-01T00:00:00Z
date_updated: 2025-11-10T15:28:49Z
day: '01'
doi: 10.1142/13476
extern: '1'
language:
- iso: eng
month: '01'
oa_version: None
publication_identifier:
  eisbn:
  - '9789811278556'
  isbn:
  - '9789811278532'
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Spin/Pin-structures and real enumerative geometry
type: book
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '20624'
abstract:
- lang: eng
  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 ${\mathbb R}\overline{\mathcal
    M}_{0,\ell}$.
article_number: '2305.08811'
article_processing_charge: No
arxiv: 1
author:
- first_name: Xujia
  full_name: Chen, Xujia
  id: 968ad14a-fd86-11ee-a420-ea29715511a3
  last_name: Chen
- first_name: Aleksey
  full_name: Zinger, Aleksey
  last_name: Zinger
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>
  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>. .
  ista: Chen X, Zinger A. Blowdowns of the Deligne-Mumford spaces of real rational
    curves. arXiv, 2305.08811.
  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>.
  short: X. Chen, A. Zinger, ArXiv (n.d.).
date_created: 2025-11-10T08:45:42Z
date_published: 2023-05-15T00:00:00Z
date_updated: 2025-11-10T15:06:21Z
day: '15'
doi: 10.48550/ARXIV.2305.08811
extern: '1'
external_id:
  arxiv:
  - '2305.08811'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2305.08811
month: '05'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
status: public
title: Blowdowns of the Deligne-Mumford spaces of real rational curves
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
OA_place: repository
OA_type: green
_id: '20625'
abstract:
- lang: eng
  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.
article_number: '2305.08798'
article_processing_charge: No
arxiv: 1
author:
- first_name: Xujia
  full_name: Chen, Xujia
  id: 968ad14a-fd86-11ee-a420-ea29715511a3
  last_name: Chen
- first_name: Penka
  full_name: Georgieva, Penka
  last_name: Georgieva
- first_name: Aleksey
  full_name: Zinger, Aleksey
  last_name: Zinger
citation:
  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>
  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>.
  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>.
    .
  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.
  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.).
date_created: 2025-11-10T08:46:11Z
date_published: 2023-05-15T00:00:00Z
date_updated: 2025-11-10T15:05:04Z
day: '15'
doi: 10.48550/ARXIV.2305.08798
extern: '1'
external_id:
  arxiv:
  - '2305.08798'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2305.08798
month: '05'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
status: public
title: The cohomology ring of the Deligne-Mumford moduli space of real rational curves
  with conjugate marked points
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
OA_place: repository
OA_type: green
_id: '20626'
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.'
article_number: '2302.03021'
article_processing_charge: No
arxiv: 1
author:
- first_name: Xujia
  full_name: Chen, Xujia
  id: 968ad14a-fd86-11ee-a420-ea29715511a3
  last_name: Chen
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>
  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>. .
  ista: Chen X. Kontsevich’s characteristic classes as topological invariants of configuration
    space bundles. arXiv, 2302.03021.
  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>.
  short: X. Chen, ArXiv (n.d.).
date_created: 2025-11-10T08:46:37Z
date_published: 2023-02-06T00:00:00Z
date_updated: 2025-11-10T15:00:28Z
day: '06'
doi: 10.48550/ARXIV.2302.03021
extern: '1'
external_id:
  arxiv:
  - '2302.03021'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2302.03021
month: '02'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
status: public
title: Kontsevich's characteristic classes as topological invariants of configuration
  space bundles
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
OA_place: repository
OA_type: green
_id: '20616'
abstract:
- lang: eng
  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.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Xujia
  full_name: Chen, Xujia
  id: 968ad14a-fd86-11ee-a420-ea29715511a3
  last_name: Chen
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>
  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.
  ista: Chen X. 2022. Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations
    for Welschinger invariants. Geometric and Functional Analysis. 32(3), 490–567.
  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>.
  short: X. Chen, Geometric and Functional Analysis 32 (2022) 490–567.
date_created: 2025-11-10T08:40:40Z
date_published: 2022-04-15T00:00:00Z
date_updated: 2025-11-10T15:18:07Z
day: '15'
doi: 10.1007/s00039-022-00596-6
extern: '1'
external_id:
  arxiv:
  - '1809.08919'
intvolume: '        32'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1809.08919
month: '04'
oa: 1
oa_version: Preprint
page: 490-567
publication: Geometric and Functional Analysis
publication_identifier:
  eissn:
  - 1420-8970
  issn:
  - 1016-443X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger
  invariants
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 32
year: '2022'
...
---
OA_place: repository
OA_type: green
_id: '20617'
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.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Xujia
  full_name: Chen, Xujia
  id: 968ad14a-fd86-11ee-a420-ea29715511a3
  last_name: Chen
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>
  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.
  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.
  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>.
  short: X. Chen, International Mathematics Research Notices 2022 (2022) 7021–7055.
date_created: 2025-11-10T08:40:57Z
date_published: 2022-05-01T00:00:00Z
date_updated: 2025-11-10T14:57:33Z
day: '01'
doi: 10.1093/imrn/rnaa318
extern: '1'
external_id:
  arxiv:
  - '1912.05437'
intvolume: '      2022'
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1912.05437
month: '05'
oa: 1
oa_version: Preprint
page: 7021-7055
publication: International Mathematics Research Notices
publication_identifier:
  eissn:
  - 1687-0247
  issn:
  - 1073-7928
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Solomon-Tukachinsky’s versus Welschinger’s open Gromov-Witten invariants of
  symplectic six-folds
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2022
year: '2022'
...
---
OA_place: repository
OA_type: green
_id: '20620'
abstract:
- lang: eng
  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.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Xujia
  full_name: Chen, Xujia
  id: 968ad14a-fd86-11ee-a420-ea29715511a3
  last_name: Chen
citation:
  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>
  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>
  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>.
  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.
  ista: Chen X. 2022. A geometric depiction of Solomon-Tukachinsky’s construction
    of open GW-invariants. Peking Mathematical Journal . 5, 279–348.
  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>.
  short: X. Chen, Peking Mathematical Journal  5 (2022) 279–348.
date_created: 2025-11-10T08:43:20Z
date_published: 2022-09-01T00:00:00Z
date_updated: 2025-11-10T13:51:17Z
day: '01'
doi: 10.1007/s42543-021-00044-8
extern: '1'
external_id:
  arxiv:
  - '1912.04119'
intvolume: '         5'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1912.04119
month: '09'
oa: 1
oa_version: Submitted Version
page: 279-348
publication: 'Peking Mathematical Journal '
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A geometric depiction of Solomon-Tukachinsky's construction of open GW-invariants
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 5
year: '2022'
...
---
_id: '20627'
abstract:
- lang: eng
  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.
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).'
article_processing_charge: No
author:
- first_name: Jiemin
  full_name: Yuan, Jiemin
  last_name: Yuan
- first_name: Haiyun
  full_name: Chen, Haiyun
  last_name: Chen
- first_name: Tao
  full_name: Yong, Tao
  last_name: Yong
- first_name: Xi
  full_name: Lai, Xi
  last_name: Lai
- first_name: Xujia
  full_name: Chen, Xujia
  id: 968ad14a-fd86-11ee-a420-ea29715511a3
  last_name: Chen
citation:
  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>'
  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>'
  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>.
  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.
  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.'
  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>.
  short: J. Yuan, H. Chen, T. Yong, X. Lai, X. Chen, in:, 6th Advanced Information
    Technology, Electronic and Automation Control Conference, IEEE, 2022.
conference:
  end_date: 2022-10-05
  location: Beijing, China
  name: 'IAEAC: Advanced Information Technology, Electronic and Automation Control
    Conference'
  start_date: 2022-10-03
date_created: 2025-11-10T08:52:47Z
date_published: 2022-11-09T00:00:00Z
date_updated: 2025-11-10T14:53:37Z
day: '09'
doi: 10.1109/iaeac54830.2022.9930026
extern: '1'
language:
- iso: eng
month: '11'
oa_version: None
publication: 6th Advanced Information Technology, Electronic and Automation Control
  Conference
publication_identifier:
  eisbn:
  - '9781665458641'
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Research on two-wheeled balance car based on improved LQR controller
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2022'
...
---
OA_place: repository
OA_type: green
_id: '20619'
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.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Xujia
  full_name: Chen, Xujia
  id: 968ad14a-fd86-11ee-a420-ea29715511a3
  last_name: Chen
- first_name: Aleksey
  full_name: Zinger, Aleksey
  last_name: Zinger
citation:
  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>
  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.
  ista: Chen X, Zinger A. 2021. WDVV-type relations for disk Gromov–Witten invariants
    in dimension 6. Mathematische Annalen. 379(3–4), 1231–1313.
  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>.
  short: X. Chen, A. Zinger, Mathematische Annalen 379 (2021) 1231–1313.
date_created: 2025-11-10T08:41:40Z
date_published: 2021-01-25T00:00:00Z
date_updated: 2025-11-10T15:11:29Z
day: '25'
doi: 10.1007/s00208-020-02130-1
extern: '1'
external_id:
  arxiv:
  - '1904.04254'
intvolume: '       379'
issue: 3-4
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1904.04254
month: '01'
oa: 1
oa_version: Preprint
page: 1231-1313
publication: Mathematische Annalen
publication_identifier:
  eissn:
  - 1432-1807
  issn:
  - 0025-5831
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: WDVV-type relations for disk Gromov–Witten invariants in dimension 6
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 379
year: '2021'
...
---
OA_place: repository
OA_type: green
_id: '20622'
abstract:
- lang: eng
  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.
article_processing_charge: No
arxiv: 1
author:
- first_name: Xujia
  full_name: Chen, Xujia
  id: 968ad14a-fd86-11ee-a420-ea29715511a3
  last_name: Chen
- first_name: Aleksey
  full_name: Zinger, Aleksey
  last_name: Zinger
citation:
  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>'
  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>'
  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>.'
  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.'
  ista: 'Chen X, Zinger A. WDVV-type relations for Welschinger’s invariants: Applications.
    Kyoto Journal of Mathematics. 61(2), 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>.'
  short: X. Chen, A. Zinger, Kyoto Journal of Mathematics 61 (n.d.) 339–376.
date_created: 2025-11-10T08:45:12Z
date_published: 2021-06-01T00:00:00Z
date_updated: 2025-11-10T15:13:58Z
day: '01'
doi: 10.1215/21562261-2021-0005
extern: '1'
external_id:
  arxiv:
  - '1809.08938'
intvolume: '        61'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1809.08938
month: '06'
oa: 1
oa_version: Preprint
page: 339-376
publication: Kyoto Journal of Mathematics
publication_identifier:
  eissn:
  - 2154-3321
publication_status: submitted
publisher: Duke University Press
quality_controlled: '1'
status: public
title: 'WDVV-type relations for Welschinger''s invariants: Applications'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 61
year: '2021'
...